diff --git a/research/p104-a2-neutral-cleanup/CLAIM.json b/research/p104-a2-neutral-cleanup/CLAIM.json
new file mode 100644
index 0000000000..b55de52dd5
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/CLAIM.json
@@ -0,0 +1,48 @@
+{
+  "schema_version": 1,
+  "status": "LOCAL author-checked conditional composition; normal and registered isolated optimized complete replays passed",
+  "kappa": "77661117/25000000000",
+  "decimal": "0.00310644468",
+  "previous_pr": 5644,
+  "previous_kappa": "62125267/20000000000",
+  "gain": "18133/100000000000",
+  "gain_decimal": "1.8133e-07",
+  "gain_percent": "0.0058375604244887995",
+  "other_comparison": {
+    "pr": 5643,
+    "kappa": "155229/50000000",
+    "gain": "46617/25000000000",
+    "gain_percent": "0.06006223063989332"
+  },
+  "raw_crossing": [
+    "310644469581/100000000000000",
+    "155322234791/50000000000000"
+  ],
+  "raw_headroom": [
+    "1581/100000000000000",
+    "791/50000000000000"
+  ],
+  "local_paid_delta_vs_pr5644": {
+    "2": 1,
+    "3": -1,
+    "5": -1,
+    "6": 1
+  },
+  "local_paid_delta_vs_pr5643": {
+    "1": -3,
+    "5": -3,
+    "6": 3
+  },
+  "target_delta": {},
+  "local_invocations": 18,
+  "complete_paid_calls": 66492,
+  "complete_productive_targets": 12958,
+  "rank_mass_surplus": 760,
+  "local_ordinary_allowance": 220220,
+  "publication": {
+    "published": false,
+    "selected": false,
+    "hosted_ci": "not run"
+  },
+  "scope": "Actual common chronological word, retaining every independent input, productive target and owned operation; conditional on inherited native, erasure, compiler, precision/tape, analytic recovery and helper endpoint contracts. No formal-kernel or independent human verification."
+}
diff --git a/research/p104-a2-neutral-cleanup/COMPONENT-TRIAGE.md b/research/p104-a2-neutral-cleanup/COMPONENT-TRIAGE.md
new file mode 100644
index 0000000000..afd44bb8e4
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/COMPONENT-TRIAGE.md
@@ -0,0 +1,46 @@
+# Which construction component is ready to remove?
+
+The best immediate opportunity is [PR #5644](https://github.com/CrocSwap/integer-mult-bounds/pull/5644)'s obsolete late helper cleanup, combined with [PR #5643](https://github.com/CrocSwap/integer-mult-bounds/pull/5643)'s A2 exchange. Its exact input-basis preparation and last-read cancellation remove contacts that force otherwise unused native stops. The resulting common word supports **conditional κ = 0.00310644468** in the fresh complete replay. This is an actual functional replacement with a recomputed invoice.
+
+The original summarized list ran through PR5612; later PR5627 consumed its compatible improvements. Current exact sources are PR5643 `a3ff5c628bfc8825553d62d913f3e91f75d6825f`, PR5644 `c5871955d89bf73506fd68b0a5bf1cf2b3153c02` and their common PR5627 source `ed4dc88a09a7d201971f6603b8c2074e95dd9c32`. All screens below bind the emitted common word, compressed SHA256 `e94809cecf9e9cba56dd7a8a11ff1edeedc4c34013ff6caebdaf3b021351cf8c`.
+
+| Rank | Component and lineage | Complete accounting and decision |
+|---|---|---|
+| 1 — positive | Late helper cleanup, [#5644](https://github.com/CrocSwap/integer-mult-bounds/pull/5644), plus A2, [#5643](https://github.com/CrocSwap/integer-mult-bounds/pull/5643) | The functional common word retains all targets. Against PR5643 it replaces 54 complete H1+H5 paths by H6; against PR5644 it retains 18 A2 rank exchanges. Extra ordinary work is charged. κ increases over both. |
+| 2 — changed interface needed | Owned delivery replaced by a complementary public relay, [#5605](https://github.com/CrocSwap/integer-mult-bounds/pull/5605)/[#5612](https://github.com/CrocSwap/integer-mult-bounds/pull/5612) | Eight paid H7 deliveries remain. All eight fail free reconstruction from current public values at their first read's literal chart and time. A new preparation or source window could still replace one, but must charge storage, routing, cleanup and any native access. |
+| 3 — changed graph needed | Vacating an intermediate frame, [#5561](https://github.com/CrocSwap/integer-mult-bounds/pull/5561)/[#5601](https://github.com/CrocSwap/integer-mult-bounds/pull/5601)/[#5580](https://github.com/CrocSwap/integer-mult-bounds/pull/5580) | Their earlier compatible retimings are already consumed. A2 shows a changed noncommuting dependency graph can escape a fixed-contact screen. The next useful object is one specific last read that can be removed or moved by an exact identity. |
+| 4 — fixed-word route exhausted in tested scope | Independent helper split, [#5599](https://github.com/CrocSwap/integer-mult-bounds/pull/5599)/[#5602](https://github.com/CrocSwap/integer-mult-bounds/pull/5602), with dyadic completion [#5611](https://github.com/CrocSwap/integer-mult-bounds/pull/5611)/[#5615](https://github.com/CrocSwap/integer-mult-bounds/pull/5615) | The complete rational prefix/suffix pairing vanishes at every tested common-chart cut for all 411 ZERO-to-FULL helpers. There is no hidden dyadic unit ideal in this scope. A changed word or charged mixed-boundary interface is required before another basis search can pay. |
+| 5 — no recursive saving by deletion alone | Prepared zero-prefix storage, [#5606](https://github.com/CrocSwap/integer-mult-bounds/pull/5606), and inverse/main wrappers | Prepared role 751's three lifetimes have zero paid MOVEs, and inverse/main adapters already add zero recursive jobs. Removing them alone changes ordinary constants. Their usefulness would be enabling a different charged word, not deleting a recursive bill they do not contain. |
+
+The older [#5413](https://github.com/CrocSwap/integer-mult-bounds/pull/5413) coupled restoration adds 144 H8 paid calls and 144 H8 productive targets. Deleting both is rankwise neutral; retaining the productive credit while deleting its paid realization would need a new source-compatible correction. The larger [#5440](https://github.com/CrocSwap/integer-mult-bounds/pull/5440) headline remains outside this ready list because its priced native primitive and actual physical caller are not matched.
+
+## Exact negative screens and their limits
+
+[Owned-delivery evidence](analysis/owned-deliveries/COMPOSED-CENTRE-RECONSTRUCTION.json) comes from a separate rational interpreter that checks all 752 scalar endpoint rows and owned zero exits. The eight H7 source rows have rational rank eight. At their first public use, the available same-frame public spans have ranks 1, 2, 1, 1, 1, 1, 1, 1; each delivery value has a nonzero residual. This excludes an ADD-only substitution at those exact frames/times. It does not exclude changed windows, preconditioning, paid transport or joint native maps.
+
+[Joint-cut evidence](analysis/helper-cuts/ALL-EVENT-CUT-SCREEN.json) covers 8,847 event/chart states at 7,253 distinct cuts, all actual cohorts of sizes 1–16 and all 411 ZERO-to-FULL helpers. Only 18 states have nonzero prefix and suffix spaces; every full rational boundary pairing matrix is zero. The [scope proof](analysis/helper-cuts/README.md) explains the exact kernels, unaffected-chart state compression and COPY handling. A separate backward-prefix/forward-suffix checker verifies all 18 witnesses; it does not independently recompute every empty kernel.
+
+Reproduce the lightweight checks from the repository root:
+
+```sh
+python3.12 -I -O -B research/p104-a2-neutral-cleanup/analysis/owned-deliveries/check_composed_centres.py
+python3.12 -I -O -B research/p104-a2-neutral-cleanup/analysis/helper-cuts/check_report.py research/p104-a2-neutral-cleanup/WORD.json.gz
+```
+
+The discovery scanner can explicitly regenerate its own receipt:
+
+```sh
+python3.12 -B research/p104-a2-neutral-cleanup/analysis/helper-cuts/scan_all_cuts.py research/p104-a2-neutral-cleanup/WORD.json.gz
+```
+
+## Why apparent accounting deletions are not automatically gains
+
+The retained caller's 3,120 whole idle jobs supply part of its actual endpoint action. Its 15 isolated query shears supply 1,560 paid H1 jobs; literal deletion changes the exact formal caller endpoint. They are not disposable line items. The BIT side is currently slack above this complex ceiling, so a stronger BIT component alone does not raise the complete κ.
+
+The useful distinction is whether a functional replacement removes paid jobs **after** surrendering any lost productive targets and charging new ownership/native access. PR5644's last-read identity and PR5643's changed A2 graph satisfy that test together. Merely dropping a wrapper, deleting both halves of an equal paid/target entry, or treating an independently prepared input as free does not.
+
+Scientific credit remains with the linked contributors and the complete source notices. The coordinating agent and three subagents produced this triage with substantial OpenAI Codex assistance. The [skeptical composition review](analysis/owned-deliveries/COMPOSITION-SKEPTICAL-REVIEW.md) is scoped agent scrutiny, not independent human or proof-kernel acceptance.
+
+## Open next questions
+
+The strongest remaining bounded task is one changed complementary-public-value window for a named H7 delivery. First show the source survives to its consumer under the changed chronology; then emit its whole restoration and native bill. A changed scalar dependency that makes a fixed helper boundary pairing nonzero is another distinct route. The current screens do not supply either construction.
diff --git a/research/p104-a2-neutral-cleanup/COMPOSITION-AUDIT.json b/research/p104-a2-neutral-cleanup/COMPOSITION-AUDIT.json
new file mode 100644
index 0000000000..d1e408d8d9
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/COMPOSITION-AUDIT.json
@@ -0,0 +1,18 @@
+{
+  "candidate_events": 25449,
+  "commuting_edit_scope": "After all three cleanup replacements, the unique original A2 motif remains; replacing it and independently reconstructing all typed monotone paths gives the identical complete emitted program.",
+  "delta_vs_pr5643": {
+    "1": -3,
+    "5": -3,
+    "6": 3
+  },
+  "delta_vs_pr5644": {
+    "2": 1,
+    "3": -1,
+    "5": -1,
+    "6": 1
+  },
+  "scalar_events": 22015,
+  "scope": "Exact common scalar skeleton, three-column A2 identity for arbitrary prefix values, reverse-order full chart-path reconstruction, fixed physical boundary data and complete paid histogram. Native phases and caller/compiler evidence remain separate.",
+  "status": "PASS_INDEPENDENT_COMPOSITION_ORDER_AND_FRAME_AUDIT"
+}
diff --git a/research/p104-a2-neutral-cleanup/COMPOSITION-PROOF.md b/research/p104-a2-neutral-cleanup/COMPOSITION-PROOF.md
new file mode 100644
index 0000000000..3aa4b1e6f2
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/COMPOSITION-PROOF.md
@@ -0,0 +1,37 @@
+# A common functional word for the A2 exchange and three helper cleanups
+
+This scoped composition combines [zxv](https://github.com/zxv)'s [PR #5643](https://github.com/CrocSwap/integer-mult-bounds/pull/5643), exact head `a3ff5c628bfc8825553d62d913f3e91f75d6825f`, with [Ali Romman](https://github.com/aliromman)'s [PR #5644](https://github.com/CrocSwap/integer-mult-bounds/pull/5644), exact head `c5871955d89bf73506fd68b0a5bf1cf2b3153c02`. Both consume the exact [PR #5627](https://github.com/CrocSwap/integer-mult-bounds/pull/5627) word at `ed4dc88a09a7d201971f6603b8c2074e95dd9c32`. This is a compatibility argument for the emitted program, not an addition of headline κ gains. All source mechanisms and notices retain their attribution. New composition and this scoped audit used substantial OpenAI Codex assistance; Apache-2.0.
+
+## The two substitutions are functional before they are priced
+
+For the A2 substitution, write A = register 715, B = register 388 and C = register 340 at its prefix. The old scalar pair `B -= 4 A; C += B` and new scalar triple `C -= 4 A; C += B; B -= 4 A` both produce `(A, B−4A, C+B−4A)` for arbitrary prefix values. This is a matrix identity on the three full input columns; it does not assume a zero register or a special incoming relation. The new gates retain their specified charts 396, 825 and 127.
+
+For a cleanup helper h, the exact checked prefix relation has the form
+
+```
+h(cut) − Σ_j b_j z_j(cut) = s u_h + Σ_{j ≠ h} a_j u_j.
+```
+
+Here s is an invertible dyadic unit, all initial inputs on the right share h's input chart, and every cancellation register on the left shares h's cut chart. Prepare `u_h' = u_h − Σ(a_j/s)u_j`. Execute the prefix on those prepared inputs, then replace the helper state by `(h(cut) − Σ b_j z_j(cut))/s`. The relation gives exactly `u_h` for every arbitrary input. There is no later read of h, and the removed suffix consists only of its own declared scalar cleanup gates. The original helper's scalar endpoint row is its independent input, while all other scalar endpoint rows have zero dependence on that helper input. Its physical endpoint retains the productive native map Φ_final Φ_initial⁻¹. Thus the preparation and replacement preserve every other endpoint and restore h's exact endpoint. This is the original cleanup proof applied to the actual composed prefix; the verifier reevaluates each relation after the preceding edits.
+
+The three helpers are 291, 321 and 369. All input preparations, dyadic scalings, cancellation gates and resulting transports are present in the emitted common word. They do not use free helper output credits or a new owned-erasure rule.
+
+## Actual composition, in both orders
+
+Applying the three retained cleanup witnesses directly to the emitted PR5643 word passes the complete rational scalar/frame replay after every cleanup. The witnesses' exact anchors, prefix relations, absence of later helper reads, fixed productive endpoint charts and retained owned-event sequence are checked on the evolving word. This supplies an actual common program.
+
+The separate audit reads the saved source, A2, cleanup and common words as data. After deleting MOVE instructions, it finds the unique old A2 scalar pair in the cleanup-only word. Replacing that pair by the specified triple gives exactly the common word's entire scalar skeleton. It independently rebuilds every typed monotone transport path from the cleanup-only initial charts and that skeleton. The resulting full chronological instruction list is exactly the common word, including every MOVE. Thus applying A2 after cleanup gives the same emitted program as applying cleanup after A2; compatibility does not follow merely from disjoint headline histograms.
+
+`audit_composition.py` also checks the three-column A2 identity, all boundary data and the complete paid histograms. A missing final A2 shear fails the functional matrix identity despite retaining all helper cleanup identities. The complete verifier separately rejects a wrong A2 frame, omitted direct A2 correction, false cleanup cancellation, wrong cleanup cut, omitted initial preparation, missing owned CLEAR, extra target credit and an unpaid query.
+
+## From scalar equality to physical action
+
+Let Φ_f be the actual native chart operator at chart f, including its global phase. The frame invariant represents each physical register by `Φ_f z`, where z is its common-coordinate value. A coframed scalar gate obeys `Φ_f z_r + q Φ_f z_s = Φ_f(z_r + qz_s)`. A paid native chart change a→b is `Φ_b Φ_a⁻¹`, so it sends `Φ_a z` to `Φ_b z`. Induction through every chronological instruction transfers the proved scalar endpoint equality to physical endpoint equality. This argument neither commutes Gaussians nor replaces a tensor power of a sum by a sum of tensor powers. All owned instructions and their inherited contracts are retained in order.
+
+The fresh native-map and full caller replays remain necessary evidence for the actual emitted chart transitions; the scalar audit alone does not claim to supply those checks. The inherited all-width realization, compiler, precision/tape, analytic recovery and helper-endpoint assumptions are unchanged.
+
+## Complete bill and limits
+
+Relative to PR5644, the common word's complete local paid change is exactly `H2 + H6 − H3 − H5`. Relative to PR5643, it is exactly `3(H6 − H1 − H5)`. Every productive target is retained. The full caller multiplies each local delta by 18. It has 66,492 paid calls, 12,958 productive fields and rank-mass surplus 760. The local ordinary allowance is 220,220, including the cleanup's extra 54 scalar units above the A2 word.
+
+Both signed moment changes are strictly favorable for `0 < t < 1`: strict concavity gives `3^t−2^t > 6^t−5^t`, and subadditivity gives `1+5^t > 6^t`. The resulting root is recomputed from the common complete invoice. Scientific admission, hosted CI, proof-kernel verification and independent human review remain separate obligations. No global optimality claim follows.
diff --git a/research/p104-a2-neutral-cleanup/COMPOSITION.json b/research/p104-a2-neutral-cleanup/COMPOSITION.json
new file mode 100644
index 0000000000..a3db58d9d4
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/COMPOSITION.json
@@ -0,0 +1,368 @@
+{
+  "candidate_payload_sha256": "42fe73e3240340aa185aab3cf976f8f6b783603b4d5513345519a260c1253d4a",
+  "cleanup_receipts": [
+    {
+      "cancellation": [
+        [
+          "ADD",
+          291,
+          293,
+          "1",
+          234
+        ],
+        [
+          "SCALE",
+          291,
+          "-1/2",
+          234
+        ]
+      ],
+      "cut": 10627,
+      "events": 25447,
+      "frame": 234,
+      "helper": 291,
+      "paid": {
+        "1": 2199,
+        "2": 457,
+        "3": 493,
+        "4": 91,
+        "5": 161,
+        "6": 20,
+        "7": 15
+      },
+      "preparation": [
+        [
+          "ADD",
+          291,
+          39,
+          "1",
+          3
+        ],
+        [
+          "ADD",
+          291,
+          293,
+          "-1/2",
+          3
+        ],
+        [
+          "ADD",
+          291,
+          303,
+          "1",
+          3
+        ]
+      ],
+      "removed_scalar_events": [
+        [
+          "SCALE",
+          291,
+          "-1/2",
+          234
+        ],
+        [
+          "ADD",
+          291,
+          289,
+          "1/2",
+          234
+        ],
+        [
+          "ADD",
+          291,
+          39,
+          "1/2",
+          234
+        ],
+        [
+          "ADD",
+          291,
+          40,
+          "1/2",
+          234
+        ],
+        [
+          "ADD",
+          291,
+          18,
+          "-1/2",
+          234
+        ],
+        [
+          "ADD",
+          291,
+          55,
+          "-1",
+          234
+        ]
+      ],
+      "scalar": 220152
+    },
+    {
+      "cancellation": [
+        [
+          "ADD",
+          321,
+          22,
+          "-2",
+          237
+        ],
+        [
+          "ADD",
+          321,
+          320,
+          "3/2",
+          237
+        ],
+        [
+          "ADD",
+          321,
+          330,
+          "-2",
+          237
+        ]
+      ],
+      "cut": 11072,
+      "events": 25447,
+      "frame": 237,
+      "helper": 321,
+      "paid": {
+        "1": 2198,
+        "2": 457,
+        "3": 493,
+        "4": 91,
+        "5": 160,
+        "6": 21,
+        "7": 15
+      },
+      "preparation": [
+        [
+          "ADD",
+          321,
+          34,
+          "2",
+          3
+        ],
+        [
+          "ADD",
+          321,
+          320,
+          "2",
+          3
+        ],
+        [
+          "ADD",
+          321,
+          330,
+          "-2",
+          3
+        ]
+      ],
+      "removed_scalar_events": [
+        [
+          "ADD",
+          321,
+          320,
+          "1",
+          237
+        ],
+        [
+          "ADD",
+          321,
+          23,
+          "-1",
+          237
+        ],
+        [
+          "ADD",
+          321,
+          22,
+          "-1",
+          237
+        ],
+        [
+          "ADD",
+          321,
+          108,
+          "1",
+          237
+        ],
+        [
+          "ADD",
+          321,
+          49,
+          "-1",
+          237
+        ]
+      ],
+      "scalar": 220176
+    },
+    {
+      "cancellation": [
+        [
+          "ADD",
+          369,
+          26,
+          "-2",
+          243
+        ],
+        [
+          "ADD",
+          369,
+          368,
+          "3/2",
+          243
+        ],
+        [
+          "ADD",
+          369,
+          378,
+          "2",
+          243
+        ]
+      ],
+      "cut": 11718,
+      "events": 25449,
+      "frame": 243,
+      "helper": 369,
+      "paid": {
+        "1": 2197,
+        "2": 457,
+        "3": 493,
+        "4": 91,
+        "5": 159,
+        "6": 22,
+        "7": 15
+      },
+      "preparation": [
+        [
+          "ADD",
+          369,
+          3,
+          "2",
+          3
+        ],
+        [
+          "ADD",
+          369,
+          372,
+          "2",
+          3
+        ],
+        [
+          "ADD",
+          369,
+          378,
+          "2",
+          3
+        ],
+        [
+          "ADD",
+          369,
+          382,
+          "2",
+          3
+        ],
+        [
+          "ADD",
+          369,
+          383,
+          "-2",
+          3
+        ]
+      ],
+      "removed_scalar_events": [
+        [
+          "ADD",
+          369,
+          368,
+          "1",
+          243
+        ],
+        [
+          "ADD",
+          369,
+          26,
+          "-1",
+          243
+        ],
+        [
+          "ADD",
+          369,
+          95,
+          "-1",
+          243
+        ],
+        [
+          "ADD",
+          369,
+          8,
+          "1",
+          243
+        ],
+        [
+          "ADD",
+          369,
+          80,
+          "-1",
+          243
+        ]
+      ],
+      "scalar": 220220
+    }
+  ],
+  "delta_vs_pr5627": {
+    "1": -3,
+    "2": 1,
+    "3": -1,
+    "5": -4,
+    "6": 4
+  },
+  "delta_vs_pr5643": {
+    "1": -3,
+    "5": -3,
+    "6": 3
+  },
+  "delta_vs_pr5644": {
+    "2": 1,
+    "3": -1,
+    "5": -1,
+    "6": 1
+  },
+  "events": 25449,
+  "local": {
+    "endpoint_coefficients": 565504,
+    "helpers": {
+      "1": 2,
+      "2": 4,
+      "4": 91,
+      "5": 6,
+      "7": 5,
+      "8": 16,
+      "9": 411
+    },
+    "owned_fields": 9,
+    "owned_lifetimes": 11,
+    "paid": {
+      "1": 2197,
+      "2": 457,
+      "3": 493,
+      "4": 91,
+      "5": 159,
+      "6": 22,
+      "7": 15
+    },
+    "paid_rank_mass": 5986,
+    "peak_owned_fields": 2,
+    "public_inputs": 743,
+    "real_scalar_allowance": 220220
+  },
+  "ordinary_scalar_delta_vs_pr5643": 54,
+  "scope": "Actual common emitted word; complete exact arbitrary-input scalar/frame replay and paid-target extraction. Native/physical/compiler/outer not yet run.",
+  "sources": {
+    "pr5643": "a3ff5c628bfc8825553d62d913f3e91f75d6825f",
+    "pr5644": "c5871955d89bf73506fd68b0a5bf1cf2b3153c02"
+  },
+  "status": "PASS_COMPOSED_SCALAR_FRAME_AND_PAID_DELTA",
+  "target_delta": {}
+}
diff --git a/research/p104-a2-neutral-cleanup/FULL-RESULT.json b/research/p104-a2-neutral-cleanup/FULL-RESULT.json
new file mode 100644
index 0000000000..e64b25fb0d
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/FULL-RESULT.json
@@ -0,0 +1,789 @@
+{
+  "candidate_payload_sha256": "42fe73e3240340aa185aab3cf976f8f6b783603b4d5513345519a260c1253d4a",
+  "cleanup_changes": [
+    {
+      "cancellation": [
+        [
+          "ADD",
+          291,
+          293,
+          "1",
+          234
+        ],
+        [
+          "SCALE",
+          291,
+          "-1/2",
+          234
+        ]
+      ],
+      "cut": 10627,
+      "events": 25447,
+      "frame": 234,
+      "helper": 291,
+      "paid": {
+        "1": 2199,
+        "2": 457,
+        "3": 493,
+        "4": 91,
+        "5": 161,
+        "6": 20,
+        "7": 15
+      },
+      "preparation": [
+        [
+          "ADD",
+          291,
+          39,
+          "1",
+          3
+        ],
+        [
+          "ADD",
+          291,
+          293,
+          "-1/2",
+          3
+        ],
+        [
+          "ADD",
+          291,
+          303,
+          "1",
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+        "4": 91,
+        "5": 162,
+        "6": 19,
+        "7": 15
+      },
+      "paid_rank_mass": 5986,
+      "peak_owned_fields": 2,
+      "public_inputs": 743,
+      "real_scalar_allowance": 220166
+    },
+    "pr5644": {
+      "endpoint_coefficients": 565504,
+      "helpers": {
+        "1": 2,
+        "2": 4,
+        "4": 91,
+        "5": 6,
+        "7": 5,
+        "8": 16,
+        "9": 411
+      },
+      "owned_fields": 9,
+      "owned_lifetimes": 11,
+      "paid": {
+        "1": 2197,
+        "2": 456,
+        "3": 494,
+        "4": 91,
+        "5": 160,
+        "6": 21,
+        "7": 15
+      },
+      "paid_rank_mass": 5986,
+      "peak_owned_fields": 2,
+      "public_inputs": 743,
+      "real_scalar_allowance": 220208
+    }
+  },
+  "sources": {
+    "pr5643": "a3ff5c628bfc8825553d62d913f3e91f75d6825f",
+    "pr5644": "c5871955d89bf73506fd68b0a5bf1cf2b3153c02"
+  },
+  "status": "PASS_P104_COMPOSED_KAPPA_00310644468",
+  "target_delta": {},
+  "transpose": {
+    "arithmetic": "Dense integer rows with binary denominators; reverse chronology",
+    "coefficients": 565504,
+    "columns": 752
+  }
+}
diff --git a/research/p104-a2-neutral-cleanup/LATEST-PR-REFRESH.json b/research/p104-a2-neutral-cleanup/LATEST-PR-REFRESH.json
new file mode 100644
index 0000000000..ea3dd78318
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/LATEST-PR-REFRESH.json
@@ -0,0 +1 @@
+{"data":{"repository":{"a":{"title":"Price the actual Gaussian reader and cut its coefficient bill by 35.6%","body":"The actual 112-port Gaussian reader reaches character rank **30**, so its sharp dirty-bank cost is **2 ceil(30/q)+2 cross-bank shears**. An explicit dyadic centre basis reduces the four-shear word from **31,608 to 20,352 coefficient ADDs** (35.6%), without a new odd denominator. This closes the actual-source rank and coefficient-cost gap left by [PR5640](https://github.com/CrocSwap/integer-mult-bounds/pull/5640) and [PR5634](https://github.com/CrocSwap/integer-mult-bounds/pull/5634). No new kappa is claimed.\n\nThe [proof and boundary](https://github.com/aliromman/integer-mult-bounds/blob/98c17101e47ad378702f8c3eb450a87b7ac7bdc2/research/actual-gaussian-reader-tariff/README.md), [basis witness](https://github.com/aliromman/integer-mult-bounds/blob/98c17101e47ad378702f8c3eb450a87b7ac7bdc2/research/actual-gaussian-reader-tariff/BASIS.json), [all-width storage tradeoff](https://github.com/aliromman/integer-mult-bounds/blob/98c17101e47ad378702f8c3eb450a87b7ac7bdc2/research/actual-gaussian-reader-tariff/RESULT.json), [exact verifier](https://github.com/aliromman/integer-mult-bounds/blob/98c17101e47ad378702f8c3eb450a87b7ac7bdc2/research/actual-gaussian-reader-tariff/verify.py), [source manifest](https://github.com/aliromman/integer-mult-bounds/blob/98c17101e47ad378702f8c3eb450a87b7ac7bdc2/research/actual-gaussian-reader-tariff/SOURCES.json) and [frozen context](https://github.com/aliromman/integer-mult-bounds/blob/98c17101e47ad378702f8c3eb450a87b7ac7bdc2/research/actual-gaussian-reader-tariff/SOURCE-CONTEXT.json) are pinned to contribution head `98c17101e47ad378702f8c3eb450a87b7ac7bdc2`. Canonical base and final refresh are `df0137efd35e11b4445734bf612bdd4c7ebc330c`, priority revision 7, selected conditional kappa 0.00310045. Only this package is added. [Coordination](https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19186810).\n\nAll 512 source character inverses, reader identities and exact rational ranks pass; modular ranks give matching lower bounds. Character 92 has rank 30. The physical inverse Walsh kernel has 15,628 reader coefficients. Ten basis changes reduce this to 9,968, with 208 scatter coefficients. The common denominator is 960, with odd part 15. The complete search over all 870 ordered row pairs and every possible improving dyadic coefficient proves that no single further row ADD reduces the bill. This is a local basis optimum, not a global ordinary-cost optimum.\n\nThe package emits exact coefficient bills and coefficient-ADD prefix/suffix bounds for every borrowed dimension 1 through 30. One borrowed field uses 62 shears and 18,331 coefficient ADDs; thirty use four and 20,352. All translation shifts and rational coefficients remain charged. A separate literal 512-address dirty-input replay agrees with the original source factors. Three controls reject a corrupted actual inverse, a wrong restoration-gather sign and a missing final scatter. The all-input endpoint follows from the checked factor identities and the written word proof; the physical test uses one deterministic payload.\n\n```sh\npython3.12 -B scripts/research_package.py --package research/actual-gaussian-reader-tariff\npython3.12 -B scripts/check_research_commit.py --package research/actual-gaussian-reader-tariff\n```\n\nExpected: `PASS_ACTUAL_GAUSSIAN_READER_TARIFF`, `PASS_REGISTERED_RESEARCH_PACKAGE`, and `PASS_RESEARCH_COMMIT_BYTES`. Normal and optimized registered checks, exact committed-byte checks, export validation and a Git-free optimized replay pass. Python 3.12 and the standard library suffice. CI is pending at publication. Full-history preflight is unavailable in this shallow checkout; source hashes and committed bytes were checked.\n\nThe lower bound uses the translation-kernel cross-bank alphabet. Unrestricted address mixing has a different contract. A smaller borrowed bank does not remove the thirty-field bank used inside the section. Rational arithmetic interiors, physical routing/tape costs, native/outer admission and a complete supplier/caller remain open. No full historical suite, selected cold replay, proof assistant or independent human scientific review was run.\n\nCredit David Ganz (@Dugongue) for PR5634 and its native/campaign lineage, PR5640 for the sharp tariff, and centre-code-services for the actual response and inverse certificate. Frozen notices retain reciprocal-native-responses, native-centre-capture, centre-metric-encoders, PR3133, PR3148, PR2588 and PR2226. New source binding, basis reduction, proof and checks: Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. Next questions are a broader physically priced basis and one complete native caller; this package reserves neither.\n","headRefOid":"98c17101e47ad378702f8c3eb450a87b7ac7bdc2"},"b":{"title":"Reconstruct a G20 native SOURCE from five prior values; ordinary BIT 0.003484629984","body":"A five-value native history reconstructs the missing SOURCE77 function at FRAME509. It lets helper444 replace H3+H1 by H4 while preserving every independent target and reusing the old zero centre. This is a new source reconstruction, distinct from PR5639's helper465/467 snapshots and PR5629's four retirements.\n\nThe complete ordinary BIT saving is **0.003484629984**, versus the pinned PR5512 value **0.003483969976**. The signed moment improves by `18*(1+3^t-4^t)` for every `0<t<1`; the full caller has 56,979 paid requests, 11,238 productive targets and eleven owned banks. No original input is erased and all five gathers, dirty clear, injection, routes and finite fees are charged. The old zero-centre work is removed from the literal program.\n\nThis is an independently usable component improvement, not a new best whole multiplication kappa. PR5641's separate four-retirement component is already numerically stronger. Combining them belongs to the integration lane; no such composition is claimed here. The selected frontier is unchanged.\n\nRead `research/g20-affine-history/PROOF.md` and `RESULT.json`. Source base: canonical main `df0137efd35e11b4445734bf612bdd4c7ebc330c`; priority7. All 152 source-closure files are pinned and declared. [Coordination](https://github.com/CrocSwap/integer-mult-bounds/discussions/5638).\n\nValidation: Python3.12 standard-library registered normal and optimized replay pass. They check all 660 local RAW/DIRTY columns, exact rational H3/H1/H4 composition, full physical controls at 101 and 101 squared, the literal eighteen-call tape, an independent 11,249-column event replay, all unchanged target descriptors, two exact interval engines and fresh ordinary compiler constants. Missing-gather, missing-dirty-clear and underpriced-move controls reject. Committed-byte and export-integrity checks pass. Git-free replay is recorded in VALIDATION.md. Full-history ancestry, independent human/formal proof and hosted CI are separate.\n\n```sh\npython3.12 -B scripts/research_package.py --package research/g20-affine-history\n```\n\nExpected marker: `PASS_G20_AFFINE_HISTORY_ORDINARY_003484629984`.\n\nCredit ai-nanachi PR5512, Ali Romman PR5421, Dugongue PR5629/PR5639, DreamingOfClouds, eumemic, Cinna Davis, rohanarun, zxv, Jacob Alan Sussman and all retained notices. Prepared by Ali Romman with substantial OpenAI Codex assistance; no subagents. New work is Apache-2.0. The retained native/all-width, ROW, compiler, owned storage, precision, fixed-tape, completed-backend and analytic assumptions remain.\n","headRefOid":"41c36785dbb72c8cfd8dabff3cf674868c54b24d"},"c":{"title":"Complete G20 snapshot fusion at ordinary BIT saving 0.003487922466","body":"**Constructive conditional ordinary BIT saving: 0.003487922466**, an exact gain of 0.000001313377 over [PR #5641](https://github.com/CrocSwap/integer-mult-bounds/pull/5641). This emits and fully prices Dugongue [PR #5639](https://github.com/CrocSwap/integer-mult-bounds/pull/5639), while reusing the old zero centre to reduce the owned reserve from 17 to 16 banks. No complete kappa or selected-frontier update is claimed.\n\n[Scope](https://github.com/aliromman/integer-mult-bounds/blob/8b1995f167471e79f77351fcdc014db3b338f818/research/g20-snapshot-native/README.md), [proof](https://github.com/aliromman/integer-mult-bounds/blob/8b1995f167471e79f77351fcdc014db3b338f818/research/g20-snapshot-native/PROOF.md), [exact checks](https://github.com/aliromman/integer-mult-bounds/blob/8b1995f167471e79f77351fcdc014db3b338f818/research/g20-snapshot-native/verify.py), [source pins](https://github.com/aliromman/integer-mult-bounds/blob/8b1995f167471e79f77351fcdc014db3b338f818/research/g20-snapshot-native/SOURCES.json), [registered replay](https://github.com/aliromman/integer-mult-bounds/blob/8b1995f167471e79f77351fcdc014db3b338f818/research/g20-snapshot-native/VERIFY.json). Base: canonical main `df0137efd35e11b4445734bf612bdd4c7ebc330c`, priority revision 7. Contribution head: `8b1995f167471e79f77351fcdc014db3b338f818`.\n\nThe snapshots preserve every retained arbitrary original and endpoint. All 546 obsolete whole-zero centre accesses are proved removable. The complete 18-call caller retains 11,166 originals, pays 56,817 queries, and allocates 16 owned banks with no output credit. Against PR5641 the paid change is `-36 H1-36 H3+36 H4`, with unchanged targets and strict gain `36*(1+3^t-4^t)>0` for `0<t<1`. [Discussion #5642](https://github.com/CrocSwap/integer-mult-bounds/discussions/5642) records the claim and scope split.\n\nNormal and optimized registered replay pass. The native word tracks all 661 original/dirty entry columns; separate adjoint checks use other address points at moduli 101 and 10201. Separate stream replay checks 445,838 events, all 56,817 query descriptors, targets, owned returns and positive costs. Two census implementations check all 667 nested blocks on every retained field, with arbitrary prior same-frame binary combinations. A third eligible window at helper444 was [handed to its active investigation](https://github.com/CrocSwap/integer-mult-bounds/discussions/5638#discussioncomment-19186960), with a direct SOURCE77 snapshot replacing five gathers. It is excluded from this emitted bill. Two rational engines certify raw crossing `(0.00348792248477,0.00348792248480)`, fresh finite thresholds, 16-bank stock and four acyclic ordinary levels. The admitted saving is less than `1.89e-11` below that crossing. Stale snapshot, missing teardown, stale epoch and unfunded price controls reject.\n\n```sh\npython3.12 -B scripts/research_package.py --package research/g20-snapshot-native\n```\n\nPython 3.12 and the standard library suffice. Committed-byte checks pass. The native/all-width, ROW, compiler, precision, tape and analytic premises remain conditional. Full historical suites and formal-kernel proofs were not rerun; separate implementations are not independent scientific acceptance. The finite uniform program and astronomical decimal threshold are algorithm-defined, not materialized. Other producers, protected-read retiming and paid frame changes are outside the frozen census. This shallow checkout cannot run the full ancestry audit. A reproduced upstream Current CI missing-link regression currently blocks the generic hosted planner; the package has complete local replay evidence. Hosted status is unconfirmed at publication.\n\nCredit Dugongue PR5639 at head 4b4f6152a4eda5f2df7add0c08caeef0692e08ed for the two fusions; ai-nanachi PR5512 for native G20 and the ordinary framework; Ali Romman PR5421/5641; DreamingOfClouds, eumemic, Cinna Davis, rohanarun, zxv, Jacob Alan Sussman and all frozen source notices. The emitted caller, zero-centre reuse, full source-window census, exact ordinary certificate and direct snapshot handoff are the contribution here.\n\nNext: complete helper444 in Discussion5638 using the direct snapshot handoff. A fourth fusion requires a changed producer or priced native frame map; the frozen 667-block census has no other candidate. Complete kappa still needs a compatible complex supplier and caller. This result reserves no further search.\n\nPrepared by Ali Romman with substantial OpenAI Codex assistance; Apache-2.0.\n","headRefOid":"8b1995f167471e79f77351fcdc014db3b338f818"}}}}
\ No newline at end of file
diff --git a/research/p104-a2-neutral-cleanup/LICENSE b/research/p104-a2-neutral-cleanup/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
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diff --git a/research/p104-a2-neutral-cleanup/NORMAL-REPLAY.log b/research/p104-a2-neutral-cleanup/NORMAL-REPLAY.log
new file mode 100644
index 0000000000..3fa7094502
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/NORMAL-REPLAY.log
@@ -0,0 +1,6 @@
+PASS actual common word: all arbitrary-input rows, frames, fixed boundaries and full local paid-target delta
+PASS every dense transpose column 752
+PASS every native map and exact phase 2916
+PASS full composed physical caller
+PASS two exact moment engines, compiler, BIT stock and all58 outer conditions ['310644469581/100000000000000', '155322234791/50000000000000']
+PASS_P104_COMPOSED_KAPPA_00310644468
diff --git a/research/p104-a2-neutral-cleanup/NOTICE b/research/p104-a2-neutral-cleanup/NOTICE
new file mode 100644
index 0000000000..329998cf2d
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/NOTICE
@@ -0,0 +1,427 @@
+A sharper exponent for integer multiplication
+Copyright 2026 Douglas Colkitt
+
+This project includes unmodified source files from OpenAI's manuscript
+"Integer multiplication below n log n" and its accompanying repository:
+https://github.com/openai/math
+Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a
+
+The original manuscript identifies OpenAI as its author. Its Apache-2.0
+license is retained at upstream/LICENSE. The exact source URLs and hashes
+are recorded in upstream/manifest.json. Proposed modifications are supplied
+as separate files under patches/; upstream source files remain unchanged.
+
+The original local research note, scripts, certificates, patches, and
+documentation were prepared by Douglas Colkitt with assistance from OpenAI
+Codex. The community release incorporates work by the contributors identified
+in the notices below; it is not solely Douglas Colkitt's work.
+This project is not an official OpenAI release or an OpenAI endorsement.
+
+Related contributions (not imported in this checkpoint):
+Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset
+motif, finite-alphabet transfer and a different compressed producer:
+https://github.com/CrocSwap/integer-mult-bounds/pull/7
+The present checkpoint claims no priority for that motif. Related compressed
+complex-network work was submitted by eumemic in PR #3:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+The pending contributions and their stronger bounds require their own review;
+this notice does not represent adoption or verification of their claims.
+
+Additional community work, including parallel and superseded submissions, is
+acknowledged in CONTRIBUTORS.md, with pinned submission metadata in
+docs/research/contribution-snapshot.json. These acknowledgements do not imply
+joint authorship of the checkpoint, incorporation of pending code, or verification
+of submitted mathematical claims. Original source-specific notices remain in force.
+
+Community release (accepted by conditional maintainer audit):
+The following original contributor notices apply to the imported PR #39 chain.
+The preceding non-import statements describe the preserved 2^-30 checkpoint.
+
+Ternary five-subset construction and common-four-point resynthesis
+Copyright 2026 Zhihao Chen (jacklightChen)
+
+This is Zhihao Chen's first submission of this specific construction to this
+repository. Research, proof development, code and verification were prepared
+with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by
+the contributor. This is not independent review or an OpenAI endorsement.
+Future research building on this contribution should explicitly acknowledge
+Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and
+retain the preceding contributors' attribution. This notice records research
+provenance; the repository's Apache-2.0 license remains unchanged.
+
+Dependencies retained from eumemic's Claude-assisted PRs #3 and #5:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+https://github.com/CrocSwap/integer-mult-bounds/pull/5
+PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893
+These include complex_circuit.py, complex_network.py, fast_gaussian.py,
+their generators, construction notes and certificates. The Gaussian input
+scaling proof is corrected in this derivative; see the modification notice below.
+Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank
+sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6.
+Their results and ideas are credited separately from this new construction.
+
+Bulk recursion and controlled tensor basis, 8 October 2026
+Copyright 2026 icekylinx
+
+The new projector batching, controlled simultaneous basis, mixed-width tape
+recursions, whole-residual complex recursion, and dependency-path precision
+guard in the batched-23 proof package are contributed by icekylinx, developed
+with substantial OpenAI GPT-6 Astra assistance. Review corrections and
+repository integration were prepared with OpenAI Codex assistance. They build on the retained
+PR #7 finite producers and the preceding contributions credited above.
+The new package retains the repository's Apache-2.0 license and the original
+authors' attribution. It is not an official OpenAI release or endorsement.
+
+Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian
+proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2).
+The P=34p precision budget and asymptotic exponent are unchanged. New batching
+checks are integrated into make verify. Existing attribution and licenses
+are retained.
+
+Partial-swap extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The partial-swap framing, binary retained-total triple construction,
+dependency-preserving positive labels and carrier reuse, unequal (25,23,57)
+common basis, improved complex batching, and exact assembly are contributed
+by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance.
+This extension directly inherits PR #10, commit
+62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters
+modify the retained paired-exclusion and shared-point implementations credited
+above. The original licenses, attribution, and Gaussian correction are retained.
+
+Endpoint-gauge extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The complementary auxiliary endpoint gauges, (32,30,40) controlled basis,
+general nondegenerate binary phase residuals, retained-center complex producer,
+updated path guard and exact assembly are contributed by icekylinx with
+substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits
+f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable
+adapters retain the paired-exclusion and shared-point contributions credited
+above. Original licenses, notices and the Gaussian correction are retained.
+
+Structured-basis and semantic-bulk extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The selected (32,30,36) bit construction, A1/A5 block refinements, fixed
+middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic
+complex centers, complete data-front batching and circuit-specific assembly
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505.
+
+The semantic/bulk compatibility argument, literal scalar charge, product row
+stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23,
+commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints
+are adopted from the same contributor's PR #21,
+commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame
+work and the earlier nested-basis contributions.
+
+Completed-child semantic precision, arbitrary-coordinate routing, phase-cell
+Gaussian inversion and bulk tape transfer are credited to the RaD project
+(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through
+PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof
+sources retain their separate CC0 license and original NOTICE under
+references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI
+Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra
+assistance. These are source attributions, not claims about this session's
+runtime model. Related contributions by Rohan Arun and Aurel Prosz remain
+acknowledged in the imported notices. No exclusive priority or additional
+license condition is asserted.
+
+Copied retained-center extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The copied retained-center schedule in both orientations, its complex-phase
+transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. This extension inherits PR #32 at
+0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work.
+
+The two-stage topology and paid copied-stream endpoint correction are due
+to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab,
+through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition,
+9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil
+Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a.
+
+The contiguous corner method, incidence factorization and exact partition
+certificates are due to Rohan Arun (PR #31), method commit
+02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate
+specializes Dominik Scholz's parameterization (PR #33),
+a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof
+snapshots are preserved in references/copied-centers. Historical OpenAI
+Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to
+the respective imported sources. Existing PR #21/#23 and RaD attribution,
+licenses and the Gaussian correction remain in force.
+
+Copied centers with reversed (23,25) data corners, 2026-10-08
+Rohan Arun with substantial OpenAI Codex assistance supplies the composition,
+exact dimension23 controls and cost/assembly integration. James Chang's PR34
+supplies the reversed boundary family; icekylinx's PR36 supplies copied retained
+centers and the selected complex graph. The balanced assembly remains attributed
+to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan
+Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx,
+eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses.
+This is not a claim of formal verification, new foundational rank identities,
+global optimality or measured runtime speedup.
+
+Fixed middle basis with copied reversed corners (2026-10-08):
+Rohan Arun, with substantial OpenAI Codex assistance. Composition and
+simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34,
+Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures,
+eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed.
+
+Changed-graph composition with copied centers and fixed bases, 8 October 2026
+Prepared with OpenAI Codex assistance.
+The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J
+projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument,
+Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and
+Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods,
+Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc)
+PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40
+reversed integration, modular data tests and both-fixed baseline;
+RaD (hipotures) PR41 changed scalar DAGs, alternating point order and
+independent role compiler; RaD balanced routing/bulk interfaces, and all
+retained predecessors.
+Complete attribution and the conditional proof boundary are recorded in
+research/copied-fixed/PROOF.md; imported originals and source pins are retained.
+Original Apache-2.0 and CC0 notices remain applicable.
+
+Community follow-up integration (PRs #49, #45 and #26), 8 October 2026:
+Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out
+orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction
+composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and
+reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD /
+hipotures's alternating pair order and independent physical role compiler (#41).
+All predecessor attribution and conditional proof interfaces remain in force.
+
+Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic
+proofs, finite tensor execution, profile precision accounting and mixed-center
+reference checks (#45), with substantial OpenAI Codex assistance. See
+research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution.
+Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic
+frame/movement/guard lemmas and independent paired-circuit checks (#26). Original
+source notices and historical snapshots are preserved. Neither formal package
+claims a full formal proof of the multiplication algorithm or a new kappa.
+
+Joint frame compilation of skip-prefix strips
+
+The local compiler and exact finite witnesses were prepared by eumemic with
+substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic
+Claude assistance supplied the unmodified PR #53 skip-prefix producer.
+The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating
+Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang,
+Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt,
+OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors
+credited in the retained sources. See references/frame-compiler/pr48/NOTICE
+and references/frame-compiler/pr53/NOTICE for their original attribution.
+No authorship or review by those predecessors is claimed for this compiler.
+
+Joint dual-skip/frame-compiler composition (2026-10-08)
+---------------------------------------------------
+Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip
+scalar graph; original LICENSE and NOTICE are retained under
+references/frame-compiler/pr55. eumemic with substantial OpenAI Codex
+assistance: PR57 joint reversible frame compiler, serialized physical-word
+replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex
+assistance: this composition, independent integration and exact certificate.
+Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all
+predecessor authors retain the notices above and in pinned source files.
+No original copyright or Apache-2.0 notice is removed.
+
+Ranked reclamation after the PR58 joint-dual composition (2026-10-08)
+----------------------------------------------------------------
+Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical
+slots by descending current frame rank, retaining slot ID as the tie-breaker;
+complete replay, exact profiles, comparison and adversarial controls.
+The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57
+compiler. Its original shared compiler remains byte-identical. The PR55
+producer and all preceding attribution remain unchanged. The complete PR58
+comparison certificate and its original source/proof provenance are retained
+under references/frame-compiler/pr58.
+
+Skip-prefix strip producer, 8 October 2026
+By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5)
+assistance. The skip-prefix leave-one-out strip layout in
+research/skip-strips/skip_graph.py is new. Everything else reuses Chafik
+Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification
+code, exact data recovery and support-order sorting, together with:
+- Rohan Arun's PR #44 weighted carrier matching optimizer;
+- RaD (hipotures) PR #41 alternating point order;
+- every predecessor credited above.
+Complete attribution and the conditional proof boundary are recorded in
+research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain
+applicable.
+
+Local split-pair skip-prefix research continuation (2026-10-08)
+Prepared with substantial OpenAI Codex assistance at the user's request.
+New contribution: singleton/pair recursive partition refinement, finite summand
+order and moment search, and verified composition with inherited paid clones.
+Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips.
+Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone
+specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51
+whole-chain/source-partition cloning and earlier producer/interfaces.
+Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all
+stated historical AI assistance. All predecessor notices remain applicable.
+
+Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones):
+Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain
+source-partition clone operation is adapted from RaD / hipotures, PR #51,
+with original envelopes retained here. The scalar base is Avi Eisenberg's
+PR #53 skip-prefix layout, prepared with Anthropic Claude assistance.
+All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain
+in force. This extension is provided under the repository's Apache-2.0 terms.
+
+Community review checkpoint #50–#61, 8 October 2026
+Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex.
+Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude.
+Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance)
+and dual-suffix strips (#55, Anthropic Claude assistance).
+Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex.
+Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked
+reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame
+composition (#56), with Anthropic Claude and stated Codex validation assistance.
+RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones
+(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone
+composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter
+refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with
+his disclosed multi-tool and Codex assistance.
+Parallel #50/#52 records are reviewed and credited without replacing the earlier
+climbed-48 implementation; their exact commit history is retained. The separate
+#51 witness is retained as research; its source-graph/negative-basis data proof
+has not received the same full replay as #56's consumed compiler machinery.
+See docs/research/community-round2-review.md for precise validation boundaries.
+All earlier licenses, contributions and notices remain applicable.
+
+Interval strips and core-aware pair assembly
+
+The interval leave-one-out strips and the core-aware group-pair assembly in
+research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic
+Claude assistance. They build on PR #53's skip-prefix pipeline and its
+inherited PR #48 sources. The stacked witness in research/pair-assembly/frame
+uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier
+are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and
+verify_skip_frame.py. Original notices are retained.
+
+Stopped product-ring extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The opposite-bank generic projector factorization, componentwise atom-ring
+adapters, stopped recurrence and outer ordinary-interchange conversion,
+aligned pair-star producer with rational centers, exact denominator-21
+grid and selected (23,23)/(24,24) composition are contributed by icekylinx
+with substantial OpenAI GPT-6 Astra and Codex assistance. This extension
+builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is
+integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37.
+
+The retained ordinary leaf uses the preceding projector, corner and
+copied-center proofs. The selected two-stage topology retains Aurel Prosz
+(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly
+retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching,
+original source notices and each imported license remain unchanged.
+
+Partial-gauge extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The pair-first cube assembly, compatible backward frame enlargement,
+partial source-gauge schedule and stopped whole-projector composition are
+contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance, extending PR #104 at 948ce1510df750f4c18b96bdaef436a86f8bf834.
+
+The physical deferred bit word, reflected event accounting, fan-order
+clarification and signed two-stage endpoint are adopted from Zhihao Chen
+(jacklightChen), PR #97, e15350b66e4bf796153a68c240a6cc1b788abe3e, with
+Codex assistance. Its deferred readouts, V leaves, lifted frames and frozen
+witness originate in Swapnil Jain's 741e7aa078392553815df7926ee17ac5e25a8c38,
+with the original Claude disclosure retained. Cyclic interval and core-aware
+pair primitives build on Avi Eisenberg (ikeboy), PR #62,
+ad0f25ff7b23cff7f08ad237c2254e6ecf74257e, with Anthropic Claude assistance.
+Prior two-stage, copied-center, ordinary-leaf, semantic/bulk, routing and
+precision credits remain in force. Imported source notices and licenses
+are preserved under references/partial-gauge/; see SOURCES.json.
+
+Three-stage cover extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The arbitrary-subspace Clifford frame theorem, three-stage Cayley geometry,
+weighted q-adic GL cover, unit-lower weighted compiler, charged local-ring
+fallback, uniform batching, internal row borrowing and exact composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. This
+repository integration uses Codex assistance and extends
+PR #115, cf60442983c153a3a0f5272ea4713f99eba13c86.
+
+The selected local complex DAG and support/label replay are adopted from
+Copyright 2026 eumemic, PR #117, cbb05ce504d571546d9b7794c186a613c659c3bf,
+with its original Apache-2.0 terms and Claude assistance disclosure.
+The unchanged bit physical word retains Zhihao Chen (jacklightChen),
+PR #97, and Swapnil Jain's underlying witness and assistance notices.
+The prior opposite-bank, stopped ordinary-leaf, copied-center, topology,
+semantic/bulk, precision and analytic credits remain applicable.
+Original source notices and license bytes are preserved in
+references/three-stage-cover/pr117/ and references/partial-gauge/.
+
+Paired-cube and shared-core extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The paired-coordinate triple-cube identity, signed overlap channels,
+original-source involution, coordinate-star centers, concrete frame/carrier
+compiler, chronological source gauges, PR97 gauge-subset selection,
+orthogonal cross-stage routing and exact supplier/assembly integration
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance.
+Repository integration uses Codex assistance and extends PR #130 at
+6a9970a530119174507904e23592fd59ede19a5d.
+
+The substantial completed-core workspace-sharing principle is credited to
+an664, PR #128, 530588a019b4a74f09180680c9e3961bf649ec89, with its reported
+OpenAI Codex assistance. No source code, partition or serialized witness
+from that PR is imported. The new routing and paired-motif integration
+are described separately and claim no exclusive priority for broad sharing,
+paired-coordinate, Fourier or carrier-matching ideas.
+
+Selected coarse queries restrict the retained eumemic PR #117 positive DAG;
+its original Apache-2.0 and Claude assistance notices remain unchanged.
+The bit word and original frames retain Zhihao Chen's PR #97 and Swapnil
+Jain's frozen witness, notices and historical assistance disclosures.
+Earlier generalized Clifford, three-stage, uniform weighted recursion,
+ordinary-leaf, semantic/bulk, precision and analytic credits remain in force.
+Source-specific license bytes are preserved under references/.
+
+October 9 recycled-bit integration:
+DaysSky (#150), William Porter/hpst3r (#147), Thomas Marchand/Th0rgal (#146),
+Rohan Gupta/gupt1156 (#148), James Chang/jamesyc (#124), SovereignSteak (#122).
+The original notices and assistance disclosures are retained under research/,
+including research/recycled-bit-integration/NOTICE. Andrew Barnes/Bortlesboat
+(#101) repairs shared verifiers using rfu08's #64 counterexample. rfu08's
+scoped finite and formal-transfer packages are included separately; they do
+not establish the full multiplication theorem. Earlier and parallel credits
+remain applicable. Douglas Colkitt integrated these with OpenAI Codex assistance.
+
+SovereignSteak PR151 independently supplies the matching gauge/recycling
+composition and the selected 473/10^6 atom refinement; its original package
+and assistance disclosure are retained under research/gauge-recycling/.
+
+October 9 coordinated-frame and completed-entrance-bank integration:
+Dugongue PR186, 166a34d75e853e933855f0f7e940fe77c4bb6b8d, builds on
+Chafik Boukhalfa/chafreaky's PR181, 7fb2194801e3a10f54772c7f0d5505035a4fc0ad,
+and eumemic's PR168 v4, 4a3c769e5c5430e7114c4d3e099ff34664677f17.
+The frozen package and prerequisite archive preserve all author, source-license
+and assistance notices, including PR175's compiler optimization. DaysSky's
+carrier closure, James Chang's terminal substitution and balanced assembly,
+geckods' stopping refinements and all preceding framework credits remain.
+Rohan Arun's PR185 bootstrap and chafreaky's PR182 bit refinement are reviewed
+parallel contributions; their gains are not added to the selected witness.
+Douglas Colkitt integrated the package and supplied the bank scheduling
+supplement with OpenAI Codex assistance, under Apache-2.0. The all-size
+interfaces remain conditional; finite verification is not full formalization.
+
+P104 A2 and neutral-helper cleanup composition, 25 October 2026
+
+New common-word construction, source-bound verifier, exact composition audit
+and scoped component triage prepared for zxv (https://github.com/zxv) with
+substantial OpenAI Codex assistance and three subagent investigations.
+Ali Romman (https://github.com/aliromman) supplies PR5644 cleanup identities
+and constructor. PR5643 supplies the emitted A2 exchange. Full predecessor
+notices and licenses are retained unchanged in the source archive and inputs.
+https://github.com/CrocSwap/integer-mult-bounds/pull/5643
+https://github.com/CrocSwap/integer-mult-bounds/pull/5644
+Apache-2.0.
diff --git a/research/p104-a2-neutral-cleanup/PR-DRAFT.md b/research/p104-a2-neutral-cleanup/PR-DRAFT.md
new file mode 100644
index 0000000000..17e9765c65
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/PR-DRAFT.md
@@ -0,0 +1,38 @@
+Conditional κ = 0.00310644468 (+1.8133e-7, +0.00583756% over #5644): combine helper cleanup with the A2 exchange
+
+The three neutral-helper cleanups in [PR #5644](https://github.com/CrocSwap/integer-mult-bounds/pull/5644) coexist with [PR #5643](https://github.com/CrocSwap/integer-mult-bounds/pull/5643)'s A2 paid-rank exchange in one emitted chronological word. The resulting **conditional κ = 0.00310644468** improves on PR5644 by **1.8133e-7 (+0.00583756%)** and on PR5643 by **1.86468e-6 (+0.06006223%)**. Both construction orders reproduce the identical full instruction list, including every MOVE.
+
+The cleanup replaces sixteen late scalar gates by an exact dyadic input preparation and cancellation after each helper's last read. Those removed contacts let three main fields bypass unused stops, replacing H1+H5 by H6. The A2 rewrite separately changes H3+H5 to H2+H6. All independent inputs, productive endpoints and owned operations/order are retained; the additional ordinary work is charged.
+
+## Significance for researchers
+
+An independent helper's late scalar restoration can force paid movement on another role after the helper's useful work is over. A functional boundary replacement removes that dependency and remains compatible with a noncommuting scalar graph rewrite. The contribution proves compatibility on the actual common program and recomputes the complete invoice, rather than adding predecessor headline gains.
+
+## Complete bill and validation
+
+The full caller has 66,492 paid calls, 12,958 productive targets and rank-mass surplus 760. The local ordinary allowance is 220,220. Two exact rational engines enclose the unique fixed-invoice raw crossing in **(0.00310644469581, 0.00310644469582)**, leaving between 1.581e-11 and 1.582e-11 above the claim. Tested saving is 0.003106444685, with the existing compiler predicates and 1e-12 reserve unchanged.
+
+```sh
+python3.12 -B scripts/research_package.py --package research/p104-a2-neutral-cleanup
+python3.12 -B scripts/check_research_commit.py --package research/p104-a2-neutral-cleanup
+```
+
+Normal full and registered isolated optimized replays check all 752 transpose columns, 2,916 signed native maps with exact phases, the complete physical caller, compiler completion, ordinary allowances, BIT stock and all 54 strict plus four functional outer conditions. A separate implementation checks the reverse construction order and arbitrary-prefix identity. Actual copied-package one-byte source corruptions are rejected before retained-code import. `VALIDATION.md` records the commands, environment and limits; `COMPOSITION-PROOF.md` gives the scoped functional proof.
+
+The exact source heads are PR5643 `a3ff5c628bfc8825553d62d913f3e91f75d6825f` and PR5644 `c5871955d89bf73506fd68b0a5bf1cf2b3153c02`. All 19 retained input files are authenticated before imports; the original [PR #5627](https://github.com/CrocSwap/integer-mult-bounds/pull/5627) export authenticates all 36 payloads. Runtime replay needs no foreign Git objects or network. The same five framework assumptions and helper-endpoint contract remain. The huge uniform word and complete rounded multiplier are not materialized. Hosted CI, independent human scientific review, formal verification and selected-frontier promotion remain separate; the checkout is shallow, so the optional full-history preflight cannot run.
+
+## Component triage
+
+The three-agent investigation also ruled out two immediate free extensions on the composed word: all eight remaining H7 delivery values lie outside their same-frame public spans at first use, and all rational boundary pairing matrices vanish across 8,847 checked event/chart states for the 411 ZERO-to-FULL helpers. These are fixed-word, fixed-interface exclusions. Prepared-prefix storage and main/inverse wrappers carry no paid recursive jobs to delete. `COMPONENT-TRIAGE.md` retains the scope, receipts and next useful changed-interface experiment.
+
+## Credit
+
+[Ali Romman](https://github.com/aliromman) supplies PR5644's cleanup identities and constructor, PR5627's helper/basis composition, checker and authenticated source export. [zxv](https://github.com/zxv) supplies PR5643's emitted A2 exchange and this composition, with substantial OpenAI Codex assistance and three complementary subagent investigations. The earlier A2 identity and scoped audits retain [Chris R](https://github.com/Clear1nsight) and [ToikY](https://github.com/ToikY)'s attribution.
+
+Credit [flyingviper](https://github.com/flyingviper), [Scratch-net](https://github.com/Scratch-net), [Pierre-Loic Doulcet](https://github.com/hexapode), [Joel Pulikkan](https://github.com/GamingPuzzled), [DreamingOfClouds](https://github.com/DreamingOfClouds), [THU New Media Research Center](https://github.com/thu-nmrc), [David Arias](https://github.com/DavidAriasC), [Gareth Davidson](https://github.com/bitplane), [Cinna Davis](https://github.com/1337isnot1337), [Jacob Alan Sussman](https://github.com/jacobalansussman), [Cao Yifan](https://github.com/intqwq) and all retained helper/native/geometry/BIT/compiler/analytic notices. Apache-2.0.
+
+## Open next questions
+
+- Replace one remaining H7 delivery through a changed public complementary-value window. First emit the source retention, preparation, all native access and complete cleanup; the current fixed-time public span is insufficient.
+- Change a scalar contact so a checked helper prefix/suffix boundary pairing becomes nonzero. A basis-only search on the current common-chart ZERO-to-FULL group is exhausted; mixed boundary charts require a charged interface.
+- Independently review the emitted common word, phase-preserving frame induction and complete funded compiler/outer argument. Agent cross-checks are not independent human or proof-kernel acceptance.
diff --git a/research/p104-a2-neutral-cleanup/PRICE-CHECKPOINT.json b/research/p104-a2-neutral-cleanup/PRICE-CHECKPOINT.json
new file mode 100644
index 0000000000..54db89edff
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/PRICE-CHECKPOINT.json
@@ -0,0 +1,237 @@
+{
+  "cost": {
+    "compiler": {
+      "H": 80511200000000000,
+      "N": "2^80511200000000000",
+      "eta": {
+        "lower": "0.000000132842965546357133068088",
+        "upper": "0.000000132842965546357133068089"
+      },
+      "gap": "1/1400000000000",
+      "integer_test_exponent": 57508,
+      "logarithm_power": 1024,
+      "theta": "63/64",
+      "uniform_saving": "2174511279/700000000000",
+      "word_materialized": false
+    },
+    "full_forward_calls": 18,
+    "gain": "18133/100000000000",
+    "kappa": "77661117/25000000000",
+    "kappa_decimal": ".00310644468",
+    "margin_at_previous": {
+      "lower": "0.044072122145674172679584329881",
+      "upper": "0.044072122145674172679584329882"
+    },
+    "negative_controls": {
+      "old_BIT": "Rejected by outer inequalities",
+      "old_cutoff": "Rejected by completion-tail ratio greater than one"
+    },
+    "nonrecursive": {
+      "fixed_scalar_growth_bound": "At most 2^(16*26000) before native factors; a declared constant, not an attained norm.",
+      "local_paid_rank_mass": 5986,
+      "local_routes": 5172000,
+      "local_scalar": 220220,
+      "peak_owned_fields": 2,
+      "raw_budget": 1000000000,
+      "raw_scalar_upper": 184647552,
+      "tensor_native_growth_bound": "Each rank-r Gaussian has row l1 norm at most 2^(rf); use local_paid_rank_mass for the whole word."
+    },
+    "ordinary_BIT": {
+      "admitted": "17/5000",
+      "after_cover": "69/20000",
+      "atom": "1/250",
+      "before_cover": "3459/1000000",
+      "ordinary_saving": "8590884599/2500000000000",
+      "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses"
+    },
+    "outer": {
+      "functional_checks": {
+        "actual_new_BIT_stock_sublinear": "348599999999253/350000000000000",
+        "fixed_halo_explicit_metadata_branch": "26950000000001/350000000000",
+        "new_BIT_row_stock_sublinear_in_active_group": "1395799999997009/1400000000000000",
+        "new_semantic_group_guard": "3/1400000000000"
+      },
+      "margins": {
+        "boundary_algebraic_matrix": "1217726315679130195489/392000000000000000000000",
+        "fused_gaussian": "1217726315677390586467/392000000000000000000000",
+        "global_coordinate_router": "1087255639/350000000000",
+        "group_bit_router": "1522157894946738233083/490000000000000000000000",
+        "group_scans": "699999999999/700000000000",
+        "main_transform": "1217726315399130195489/392000000000000000000000",
+        "microbox_face_corrections": "26950000000001/350000000000",
+        "polynomial_products": "1399999999999/1400000000000",
+        "sparse_union_movement": "160467726315679130195489/392000000000000000000000"
+      },
+      "parameters": {
+        "a": "1087255639/350000000000",
+        "b": "4349022557/1400000000000",
+        "beta": "1399999999997/1400000000000",
+        "bit_saving": "17/5000",
+        "cap_xi": "356467726315399130195489/392000000000000000000000",
+        "complex_uniform_saving": "2174511279/700000000000",
+        "d": "1/1400000000000",
+        "epsilon": "1399999999999/1400000000000",
+        "kappa": "77661117/25000000000",
+        "lambda_": "398757422127/400000000000",
+        "lambda_prime": "279130195489/280000000000",
+        "layout": "1/1400000000000",
+        "q": "869804511/280000000000",
+        "r0": "1/14000000000000",
+        "stop": "1/1400000000000",
+        "tested_saving": "621288937/200000000000"
+      },
+      "strict_checks": {
+        "actual_bit_above_effective": "102744361/350000000000",
+        "actual_logarithmic_gamma_guard": "1/1400000000000",
+        "actual_logarithmic_group_guard": "35532273685020869804511/196000000000000000000000",
+        "alpha_logarithm_absorption": "1/14000000000000",
+        "boundary_algebraic_matrix_above_kappa": "1119130195489/392000000000000000000000",
+        "cap_above_band": "160467726315399130195489/392000000000000000000000",
+        "cap_below_cell": "35532273684320869804511/392000000000000000000000",
+        "cap_below_phase_cell_power": "427532273684600869804511/392000000000000000000000",
+        "complex_above_effective": "1/1400000000000",
+        "complex_below_one_over_32": "39400977443/1400000000000",
+        "complex_endpoint": "1/700000000000",
+        "epsilon_below_one": "1/1400000000000",
+        "epsilon_positive": "1399999999999/1400000000000",
+        "fine_prime_halo_umbrella": "7/2",
+        "fused_gaussian_above_kappa": "1117390586467/392000000000000000000000",
+        "gaussian_above_main": "139130195489/196000000000000000000000",
+        "global_coordinate_router_above_kappa": "1/350000000000",
+        "global_gamma_power_slack": "9/14000000000000",
+        "group_below_dimension": "1/700000000000",
+        "group_bit_router_above_kappa": "1746738233083/490000000000000000000000",
+        "group_gauge_power_slack": "35532273685006869804511/196000000000000000000000",
+        "group_key_fits_record": "1/700000000000",
+        "group_positive": "1399999999997/1400000000000",
+        "group_scans_above_kappa": "697825488723/700000000000",
+        "halo_covers_generic_inverse_radius": "5",
+        "improvement_over_user_baseline": "687737130400418148631/500000000000000000000000",
+        "lambda_above_internal": "1/2800000000000",
+        "lambda_above_sigma": "3/2800000000000",
+        "lambda_above_tau": "1/2800000000000",
+        "lambda_prime_above_lambda": "1/2800000000000",
+        "lambda_prime_above_leaf": "2795650977443/1960000000000000000000000",
+        "leaf_saving_above_effective": "1395650977443/1960000000000000000000000",
+        "main_transform_above_kappa": "839130195489/392000000000000000000000",
+        "membership_arithmetic_fits_record": "1/1400000000000",
+        "microbox_face_corrections_above_kappa": "26948912744363/350000000000",
+        "microbox_halo_volume": "110600000000003/1400000000000",
+        "new_complex_uniform_saving_above_b": "1/1400000000000",
+        "new_semantic_guard_with_C1_one": "1/1400000000000",
+        "polynomial_products_above_kappa": "1395650977447/1400000000000",
+        "positive_layout_slack": "1/1400000000000",
+        "q_below_effective": "1/1400000000000",
+        "q_below_internal": "1/1400000000000",
+        "q_below_leaf": "2795650977443/1960000000000000000000000",
+        "q_positive": "869804511/280000000000",
+        "short_record_fallback": "1395650977443/1400000000000",
+        "source_axis_superpolynomial": "1/1400000000000",
+        "sparse_union_movement_above_kappa": "159250000001119130195489/392000000000000000000000",
+        "stop_below_one": "1399999999999/1400000000000",
+        "stop_positive": "1/1400000000000",
+        "strassen_integer_power_gap": "1951441519231",
+        "support_router_span": "3/1400000000000",
+        "theta_positive_polynomial_power": "2",
+        "union_header_fits_record": "3/1400000000000",
+        "union_tag_work_per_visit_fits_record": "3/1400000000000"
+      }
+    },
+    "paid": {
+      "1": 41106,
+      "16": 416,
+      "2": 8226,
+      "24": 416,
+      "3": 8874,
+      "32": 416,
+      "4": 1638,
+      "40": 416,
+      "48": 416,
+      "5": 2862,
+      "56": 416,
+      "6": 396,
+      "64": 416,
+      "7": 270,
+      "72": 208
+    },
+    "paid_calls": 66492,
+    "previous_open_pr5627": "62125267/20000000000",
+    "productive_fields": 12958,
+    "query_shears": 15,
+    "rank_mass_surplus": 760,
+    "raw_ceiling": {
+      "derivative_upper": "-46262147594541099508843083517426769431530571502553738606261941/196159429230833773869868419475239575503198607639501078528",
+      "interval": [
+        "0",
+        "17/5000"
+      ]
+    },
+    "raw_headroom": [
+      "1581/100000000000000",
+      "791/50000000000000"
+    ],
+    "raw_root_interval": [
+      "310644469581/100000000000000",
+      "155322234791/50000000000000"
+    ],
+    "relative_gain_percent": "362660/62125267",
+    "strictification": {
+      "alpha": {
+        "lower": "0.999999999989000727034318538265",
+        "upper": "0.999999999989000727034318538266"
+      },
+      "cutoff": 17,
+      "delta": {
+        "lower": "0.967531019705250195840076347630",
+        "upper": "0.967531019705250195840076347631"
+      },
+      "floor": 18,
+      "gamma": {
+        "lower": "0.968151249902445992824910038589",
+        "upper": "0.968151249902445992824910038590"
+      },
+      "normalized_paid_upper": "1048576000976562501/1048576001073741824",
+      "power": 1024,
+      "reserve": "1/1000000000000",
+      "tail_block": 128,
+      "tail_decay": "39/40",
+      "tail_offset": "1/5",
+      "tested": "621288937/200000000000"
+    },
+    "targets": {
+      "1": 36,
+      "145": 208,
+      "17": 416,
+      "2": 72,
+      "25": 416,
+      "33": 416,
+      "4": 1638,
+      "41": 416,
+      "49": 416,
+      "5": 108,
+      "57": 416,
+      "65": 416,
+      "7": 90,
+      "73": 208,
+      "8": 288,
+      "9": 7398
+    },
+    "whole_idle_jobs": 3120
+  },
+  "declared_price_edits": [
+    [
+      "Q('.00310626335'), Q('.003106263355')",
+      "Q('.00310644468'), Q('.003106444685')"
+    ],
+    [
+      "PREVIOUS = Q('.00310440546')",
+      "PREVIOUS = Q('.00310626335')"
+    ],
+    [
+      "'kappa_decimal':'.00310626335'",
+      "'kappa_decimal':'.00310644468'"
+    ]
+  ],
+  "scope": "Exact rational complete caller invoice and compiler/outer price from new scalar/frame word; caller/native-boundary receipts reused. Fresh native-map and physical execution check pending.",
+  "status": "PASS_EXACT_PRICE_PENDING_FRESH_NATIVE_PHYSICAL_REPLAY"
+}
diff --git a/research/p104-a2-neutral-cleanup/README.md b/research/p104-a2-neutral-cleanup/README.md
new file mode 100644
index 0000000000..c1346da6f5
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/README.md
@@ -0,0 +1,72 @@
+# Conditional κ = 0.00310644468 from compatible functional cleanup
+
+This author-checked conditional construction combines [PR #5644](https://github.com/CrocSwap/integer-mult-bounds/pull/5644)'s three neutral-helper cleanups with [PR #5643](https://github.com/CrocSwap/integer-mult-bounds/pull/5643)'s A2 paid-rank exchange. The two construction orders produce the **identical complete chronological program**, including every native chart change. The gain comes from a changed fully charged word with fixed productive targets.
+
+| Quantity | PR5643 | PR5644 | Common word |
+|---|---:|---:|---:|
+| Conditional κ | 0.00310458 | 0.00310626335 | **0.00310644468** |
+| Complete paid calls | 66,546 | 66,492 | **66,492** |
+| Complete productive targets | 12,958 | 12,958 | **12,958** |
+| Rank-mass surplus | 760 | 760 | **760** |
+| Local ordinary scalar allowance | 220,166 | 220,208 | **220,220** |
+
+The increase is **1.8133e-7 (+0.00583756%) over PR5644** and **1.86468e-6 (+0.06006223%) over PR5643**. Two exact rational engines enclose the unique complete-invoice raw crossing in **(0.00310644469581, 0.00310644469582)**. The claim leaves between 1.581e-11 and 1.582e-11 of raw headroom. The tested saving is 0.003106444685; all compiler predicates and the existing 1e-12 reserve are retained.
+
+## What is deleted and what replaces it
+
+For helpers 291, 321 and 369, an invertible dyadic input basis preparation and a checked cancellation at the helper's last read replace sixteen late scalar cleanup gates. Every arbitrary independent input and productive helper endpoint is retained. The deleted contacts let main roles 55, 49 and 80 bypass an intermediate chart: each paid H1+H5 path becomes H6. All preparation, cancellation, scaling, movement and ordinary work appears in the emitted word and invoice.
+
+The A2 substitution separately replaces `B -= 4A; C += B` by `C -= 4A; C += B; B -= 4A`. It preserves the three-register endpoint on arbitrary prefix values while changing source 715's legal chart path from H5+H3 to H2+H6. The elementary identity and its earlier investigations retain their predecessor credit.
+
+For 0 < t < 1, the complete paid changes are strictly favorable:
+
+```
+relative to PR5644:  18 (2^t + 6^t - 3^t - 5^t) < 0
+relative to PR5643:  54 (6^t - 1 - 5^t) < 0
+productive-target change: 0
+```
+
+The exact common-word reconstruction and reverse-order audit establish compatibility before pricing. [COMPOSITION-PROOF.md](COMPOSITION-PROOF.md) gives the boundary identity, phase-preserving chart induction and limits. A histogram sum alone would not establish this result.
+
+## Reproduce
+
+Python 3.12 and the standard library suffice. From the repository root:
+
+```sh
+python3.12 -B scripts/research_package.py --package research/p104-a2-neutral-cleanup
+```
+
+Standalone checks, independent of the working directory:
+
+```sh
+python3.12 -I -O -B /absolute/path/to/p104-a2-neutral-cleanup/verify.py
+python3.12 -I -O -B /absolute/path/to/p104-a2-neutral-cleanup/audit_composition.py
+```
+
+`verify.py --quick` authenticates retained sources, regenerates both predecessors and the common word, and checks all rational scalar/frame rows and complete local paid/target changes. The full verifier checks 752 transpose columns, signed native maps with full global phases, the complete physical caller, both exact moment engines, compiler completion, ordinary allowances, BIT stock and all 54 strict plus four functional outer conditions. It compares the complete result with [FULL-RESULT.json](FULL-RESULT.json). Rejection controls cover invalid cancellation, wrong cut/frame, omitted preparation/A2 correction/owned erasure, excess target credit and unpaid children. `--write` explicitly regenerates the complete result receipt.
+
+[VALIDATION.md](VALIDATION.md) records executed commands, environment, actual source-corruption controls and unrun obligations. The separately implemented `audit_composition.py` reconstructs the entire program in the reverse construction order and tests the arbitrary-prefix A2 identity. It does not replace full physical or outer verification.
+
+## Sources and scope
+
+Exact scientific sources are PR5643 head `a3ff5c628bfc8825553d62d913f3e91f75d6825f` and PR5644 head `c5871955d89bf73506fd68b0a5bf1cf2b3153c02`, both consuming PR5627 head `ed4dc88a09a7d201971f6603b8c2074e95dd9c32`. Nineteen retained input files are bound by size, SHA256 and Git blob in [REPLAY-SOURCES.json](REPLAY-SOURCES.json) before any retained code import. The retained export authenticates all 36 predecessor payloads. Nineteen available PR5627 source-manifest rows are additionally checked against their declared hashes. Runtime replay needs no foreign Git objects or network access.
+
+Canonical main was refreshed to `df0137efd35e11b4445734bf612bdd4c7ebc330c`, selecting conditional κ = 0.00310045; priorities remain revision 7. TASK.json preserves the original pinned scalar-to-moment card at `f626db5c`, refined for this concrete component-deletion request. Current guidance, open PRs, recent handoffs and active discussions were checked. The original summarized claims through PR5612 are treated as a lineage, with PR5627/5643/5644 providing the current source words. This is not an exhaustive novelty certificate.
+
+The historical hosted nine-stage packing cap is outside this mixed-target productive-helper model. Its replacement is the proved unique complete-invoice raw ceiling on [0, 0.0034], of which the claim realizes more than 99.99999949%. This ceiling covers the fixed invoice rather than changed constructions. The same five framework assumptions and helper-endpoint contract remain. The enormous uniform word and full rounded multiplier are algorithm-defined rather than materialized. No selected-result change, formal proof, independent human acceptance or global optimum is claimed.
+
+## Significance for researchers
+
+The most immediately useful component is a cleanup contact that only restores an independent helper after its last use. An exact earlier basis preparation can replace that cleanup and remove a forced native stop on another role. The common-word audit shows this mechanism coexists with a noncommuting A2 graph rewrite. [COMPONENT-TRIAGE.md](COMPONENT-TRIAGE.md) ranks the remaining opportunities and records why zero-paid wrappers and the tested fixed helper cuts do not offer an immediate further gain.
+
+## Attribution
+
+[Ali Romman](https://github.com/aliromman) supplies the three cleanup identities, constructor, PR5627 helper/basis composition and retained source checker. [zxv](https://github.com/zxv) supplies PR5643's emitted A2 exchange and the new composition, developed with substantial OpenAI Codex assistance and three complementary subagent investigations. The A2 identity and earlier scoped investigations retain [Chris R](https://github.com/Clear1nsight) and [ToikY](https://github.com/ToikY)'s credit.
+
+Credit [flyingviper](https://github.com/flyingviper)'s relays, [Scratch-net](https://github.com/Scratch-net)'s prepared prefix, [Pierre-Loic Doulcet](https://github.com/hexapode)'s cascade, [Joel Pulikkan](https://github.com/GamingPuzzled), [DreamingOfClouds](https://github.com/DreamingOfClouds), [THU New Media Research Center](https://github.com/thu-nmrc), [David Arias](https://github.com/DavidAriasC), [Gareth Davidson](https://github.com/bitplane), [Cinna Davis](https://github.com/1337isnot1337), [Jacob Alan Sussman](https://github.com/jacobalansussman), [Cao Yifan](https://github.com/intqwq) and all retained helper/native/geometry/BIT/compiler/analytic notices. Root and archived NOTICE/LICENSE files retain the source-specific attribution. Apache-2.0.
+
+## Open next questions
+
+1. Change one named public-relay/preconditioning window to replace a remaining paid H7 delivery. Current same-frame public reconstruction is the discriminating first check; changing its window requires charging access, storage, restoration and every native job.
+2. Find a scalar/consumer edit that changes a checked ZERO-to-FULL prefix/suffix pairing. The fixed common-chart matrices vanish in the scoped all-event screen; another basis-only search on that word cannot add a target. Mixed initial/final charts require a charged interface.
+3. Independently review the common-word identity, native chart induction and complete funded compiler/outer argument. Author-side and subagent checks retain the inherited assumptions and are not independent human or proof-kernel admission.
diff --git a/research/p104-a2-neutral-cleanup/REGISTERED-REPLAY.log b/research/p104-a2-neutral-cleanup/REGISTERED-REPLAY.log
new file mode 100644
index 0000000000..8a1efc9464
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/REGISTERED-REPLAY.log
@@ -0,0 +1,30 @@
+CHECK Authenticate retained sources, regenerate both predecessors and the actual common word, replay all rational scalar/frame rows and complete paid-target deltas.
+PASS actual common word: all arbitrary-input rows, frames, fixed boundaries and full local paid-target delta
+PASS_P104_COMPOSITION_QUICK
+CHECK Fresh exact transpose/native phases/full caller, two moment engines, unchanged compiler predicates, BIT stock, all58 outer conditions and meaningful corruption controls; compare saved complete result.
+PASS actual common word: all arbitrary-input rows, frames, fixed boundaries and full local paid-target delta
+PASS every dense transpose column 752
+PASS every native map and exact phase 2916
+PASS full composed physical caller
+PASS two exact moment engines, compiler, BIT stock and all58 outer conditions ['310644469581/100000000000000', '155322234791/50000000000000']
+PASS_P104_COMPOSED_KAPPA_00310644468
+CHECK Separate scalar interpreter proves the arbitrary-prefix A2 identity and reverse construction order yields the identical complete chronological program.
+{
+  "candidate_events": 25449,
+  "commuting_edit_scope": "After all three cleanup replacements, the unique original A2 motif remains; replacing it and independently reconstructing all typed monotone paths gives the identical complete emitted program.",
+  "delta_vs_pr5643": {
+    "1": -3,
+    "5": -3,
+    "6": 3
+  },
+  "delta_vs_pr5644": {
+    "2": 1,
+    "3": -1,
+    "5": -1,
+    "6": 1
+  },
+  "scalar_events": 22015,
+  "scope": "Exact common scalar skeleton, three-column A2 identity for arbitrary prefix values, reverse-order full chart-path reconstruction, fixed physical boundary data and complete paid histogram. Native phases and caller/compiler evidence remain separate.",
+  "status": "PASS_INDEPENDENT_COMPOSITION_ORDER_AND_FRAME_AUDIT"
+}
+PASS_REGISTERED_RESEARCH_PACKAGE research/p104-a2-neutral-cleanup outcome=completed
diff --git a/research/p104-a2-neutral-cleanup/REPLAY-SOURCES.json b/research/p104-a2-neutral-cleanup/REPLAY-SOURCES.json
new file mode 100644
index 0000000000..1f7e9064ef
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/REPLAY-SOURCES.json
@@ -0,0 +1,123 @@
+{
+  "files": [
+    {
+      "git_blob": "7cf851189d95a471f7e50a7c9b0a60b8958734c9",
+      "local_path": "inputs/pr5643/WORD.json.gz",
+      "sha256": "b2ab778bdd5d68c62df0b51c12dc33fde93ad89213639a8e7da23e4b9cf6c3dc",
+      "size": 106609
+    },
+    {
+      "git_blob": "9500a34a537e6b40d31c73d4d17ca010c61d81dd",
+      "local_path": "inputs/pr5643/construct.py",
+      "sha256": "72ec32be21cf1bdb22bd68532947b2cf59625c8150c824ab958c0802aac97218",
+      "size": 3792
+    },
+    {
+      "git_blob": "b60955f312f76d08ee4f86ac2ad664e3ab4e46ea",
+      "local_path": "inputs/pr5643/inputs/pr5627-WORD.json.gz",
+      "sha256": "162e6f13a6e3805517946309bd6247eaa45b337ab9c39621806b254b415075ec",
+      "size": 107885
+    },
+    {
+      "git_blob": "e72cb02dba9b68d3bd5934371b5d25a44589c482",
+      "local_path": "inputs/pr5643/inputs/pr5627-local.py",
+      "sha256": "716d01a342467f87b14d67853d8de30740f9f2fa881afe271db0df5ef8b19697",
+      "size": 9392
+    },
+    {
+      "git_blob": "52b80e08828bdfd414fccc73d63ca064de88543d",
+      "local_path": "inputs/pr5644/NOTICE",
+      "sha256": "8ae3e07251d69074dddb5f94688f9d0ffd323214b4e48293c26c2d79b9acffe7",
+      "size": 296
+    },
+    {
+      "git_blob": "8572bf7a3ad40a1585222e3d4be729f02e07d80a",
+      "local_path": "inputs/pr5644/PROOF.md",
+      "sha256": "a599da8788777e8d703665322641ce4be6e025bddf96d79b07c1b7977e72dd50",
+      "size": 6057
+    },
+    {
+      "git_blob": "d21c40e63f2ebf999c1f6667374b50f3f79855a0",
+      "local_path": "inputs/pr5644/README.md",
+      "sha256": "e7f7f83f70ab231067bcfeadb7a03ecbcb69a18cccff6cf7085ef38c1f46d04a",
+      "size": 6530
+    },
+    {
+      "git_blob": "2908bf95db749ecb34b14e59e8d6bf3e2f200eea",
+      "local_path": "inputs/pr5644/RESULT.json",
+      "sha256": "b4252113207b900c8b853450ba6fdd5c030e563698dd1d90b04f79195ee96699",
+      "size": 16949
+    },
+    {
+      "git_blob": "410fd77bfdd18cfd89b460f03f59a394b0c19669",
+      "local_path": "inputs/pr5644/SOURCES.json",
+      "sha256": "bc32dcab5cc31a944c67cb25d59fe5c9822ec4cc397f6179f3349117cbdb9dc7",
+      "size": 1384
+    },
+    {
+      "git_blob": "4e04ce714ebf41ad9b523da434f93c89534d9ee7",
+      "local_path": "inputs/pr5644/TASK.json",
+      "sha256": "2145cc4b2483da5bac5eec0a875c42026d8c2720be7803f9f167ad28508f5170",
+      "size": 5754
+    },
+    {
+      "git_blob": "c2c3fc079f4b0946bfebbec92ca1440fa2fb0542",
+      "local_path": "inputs/pr5644/VALIDATION.md",
+      "sha256": "e05b47a509bc4a65b1aaba768f525ec593c6d984b67df89b61f0ed610b032e4c",
+      "size": 4771
+    },
+    {
+      "git_blob": "8773470dc510b4ced8ced40c203a7f8facb6e776",
+      "local_path": "inputs/pr5644/VERIFY.json",
+      "sha256": "399b47b4e31f19a262e5e995cbc3be59751cd2a285e1942d91b2c7cb0835469c",
+      "size": 1122
+    },
+    {
+      "git_blob": "8d4f38c5c9ac9ccbcdf47ee1c95a76e2441b7c8e",
+      "local_path": "inputs/pr5644/WITNESS.json",
+      "sha256": "0cf78fcbdb62bd4965536dd7d2f74f96761fcd95b11d750bc68ac81ceb1ec58c",
+      "size": 1124
+    },
+    {
+      "git_blob": "0bd3cff77581895917206a410b685ce4959e3e3e",
+      "local_path": "inputs/pr5644/WORD.json.gz",
+      "sha256": "3f2563d3c98f9d1170a583ba78bf171d5eb24e21976ddb026216bc637fc8a2ad",
+      "size": 107894
+    },
+    {
+      "git_blob": "1d9ff07f573bdbcf0e68d26eaa11862f958b2412",
+      "local_path": "inputs/pr5644/construct.py",
+      "sha256": "99ff4814b7c106973b149d1d4342c7e4608a027445bf07b19b5364658970099e",
+      "size": 5361
+    },
+    {
+      "git_blob": "bc900f0a1561b17b35492a80d10ae94f790d8378",
+      "local_path": "inputs/pr5644/inputs/pr5627-source.tar",
+      "sha256": "86c6bb839e14d79175ff8f3ed80b51a02d5c51a04deb0eff7ccea1afbe72923b",
+      "size": 1648640
+    },
+    {
+      "git_blob": "dc7f71a7814213d847c13460f8194e9e2f319de1",
+      "local_path": "inputs/pr5644/pricing.py",
+      "sha256": "1ceef843721af011c3af32b95e20486c3f53ef937489d559bec721c250499801",
+      "size": 10149
+    },
+    {
+      "git_blob": "ea32e0a12071cd921bb51e804667bf1ccbf2516f",
+      "local_path": "inputs/pr5644/sources.py",
+      "sha256": "add4c3a2567a11f36c88bbdd1c4f551044b68141e3faf7053da71b39972e8f41",
+      "size": 2617
+    },
+    {
+      "git_blob": "b8763f22ea159a3c504952830387b4e8a622394d",
+      "local_path": "inputs/pr5644/verify.py",
+      "sha256": "4735bc6a6fb148ee44bee27d9ba1cbe681d4a4451dea00e43d355d9c13e4a512",
+      "size": 5571
+    }
+  ],
+  "schema_version": 1,
+  "sources": {
+    "pr5643": "a3ff5c628bfc8825553d62d913f3e91f75d6825f",
+    "pr5644": "c5871955d89bf73506fd68b0a5bf1cf2b3153c02"
+  }
+}
diff --git a/research/p104-a2-neutral-cleanup/SOURCE-CONTROLS.json b/research/p104-a2-neutral-cleanup/SOURCE-CONTROLS.json
new file mode 100644
index 0000000000..ff7beb4a31
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/SOURCE-CONTROLS.json
@@ -0,0 +1,21 @@
+{
+  "status": "PASS_ACTUAL_COPIED_PACKAGE_SOURCE_CORRUPTION_CONTROLS",
+  "checks": [
+    {
+      "source": "inputs/pr5643/construct.py",
+      "exit_code": 1,
+      "reason": "Exact retained source SHA256 rejection before retained-code import"
+    },
+    {
+      "source": "inputs/pr5644/construct.py",
+      "exit_code": 1,
+      "reason": "Exact retained source SHA256 rejection before retained-code import"
+    },
+    {
+      "source": "inputs/pr5644/inputs/pr5627-source.tar",
+      "exit_code": 1,
+      "reason": "Exact retained source SHA256 rejection before retained-code import"
+    }
+  ],
+  "scope": "One byte changed in each of three temporary retained inputs; actual isolated optimized verifier --quick invoked. Original package and source bytes were never modified."
+}
diff --git a/research/p104-a2-neutral-cleanup/SOURCES.json b/research/p104-a2-neutral-cleanup/SOURCES.json
new file mode 100644
index 0000000000..cb99bc17e9
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/SOURCES.json
@@ -0,0 +1,32 @@
+{
+  "schema_version": 1,
+  "base_commit": "f626db5c3a3d781d8f7695038776c621651f75e1",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "ed33caef5c5827693e9572d252a66f99cbb73d40",
+      "sha256": "5732707cc1e460b090b53f2463162749ad860de878a18f7408938671d295a9d9"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65",
+      "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96"
+    }
+  ],
+  "scientific_predecessors": [
+    {
+      "pr": 5643,
+      "head": "a3ff5c628bfc8825553d62d913f3e91f75d6825f",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5643"
+    },
+    {
+      "pr": 5644,
+      "head": "c5871955d89bf73506fd68b0a5bf1cf2b3153c02",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5644"
+    }
+  ],
+  "runtime_source_inventory": "REPLAY-SOURCES.json",
+  "runtime_source_policy": "All retained code/data are authenticated by size, SHA256 and Git blob before import; PR5644 sources.py authenticates all36 original PR5627 export payloads. No runtime Git object or network dependency."
+}
diff --git a/research/p104-a2-neutral-cleanup/TASK.json b/research/p104-a2-neutral-cleanup/TASK.json
new file mode 100644
index 0000000000..fdea20ee7a
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/TASK.json
@@ -0,0 +1,124 @@
+{
+  "schema_version": 1,
+  "task_id": "scalar-to-moment",
+  "priority_revision": 7,
+  "base_commit": "f626db5c3a3d781d8f7695038776c621651f75e1",
+  "original_card": {
+    "id": "scalar-to-moment",
+    "question": "Can a changed frame itinerary remove a paid transition beyond the already covered scalar A2 contractions?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "certificates/selected-result.json",
+      "research/staged544-a2-graph-rewrite/README.md",
+      "research/staged544-separated-a2/README.md",
+      "research/staged544-a2-composition-audit/README.md",
+      "research/staged544-a1858-contraction-audit/README.md"
+    ],
+    "methods": [
+      "Derive the changed legal frame itinerary and exact child histogram.",
+      "Prove a scoped obstruction showing why that scalar gain cannot change the paid contract."
+    ],
+    "acceptance_gate": "An unchanged histogram is not a kappa gain; record any separate runtime or proof benefit explicitly.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read the A2 and separated-A2 constructions and their composition/contraction audits. Scalar contractions can preserve the complete recursive histogram; fewer ADDs alone do not justify further scans.",
+      "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+    },
+    "first_experiment": "Identify an actual paid transition to remove and construct a legal replacement frame itinerary, charging restoration, source windows and changed helpers. Compare complete before/after histograms. Stop if only scalar count changes; report that benefit honestly, without expanding the same scalar-only census.",
+    "bottleneck_link": "A legal change to the histogram, not addition count alone, is the bridge to an exponent gain.",
+    "allowed_variations": [
+      "One existing scalar simplification and one proposed frame-path change."
+    ],
+    "scope_change_triggers": [
+      "Submitting only another scalar count as completion of a paid-profile task."
+    ],
+    "overlap_terms": [
+      "scalar simplification",
+      "paid profile",
+      "R439",
+      "3998",
+      "4019",
+      "4112",
+      "4152",
+      "staged544-a2-graph-rewrite",
+      "staged544-separated-a2",
+      "staged544-a2-composition-audit",
+      "staged544-a1858-contraction-audit"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #3998: consecutive A2 scalar contraction",
+        "evidence": "research/staged544-a2-graph-rewrite/README.md",
+        "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+        "status": "author-checked",
+        "source_commit": "389268a6b5e0373a3125d5c6fcd6995f4ea324f5",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4019: separated A2 sites with unchanged recursive histogram",
+        "evidence": "research/staged544-separated-a2/README.md",
+        "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+        "status": "author-checked",
+        "source_commit": "f408e09df300b575235f7f77f81948071397e16d",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4112: composition audit",
+        "evidence": "research/staged544-a2-composition-audit/README.md",
+        "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+        "status": "author-checked",
+        "source_commit": "205b7380656ba4b6316a8a493b1a3c679b8f7a0e",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4152: A1858 contraction audit",
+        "evidence": "research/staged544-a1858-contraction-audit/README.md",
+        "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+        "status": "author-checked",
+        "source_commit": "caaa14cde5962adc372fdca71f63d0f29e73c8b2",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      }
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Compose PR5644 neutral-helper cleanup with PR5643 A2 rank exchange in one fully charged chronological word, and rank remaining component-deletion opportunities.",
+  "scope_change_reason": "The donor requested functional component deletions after the PR5643 submission; newly published PR5644 changes the same PR5627 source and offers three compatible cleanup deletions.",
+  "bottleneck_link": "Delete obsolete scalar contacts so main fields bypass paid stops, retaining every productive target and combining with a proved changed A2 dependency graph.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop at one complete source-bound conditional improvement over both PR5643 and PR5644, or a precise compatibility/pricing obstruction; preserve scoped negative sidequests.",
+  "outcome": "completed",
+  "evidence": "FULL-RESULT.json, NORMAL-REPLAY.log and registered replay; COMPOSITION-AUDIT.json and COMPOSITION-PROOF.md bind the common functional program. Scoped component screens are retained under analysis/.",
+  "author": "zxv (https://github.com/zxv), with substantial OpenAI Codex assistance",
+  "ai_assistance": "The coordinating Codex agent and three subagents performed compatibility construction, component triage and exact joint-cut investigation. Agent audits are not independent human or formal verification.",
+  "open_questions": [
+    {
+      "question": "Can a changed public relay or preconditioning window replace one of the remaining paid H7 owned deliveries?",
+      "why_it_matters": "Each successful fully charged replacement removes recursive cost, whereas the prepared-prefix lifetimes have no paid MOVE to remove.",
+      "first_step": "Change one named delivery window and emit its preparation, transport, cleanup and full original-input action; price every new job.",
+      "blocked_by": "Current same-frame public row-span reconstruction fails at all eight first delivery reads in the screened word; changed windows or paid access require new evidence."
+    },
+    {
+      "question": "Can changed scalar contacts create a nonzero prefix/suffix pairing in the large ZERO-to-FULL helper group?",
+      "why_it_matters": "The fixed common-chart boundary pairing matrices vanish, so another basis search on that word cannot add a target.",
+      "first_step": "Name a scalar/consumer edit that changes a checked boundary pairing, then reconstruct and price its whole word.",
+      "blocked_by": "The exact all-event common-chart screen is zero over Q on the composed word; mixed boundary charts are not free to mix."
+    },
+    {
+      "question": "Does independent scientific review accept the composed physical/outer argument under the retained framework assumptions?",
+      "why_it_matters": "Author and agent checks do not admit a new selected result.",
+      "first_step": "Replay the package from its retained source closure and inspect the reverse-order program equality and frame-induction proof.",
+      "blocked_by": "No proof-kernel or independent human verification is supplied."
+    }
+  ],
+  "source_comparison": {
+    "pr": 5644,
+    "head": "c5871955d89bf73506fd68b0a5bf1cf2b3153c02",
+    "kappa": "0.00310626335"
+  },
+  "refresh_limitation": "Canonical main refreshed successfully to df0137efd35e11b4445734bf612bdd4c7ebc330c; priority7. Checkout is shallow; optional full source-history preflight cannot run. Runtime sources are self-contained authenticated retained bytes."
+}
diff --git a/research/p104-a2-neutral-cleanup/VALIDATION.md b/research/p104-a2-neutral-cleanup/VALIDATION.md
new file mode 100644
index 0000000000..dc50028f74
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/VALIDATION.md
@@ -0,0 +1,46 @@
+# Validation of the common cleanup/A2 word
+
+Environment: Python 3.12.8, macOS 26.5.1, arm64; standard library only. Canonical publication base `df0137efd35e11b4445734bf612bdd4c7ebc330c`, priority revision 7. The scientific predecessor heads and retained input hashes are in REPLAY-SOURCES.json. Original frozen predecessor files remain unchanged.
+
+## Complete scientific replay
+
+```sh
+python3.12 -B research/p104-a2-neutral-cleanup/verify.py --write
+python3.12 -B scripts/research_package.py --package research/p104-a2-neutral-cleanup
+```
+
+The first command generated FULL-RESULT.json after a fresh normal full replay. The registered replay then checked quick source/word reconstruction, isolated optimized full replay against that saved receipt, and the separately implemented reverse-order composition audit. Both full runs include actual native-map and physical-caller checks; the earlier PRICE-CHECKPOINT.json reused source boundary receipts and is historical pricing-only evidence.
+
+Normal/registered logs record the outcomes. The complete receipt includes:
+
+- 743 independent public inputs, nine owned roles, eleven owned lifetimes and peak occupancy two; every productive target retained.
+- 752 exact dense transpose columns / 565,504 coefficients.
+- 2,916 signed native maps with exact phases and rejected wrong-phase control.
+- 7,488 physical contacts and 53,248 central-square columns; full main action and all 3,120 whole idle jobs.
+- Two exact rational moment engines, proved negative derivative through [0, 0.0034], strict compiler/floor/tail/rounding tests, BIT stock and all 54 strict plus four functional outer predicates.
+- 66,492 paid calls, 12,958 productive targets and surplus 760. Ordinary local allowance 220,220; complete nonrecursive upper bound 184,647,552 < 1e9.
+- 29 scoped rejection controls in FULL-RESULT.json, including source-hash checks. These controls differ in scope; source-hash function tests alone are not import-order tests.
+
+The tighter claim is κ = 0.00310644468, tested at 0.003106444685. The raw crossing is (0.00310644469581, 0.00310644469582). Compiler gap 1/1400000000000, logarithm/tensor power 1024, reserve 1e-12 and finite threshold N = 2^80511200000000000 all pass unchanged mathematical predicates.
+
+## Source authentication and actual corruption controls
+
+The verifier authenticates the frozen 19-file input inventory by size, SHA256 and Git blob before importing retained code. PR5644's original source reader then authenticates all 36 PR5627 export payloads. All 19 available original source-manifest rows match their declared SHA256 values. Runtime imports use a fresh private Python bytecode-cache directory.
+
+SOURCE-CONTROLS.json records three actual copied-package controls. One byte was independently changed in the retained PR5643 constructor, PR5644 constructor and PR5627 source archive in a temporary copy, then the real verifier ran with `-I -O -B --quick`. Every run rejected the exact source hash before any retained-code import. Original source bytes were never modified.
+
+## Separate scoped checks
+
+`audit_composition.py` proves reverse construction order reproduces the identical complete program, not only its histogram. The separate triage interpreter verifies every scalar endpoint row and owned zero exit on the common word. All eight H7 first-delivery same-frame public-span reconstructions fail in that stated model. The complete common-chart helper-cut scanner covers 8,847 event/chart states at 7,253 cuts for 411 ZERO-to-FULL helpers; all full rational boundary pairings vanish. Its 18 nontrivial states pass a separate backward-prefix/forward-suffix witness check. Portable copies reproduce the original saved JSON receipts.
+
+Read COMPONENT-TRIAGE.md and the analysis subdirectory for exact domain and completeness limitations. The source helper-cut scanner intentionally regenerates its own receipt; the independent witness checker does not regenerate it.
+
+## Signed-invoice preflight
+
+`export_invoices.py` extracts both complete paid/target histograms from the frozen PR5644 receipt and FULL-RESULT.json. The shared `scripts/compare_recursive_invoices.py` reports `uniformly_better`, Δpaid = 18(H2 + H6 − H3 − H5), and Δtargets = 0; the exact inputs and output are in invoices/. This is a uniform concave-tariff arithmetic check, separate from physical legality and supplier admission.
+
+## Publication and remaining obligations
+
+The local package metadata/source-pin check and final committed-byte check are separate from scientific replay. The optional full-history preflight cannot run because the shared repository is shallow. Pending scientific dependencies are retained as authenticated bytes and an archive, not supplied only by cached unmerged Git objects.
+
+No hosted CI, independent human review, Lean/proof-kernel check, historical all-suite replay or selected-frontier change is claimed. The same native all-width, owned erasure, compiler, precision/fixed-tape, analytic recovery and helper-endpoint hypotheses remain. The complete huge uniform program and rounded multiplier are not materialized. Agent cross-checks are author-side evidence.
diff --git a/research/p104-a2-neutral-cleanup/VERIFY.json b/research/p104-a2-neutral-cleanup/VERIFY.json
new file mode 100644
index 0000000000..5f80c2ea4b
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/VERIFY.json
@@ -0,0 +1,41 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py",
+        "--quick"
+      ],
+      "timeout_seconds": 60,
+      "checks": "Authenticate retained sources, regenerate both predecessors and the actual common word, replay all rational scalar/frame rows and complete paid-target deltas."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 600,
+      "checks": "Fresh exact transpose/native phases/full caller, two moment engines, unchanged compiler predicates, BIT stock, all58 outer conditions and meaningful corruption controls; compare saved complete result."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-B",
+        "{package}/audit_composition.py"
+      ],
+      "timeout_seconds": 60,
+      "checks": "Separate scalar interpreter proves the arbitrary-prefix A2 identity and reverse construction order yields the identical complete chronological program."
+    }
+  ]
+}
diff --git a/research/p104-a2-neutral-cleanup/WORD.json.gz b/research/p104-a2-neutral-cleanup/WORD.json.gz
new file mode 100644
index 0000000000..92e858d5db
Binary files /dev/null and b/research/p104-a2-neutral-cleanup/WORD.json.gz differ
diff --git a/research/p104-a2-neutral-cleanup/analysis/helper-cuts/ALL-EVENT-CUT-SCREEN.json b/research/p104-a2-neutral-cleanup/analysis/helper-cuts/ALL-EVENT-CUT-SCREEN.json
new file mode 100644
index 0000000000..c055049963
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/analysis/helper-cuts/ALL-EVENT-CUT-SCREEN.json
@@ -0,0 +1,1222 @@
+{
+  "status": "EXACT_FIXED_WORD_COMMON_CHART_BOUNDARY_PAIRING_EXCLUSION",
+  "source_word_sha256": "e94809cecf9e9cba56dd7a8a11ff1edeedc4c34013ff6caebdaf3b021351cf8c",
+  "group": [
+    3,
+    21,
+    34,
+    39,
+    61,
+    93,
+    115,
+    126,
+    133,
+    146,
+    151,
+    173,
+    188,
+    205,
+    224,
+    226,
+    227,
+    228,
+    229,
+    230,
+    231,
+    232,
+    233,
+    234,
+    235,
+    236,
+    237,
+    238,
+    239,
+    240,
+    241,
+    242,
+    243,
+    244,
+    245,
+    246,
+    247,
+    248,
+    249,
+    250,
+    251,
+    252,
+    253,
+    254,
+    255,
+    256,
+    257,
+    258,
+    260,
+    261,
+    262,
+    263,
+    264,
+    265,
+    266,
+    267,
+    268,
+    269,
+    270,
+    271,
+    272,
+    274,
+    276,
+    278,
+    279,
+    280,
+    281,
+    283,
+    284,
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+      "cut_after": 14980,
+      "frame": 396,
+      "dimension": 3,
+      "cohort": [
+        340,
+        525,
+        715
+      ],
+      "prefix_dimension": 1,
+      "suffix_dimension": 1,
+      "gcd_odd_numerators": 0,
+      "nonzero_internal_pairs": 0,
+      "nonzero_boundary_pairs": 0,
+      "active_owned": [
+        751
+      ],
+      "A": [
+        [
+          {
+            "525": "1",
+            "340": "-1"
+          },
+          {
+            "525": "1",
+            "712": "-4",
+            "715": "4"
+          }
+        ]
+      ],
+      "B": [
+        [
+          {
+            "715": "1/2"
+          },
+          {
+            "715": "1/2",
+            "525": "-2",
+            "471": "1",
+            "343": "1",
+            "338": "1"
+          }
+        ]
+      ],
+      "pairing": []
+    }
+  ],
+  "hits": []
+}
diff --git a/research/p104-a2-neutral-cleanup/analysis/helper-cuts/README.md b/research/p104-a2-neutral-cleanup/analysis/helper-cuts/README.md
new file mode 100644
index 0000000000..259380dd10
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/analysis/helper-cuts/README.md
@@ -0,0 +1,36 @@
+# The composed P104 word has no additional common-chart ZERO→FULL split
+
+**LOCAL-ONLY, exact finite fixed-word exclusion; no new κ claim.** The scientific input is the PR5643 A2 word composed with PR5644's three late-contact deletions, supplied by the coordinating agent as `../../WORD.json.gz`. Exact compressed SHA256: `e94809cecf9e9cba56dd7a8a11ff1edeedc4c34013ff6caebdaf3b021351cf8c`. The parent owns the full native/caller/compiler verification of that composition.
+
+This tests the previously unfinished joint multi-channel cut question for all 411 independent helper roles with initial chart 3 (ZERO) and final chart 127 (FULL). It permits arbitrary rational combinations of every role coframed at a proper intermediate chart; it therefore contains the dyadic dual-pair/unit-ideal search as a relaxation. It does not change the word, add charged boundary transports, combine different initial/final chart groups, or create a new owned-erasure contract.
+
+## Exact result and coverage
+
+The scan checks 8,847 event/chart states at 7,253 distinct event cuts, with all actual coframed cohorts of sizes 1 through 16. Nothing is omitted by a cohort-size bound. Only 18 states have both a nonzero admissible prefix-functional space and a nonzero admissible suffix-direction space. At each, both image spaces have dimension one and their exact boundary pairing is zero. Every other state has an empty prefix or suffix space. The complete pairing matrix is therefore zero at every covered cut, even over Q. There is no hidden multi-channel dyadic unit ideal to complete in this domain.
+
+`ALL-EVENT-CUT-SCREEN.json` records the word hash, all 411 boundary roles, a hash of the enumerated event/chart/cohort inventory, dimension census, and the exact coframe/boundary witnesses for all 18 nontrivial states. The state-inventory SHA256 is `d0a8a54552223d6d7e10cb850c82edadd4d006ee0836295b6354e40cff3784bf`.
+
+## Why this is a complete screen within the stated boundary
+
+At a cut let E be the current roles in one proper intermediate chart, P the actual scalar prefix, S the actual suffix, and G the 411-role boundary group. Row elimination computes all a supported in E for which c=aP is supported in G, then removes zero/dependent c images. Column elimination computes all b supported in E for which d=Sb is supported in G, again retaining a basis of boundary images. These are homogeneous exact-rational kernels of the unwanted boundary coordinates. Elementary elimination spans each full kernel; the second elimination retains the full boundary image space.
+
+Every legal old-input/fresh-suffix channel split must have c·d=1, in addition to the internal pairing and native/chart conditions. A zero pairing matrix between the two full rational boundary image spaces makes that necessary equation impossible. Null-prefix or null-suffix image directions cannot change c·d and need not be retained. This is stronger than failure of a particular pivot test; no dyadic basis compiler can make a zero rational pairing into one.
+
+All scalar ADD, SCALE and COPY events are explicitly considered on their chart. MOVE, INIT and CLEAR events are considered on each chart they touch after the membership change. Any chart untouched by an event has identical prefix rows and suffix columns: the event updates only its operands, all in another chart. Thus its latest recorded event/chart state has exactly the same two spaces and pairing. Initially no proper-chart role carries a G input, so the prefix space is zero before the first touched event. This compresses repeated unaffected states without omitting any cut/chart pairing. COPY is handled explicitly; no invertibility assumption about COPY is used.
+
+## Reproduce and independently check the nontrivial witnesses
+
+```sh
+python3.12 -B scan_all_cuts.py ../../WORD.json.gz
+python3.12 -I -O -B check_report.py ../../WORD.json.gz
+```
+
+Both use only Python's standard library. The independent check propagates each saved prefix functional backwards through the prefix and each suffix direction forwards through the suffix, checking the declared boundary images and all 18 zero pairings. This uses a different chronological direction from the discovery scan for the prefix evidence and directly executes each suffix vector. It also checks source hash and census totals. This check does not independently rederive completeness of every empty kernel; that claim follows the explicit elimination algorithm and its argument above.
+
+## Significance and open next questions
+
+The pending dyadic basis-completion algorithm in [PR #5611](https://github.com/CrocSwap/integer-mult-bounds/pull/5611) removes an individual-unit-pivot limitation, but it cannot help where the full boundary pairing matrix is zero. On this frozen composed word, the large ZERO→FULL group is not a remaining free helper-split opportunity.
+
+A mixed initial/final boundary group is a different construction question. Its bases cannot be freely mixed at their distinct boundary charts; the necessary native boundary transports and changed productive credits must be priced before using a union-group kernel as a claimed improvement. No such charged construction is supplied here. Changed words or changed boundary contracts can reopen this direction.
+
+Credit [Ali Romman](https://github.com/aliromman) for the helper-cut interface, source P104 construction and dyadic basis completion; the PR5643/PR5644 source notices retain the full native/helper/controller/compiler lineage. Prepared for [zxv](https://github.com/zxv) with substantial OpenAI Codex assistance; Apache-2.0. No new native or outer replay was run in this scoped investigation.
diff --git a/research/p104-a2-neutral-cleanup/analysis/helper-cuts/check_report.py b/research/p104-a2-neutral-cleanup/analysis/helper-cuts/check_report.py
new file mode 100644
index 0000000000..c6bf9ac9e2
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/analysis/helper-cuts/check_report.py
@@ -0,0 +1,59 @@
+"""Independent chronological checks of each saved nontrivial boundary pair.
+Prepared for zxv with substantial OpenAI Codex assistance; Apache-2.0.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from hashlib import sha256
+import gzip,json,sys
+def need(ok,why):
+ if not ok:raise ValueError(why)
+HERE=Path(__file__).resolve().parent
+word=Path(sys.argv[1]);w=json.loads(gzip.decompress(word.read_bytes()))
+p=json.loads((HERE/'ALL-EVENT-CUT-SCREEN.json').read_bytes())
+need(sha256(word.read_bytes()).hexdigest()==p['source_word_sha256'],'Independent boundary receipt check')
+need(p['all_snapshots']==p['bounded_snapshots']==sum(p['dimension_counts'].values()),'Independent boundary receipt check')
+need(not p['hits'],'Independent boundary receipt check')
+def add(row,k,v):
+ z=row.get(k,0)+v
+ if z:row[k]=z
+ else:row.pop(k,None)
+def vector(d):return {int(k):Q(v) for k,v in d.items()}
+def prefix(a,cut):
+ out=a.copy()
+ for e in reversed(w['program'][:cut+1]):
+  op,r=e[:2]
+  if op in ('INIT','CLEAR'):out.pop(r,None)
+  elif op=='SCALE':
+   if r in out:out[r]*=Q(e[-2])
+  elif op in ('ADD','COPY'):
+   add(out,e[2],Q(e[-2])*out.get(r,0))
+   if op=='COPY':out.pop(r,None)
+ return out
+def suffix(b,cut):
+ out=b.copy()
+ for e in w['program'][cut+1:]:
+  op,r=e[:2]
+  if op in ('INIT','CLEAR'):out.pop(r,None)
+  elif op=='SCALE':
+   if r in out:out[r]*=Q(e[-2])
+  elif op in ('ADD','COPY'):
+   val=Q(e[-2])*out.get(e[2],0)
+   if op=='COPY':out.pop(r,None)
+   add(out,r,val)
+ return out
+checks=0
+for state in p['reports']:
+ cut=state['cut_after'];A=[(vector(a),vector(c)) for a,c in state['A']];B=[(vector(b),vector(d)) for b,d in state['B']]
+ need(A and B and state['prefix_dimension']==state['suffix_dimension']==1,'Independent boundary receipt check')
+ for a,c in A:
+  need(prefix(a,cut)==c,'Independent boundary receipt check')
+  need(set(c)<=set(p['group']),'Independent boundary receipt check')
+ for b,d in B:
+  need(suffix(b,cut)==d,'Independent boundary receipt check')
+  need(set(d)<=set(p['group']),'Independent boundary receipt check')
+ for a,c in A:
+  for b,d in B:
+   need(sum(q*d.get(r,0) for r,q in c.items())==0,'Independent boundary receipt check')
+ checks+=1
+need(checks==18,'Independent boundary receipt check')
+print('PASS_INDEPENDENT_18_BOUNDARY_PAIRINGS_AND_COMPLETE_SNAPSHOT_COUNTS')
diff --git a/research/p104-a2-neutral-cleanup/analysis/helper-cuts/scan_all_cuts.py b/research/p104-a2-neutral-cleanup/analysis/helper-cuts/scan_all_cuts.py
new file mode 100644
index 0000000000..ec13953130
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/analysis/helper-cuts/scan_all_cuts.py
@@ -0,0 +1,125 @@
+"""Exact common-chart multi-channel cut screen on an explicitly supplied word.
+Prepared for zxv with OpenAI Codex assistance; Apache-2.0.
+Ali Romman supplies the cut interface and predecessor P104 construction.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import defaultdict,Counter
+from hashlib import sha256
+import gzip,json,pickle,time,math,sys
+HERE=Path(__file__).resolve().parent
+P=HERE.parents[1]
+OUT=HERE
+WORD=Path(sys.argv[1]) if len(sys.argv)>1 else P/'WORD.json.gz'
+w=json.loads(gzip.decompress(WORD.read_bytes()))
+n=w['public'];N=n+w['owned_fields'];main=set(w['live'])|{r+112 for r in w['live']}
+group={r for r in range(n) if r not in main and (w['initial'][r],w['final'][r])==(3,127)}
+frames=w['frames'];program=w['program']
+def add(a,b,q):
+ for k,v in b.items():
+  z=a.get(k,0)+q*v
+  if z:a[k]=z
+  else:a.pop(k,None)
+def enc(v):return {str(k):str(x) for k,x in v.items()}
+def span(b):
+ s={0}
+ for x in b:s|={a^x for a in tuple(s)}
+ return s
+# Record each event on every chart it touches. All other chart rows and suffix
+# columns are unchanged, so their previous recorded cut has identical spaces.
+current=w['initial']+[None]*w['owned_fields'];at=defaultdict(set)
+for r,f in enumerate(current):
+ if f is not None:at[f].add(r)
+snapshots={};active=set()
+for i,e in enumerate(program):
+ op,r=e[:2];touched=set()
+ if op in ('MOVE','INIT','CLEAR'):
+  if current[r] is not None:touched.add(current[r]);at[current[r]].remove(r)
+  if op=='MOVE':f=e[3]
+  elif op=='INIT':f=e[2];active.add(r)
+  else:f=None;active.remove(r)
+  current[r]=f
+  if f is not None:touched.add(f);at[f].add(r)
+ else:touched.add(e[-1])
+ for chart in touched:
+  E=tuple(sorted(at[chart]))
+  if chart not in (3,127) and len(E)>=1:snapshots.setdefault(i,[]).append((chart,E,tuple(active)))
+print('candidate',n,N,'group',len(group),'snapshots',sum(map(len,snapshots.values())),'maxcohort',max(len(s[1]) for ss in snapshots.values() for s in ss),flush=True)
+allcount=sum(map(len,snapshots.values()))
+state_hash=sha256(json.dumps([(i,f,E) for i,ss in snapshots.items() for f,E,_ in ss],separators=(',',':')).encode()).hexdigest()
+print('all event states',allcount,flush=True)
+# Suffix columns: reverse scalar execution updates the source column.
+columns=[{r:Q(1)} for r in range(N)];suffix={}
+for i in range(len(program)-1,-1,-1):
+ if i in snapshots:
+  suffix[i]={r:columns[r].copy() for r in set(r for _,E,_ in snapshots[i] for r in E)}
+ e=program[i];op,r=e[:2]
+ if op in ('INIT','CLEAR'):columns[r]={}
+ elif op=='SCALE':columns[r]={k:Q(e[-2])*v for k,v in columns[r].items()}
+ elif op in ('ADD','COPY'):
+  add(columns[e[2]],columns[r],Q(e[-2]))
+  if op=='COPY':columns[r]={}
+print('suffix snapshots complete',len(suffix),flush=True)
+def kernel_vectors(vectors,E):
+ """Return exact coframe vectors whose image is supported inside helper group."""
+ pivots={};out=[]
+ for r in E:
+  v={k:x for k,x in vectors[r].items() if k not in group};a={r:Q(1)}
+  while v:
+   k=min(v)
+   if k not in pivots:
+    q=v[k];pivots[k]=({j:x/q for j,x in v.items()},{j:x/q for j,x in a.items()});break
+   b,c=pivots[k];q=v[k];add(v,b,-q);add(a,c,-q)
+  if not v:
+   image={}
+   for s,q in a.items():add(image,vectors[s],q)
+   if not set(image)<=group:raise ValueError('Kernel image leaves the declared boundary group')
+   if image:out.append((a,image))
+ # Remove dependent image generators while retaining their coframe witnesses.
+ # Zero-image kernel directions cannot produce a unit boundary pairing.
+ image_basis={}
+ for a,image in out:
+  a=a.copy();image=image.copy()
+  while image:
+   k=min(image)
+   if k not in image_basis:
+    q=image[k]
+    image_basis[k]=({j:x/q for j,x in a.items()},{j:x/q for j,x in image.items()})
+    break
+   ba,bi=image_basis[k];q=image[k];add(a,ba,-q);add(image,bi,-q)
+ return list(image_basis.values())
+def dyadic(q):return q.denominator&(q.denominator-1)==0
+def oddpart(k):
+ k=abs(k)
+ while k and k%2==0:k//=2
+ return k
+rows=[{r:Q(1)} if r<n else {} for r in range(N)];reports=[];hits=[];coverage=Counter();started=time.time()
+for i,e in enumerate(program):
+ op,r=e[:2]
+ if op in ('INIT','CLEAR'):rows[r]={}
+ elif op=='SCALE':rows[r]={k:Q(e[-2])*v for k,v in rows[r].items()}
+ elif op=='COPY':rows[r]={k:Q(e[-2])*v for k,v in rows[e[2]].items()}
+ elif op=='ADD':add(rows[r],rows[e[2]],Q(e[-2]))
+ if i not in snapshots:continue
+ for f,E,active in snapshots[i]:
+  A=kernel_vectors(rows,E);B=kernel_vectors(suffix[i],E)
+  coverage[str((len(A),len(B)))]+=1
+  if not A or not B:continue
+  pairs=[];g=0
+  for ai,(a,c) in enumerate(A):
+   for bi,(b,d) in enumerate(B):
+    v=sum(x*b.get(r,0) for r,x in a.items());v2=sum(x*d.get(r,0) for r,x in c.items())
+    if v or v2:
+     pairs.append((ai,bi,v,v2));g=math.gcd(g,oddpart(v2.numerator))
+  rep=dict(cut_after=i,frame=f,dimension=len(frames[f]),cohort=list(E),prefix_dimension=len(A),suffix_dimension=len(B),gcd_odd_numerators=g,nonzero_internal_pairs=sum(v!=0 for _,_,v,v2 in pairs),nonzero_boundary_pairs=sum(v2!=0 for _,_,v,v2 in pairs),active_owned=list(active))
+  rep['A']=[(enc(a),enc(c)) for a,c in A]
+  rep['B']=[(enc(b),enc(d)) for b,d in B]
+  rep['pairing']=[(ai,bi,str(v),str(v2)) for ai,bi,v,v2 in pairs]
+  reports.append(rep)
+  if g==1:
+   hit={**rep,'A':[(enc(a),enc(c)) for a,c in A],'B':[(enc(b),enc(d)) for b,d in B],'pairing':[(ai,bi,str(v),str(v2)) for ai,bi,v,v2 in pairs]};hits.append(hit)
+   print('HIT',i,'frame',f,'dims',len(A),len(B),'pairs',len(pairs),'unitentries',sum(oddpart(v.numerator)==1 for _,_,v,_ in pairs),'dyadic',all(all(dyadic(x) for x in a.values()) for a,c in A+B),flush=True)
+ if i%500==0:print('at',i,'reports',len(reports),'hits',len(hits),'seconds',round(time.time()-started,1),flush=True)
+result={'status':'EXACT_FIXED_WORD_COMMON_CHART_BOUNDARY_PAIRING_EXCLUSION','source_word_sha256':sha256(WORD.read_bytes()).hexdigest(),'group':sorted(group),'all_snapshots':allcount,'bounded_snapshots':sum(map(len,snapshots.values())),'event_cuts':len(snapshots),'state_sha256':state_hash,'max_cohort':max(len(E) for ss in snapshots.values() for f,E,_ in ss),'dimension_counts':dict(coverage),'reports':reports,'hits':hits}
+(OUT/'ALL-EVENT-CUT-SCREEN.json').write_text(json.dumps(result,indent=2)+'\n')
+print('DONE',len(reports),'reports',len(hits),'hits',round(time.time()-started,1),flush=True)
diff --git a/research/p104-a2-neutral-cleanup/analysis/owned-deliveries/COMPOSED-CENTRE-RECONSTRUCTION.json b/research/p104-a2-neutral-cleanup/analysis/owned-deliveries/COMPOSED-CENTRE-RECONSTRUCTION.json
new file mode 100644
index 0000000000..ef1e5963f7
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/analysis/owned-deliveries/COMPOSED-CENTRE-RECONSTRUCTION.json
@@ -0,0 +1,168 @@
+{
+  "all_endpoint_rows_checked": 752,
+  "scope": "Exact scalar reference-coordinate necessity for replacing each first owned read by ordinary operations on public registers at the SAME literal frame; no new paid transports, ownership changes, or multi-frame/native maps are allowed. Not a global impossibility proof.",
+  "source_sha256": "e94809cecf9e9cba56dd7a8a11ff1edeedc4c34013ff6caebdaf3b021351cf8c",
+  "checks": [
+    {
+      "event": 32,
+      "owned": 751,
+      "frame": 3,
+      "dimension": 0,
+      "available_public_rows": 569,
+      "public_span_rank": 569,
+      "owned_value_support": 1,
+      "free_public_reconstructible": true,
+      "nonzero_residual_support": 0
+    },
+    {
+      "event": 13519,
+      "owned": 743,
+      "frame": 593,
+      "dimension": 1,
+      "available_public_rows": 1,
+      "public_span_rank": 1,
+      "owned_value_support": 115,
+      "free_public_reconstructible": false,
+      "nonzero_residual_support": 115
+    },
+    {
+      "event": 13530,
+      "owned": 744,
+      "frame": 594,
+      "dimension": 1,
+      "available_public_rows": 2,
+      "public_span_rank": 2,
+      "owned_value_support": 110,
+      "free_public_reconstructible": false,
+      "nonzero_residual_support": 110
+    },
+    {
+      "event": 13541,
+      "owned": 745,
+      "frame": 595,
+      "dimension": 1,
+      "available_public_rows": 1,
+      "public_span_rank": 1,
+      "owned_value_support": 118,
+      "free_public_reconstructible": false,
+      "nonzero_residual_support": 118
+    },
+    {
+      "event": 13550,
+      "owned": 746,
+      "frame": 597,
+      "dimension": 1,
+      "available_public_rows": 1,
+      "public_span_rank": 1,
+      "owned_value_support": 109,
+      "free_public_reconstructible": false,
+      "nonzero_residual_support": 109
+    },
+    {
+      "event": 13570,
+      "owned": 747,
+      "frame": 598,
+      "dimension": 1,
+      "available_public_rows": 1,
+      "public_span_rank": 1,
+      "owned_value_support": 105,
+      "free_public_reconstructible": false,
+      "nonzero_residual_support": 105
+    },
+    {
+      "event": 13585,
+      "owned": 748,
+      "frame": 599,
+      "dimension": 1,
+      "available_public_rows": 1,
+      "public_span_rank": 1,
+      "owned_value_support": 108,
+      "free_public_reconstructible": false,
+      "nonzero_residual_support": 108
+    },
+    {
+      "event": 13600,
+      "owned": 749,
+      "frame": 600,
+      "dimension": 1,
+      "available_public_rows": 1,
+      "public_span_rank": 1,
+      "owned_value_support": 101,
+      "free_public_reconstructible": false,
+      "nonzero_residual_support": 101
+    },
+    {
+      "event": 13615,
+      "owned": 750,
+      "frame": 601,
+      "dimension": 1,
+      "available_public_rows": 1,
+      "public_span_rank": 1,
+      "owned_value_support": 102,
+      "free_public_reconstructible": false,
+      "nonzero_residual_support": 102
+    },
+    {
+      "event": 13691,
+      "owned": 751,
+      "frame": 603,
+      "dimension": 2,
+      "available_public_rows": 3,
+      "public_span_rank": 3,
+      "owned_value_support": 120,
+      "free_public_reconstructible": true,
+      "nonzero_residual_support": 0
+    }
+  ],
+  "eight_centre_source_rank": 8,
+  "eight_centre_sources": [
+    {
+      "event": 13515,
+      "owned": 743,
+      "source": 173,
+      "support": 115
+    },
+    {
+      "event": 13526,
+      "owned": 744,
+      "source": 151,
+      "support": 110
+    },
+    {
+      "event": 13537,
+      "owned": 745,
+      "source": 146,
+      "support": 118
+    },
+    {
+      "event": 13546,
+      "owned": 746,
+      "source": 133,
+      "support": 109
+    },
+    {
+      "event": 13566,
+      "owned": 747,
+      "source": 256,
+      "support": 105
+    },
+    {
+      "event": 13581,
+      "owned": 748,
+      "source": 92,
+      "support": 108
+    },
+    {
+      "event": 13596,
+      "owned": 749,
+      "source": 9,
+      "support": 101
+    },
+    {
+      "event": 13611,
+      "owned": 750,
+      "source": 240,
+      "support": 102
+    }
+  ]
+}
diff --git a/research/p104-a2-neutral-cleanup/analysis/owned-deliveries/COMPOSITION-SKEPTICAL-REVIEW.md b/research/p104-a2-neutral-cleanup/analysis/owned-deliveries/COMPOSITION-SKEPTICAL-REVIEW.md
new file mode 100644
index 0000000000..a2ed20f540
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/analysis/owned-deliveries/COMPOSITION-SKEPTICAL-REVIEW.md
@@ -0,0 +1,25 @@
+# Scoped skeptical review of the common word
+
+Local-only separate agent review; substantial OpenAI Codex assistance. This is not independent human review, formal verification or a full inherited theorem audit.
+
+Candidate: `/private/tmp/integer-mult-p104-a2-submit/research/p104-a2-neutral-cleanup/WORD.json.gz`, compressed SHA256 `e94809cecf9e9cba56dd7a8a11ff1edeedc4c34013ff6caebdaf3b021351cf8c`.
+
+Sources read: COMPOSITION-PROOF.md, audit_composition.py, verify.py, pricing.py, COMPOSITION.json, and the retained [Ali Romman](https://github.com/aliromman) [PR #5644](https://github.com/CrocSwap/integer-mult-bounds/pull/5644) constructor, WITNESS.json and PROOF.md. The A2 source is [zxv](https://github.com/zxv)'s [PR #5643](https://github.com/CrocSwap/integer-mult-bounds/pull/5643). Exact heads remain c5871955d89bf73506fd68b0a5bf1cf2b3153c02 and a3ff5c628bfc8825553d62d913f3e91f75d6825f, respectively.
+
+No concrete objection was found to the changed local functional argument:
+
+1. For a cleanup helper h, the checked prefix relation is a full rational row equality. Preconditioning changes only the initial coordinate h; substitution turns the canceled prefix row into s*x_h. All involved input operations share the initial chart, and cut operations share the final chart. Division by the dyadic unit s is an ordinary SCALE already emitted and charged.
+2. The original complete scalar endpoint has helper h only in its own output. Therefore preparing h cannot change the other final rows. No later operation reads h as a source, so replacing its cut value and deleting only its own scalar suffix cannot feed a changed value into another output.
+3. The A2 identity holds for every prefix triple, without a zero-input assumption. The lightweight audit confirms that applying A2 after cleanup produces the exact common scalar skeleton and independently reconstructs the identical entire typed MOVE/scalar program. This is stronger than assuming disjoint histogram deltas.
+4. Public/owned inventories and boundary charts remain fixed. The complete owned-event subsequence is retained. The extra ordinary scalar charge is explicit: 220,220 total, +54 above the A2 word and +12 above cleanup alone. Every productive target is retained; the changed local paid deltas are exactly the declared A2 and three cleanup deltas.
+5. The frame-invariant proof uses full chart maps with phase and exact chronological native transports. It does not commute noncommuting operators or distribute tensor powers over sums. Actual phase/native/caller verification remains necessary and belongs to the parent's separate full replay.
+
+Executed only cheap checks:
+
+- `python3.12 -B research/p104-a2-neutral-cleanup/audit_composition.py`: PASS_INDEPENDENT_COMPOSITION_ORDER_AND_FRAME_AUDIT; 25,449 chronological events and 22,015 scalar events.
+- A separately implemented scalar interpreter in `check_composed_centres.py` checks every one of the 752 complete endpoint rows and all final owned zero states. This interpreter does not import the construction or local checker.
+- The same interpreter repeats the current-frame public-span screen on the actual composed word. All eight H7 centre sources remain independent and none is already reconstructible from available public values at its first delivery chart/time. Prepared751 first reads are reconstructible but carry no paid MOVE. See COMPOSED-CENTRE-RECONSTRUCTION.json.
+
+Suggested wording clarification: the original helper's endpoint is its independent input **as a scalar row in normalized reference coordinates**; physically it is still the credited map Φ_final Φ_initial^-1. This is a clarity point, not a mathematical objection.
+
+Not rerun here: native phases, physical caller, rational price engines, compiler/outer suite, source archive import or hosted CI. No new ownership, erasure, native alphabet or all-width realization premise was identified in this local review; the inherited five framework assumptions and helper-endpoint contract remain.
diff --git a/research/p104-a2-neutral-cleanup/analysis/owned-deliveries/check_composed_centres.py b/research/p104-a2-neutral-cleanup/analysis/owned-deliveries/check_composed_centres.py
new file mode 100644
index 0000000000..37821b2911
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/analysis/owned-deliveries/check_composed_centres.py
@@ -0,0 +1,60 @@
+"""Source-bound same-frame owned-delivery screen; zxv with OpenAI Codex assistance. Apache-2.0."""
+from pathlib import Path
+from fractions import Fraction as Q
+from hashlib import sha256
+import gzip,json
+HERE=Path(__file__).resolve().parent
+src=HERE.parents[1]/'WORD.json.gz'
+w=json.loads(gzip.decompress(src.read_bytes()))
+n=w['public']+w['owned_fields']; rows=[{i:Q(1)}for i in range(n)]
+frames=w['initial']+[None]*w['owned_fields'];active=set();probed=set();copies=[];checks=[]
+def add(a,b,q):
+ for k,v in b.items():
+  z=a.get(k,0)+q*v
+  if z:a[k]=z
+  else:a.pop(k,None)
+def basis(vectors):
+ out={}
+ for row in vectors:
+  row=dict(row)
+  while row:
+   p=min(row)
+   if p not in out:
+    q=row[p];out[p]={k:v/q for k,v in row.items()};break
+   add(row,out[p],-row[p])
+ return out
+def residue(row,b):
+ row=dict(row)
+ while row:
+  p=min(row)
+  if p not in b:break
+  add(row,b[p],-row[p])
+ return row
+for i,e in enumerate(w['program']):
+ op,r=e[:2]
+ if op=='INIT':rows[r]={};frames[r]=e[2];active.add(r);probed.discard(r)
+ elif op=='CLEAR':rows[r]={};frames[r]=None;active.remove(r)
+ elif op=='MOVE':frames[r]=e[3]
+ else:
+  q=Q(e[-2]);f=e[-1]
+  if op=='SCALE':rows[r]={k:q*v for k,v in rows[r].items()}
+  else:
+   s=e[2]
+   if s in active and s not in probed:
+    avail=[j for j in range(w['public']) if frames[j]==f]
+    b=basis(rows[j]for j in avail)
+    rem=residue(rows[s],b)
+    checks.append({'event':i,'owned':s,'frame':f,'dimension':len(w['frames'][f]),'available_public_rows':len(avail),'public_span_rank':len(b),'owned_value_support':len(rows[s]),'free_public_reconstructible':not rem,'nonzero_residual_support':len(rem)})
+    probed.add(s)
+   if op=='COPY':
+    rows[r]={k:q*v for k,v in rows[s].items()}
+    if r in active and r<751:copies.append({'event':i,'owned':r,'source':s,'row':dict(rows[r])})
+   else:add(rows[r],rows[s],q)
+for r,row in enumerate(rows):
+ expected={r:Q(1)}if r<w['public']else{}
+ if r-112 in w['live']:expected[r-112]=Q(1)
+ if row!=expected:raise ValueError('Independent endpoint mismatch on row '+str(r))
+if active or frames[:w['public']]!=w['final']:raise ValueError('Final chart/owned lifetime mismatch')
+out={'all_endpoint_rows_checked':len(rows),'scope':'Exact scalar reference-coordinate necessity for replacing each first owned read by ordinary operations on public registers at the SAME literal frame; no new paid transports, ownership changes, or multi-frame/native maps are allowed. Not a global impossibility proof.','source_sha256':sha256(src.read_bytes()).hexdigest(),'checks':checks,'eight_centre_source_rank':len(basis(x['row']for x in copies)),'eight_centre_sources':[{'event':x['event'],'owned':x['owned'],'source':x['source'],'support':len(x['row'])}for x in copies]}
+(HERE/'COMPOSED-CENTRE-RECONSTRUCTION.json').write_text(json.dumps(out,indent=2)+'\n')
+print(json.dumps(out,indent=2))
diff --git a/research/p104-a2-neutral-cleanup/audit_composition.py b/research/p104-a2-neutral-cleanup/audit_composition.py
new file mode 100644
index 0000000000..4319b83c74
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/audit_composition.py
@@ -0,0 +1,71 @@
+"""Independent audit of the common scalar skeleton and typed frame lowering.
+
+Prepared for zxv with substantial OpenAI Codex assistance; Apache-2.0.
+This is a scoped composition audit, not independent human or kernel review.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter
+import gzip,json
+HERE=Path(__file__).resolve().parent
+def read(p):return json.loads(gzip.decompress(p.read_bytes()))
+def need(ok,why):
+ if not ok:raise ValueError(why)
+def scalar(w):return[e for e in w['program']if e[0]!='MOVE']
+def span(b):
+ s={0}
+ for v in b:s|={x^v for x in tuple(s)}
+ return s
+source=read(HERE/'inputs/pr5643/inputs/pr5627-WORD.json.gz')
+a2=read(HERE/'inputs/pr5643/WORD.json.gz')
+cleanup=read(HERE/'inputs/pr5644/WORD.json.gz')
+composed=read(HERE/'WORD.json.gz')
+old=[['ADD',388,715,'-4',825],['ADD',340,388,'1',825]]
+new=[['ADD',340,715,'-4',396],['ADD',340,388,'1',825],['ADD',388,715,'-4',127]]
+def replace(w):
+ seq=scalar(w);hits=[i for i in range(len(seq)-1)if seq[i:i+2]==old]
+ need(len(hits)==1,'One source A2 motif survives cleanup');i=hits[0]
+ return seq[:i]+new+seq[i+2:]
+need(scalar(a2)==replace(source),'Exact original A2 scalar replacement')
+need(scalar(composed)==replace(cleanup),'Common scalar skeleton equals A2 applied after cleanup')
+# Reconstruct typed monotone paths independently from this common skeleton.
+frames=[span(b)for b in cleanup['frames']]
+current=cleanup['initial']+[None]*cleanup['owned_fields'];active=set();events=[]
+def move(r,f):
+ a=current[r]
+ if a==f:return
+ need(a is not None and (frames[f]<frames[a]if r in active else frames[a]<frames[f]),'Legal strict nested chart path')
+ events.append(['MOVE',r,a,f,r in active]);current[r]=f
+for e in replace(cleanup):
+ op,r=e[:2]
+ if op=='INIT':
+  need(current[r]is None,'Fresh owned role');active.add(r);current[r]=e[2]
+ elif op=='CLEAR':
+  move(r,e[2]);active.remove(r);current[r]=None
+ else:
+  move(r,e[-1])
+  if op!='SCALE':move(e[2],e[-1])
+ events.append(e)
+for r,f in enumerate(cleanup['final']):move(r,f)
+need(events==composed['program'],'Reverse construction order gives identical chronological native/scalar word')
+need(all(composed[k]==source[k]for k in ('initial','final','frames','ports','live','public','owned_fields')),'All physical boundary data unchanged')
+def matrix(seq):
+ rows={r:{r:Q(1)}for r in (340,388,715)}
+ for e in seq:
+  dst,src,q=e[1],e[2],Q(e[-2])
+  for j,x in rows[src].items():
+   z=rows[dst].get(j,0)+q*x
+   if z:rows[dst][j]=z
+   else:rows[dst].pop(j,None)
+ return rows
+need(matrix(old)==matrix(new),'A2 acts identically on every possible prefix triple')
+def paid(w):return Counter(abs(len(w['frames'][e[3]])-len(w['frames'][e[2]]))for e in w['program']if e[0]=='MOVE')
+def delta(a,b):
+ d=paid(a);d.subtract(paid(b));return{r:n for r,n in d.items()if n}
+need(delta(composed,cleanup)=={2:1,3:-1,5:-1,6:1},'Exact full A2 paid delta after cleanup')
+need(delta(composed,a2)=={1:-3,5:-3,6:3},'Exact full cleanup paid delta after A2')
+# Incorrectly replacing the old pair by only its first two proposed gates fails
+# for arbitrary values even when all helper-cleanup identities are retained.
+need(matrix(old)!=matrix(new[:-1]),'Missing final shear fails the composed functional identity')
+result={'status':'PASS_INDEPENDENT_COMPOSITION_ORDER_AND_FRAME_AUDIT','candidate_events':len(events),'scalar_events':len(scalar(composed)),'commuting_edit_scope':'After all three cleanup replacements, the unique original A2 motif remains; replacing it and independently reconstructing all typed monotone paths gives the identical complete emitted program.','delta_vs_pr5644':delta(composed,cleanup),'delta_vs_pr5643':delta(composed,a2),'scope':'Exact common scalar skeleton, three-column A2 identity for arbitrary prefix values, reverse-order full chart-path reconstruction, fixed physical boundary data and complete paid histogram. Native phases and caller/compiler evidence remain separate.'}
+print(json.dumps(result,sort_keys=True,indent=2))
diff --git a/research/p104-a2-neutral-cleanup/export_invoices.py b/research/p104-a2-neutral-cleanup/export_invoices.py
new file mode 100644
index 0000000000..98993e1537
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/export_invoices.py
@@ -0,0 +1,37 @@
+"""Export complete source-bound invoices for the shared concave-order preflight.
+
+Prepared for zxv with substantial OpenAI Codex assistance; Apache-2.0.
+This is receipt extraction, not a circuit or supplier-admission verifier.
+"""
+from pathlib import Path
+import json
+
+HERE = Path(__file__).resolve().parent
+CONTRACT = {
+    'model': 'mixed-target-unnormalized-power-v1',
+    'rank_semantics': 'H_r costs r^(1-C); debit surrendered productive fields',
+    'ambient_rank': 145,
+    'boundary': 'Complete PR5627-derived p16/a7 caller before the same mixed-target compiler',
+}
+
+
+def main():
+    output = HERE/'invoices'
+    output.mkdir(exist_ok=True)
+    for name, source in (
+        ('pr5644', HERE/'inputs/pr5644/RESULT.json'),
+        ('common', HERE/'FULL-RESULT.json'),
+    ):
+        cost = json.loads(source.read_bytes())['complete_cost']
+        invoice = {
+            'schema': 'integer-mult-recursive-invoice/v1',
+            'contract': CONTRACT,
+            'paid': cost['paid'],
+            'targets': cost['targets'],
+        }
+        (output/(name+'.json')).write_text(json.dumps(invoice, indent=2)+'\n')
+    print('EXPORTED_COMPLETE_RECURSIVE_INVOICES')
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/p104-a2-neutral-cleanup/inputs/pr5643/WORD.json.gz b/research/p104-a2-neutral-cleanup/inputs/pr5643/WORD.json.gz
new file mode 100644
index 0000000000..7cf851189d
Binary files /dev/null and b/research/p104-a2-neutral-cleanup/inputs/pr5643/WORD.json.gz differ
diff --git a/research/p104-a2-neutral-cleanup/inputs/pr5643/construct.py b/research/p104-a2-neutral-cleanup/inputs/pr5643/construct.py
new file mode 100644
index 0000000000..9500a34a53
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/inputs/pr5643/construct.py
@@ -0,0 +1,64 @@
+"""Construct a complete P104 A2 paid-rank exchange against exact PR5627 bytes.
+
+Retains Ali Romman's P104 local checker and all predecessor notices. The A2
+identity and complete-boundary discipline are credited to Chris R/Clear1nsight
+(PR3998), ToikY(PR4019), and the scoped audits(PR4112/4152). New P104 witness,
+construction and checks with substantial OpenAI Codex assistance. Apache-2.0.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter
+from copy import deepcopy
+from hashlib import sha256
+import argparse,gzip,importlib.util,json,sys
+HERE=Path(__file__).resolve().parent
+SOURCE_WORD='162e6f13a6e3805517946309bd6247eaa45b337ab9c39621806b254b415075ec'
+SOURCE_CHECKER='716d01a342467f87b14d67853d8de30740f9f2fa881afe271db0df5ef8b19697'
+EXPECTED='c7545eab4e1394ba942a7ac8e4d70860d172cabda151a559fd566478aa38204b'
+def need(ok,why):
+ if not ok:raise ValueError(why)
+def construct():
+ for rel,digest in [('inputs/pr5627-WORD.json.gz',SOURCE_WORD),('inputs/pr5627-local.py',SOURCE_CHECKER)]:
+  need(sha256((HERE/rel).read_bytes()).hexdigest()==digest,'Exact source pin '+rel)
+ spec=importlib.util.spec_from_file_location('retained_p104_checker',HERE/'inputs/pr5627-local.py');L=importlib.util.module_from_spec(spec);spec.loader.exec_module(L)
+ w=json.loads(gzip.decompress((HERE/'inputs/pr5627-WORD.json.gz').read_bytes()));v=deepcopy(w)
+ need(w['program'][14975]==['ADD',388,715,'-4',825] and w['program'][14977]==['ADD',340,388,'1',825],'Literal old pair')
+ need(w['program'][14976]==['MOVE',340,396,825,False],'Only the declared intermediate transport')
+ replacement=[['ADD',340,715,'-4',396],['ADD',340,388,'1',825],['ADD',388,715,'-4',127]]
+ need([w['frames'][f]for f in[396,825,127]]==[[13,70,416],[7,10,32,65,144,272],[1,2,4,8,16,32,64,128,256]],'Exact existing frames')
+ scalar=[]
+ for i,e in enumerate(w['program']):
+  if i==14975:scalar.extend(replacement)
+  if i not in(14975,14977) and e[0]!='MOVE':scalar.append(e[:])
+ frames=[L.span(b)for b in w['frames']];n=w['public'];current=w['initial']+[None]*w['owned_fields'];active=set();out=[]
+ def move(r,f):
+  a=current[r]
+  if a==f:return
+  private=r in active
+  need(a is not None and (frames[f]<frames[a]if private else frames[a]<frames[f]),'Strict nested typed transport')
+  out.append(['MOVE',r,a,f,private]);current[r]=f
+ for e in scalar:
+  op,r=e[:2]
+  if op=='INIT':need(current[r]is None,'Owned slot available');active.add(r);current[r]=e[2]
+  elif op=='CLEAR':move(r,e[2]);active.remove(r);current[r]=None
+  else:
+   move(r,e[-1])
+   if op!='SCALE':move(e[2],e[-1])
+  out.append(e)
+ for r in range(n):move(r,w['final'][r])
+ v['program']=out;v['schema']='p104-a2-paid-rank-exchange/1'
+ before,after=L.replay(w),L.replay(v)
+ delta=Counter(after['paid']);delta.subtract(before['paid']);delta={r:c for r,c in delta.items()if c}
+ need(delta=={2:1,3:-1,5:-1,6:1},'Exact full paid-rank exchange')
+ need(before['helpers']==after['helpers'],'Every target retained')
+ need(after['real_scalar_allowance']-before['real_scalar_allowance']==12,'Correction ADD fully counted')
+ payload=(json.dumps(v,separators=(',',':'))).encode()
+ need(sha256(payload).hexdigest()==EXPECTED,'Entire regenerated candidate payload')
+ need(gzip.decompress((HERE/'WORD.json.gz').read_bytes())==payload,'Exact saved candidate')
+ return payload,{'status':'PASS_P104_A2_PAID_RANK_EXCHANGE','paid_delta':delta,'target_delta':{},'local':after,'source_local':before,'candidate_decompressed_sha256':EXPECTED}
+def main():
+ ap=argparse.ArgumentParser(description=__doc__);ap.add_argument('--out',type=Path);args=ap.parse_args();payload,result=construct()
+ if args.out:
+  with args.out.open('xb')as f:f.write(gzip.compress(payload,mtime=0))
+ print(json.dumps(result,indent=2,sort_keys=True))
+if __name__=='__main__':main()
diff --git a/research/p104-a2-neutral-cleanup/inputs/pr5643/inputs/pr5627-WORD.json.gz b/research/p104-a2-neutral-cleanup/inputs/pr5643/inputs/pr5627-WORD.json.gz
new file mode 100644
index 0000000000..b60955f312
Binary files /dev/null and b/research/p104-a2-neutral-cleanup/inputs/pr5643/inputs/pr5627-WORD.json.gz differ
diff --git a/research/p104-a2-neutral-cleanup/inputs/pr5643/inputs/pr5627-local.py b/research/p104-a2-neutral-cleanup/inputs/pr5643/inputs/pr5627-local.py
new file mode 100644
index 0000000000..e72cb02dba
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/inputs/pr5643/inputs/pr5627-local.py
@@ -0,0 +1,208 @@
+"""Check the complete P104 word with an independent helper inventory.
+
+Adapted from Ali Romman's PR5544/5545. David Arias supplied the word;
+Cinna Davis supplied private reuse; Gareth Davidson supplied composition.
+Prepared by Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from functools import lru_cache
+from hashlib import sha256
+from pathlib import Path
+import gzip
+import importlib.util
+import json
+import sys
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+
+def need(ok, why):
+    if not ok:
+        raise ValueError(why)
+
+def read(path):
+    raw = path.read_bytes()
+    return json.loads(gzip.decompress(raw) if path.suffix == '.gz' else raw)
+
+def load(path, name):
+    spec = importlib.util.spec_from_file_location(name, path)
+    module = importlib.util.module_from_spec(spec)
+    sys.modules[name] = module
+    spec.loader.exec_module(module)
+    return module
+
+def add(dst, src, q):
+    for k, v in tuple(src.items()):
+        value = dst.get(k, 0) + q*v
+        if value:
+            dst[k] = value
+        else:
+            dst.pop(k, None)
+
+def span(basis):
+    out = {0}
+    for v in basis:
+        need(type(v) is int and 0 < v < 512 and v not in out, 'Independent binary basis')
+        out |= {x ^ v for x in tuple(out)}
+    return frozenset(out)
+
+def replay(w):
+    public = w['public']
+    owned = w.get('owned_fields', 8)
+    need(type(owned) is int and 8 <= owned <= 9, 'Owned inventory bound')
+    need(type(public) is int and 735 <= public <= 750, 'Public inventory bound')
+    need(len(w['initial']) == len(w['final']) == public, 'Public boundary size')
+    need(len(w['program']) < 26000, 'Fixed operation bound')
+    frames = [span(x) for x in w['frames']]
+    rows = [{r:Q(1)} for r in range(public+owned)]
+    current = list(w['initial']) + [None]*owned
+    paid, scalar, live_owned, peak = Counter(), 0, set(), 0
+    lifetimes = 0
+    for e in w['program']:
+        op, r = e[:2]
+        need(0 <= r < public+owned, 'Role index')
+        if op == 'MOVE':
+            _, r, a, b, private = e
+            need(current[r] == a and (r in live_owned) == private, 'Transport source and ownership')
+            need(frames[b] < frames[a] if private else frames[a] < frames[b], 'Nested chronological transport')
+            paid[abs(len(w['frames'][b])-len(w['frames'][a]))] += 1
+            current[r] = b
+        elif op == 'INIT':
+            need(r >= public and r not in live_owned, 'Owned initialization')
+            live_owned.add(r)
+            lifetimes += 1
+            peak = max(peak, len(live_owned))
+            rows[r] = {}
+            current[r] = e[2]
+            scalar += 2
+        elif op == 'CLEAR':
+            need(r in live_owned and current[r] == e[2], 'Owned erasure at declared frame')
+            rows[r] = {}
+            current[r] = None
+            live_owned.remove(r)
+            scalar += 2
+        else:
+            q, f = Q(e[-2]), e[-1]
+            need(q and current[r] == f, 'Scalar destination and coefficient')
+            n, d = abs(q.numerator), q.denominator
+            need(d & (d-1) == 0, 'Dyadic scalar coefficient')
+            need(abs(q)+1 < 2**16, 'Fixed scalar growth bound')
+            if op == 'SCALE':
+                need(n & (n-1) == 0, 'Dyadic unit SCALE')
+                rows[r] = {k:q*x for k,x in rows[r].items()}
+                scalar += 2*(abs(n.bit_length()-d.bit_length()) + int(q < 0))
+            else:
+                s = e[2]
+                need(s != r and 0 <= s < public+owned and current[s] == f, 'Common scalar chart')
+                if op == 'COPY':
+                    need(r in live_owned and not rows[r], 'COPY into cleared owned field')
+                    rows[r] = {k:q*x for k,x in rows[s].items()}
+                else:
+                    need(op == 'ADD', 'Scalar opcode')
+                    add(rows[r], rows[s], q)
+                scalar += 2*(3+n.bit_length()-1+n.bit_count()+d.bit_length()-1)
+    need(not live_owned and 0 < peak <= 2 and current[:public] == w['final'], 'All public and owned exits')
+    live = set(w['live'])
+    for r,row in enumerate(rows):
+        expected = {r:Q(1)} if r < public else {}
+        if r-112 in live:
+            expected[r-112] = Q(1)
+        need(row == expected, 'All public and owned rows')
+    main = live | {r+112 for r in live}
+    helpers = Counter(len(w['frames'][w['final'][r]])-len(w['frames'][w['initial'][r]]) for r in range(public) if r not in main)
+    need(len(live) == len(w['ports']) == 104 and len(main) == 208 and min(helpers) > 0, 'Independent productive inputs')
+    return {'paid':dict(paid), 'helpers':dict(helpers), 'public_inputs':public, 'owned_fields':owned, 'owned_lifetimes':lifetimes,
+            'peak_owned_fields':peak, 'real_scalar_allowance':scalar, 'endpoint_coefficients':(public+owned)*(public+owned),
+            'paid_rank_mass':sum(r*count for r,count in paid.items())}
+
+def reverse_columns(w):
+    """Check the transpose with dense dyadic rows and the reverse chronology."""
+    public = w['public']
+    n = public+w.get('owned_fields', 8)
+    rows = [[int(i == j) for j in range(n)] for i in range(n)]
+    exponents = [0]*n
+    for e in reversed(w['program']):
+        op,r = e[:2]
+        if op == 'MOVE':
+            continue
+        if op in ('INIT','CLEAR'):
+            rows[r] = [0]*n
+            exponents[r] = 0
+            continue
+        q = Q(e[-2])
+        qe = q.denominator.bit_length()-1
+        if op == 'SCALE':
+            rows[r] = [q.numerator*x for x in rows[r]]
+            exponents[r] += qe
+        else:
+            s = e[2]
+            level = max(exponents[s], exponents[r]+qe)
+            a, b = 1 << (level-exponents[s]), q.numerator << (level-exponents[r]-qe)
+            rows[s] = [a*x+b*y for x,y in zip(rows[s],rows[r])]
+            exponents[s] = level
+            if op == 'COPY':
+                rows[r] = [0]*n
+                exponents[r] = 0
+            r = s
+        while exponents[r] and not any(x & 1 for x in rows[r]):
+            rows[r] = [x//2 for x in rows[r]]
+            exponents[r] -= 1
+    for r,row in enumerate(rows):
+        expected = [0]*n
+        if r < public:
+            expected[r] = 1 << exponents[r]
+        if r in w['live']:
+            expected[r+112] = 1 << exponents[r]
+        need(row == expected, 'Independent dense transpose columns')
+    return {'columns':n, 'coefficients':n*n, 'arithmetic':'Dense integer rows with binary denominators; reverse chronology'}
+
+def native(w):
+    n = w['public']
+    C = load(ROOT/'research/p104-native-channel/vendor/clifford_exact.py', 'p104_productive_clifford')
+    V = load(ROOT/'research/p104-native-channel/vendor/native_verify.py', 'p104_productive_gaussian')
+    @lru_cache(None)
+    def chart(i):
+        return C.canonical_frame(9, tuple(w['frames'][i]))
+    recipes = {}
+    def check(a,b):
+        if (a,b) not in recipes:
+            recipe,_ = C.lower_child(chart(a).adjoint().then(chart(b)))
+            expected = V.adjoint(V.frame(w['frames'][a],9)) + V.frame(w['frames'][b],9)
+            V.equal(V.recipe(recipe),expected,'Native chart change and exact global phase')
+            need(recipe['rank'] == abs(len(w['frames'][a])-len(w['frames'][b])), 'Native boundary rank')
+            recipes[a,b] = recipe
+        return recipes[a,b]
+    for e in w['program']:
+        if e[0] == 'MOVE':
+            check(e[2],e[3])
+    main = set(w['live']) | {r+112 for r in w['live']}
+    helper_profile = Counter()
+    for r in range(n):
+        if r not in main:
+            helper_profile[check(w['initial'][r],w['final'][r])['rank']] += 1
+    adapters = []
+    for r,q in zip(w['live'],w['ports']):
+        need(w['frames'][w['initial'][r]] == [q], 'Literal central port')
+        need(span(w['frames'][w['final'][r+112]]) == frozenset(x for x in range(512) if not (x&q).bit_count()%2), 'Literal output hyperplane')
+        tests = [
+            (C.cgate(9,q,1).adjoint().then(chart(w['initial'][r])), V.adjoint((('C',q,1),))+V.frame(w['frames'][w['initial'][r]],9)),
+            (chart(w['final'][r+112]).adjoint().then(C.cgate(9,q,-1).then(C.fourier(9))), V.adjoint(V.frame(w['frames'][w['final'][r+112]],9))+(('C',q,-1),)+V.fourier(9))]
+        for actual,expected in tests:
+            recipe,_ = C.lower_child(actual)
+            need(recipe['rank'] == 0, 'Free intrinsic main adapter')
+            V.equal(V.recipe(recipe),expected,'Main endpoint phase')
+            adapters.append(recipe)
+    bad = json.loads(json.dumps(next(iter(recipes.values()))))
+    bad['left']['phase'] = (bad['left']['phase']+1)%4
+    a,b = next(iter(recipes))
+    try:
+        V.equal(V.recipe(bad),V.adjoint(V.frame(w['frames'][a],9))+V.frame(w['frames'][b],9),'Wrong phase control')
+    except ValueError:
+        pass
+    else:
+        raise ValueError('Wrong native phase accepted')
+    payload = [[a,b,recipes[a,b]] for a,b in sorted(recipes)] + adapters
+    return {'distinct_maps':len(recipes),'main_adapters':len(adapters),'helper_normalizers':2*sum(helper_profile.values()),
+            'helpers':dict(helper_profile),'recipe_payload_sha256':sha256(json.dumps(payload,sort_keys=True,separators=(',',':')).encode()).hexdigest(),
+            'wrong_phase_rejected':True, 'proof':'Every signed Pauli image and exact global phase; frame induction at every positive tensor width'}
diff --git a/research/p104-a2-neutral-cleanup/inputs/pr5644/NOTICE b/research/p104-a2-neutral-cleanup/inputs/pr5644/NOTICE
new file mode 100644
index 0000000000..52b80e0882
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/inputs/pr5644/NOTICE
@@ -0,0 +1,6 @@
+P104 neutral helper cleanup
+Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+
+The retained PR5627 archive contains the full source notices. The source
+pricing module retains its predecessor notices. Read README.md for links
+and the contribution map. No source notice was removed.
diff --git a/research/p104-a2-neutral-cleanup/inputs/pr5644/PROOF.md b/research/p104-a2-neutral-cleanup/inputs/pr5644/PROOF.md
new file mode 100644
index 0000000000..8572bf7a3a
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/inputs/pr5644/PROOF.md
@@ -0,0 +1,136 @@
+# Three neutral helper relations remove paid calls
+
+This construction starts from the exact PR5627 word at
+`ed4dc88a09a7d201971f6603b8c2074e95dd9c32`. It keeps all 743 independent
+inputs, all 535 helper targets and the 104 main pairs. The selected frontier
+is unchanged. The five source framework assumptions and the helper endpoint
+contract remain.
+
+## 1. The boundary identity
+
+Write the scalar state in native normalized coordinates. Let h be a helper
+with initial chart S and final chart F. At a chronological cut, suppose h
+and each cancellation supplier are at F. Suppose the exact prefix rows give
+
+```math
+r_h-\sum_j b_j r_j=c x_h+\sum_{j\ne h} a_j x_j.
+```
+
+Every input on the right has initial chart S, and c is a dyadic unit. Suppose
+there is no later source read of h. Before the word, apply
+`h += -a_j/c * j` for every j other than h. At the cut, apply
+`h -= b_j * j` and then `h *= 1/c`. The resulting h is exactly the original
+independent input x_h. Delete the later scalar operations whose destination
+is h. They have no effect on another output.
+
+The source returns every helper unchanged and has no helper contribution
+to a main output. Thus the input basis change can affect only the old h
+output. The cut repairs that output exactly. No helper is set to zero,
+no new input is created and no productive target is removed or added.
+All basis coefficients are dyadic, and every SCALE has a dyadic inverse.
+
+The constructor checks the complete prefix relation, common charts, the
+last-read condition, the exact removed operations and the full arbitrary-input
+endpoint after each step. It also checks that the complete chronological
+subsequence of owned operations is unchanged.
+
+## 2. Exact witnesses
+
+The cuts below are zero-based and refer to each successive word after
+transport coalescing. `WITNESS.json` retains the full event anchors and vectors.
+Here `e_j` denotes the j-th independent input.
+
+| Helper | Cut | Final chart | Prefix row after cancellation |
+| ---: | ---: | ---: | --- |
+| 291 | 10627 | 234 | -2 e291 - e293 + 2 e39 + 2 e303 |
+| 321 | 11072 | 237 | e321 - 2 e320 - 2 e34 + 2 e330 |
+| 369 | 11718 | 243 | e369 + 2 e383 - 2 e372 - 2 e3 - 2 e382 - 2 e378 |
+
+Their cancellation vectors are respectively
+`{293:-1}`, `{22:2,320:-3/2,330:2}`, and
+`{368:-3/2,26:2,378:-2}`. All initial basis operations use chart 3.
+The three steps remove six, five and five old scalar cleanup events.
+The inserted cancellation and input operations are included in the cost.
+
+## 3. The paid change
+
+The removed cleanup contacts let main roles 55, 49 and 80 bypass one
+intermediate chart each. Their old paths are
+
+```text
+role 55: 722 -> 234 -> 127
+role 49: 734 -> 237 -> 127
+role 80: 749 -> 243 -> 127
+```
+
+Each path has ranks 1 and 5. The new direct path has rank 6. For chart
+operators C_A, C_B and C_D, the exact product is
+
+```math
+(C_D C_B^{-1})(C_B C_A^{-1})=C_D C_A^{-1}.
+```
+
+No scalar operation uses that role between these transports. The chronological
+replay checks strict chart containment, and the native verifier checks the
+exact signed map and global phase. This identity applies at every positive
+tensor width under the retained native implementation assumption.
+
+The local paid delta is `-3 H1 -3 H5 +3 H6`. Every target stays fixed.
+For 0<t<1, the complete target-minus-paid moment therefore increases by
+
+```math
+54[1+5^t-6^t]>0.
+```
+
+This is a changed physical invoice. It does not add predecessor kappa gains.
+The alternative PR5613 inventory has 72 additional H5 paid calls and 72
+additional H5 targets. It has the same signed source moment, but this package
+uses only the smaller PR5627 inventory.
+
+## 4. Complete cost and verification
+
+The final local word has 25,448 events, 743 independent inputs, 535 helpers,
+nine owned roles, eleven owned lifetimes and peak owned occupancy two.
+Its paid profile is
+
+```text
+{1:2197, 2:456, 3:494, 4:91, 5:160, 6:21, 7:15}.
+```
+
+The complete caller retains 18 full forward calls, 15 thin query sites,
+3,120 whole idle jobs and 3,328 main targets. Its complete invoice has
+66,492 paid calls and 12,958 productive targets. The rank-mass surplus is 760.
+Helpers, native normalizers, main adapters, basis operations, COPY/CLEAR,
+all owned lifetimes, routes, thin queries and idles are charged.
+
+A separate dense integer transpose checks all 565,504 matrix entries.
+The native check verifies 2,916 distinct maps. The physical caller verifies
+all 7,488 contacts, 53,248 central-square columns and complete main phases.
+Two rational interval engines check the same complete moment.
+
+The exact raw crossing lies in
+`(0.00310626336369, 0.00310626336370)`. The claim is `0.00310626335`, tested
+at `0.003106263355`. The gain over PR5627's claim is `0.00000185789`,
+about 0.05985%. This is a small gain.
+The raw ceiling is proved only for this fixed invoice on `[0,0.0034]`.
+Its headroom above the claim is between `1.369e-11` and `1.370e-11`.
+It is not an optimum over constructions.
+
+The source strictification parameters remain: power 1024, cutoff 17,
+target floor 18, tail offset 1/5, reserve 10^-12 and tail decay 39/40.
+The compiler checks its finite integer threshold, the preceding integer,
+initial range, shifted exits and complement capacity. All 54 strict outer
+conditions and four functional conditions pass. The ordinary BIT contract
+remains 0.0034.
+
+The local scalar allowance is 220,208 and the local route allowance is
+5,172,000, below the retained 10^7 bound. The complete ordinary-work bound
+is 184,647,552, below 10^9. Fewer than 26,000 scalar events and the checked
+coefficient bound retain the source growth bound. The paid native rank sum
+is 5,986 per local word. No growth or route cost is omitted.
+
+The huge uniform word and complete rounded multiplier are not materialized.
+These are author checks by the same AI-assisted author. Independent scientific
+acceptance and a proof-kernel theorem remain absent. Source native, owned
+erasure, uniform compiler, precision/tape and analytic recovery assumptions
+remain. The package makes no large-gain or global-optimum claim.
diff --git a/research/p104-a2-neutral-cleanup/inputs/pr5644/README.md b/research/p104-a2-neutral-cleanup/inputs/pr5644/README.md
new file mode 100644
index 0000000000..d21c40e63f
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/inputs/pr5644/README.md
@@ -0,0 +1,121 @@
+# Conditional kappa 0.00310626335 from three helper cleanups
+
+This construction raises complete conditional kappa from
+**0.00310440546 to 0.00310626335**, a gain of **0.00000185789**
+(about **0.05985%**) over
+[PR #5627](https://github.com/CrocSwap/integer-mult-bounds/pull/5627).
+This is a small gain. The requested large improvement is not established.
+The selected frontier is not changed by this package.
+
+Three exact helper relations remove scalar contacts on main roles 55, 49
+and 80. Each role can then replace an H1+H5 path with H6. The local paid
+delta is `-3 H1 -3 H5 +3 H6`. All independent inputs, productive targets
+and owned operations stay fixed. The complete caller saves 54 paid calls.
+
+Read [PROOF.md](PROOF.md), [WITNESS.json](WITNESS.json),
+[RESULT.json](RESULT.json), [SOURCES.json](SOURCES.json), and
+[VALIDATION.md](VALIDATION.md). The constructor checks every relation before
+it emits the new [word](WORD.json.gz).
+
+| Complete quantity | Value |
+| --- | ---: |
+| Paid calls | 66,492 |
+| Productive targets | 12,958 |
+| Rank-mass surplus | 760 |
+| Public inputs / helpers per full call | 743 / 535 |
+| Owned roles / lifetimes / peak | 9 / 11 / 2 |
+| Local events | 25,448 |
+| Raw crossing | (0.00310626336369, 0.00310626336370) |
+| Tested saving | 0.003106263355 |
+| Claimed conditional kappa | 0.00310626335 |
+
+The complete cost includes helpers, native maps, input/output normalizers,
+main adapters, scalar bases, COPY/CLEAR, allocation, routes, thin queries,
+whole idles, compiler completion and rounding. Two rational interval engines,
+all compiler conditions and all 58 outer conditions pass. The ordinary BIT
+contract stays at 0.0034. The fixed-invoice ceiling is the raw crossing above;
+it is not a ceiling over constructions.
+
+## Reproduce
+
+Use Python 3.12 and its standard library, from the repository root:
+
+```sh
+python3 -B scripts/research_package.py --package research/p104-neutral-helper-cleanup --check-only
+python3 -B scripts/research_package.py --package research/p104-neutral-helper-cleanup
+```
+
+The registered command runs normally and with `-O`. Expected markers are
+`PASS_P104_NEUTRAL_HELPER_KAPPA_00310626335` and
+`PASS_REGISTERED_RESEARCH_PACKAGE`. Direct replay needs no Git or network:
+
+```sh
+python3 -I -W error -B research/p104-neutral-helper-cleanup/verify.py
+python3 -I -W error -B -O research/p104-neutral-helper-cleanup/verify.py
+```
+
+Normal replay is read-only. `--write` regenerates the word and receipt.
+The verifier authenticates the exact source archive and all 36 payload files
+before it imports source code. It checks all 565,504 endpoint coefficients,
+2,916 signed native maps, the complete physical caller and the full cost.
+Controls reject a false cancellation, wrong cut, missing input basis,
+missing owned erasure, extra target credit and unpaid query. The native,
+controller and pricing checks retain their own controls.
+
+## Source and credit
+
+The consumed source is [PR #5627](https://github.com/CrocSwap/integer-mult-bounds/pull/5627)
+at `ed4dc88a09a7d201971f6603b8c2074e95dd9c32`:
+[source proof](https://github.com/aliromman/integer-mult-bounds/blob/ed4dc88a09a7d201971f6603b8c2074e95dd9c32/research/p104-helper-subspace-splits/PROOF.md),
+[source word](https://github.com/aliromman/integer-mult-bounds/blob/ed4dc88a09a7d201971f6603b8c2074e95dd9c32/research/p104-helper-subspace-splits/WORD.json.gz),
+and [source notices](https://github.com/aliromman/integer-mult-bounds/blob/ed4dc88a09a7d201971f6603b8c2074e95dd9c32/research/p104-helper-subspace-splits/NOTICE).
+Its official self-contained export is retained. Reproduction does not require
+a cached unmerged Git object. The exact word, caller and all shared proof
+engines are unchanged source inputs. The derived pricing file changes only
+the declared claim, comparison and paid count; its byte-level derivation is checked.
+
+Ali Romman supplied the new three relations with substantial OpenAI Codex
+assistance. The same assistant performed the author checks; no subagents or
+independent scientific review. The helper-boundary method extends
+[PR #5602](https://github.com/CrocSwap/integer-mult-bounds/pull/5602).
+The source package supplies the complete composition of
+[PR #5601](https://github.com/CrocSwap/integer-mult-bounds/pull/5601),
+[PR #5605](https://github.com/CrocSwap/integer-mult-bounds/pull/5605),
+[PR #5612](https://github.com/CrocSwap/integer-mult-bounds/pull/5612),
+[PR #5606](https://github.com/CrocSwap/integer-mult-bounds/pull/5606)
+and [PR #5599](https://github.com/CrocSwap/integer-mult-bounds/pull/5599).
+Its notices credit flyingviper's relays, Scratch-net's prepared helper,
+Pierre-Loic Doulcet's cascade, Joel Pulikkan, DreamingOfClouds, thu-nmrc,
+Gareth Davidson, David Arias, Cinna Davis, Jacob Alan Sussman, zxv and
+Cao Yifan, with the earlier geometry, BIT and analytic sources.
+All notices remain in the retained export and pricing module. Apache-2.0.
+
+The discovery first passed on
+[PR #5613](https://github.com/CrocSwap/integer-mult-bounds/pull/5613) at
+`32f23af8790cc3c435bb1f495d861332b4f000e3`. That source has the same signed
+moment but 72 more H5 paid calls and 72 more H5 targets. It is comparison
+evidence, not the consumed input. Its counts are not combined with this receipt.
+
+## Coordination and limits
+
+The frozen research base is canonical main
+`6cf7a683f447b9f1e2333791907fd92be5009a63`, priority revision 7.
+The [canonical claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19154639)
+records the source pins, live overlap checks and released finite screens.
+The separate Discussion5600 main-port retirement campaign is excluded.
+The final publication checkpoint is recorded in `VALIDATION.md`.
+
+The five selected assumptions remain: native implementation at all widths,
+owned erasure, uniform compiler closure, precision/tape cost and analytic
+recovery. The helper endpoint contract also remains. The huge uniform word
+and complete rounded multiplier are not materialized. This package does not
+claim independent acceptance, a proof-kernel theorem or global optimality.
+
+## Open next questions
+
+An independent reviewer can check the three prefix relations and transport
+products, then replay the full package. Further coordinated bases may remove
+more scalar contacts, but the larger exploratory screens have not produced
+a new complete gain. A new construction must first check current claims and
+must include every changed target and paid operation. [TASK.json](TASK.json)
+records the next bounded question and its blockers.
diff --git a/research/p104-a2-neutral-cleanup/inputs/pr5644/RESULT.json b/research/p104-a2-neutral-cleanup/inputs/pr5644/RESULT.json
new file mode 100644
index 0000000000..2908bf95db
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/inputs/pr5644/RESULT.json
@@ -0,0 +1,680 @@
+{
+  "authenticated_source_files": 36,
+  "changes": [
+    {
+      "cancellation": [
+        [
+          "ADD",
+          291,
+          293,
+          "1",
+          234
+        ],
+        [
+          "SCALE",
+          291,
+          "-1/2",
+          234
+        ]
+      ],
+      "cut": 10627,
+      "events": 25446,
+      "frame": 234,
+      "helper": 291,
+      "paid": {
+        "1": 2199,
+        "2": 456,
+        "3": 494,
+        "4": 91,
+        "5": 162,
+        "6": 19,
+        "7": 15
+      },
+      "preparation": [
+        [
+          "ADD",
+          291,
+          39,
+          "1",
+          3
+        ],
+        [
+          "ADD",
+          291,
+          293,
+          "-1/2",
+          3
+        ],
+        [
+          "ADD",
+          291,
+          303,
+          "1",
+          3
+        ]
+      ],
+      "removed_scalar_events": [
+        [
+          "SCALE",
+          291,
+          "-1/2",
+          234
+        ],
+        [
+          "ADD",
+          291,
+          289,
+          "1/2",
+          234
+        ],
+        [
+          "ADD",
+          291,
+          39,
+          "1/2",
+          234
+        ],
+        [
+          "ADD",
+          291,
+          40,
+          "1/2",
+          234
+        ],
+        [
+          "ADD",
+          291,
+          18,
+          "-1/2",
+          234
+        ],
+        [
+          "ADD",
+          291,
+          55,
+          "-1",
+          234
+        ]
+      ],
+      "scalar": 220140
+    },
+    {
+      "cancellation": [
+        [
+          "ADD",
+          321,
+          22,
+          "-2",
+          237
+        ],
+        [
+          "ADD",
+          321,
+          320,
+          "3/2",
+          237
+        ],
+        [
+          "ADD",
+          321,
+          330,
+          "-2",
+          237
+        ]
+      ],
+      "cut": 11072,
+      "events": 25446,
+      "frame": 237,
+      "helper": 321,
+      "paid": {
+        "1": 2198,
+        "2": 456,
+        "3": 494,
+        "4": 91,
+        "5": 161,
+        "6": 20,
+        "7": 15
+      },
+      "preparation": [
+        [
+          "ADD",
+          321,
+          34,
+          "2",
+          3
+        ],
+        [
+          "ADD",
+          321,
+          320,
+          "2",
+          3
+        ],
+        [
+          "ADD",
+          321,
+          330,
+          "-2",
+          3
+        ]
+      ],
+      "removed_scalar_events": [
+        [
+          "ADD",
+          321,
+          320,
+          "1",
+          237
+        ],
+        [
+          "ADD",
+          321,
+          23,
+          "-1",
+          237
+        ],
+        [
+          "ADD",
+          321,
+          22,
+          "-1",
+          237
+        ],
+        [
+          "ADD",
+          321,
+          108,
+          "1",
+          237
+        ],
+        [
+          "ADD",
+          321,
+          49,
+          "-1",
+          237
+        ]
+      ],
+      "scalar": 220164
+    },
+    {
+      "cancellation": [
+        [
+          "ADD",
+          369,
+          26,
+          "-2",
+          243
+        ],
+        [
+          "ADD",
+          369,
+          368,
+          "3/2",
+          243
+        ],
+        [
+          "ADD",
+          369,
+          378,
+          "2",
+          243
+        ]
+      ],
+      "cut": 11718,
+      "events": 25448,
+      "frame": 243,
+      "helper": 369,
+      "paid": {
+        "1": 2197,
+        "2": 456,
+        "3": 494,
+        "4": 91,
+        "5": 160,
+        "6": 21,
+        "7": 15
+      },
+      "preparation": [
+        [
+          "ADD",
+          369,
+          3,
+          "2",
+          3
+        ],
+        [
+          "ADD",
+          369,
+          372,
+          "2",
+          3
+        ],
+        [
+          "ADD",
+          369,
+          378,
+          "2",
+          3
+        ],
+        [
+          "ADD",
+          369,
+          382,
+          "2",
+          3
+        ],
+        [
+          "ADD",
+          369,
+          383,
+          "-2",
+          3
+        ]
+      ],
+      "removed_scalar_events": [
+        [
+          "ADD",
+          369,
+          368,
+          "1",
+          243
+        ],
+        [
+          "ADD",
+          369,
+          26,
+          "-1",
+          243
+        ],
+        [
+          "ADD",
+          369,
+          95,
+          "-1",
+          243
+        ],
+        [
+          "ADD",
+          369,
+          8,
+          "1",
+          243
+        ],
+        [
+          "ADD",
+          369,
+          80,
+          "-1",
+          243
+        ]
+      ],
+      "scalar": 220208
+    }
+  ],
+  "complete_cost": {
+    "compiler": {
+      "H": 80511200000000000,
+      "N": "2^80511200000000000",
+      "eta": {
+        "lower": "0.000000132965805256205580454152",
+        "upper": "0.000000132965805256205580454153"
+      },
+      "gap": "1/1400000000000",
+      "integer_test_exponent": 57508,
+      "logarithm_power": 1024,
+      "theta": "63/64",
+      "uniform_saving": "543596087/175000000000",
+      "word_materialized": false
+    },
+    "full_forward_calls": 18,
+    "gain": "185789/100000000000",
+    "kappa": "62125267/20000000000",
+    "kappa_decimal": ".00310626335",
+    "margin_at_previous": {
+      "lower": "0.451550879336614603359787426152",
+      "upper": "0.451550879336614603359787426153"
+    },
+    "negative_controls": {
+      "old_BIT": "Rejected by outer inequalities",
+      "old_cutoff": "Rejected by completion-tail ratio greater than one"
+    },
+    "nonrecursive": {
+      "fixed_scalar_growth_bound": "At most 2^(16*26000) before native factors; a declared constant, not an attained norm.",
+      "local_paid_rank_mass": 5986,
+      "local_routes": 5172000,
+      "local_scalar": 220208,
+      "peak_owned_fields": 2,
+      "raw_budget": 1000000000,
+      "raw_scalar_upper": 184647552,
+      "tensor_native_growth_bound": "Each rank-r Gaussian has row l1 norm at most 2^(rf); use local_paid_rank_mass for the whole word."
+    },
+    "ordinary_BIT": {
+      "admitted": "17/5000",
+      "after_cover": "69/20000",
+      "atom": "1/250",
+      "before_cover": "3459/1000000",
+      "ordinary_saving": "8590884599/2500000000000",
+      "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses"
+    },
+    "outer": {
+      "functional_checks": {
+        "actual_new_BIT_stock_sublinear": "348599999999253/350000000000000",
+        "fixed_halo_explicit_metadata_branch": "26950000000001/350000000000",
+        "new_BIT_row_stock_sublinear_in_active_group": "1395799999997009/1400000000000000",
+        "new_semantic_group_guard": "3/1400000000000"
+      },
+      "margins": {
+        "boundary_algebraic_matrix": "6088276171595651231307/1960000000000000000000000",
+        "fused_gaussian": "6088276171586953693921/1960000000000000000000000",
+        "global_coordinate_router": "2174384347/700000000000",
+        "group_bit_router": "3044138086493476846959/980000000000000000000000",
+        "group_scans": "699999999999/700000000000",
+        "main_transform": "6088276170195651231307/1960000000000000000000000",
+        "microbox_face_corrections": "26950000000001/350000000000",
+        "polynomial_products": "1399999999999/1400000000000",
+        "sparse_union_movement": "802338276171595651231307/1960000000000000000000000"
+      },
+      "parameters": {
+        "a": "2174384347/700000000000",
+        "b": "869753739/280000000000",
+        "beta": "1399999999997/1400000000000",
+        "bit_saving": "17/5000",
+        "cap_xi": "1782338276170195651231307/1960000000000000000000000",
+        "complex_uniform_saving": "543596087/175000000000",
+        "d": "1/1400000000000",
+        "epsilon": "1399999999999/1400000000000",
+        "kappa": "62125267/20000000000",
+        "lambda_": "398757494659/400000000000",
+        "lambda_prime": "1395651231307/1400000000000",
+        "layout": "1/1400000000000",
+        "q": "4348768693/1400000000000",
+        "r0": "1/14000000000000",
+        "stop": "1/1400000000000",
+        "tested_saving": "621252671/200000000000"
+      },
+      "strict_checks": {
+        "actual_bit_above_effective": "205615653/700000000000",
+        "actual_logarithmic_gamma_guard": "1/1400000000000",
+        "actual_logarithmic_group_guard": "177661723831904348768693/980000000000000000000000",
+        "alpha_logarithm_absorption": "1/14000000000000",
+        "boundary_algebraic_matrix_above_kappa": "5595651231307/1960000000000000000000000",
+        "cap_above_band": "802338276170195651231307/1960000000000000000000000",
+        "cap_below_cell": "177661723828404348768693/1960000000000000000000000",
+        "cap_below_phase_cell_power": "2137661723829804348768693/1960000000000000000000000",
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+        "complex_below_one_over_32": "7880246261/280000000000",
+        "complex_endpoint": "1/700000000000",
+        "epsilon_below_one": "1/1400000000000",
+        "epsilon_positive": "1399999999999/1400000000000",
+        "fine_prime_halo_umbrella": "7/2",
+        "fused_gaussian_above_kappa": "5586953693921/1960000000000000000000000",
+        "gaussian_above_main": "695651231307/980000000000000000000000",
+        "global_coordinate_router_above_kappa": "1/350000000000",
+        "global_gamma_power_slack": "9/14000000000000",
+        "group_below_dimension": "1/700000000000",
+        "group_bit_router_above_kappa": "3493476846959/980000000000000000000000",
+        "group_gauge_power_slack": "177661723831834348768693/980000000000000000000000",
+        "group_key_fits_record": "1/700000000000",
+        "group_positive": "1399999999997/1400000000000",
+        "group_scans_above_kappa": "348912807827/350000000000",
+        "halo_covers_generic_inverse_radius": "5",
+        "improvement_over_user_baseline": "687646465400418148631/500000000000000000000000",
+        "lambda_above_internal": "1/2800000000000",
+        "lambda_above_sigma": "3/2800000000000",
+        "lambda_above_tau": "1/2800000000000",
+        "lambda_prime_above_lambda": "1/2800000000000",
+        "lambda_prime_above_leaf": "559130246261/392000000000000000000000",
+        "leaf_saving_above_effective": "279130246261/392000000000000000000000",
+        "main_transform_above_kappa": "4195651231307/1960000000000000000000000",
+        "membership_arithmetic_fits_record": "1/1400000000000",
+        "microbox_face_corrections_above_kappa": "53897825615657/700000000000",
+        "microbox_halo_volume": "110600000000003/1400000000000",
+        "new_complex_uniform_saving_above_b": "1/1400000000000",
+        "new_semantic_guard_with_C1_one": "1/1400000000000",
+        "polynomial_products_above_kappa": "1395651231309/1400000000000",
+        "positive_layout_slack": "1/1400000000000",
+        "q_below_effective": "1/1400000000000",
+        "q_below_internal": "1/1400000000000",
+        "q_below_leaf": "559130246261/392000000000000000000000",
+        "q_positive": "4348768693/1400000000000",
+        "short_record_fallback": "279130246261/280000000000",
+        "source_axis_superpolynomial": "1/1400000000000",
+        "sparse_union_movement_above_kappa": "796250000005595651231307/1960000000000000000000000",
+        "stop_below_one": "1399999999999/1400000000000",
+        "stop_positive": "1/1400000000000",
+        "strassen_integer_power_gap": "1951441519231",
+        "support_router_span": "3/1400000000000",
+        "theta_positive_polynomial_power": "2",
+        "union_header_fits_record": "3/1400000000000",
+        "union_tag_work_per_visit_fits_record": "3/1400000000000"
+      }
+    },
+    "paid": {
+      "1": 41106,
+      "16": 416,
+      "2": 8208,
+      "24": 416,
+      "3": 8892,
+      "32": 416,
+      "4": 1638,
+      "40": 416,
+      "48": 416,
+      "5": 2880,
+      "56": 416,
+      "6": 378,
+      "64": 416,
+      "7": 270,
+      "72": 208
+    },
+    "paid_calls": 66492,
+    "previous_open_pr5627": "155220273/50000000000",
+    "productive_fields": 12958,
+    "query_shears": 15,
+    "rank_mass_surplus": 760,
+    "raw_ceiling": {
+      "derivative_upper": "-185059801945251167500572380988789019128885006440939063323697675/784637716923335095479473677900958302012794430558004314112",
+      "interval": [
+        "0",
+        "17/5000"
+      ]
+    },
+    "raw_headroom": [
+      "1369/100000000000000",
+      "137/10000000000000"
+    ],
+    "raw_root_interval": [
+      "310626336369/100000000000000",
+      "31062633637/10000000000000"
+    ],
+    "relative_gain_percent": "9289450/155220273",
+    "strictification": {
+      "alpha": {
+        "lower": "0.999999999991151995165679182213",
+        "upper": "0.999999999991151995165679182214"
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+      "cutoff": 17,
+      "delta": {
+        "lower": "0.967530914044170735058316873915",
+        "upper": "0.967530914044170735058316873916"
+      },
+      "floor": 18,
+      "gamma": {
+        "lower": "0.968140817783099208114307070153",
+        "upper": "0.968140817783099208114307070154"
+      },
+      "normalized_paid_upper": "1048576000976562501/1048576001073741824",
+      "power": 1024,
+      "reserve": "1/1000000000000",
+      "tail_block": 128,
+      "tail_decay": "39/40",
+      "tail_offset": "1/5",
+      "tested": "621252671/200000000000"
+    },
+    "targets": {
+      "1": 36,
+      "145": 208,
+      "17": 416,
+      "2": 72,
+      "25": 416,
+      "33": 416,
+      "4": 1638,
+      "41": 416,
+      "49": 416,
+      "5": 108,
+      "57": 416,
+      "65": 416,
+      "7": 90,
+      "73": 208,
+      "8": 288,
+      "9": 7398
+    },
+    "whole_idle_jobs": 3120
+  },
+  "limits": [
+    "The five selected framework assumptions and helper-endpoint contract remain.",
+    "The enormous uniform word and complete rounded multiplier are not materialized.",
+    "These author checks are not independent scientific review or a proof-kernel theorem.",
+    "The improvement is small. No large gain or global optimum is established."
+  ],
+  "local": {
+    "endpoint_coefficients": 565504,
+    "helpers": {
+      "1": 2,
+      "2": 4,
+      "4": 91,
+      "5": 6,
+      "7": 5,
+      "8": 16,
+      "9": 411
+    },
+    "owned_fields": 9,
+    "owned_lifetimes": 11,
+    "paid": {
+      "1": 2197,
+      "2": 456,
+      "3": 494,
+      "4": 91,
+      "5": 160,
+      "6": 21,
+      "7": 15
+    },
+    "paid_rank_mass": 5986,
+    "peak_owned_fields": 2,
+    "public_inputs": 743,
+    "real_scalar_allowance": 220208
+  },
+  "local_helper_delta": {},
+  "local_paid_delta": {
+    "1": -3,
+    "5": -3,
+    "6": 3
+  },
+  "native": {
+    "distinct_maps": 2916,
+    "helper_normalizers": 1070,
+    "helpers": {
+      "1": 2,
+      "2": 4,
+      "4": 91,
+      "5": 6,
+      "7": 5,
+      "8": 16,
+      "9": 411
+    },
+    "main_adapters": 208,
+    "proof": "Every signed Pauli image and exact global phase; frame induction at every positive tensor width",
+    "recipe_payload_sha256": "92eef26313b53686f5f78c181e8a75549280be0a714dbd069ae2cc2f24bbd820",
+    "wrong_phase_rejected": true
+  },
+  "negative_controls": {
+    "extra_target_credit": "Every productive helper has a native target",
+    "false_cancellation": "Exact prefix relation on every input",
+    "missing_central_translation": "Rejected by the complete Laurent endpoint",
+    "missing_input_basis": "All public and owned rows",
+    "missing_owned_erasure": "All public and owned exits",
+    "unpaid_query": "Complete field and call counts",
+    "wrong_cut": "Exact chronological anchor"
+  },
+  "physical_caller": {
+    "central_square_columns": 53248,
+    "full_calls": 18,
+    "main_targets": {
+      "145": 208,
+      "17": 416,
+      "25": 416,
+      "33": 416,
+      "41": 416,
+      "49": 416,
+      "57": 416,
+      "65": 416,
+      "73": 208
+    },
+    "new_paid_jobs": 0,
+    "physical_contacts": 7488,
+    "ports": 104,
+    "route_payload_sha256": "7f4f0ca768ffbc4f93dcff575592c4c67411f46b4289e45b73f715a2ad47b142",
+    "tensor_rule": "Factorwise native maps; scalar signs stay outside the tensor power.",
+    "whole_idle_jobs": {
+      "16": 416,
+      "24": 416,
+      "32": 416,
+      "40": 416,
+      "48": 416,
+      "56": 416,
+      "64": 416,
+      "72": 208
+    },
+    "wrapper_sites": [
+      1,
+      3,
+      5,
+      7,
+      9,
+      11,
+      13,
+      15,
+      17,
+      19,
+      21,
+      23,
+      25,
+      27,
+      29,
+      31
+    ]
+  },
+  "separate_columns": {
+    "arithmetic": "Dense integer rows with binary denominators; reverse chronology",
+    "coefficients": 565504,
+    "columns": 752
+  },
+  "source_commit": "ed4dc88a09a7d201971f6603b8c2074e95dd9c32",
+  "source_local": {
+    "endpoint_coefficients": 565504,
+    "helpers": {
+      "1": 2,
+      "2": 4,
+      "4": 91,
+      "5": 6,
+      "7": 5,
+      "8": 16,
+      "9": 411
+    },
+    "owned_fields": 9,
+    "owned_lifetimes": 11,
+    "paid": {
+      "1": 2200,
+      "2": 456,
+      "3": 494,
+      "4": 91,
+      "5": 163,
+      "6": 18,
+      "7": 15
+    },
+    "paid_rank_mass": 5986,
+    "peak_owned_fields": 2,
+    "public_inputs": 743,
+    "real_scalar_allowance": 220154
+  },
+  "status": "PASS_P104_NEUTRAL_HELPER_KAPPA_00310626335"
+}
diff --git a/research/p104-a2-neutral-cleanup/inputs/pr5644/SOURCES.json b/research/p104-a2-neutral-cleanup/inputs/pr5644/SOURCES.json
new file mode 100644
index 0000000000..410fd77bfd
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/inputs/pr5644/SOURCES.json
@@ -0,0 +1,34 @@
+{
+  "base_commit": "6cf7a683f447b9f1e2333791907fd92be5009a63",
+  "files": [
+    {
+      "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602",
+      "path": "docs/research/agent-task-catalog.json",
+      "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72",
+      "usage": "provenance"
+    },
+    {
+      "git_blob": "fc3d4ba105e1f097d0d7d051a308281e86ab1446",
+      "path": "certificates/selected-result.json",
+      "sha256": "66974efdced4083c00025f97d95d83909a226cdf801edb9301c195c6641f6903",
+      "usage": "provenance"
+    },
+    {
+      "git_blob": "bc900f0a1561b17b35492a80d10ae94f790d8378",
+      "path": "research/p104-neutral-helper-cleanup/inputs/pr5627-source.tar",
+      "pin": "head:47da58a1446ff744c6a558a16719024375e77e81:research/p104-neutral-helper-cleanup/inputs/pr5627-source.tar",
+      "sha256": "86c6bb839e14d79175ff8f3ed80b51a02d5c51a04deb0eff7ccea1afbe72923b",
+      "usage": "input"
+    }
+  ],
+  "schema_version": 1,
+  "source_export": {
+    "commit": "ed4dc88a09a7d201971f6603b8c2074e95dd9c32",
+    "files": 36,
+    "git_blob": "bc900f0a1561b17b35492a80d10ae94f790d8378",
+    "local_path": "inputs/pr5627-source.tar",
+    "package": "research/p104-helper-subspace-splits",
+    "sha256": "86c6bb839e14d79175ff8f3ed80b51a02d5c51a04deb0eff7ccea1afbe72923b",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5627"
+  }
+}
diff --git a/research/p104-a2-neutral-cleanup/inputs/pr5644/TASK.json b/research/p104-a2-neutral-cleanup/inputs/pr5644/TASK.json
new file mode 100644
index 0000000000..4e04ce714e
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/inputs/pr5644/TASK.json
@@ -0,0 +1,106 @@
+{
+  "actual_scope": "Use three exact helper relations to remove main scalar contacts and fuse three paid paths. Verify the complete conditional kappa.",
+  "ai_assistance": "Substantial OpenAI Codex assistance. The same assistant performed the author checks. No subagents or independent review.",
+  "author": "Ali Romman",
+  "base_commit": "6cf7a683f447b9f1e2333791907fd92be5009a63",
+  "bottleneck_link": "Three H1+H5 paths become H6 in each of eighteen full calls.",
+  "budget_minutes": 240,
+  "evidence": "PROOF.md, WITNESS.json and RESULT.json",
+  "open_questions": [
+    {
+      "blocked_by": "No further large gain is established. Complete native, caller and compiler checks are required.",
+      "first_step": "Check live claims, then test a changed basis on the exact new word and retain every target debit.",
+      "question": "Can coordinated helper basis changes remove more main scalar contacts?",
+      "why_it_matters": "A longer paid path can improve the complete moment."
+    }
+  ],
+  "original_card": {
+    "acceptance_gate": "An unchanged histogram is not a kappa gain; record any separate runtime or proof benefit explicitly.",
+    "allowed_variations": [
+      "One existing scalar simplification and one proposed frame-path change."
+    ],
+    "bottleneck_link": "A legal change to the histogram, not addition count alone, is the bridge to an exponent gain.",
+    "existing_checks": [
+      {
+        "evidence": "research/staged544-a2-graph-rewrite/README.md",
+        "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+        "scope": "PR #3998: consecutive A2 scalar contraction",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129",
+        "source_commit": "389268a6b5e0373a3125d5c6fcd6995f4ea324f5",
+        "status": "author-checked"
+      },
+      {
+        "evidence": "research/staged544-separated-a2/README.md",
+        "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+        "scope": "PR #4019: separated A2 sites with unchanged recursive histogram",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129",
+        "source_commit": "f408e09df300b575235f7f77f81948071397e16d",
+        "status": "author-checked"
+      },
+      {
+        "evidence": "research/staged544-a2-composition-audit/README.md",
+        "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+        "scope": "PR #4112: composition audit",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129",
+        "source_commit": "205b7380656ba4b6316a8a493b1a3c679b8f7a0e",
+        "status": "author-checked"
+      },
+      {
+        "evidence": "research/staged544-a1858-contraction-audit/README.md",
+        "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+        "scope": "PR #4152: A1858 contraction audit",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129",
+        "source_commit": "caaa14cde5962adc372fdca71f63d0f29e73c8b2",
+        "status": "author-checked"
+      }
+    ],
+    "first_experiment": "Identify an actual paid transition to remove and construct a legal replacement frame itinerary, charging restoration, source windows and changed helpers. Compare complete before/after histograms. Stop if only scalar count changes; report that benefit honestly, without expanding the same scalar-only census.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read the A2 and separated-A2 constructions and their composition/contraction audits. Scalar contractions can preserve the complete recursive histogram; fewer ADDs alone do not justify further scans.",
+      "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+    },
+    "id": "scalar-to-moment",
+    "methods": [
+      "Derive the changed legal frame itinerary and exact child histogram.",
+      "Prove a scoped obstruction showing why that scalar gain cannot change the paid contract."
+    ],
+    "overlap_terms": [
+      "scalar simplification",
+      "paid profile",
+      "R439",
+      "3998",
+      "4019",
+      "4112",
+      "4152",
+      "staged544-a2-graph-rewrite",
+      "staged544-separated-a2",
+      "staged544-a2-composition-audit",
+      "staged544-a1858-contraction-audit"
+    ],
+    "question": "Can a changed frame itinerary remove a paid transition beyond the already covered scalar A2 contractions?",
+    "scope_change_triggers": [
+      "Submitting only another scalar count as completion of a paid-profile task."
+    ],
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "certificates/selected-result.json",
+      "research/staged544-a2-graph-rewrite/README.md",
+      "research/staged544-separated-a2/README.md",
+      "research/staged544-a2-composition-audit/README.md",
+      "research/staged544-a1858-contraction-audit/README.md"
+    ]
+  },
+  "outcome": "completed",
+  "priority_revision": 7,
+  "schema_version": 1,
+  "scope_change_reason": "The user assigned helper-basis work and a complete cost improvement. The paid paths change; scalar counts alone do not establish the result.",
+  "scope_status": "refined",
+  "stop_rule": "Publish one exact complete gain. Do not change the selected frontier.",
+  "task_id": "scalar-to-moment"
+}
diff --git a/research/p104-a2-neutral-cleanup/inputs/pr5644/VALIDATION.md b/research/p104-a2-neutral-cleanup/inputs/pr5644/VALIDATION.md
new file mode 100644
index 0000000000..c2c3fc079f
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/inputs/pr5644/VALIDATION.md
@@ -0,0 +1,91 @@
+# Validation record
+
+Scientific source: PR5627 `ed4dc88a09a7d201971f6603b8c2074e95dd9c32`.
+Frozen task provenance: canonical main
+`6cf7a683f447b9f1e2333791907fd92be5009a63`, priority revision 7.
+The publication branch was refreshed to canonical main
+`df0137efd35e11b4445734bf612bdd4c7ebc330c`. Its selected result is
+0.00310045. The priority and task catalogue are unchanged. This package does
+not edit the selection or a predecessor package.
+
+## Completed author checks
+
+Python 3.12, standard library, macOS arm64. No subagents.
+
+```sh
+python3 -I -W error -B research/p104-neutral-helper-cleanup/verify.py --write
+python3 -B scripts/research_package.py --package research/p104-neutral-helper-cleanup --check-only
+```
+
+Both commands passed. The first reconstructed all three relations, checked
+unchanged targets and owned lifetimes, all 565,504 matrix entries, 2,916
+signed native maps, the complete physical caller, both exact moment engines,
+compiler costs, 54 strict and four functional outer conditions. It rejected
+all declared semantic controls and saved the deterministic word and receipt.
+The metadata result is `PASS_PACKAGE_METADATA_AND_PINS`; it is not a
+mathematical acceptance check.
+
+The same three relations first passed full standalone checks on the PR5613
+inventory. They were then reconstructed on the smaller PR5627 inventory and
+passed full standalone checks again. Only the latter is the package input.
+No source gain or paid/target count is transferred by addition of PR claims.
+
+The final source export is an uncompressed tar file. Its exact bytes, Git
+blob, archive manifest and all 36 payload files are checked before imports.
+The export bytes are retained in an ancestor of this branch.
+
+## Completed publication checks
+
+The registered normal and optimized replays both passed. They compared the
+complete regenerated receipt and word with the saved artifacts.
+
+```sh
+python3 -B scripts/research_package.py --package research/p104-neutral-helper-cleanup
+python3 -B scripts/check_research_commit.py --package research/p104-neutral-helper-cleanup
+python3 -B scripts/export_research_package.py export --package research/p104-neutral-helper-cleanup --ref 034db9706c0b4b6913a2347351656d52a2cbfe66 --output /tmp/p104-neutral-clean.tar
+python3 -B scripts/export_research_package.py check /tmp/p104-neutral-clean.tar
+```
+
+Expected and observed markers were `PASS_REGISTERED_RESEARCH_PACKAGE`,
+`PASS_RESEARCH_COMMIT_BYTES` and `PASS_RESEARCH_EXPORT`. All 15 package files
+matched scientific commit `034db9706c0b4b6913a2347351656d52a2cbfe66`.
+
+A fresh export passed optimized replay without Git and with an empty PATH.
+All 16 exported files, including the export manifest, were read-only. Their
+hashes and modes stayed unchanged. Replay took 73.01 seconds. It used the
+same Python 3.12 standard library and compared the complete receipt and word.
+
+Three separate source-corruption cases were rejected in normal and optimized
+mode: a changed archive byte, a changed payload with rebound outer archive
+hashes, and an omitted payload with rebound outer hashes. The last two reach
+the payload and inventory checks. No source code from a damaged export is
+imported. Controls ran in isolated temporary copies.
+
+The full-history source-ancestry mode was not run. This checkout is shallow
+and the tool requires full history. The task base and retained-export commit
+are direct ancestors of the publication commit; their source bytes and the
+Git-free replay are checked. Hosted CI and independent scientific acceptance
+remain separate. GitHub body rendering and link checks will be retained in
+the Discussion handoff after publication.
+
+## Coordination
+
+The last full remote snapshot at 2026-10-26 01:42-01:43 UTC covered 334 open
+PRs and 4,919 Discussion records with complete pagination. Sparse local note
+coverage is incomplete. The current arbitrary-carrier/paid-extension screens
+were released by the PR5627 thread; its active scope is MOVE-window scheduling.
+Discussion5600 now tests paid history reconstruction. Neither active scope is
+part of this package. The three exact helper cleanups remain in the canonical
+claim linked from README.md.
+
+Some local broader screens overlapped newly posted, released negative screens
+for arbitrary carriers and single endpoint extensions. No novelty or κ gain is
+claimed for them. They are not inputs to this proof. Subsequent work tests
+changed scalar contacts with boundary repair, separate from the active claims.
+
+## Limits
+
+All checks are author checks by the same assistant. The five inherited
+framework assumptions and helper endpoint contract remain. The huge uniform
+word and complete rounded multiplier are not materialized. No independent
+human acceptance, proof-kernel theorem or global optimum is claimed.
diff --git a/research/p104-a2-neutral-cleanup/inputs/pr5644/VERIFY.json b/research/p104-a2-neutral-cleanup/inputs/pr5644/VERIFY.json
new file mode 100644
index 0000000000..8773470dc5
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/inputs/pr5644/VERIFY.json
@@ -0,0 +1,36 @@
+{
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-W",
+        "error",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "checks": "Authenticate all 36 exported source files; reconstruct three relations; check all rows and dense columns, native phases, complete caller, two exact moment engines, compiler costs and 58 outer conditions; reject semantic corruptions and compare saved artifacts.",
+      "timeout_seconds": 540
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-W",
+        "error",
+        "-B",
+        "-O",
+        "{package}/verify.py"
+      ],
+      "checks": "Authenticate all 36 exported source files; reconstruct three relations; check all rows and dense columns, native phases, complete caller, two exact moment engines, compiler costs and 58 outer conditions; reject semantic corruptions and compare saved artifacts.",
+      "timeout_seconds": 540
+    }
+  ],
+  "inputs": [
+    "research/p104-neutral-helper-cleanup/inputs/pr5627-source.tar"
+  ],
+  "python": "3.12",
+  "requirements": [],
+  "schema_version": 1,
+  "status": "ready"
+}
diff --git a/research/p104-a2-neutral-cleanup/inputs/pr5644/WITNESS.json b/research/p104-a2-neutral-cleanup/inputs/pr5644/WITNESS.json
new file mode 100644
index 0000000000..8d4f38c5c9
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/inputs/pr5644/WITNESS.json
@@ -0,0 +1,80 @@
+[
+  {
+    "anchor": [
+      "ADD",
+      18,
+      291,
+      "-1/2",
+      234
+    ],
+    "cancel": {
+      "293": "-1"
+    },
+    "cut": 10627,
+    "frame": 234,
+    "gain": 0.0,
+    "helper": 291,
+    "output": {
+      "291": "-2",
+      "293": "-1",
+      "303": "2",
+      "39": "2"
+    },
+    "removed": 6,
+    "reverse": false
+  },
+  {
+    "anchor": [
+      "ADD",
+      320,
+      321,
+      "-1",
+      237
+    ],
+    "cancel": {
+      "22": "2",
+      "320": "-3/2",
+      "330": "2"
+    },
+    "cut": 11072,
+    "frame": 237,
+    "gain": 0.0,
+    "helper": 321,
+    "output": {
+      "320": "-2",
+      "321": "1",
+      "330": "2",
+      "34": "-2"
+    },
+    "removed": 5,
+    "reverse": false
+  },
+  {
+    "anchor": [
+      "ADD",
+      368,
+      369,
+      "-1",
+      243
+    ],
+    "cancel": {
+      "26": "2",
+      "368": "-3/2",
+      "378": "-2"
+    },
+    "cut": 11718,
+    "frame": 243,
+    "gain": 0.0,
+    "helper": 369,
+    "output": {
+      "3": "-2",
+      "369": "1",
+      "372": "-2",
+      "378": "-2",
+      "382": "-2",
+      "383": "2"
+    },
+    "removed": 5,
+    "reverse": false
+  }
+]
diff --git a/research/p104-a2-neutral-cleanup/inputs/pr5644/WORD.json.gz b/research/p104-a2-neutral-cleanup/inputs/pr5644/WORD.json.gz
new file mode 100644
index 0000000000..0bd3cff775
Binary files /dev/null and b/research/p104-a2-neutral-cleanup/inputs/pr5644/WORD.json.gz differ
diff --git a/research/p104-a2-neutral-cleanup/inputs/pr5644/construct.py b/research/p104-a2-neutral-cleanup/inputs/pr5644/construct.py
new file mode 100644
index 0000000000..1d9ff07f57
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/inputs/pr5644/construct.py
@@ -0,0 +1,117 @@
+"""Apply three exact neutral helper relations and join unused transports.
+
+Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+The helper boundary identity extends the retained PR5602 construction.
+"""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction as Q
+
+
+def coalesce(word, L):
+    out = deepcopy(word)
+    actual = word['initial'] + [None]*word['owned_fields']
+    desired, program = actual[:], []
+
+    def flush(role):
+        if actual[role] != desired[role]:
+            program.append(['MOVE', role, actual[role], desired[role], role >= word['public']])
+            actual[role] = desired[role]
+
+    for event in word['program']:
+        op, role = event[:2]
+        if op == 'MOVE':
+            L.need(desired[role] == event[2], 'Chronological transport source')
+            desired[role] = event[3]
+        elif op == 'INIT':
+            L.need(actual[role] is None, 'Fresh owned lifetime')
+            actual[role] = desired[role] = event[2]
+            program.append(event[:])
+        else:
+            flush(role)
+            if op in ('ADD', 'COPY'):
+                flush(event[2])
+            program.append(event[:])
+            if op == 'CLEAR':
+                actual[role] = desired[role] = None
+    for role in range(word['public']):
+        flush(role)
+    out['program'] = program
+    return out
+
+
+def relation(word, witness, L):
+    h, cut, frame = (witness[k] for k in ('helper', 'cut', 'frame'))
+    n, owned = word['public'], word['owned_fields']
+    main = set(word['live']) | {r+112 for r in word['live']}
+    L.need(h < n and h not in main and witness['reverse'] is False, 'Forward public helper')
+    L.need(word['program'][cut] == witness['anchor'], 'Exact chronological anchor')
+    L.need(word['final'][h] == frame, 'The target boundary stays fixed')
+    rows = [{r:Q(1)} if r < n else {} for r in range(n+owned)]
+    current = word['initial'] + [None]*owned
+    for event in word['program'][:cut+1]:
+        op, role = event[:2]
+        if op == 'MOVE':
+            current[role] = event[3]
+        elif op in ('INIT', 'CLEAR'):
+            rows[role] = {}
+            current[role] = event[2] if op == 'INIT' else None
+        elif op == 'SCALE':
+            rows[role] = {j:Q(event[-2])*a for j,a in rows[role].items()}
+        elif op == 'COPY':
+            rows[role] = {j:Q(event[-2])*a for j,a in rows[event[2]].items()}
+        else:
+            L.add(rows[role], rows[event[2]], Q(event[-2]))
+    output = {int(j):Q(a) for j,a in witness['output'].items()}
+    cancel = {int(j):Q(a) for j,a in witness['cancel'].items()}
+    initial = word['initial'][h]
+    L.need(h in output and h not in cancel and all(j < n and word['initial'][j] == initial
+           for j in output), 'One independent input chart')
+    L.need(current[h] == frame and all(current[j] == frame for j in cancel),
+           'One cancellation chart')
+    row = rows[h].copy()
+    for role, coefficient in cancel.items():
+        L.add(row, rows[role], -coefficient)
+    L.need(row == output, 'Exact prefix relation on every input')
+    scale = output[h]
+    L.need(scale and abs(scale.numerator) & (abs(scale.numerator)-1) == 0
+           and scale.denominator & (scale.denominator-1) == 0, 'Invertible dyadic coefficient')
+    tail = word['program'][cut+1:]
+    L.need(not any(e[0] in ('ADD', 'COPY') and e[2] == h for e in tail), 'No later helper read')
+    removed = [e for e in tail if e[1] == h]
+    L.need(len(removed) == witness['removed'] and all(e[0] in ('ADD', 'SCALE') for e in removed),
+           'Only declared scalar cleanup is removed')
+    preparation = [['ADD', h, j, str(-a/scale), initial] for j,a in sorted(output.items()) if j != h]
+    cancellation = [['ADD', h, j, str(-a), frame] for j,a in sorted(cancel.items())]
+    if scale != 1:
+        cancellation.append(['SCALE', h, str(1/scale), frame])
+    out = deepcopy(word)
+    out['program'] = preparation + word['program'][:cut+1] + cancellation + [e for e in tail if e[1] != h]
+    out = coalesce(out, L)
+    return out, {'helper':h, 'cut':cut, 'frame':frame, 'removed_scalar_events':removed,
+                 'preparation':preparation, 'cancellation':cancellation}
+
+
+def owned_events(word):
+    n = word['public']
+    return [e for e in word['program'] if e[1] >= n or (e[0] in ('ADD', 'COPY') and e[2] >= n)]
+
+
+def construct(source, witnesses, L):
+    L.need([c['helper'] for c in witnesses] == [291,321,369], 'Three declared helper relations')
+    word, receipts = deepcopy(source), []
+    before = L.replay(word)
+    for witness in witnesses:
+        old = word
+        word, receipt = relation(word, witness, L)
+        after = L.replay(word)
+        delta = Counter(after['paid'])
+        delta.subtract(before['paid'])
+        L.need({r:v for r,v in delta.items() if v} == {1:-1,5:-1,6:1}, 'One H1+H5 path becomes H6')
+        L.need(after['helpers'] == before['helpers'] and word['initial'] == old['initial']
+               and word['final'] == old['final'], 'Every target and independent input stays fixed')
+        L.need(owned_events(word) == owned_events(old), 'Every owned operation is retained in order')
+        receipt.update(paid=after['paid'], events=len(word['program']), scalar=after['real_scalar_allowance'])
+        receipts.append(receipt)
+        before = after
+    return word, receipts, before
diff --git a/research/p104-a2-neutral-cleanup/inputs/pr5644/inputs/pr5627-source.tar b/research/p104-a2-neutral-cleanup/inputs/pr5644/inputs/pr5627-source.tar
new file mode 100644
index 0000000000..bc900f0a15
Binary files /dev/null and b/research/p104-a2-neutral-cleanup/inputs/pr5644/inputs/pr5627-source.tar differ
diff --git a/research/p104-a2-neutral-cleanup/inputs/pr5644/pricing.py b/research/p104-a2-neutral-cleanup/inputs/pr5644/pricing.py
new file mode 100644
index 0000000000..dc7f71a781
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/inputs/pr5644/pricing.py
@@ -0,0 +1,174 @@
+"""Complete mixed-target price, compiler and outer transfer.
+
+The interval and compiler bounds follow zxv and Cao Yifan. The productive
+recursion is by Jacob Alan Sussman. The controller is by Cinna Davis.
+Adapted from Ali Romman's PR5544/5545 for the two coupled contact changes.
+Successor choices were prepared for thu-nmrc with OpenAI Codex assistance.
+Helper-subspace targets were added by Ali Romman with OpenAI Codex assistance.
+The source commuting-contact construction is by Pierre-Loic Doulcet (hexapode) in PR5565.
+The source coupled-frame change is by Ali Romman with OpenAI Codex in PR5601.
+Five fixed boundary relations are from Ali Romman's PR5602.
+The shared and delayed relays are from flyingviper's PR5605 and PR5612. The preparation is from
+Scratch-net's PR5606. Their costs and target debit are included.
+Ali Romman's complete caller/price proof and all predecessor credit are retained.
+Apache-2.0.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+import local as L
+
+KAPPA, TESTED = Q('.00310626335'), Q('.003106263355')
+PREVIOUS = Q('.00310440546')
+
+
+def encode(x):
+    if isinstance(x,Q):
+        return str(x)
+    if isinstance(x,dict):
+        return {str(k):encode(v) for k,v in x.items()}
+    if isinstance(x,(list,tuple)):
+        return [encode(v) for v in x]
+    return x
+
+
+def assemble(local, native, word, physical):
+    paid, targets = Counter(), Counter()
+    counts = Counter()
+    L.need(local['helpers'] == native['helpers'], 'Every productive helper has a native target')
+    for e in word['physical_events']:
+        counts[e[0]] += 1
+        if e[0] == 'LOCAL':
+            L.need(e[3] is False, 'Every source invocation is forward')
+            paid.update(local['paid'])
+            targets.update(local['helpers'])
+        elif e[0] == 'QUERY_SHEAR':
+            paid[1] += 104
+        elif e[0] == 'IDLE':
+            paid[8*len(e[2])] += 208
+    main = Counter()
+    idle = Counter({8*len(e[2]):0 for e in word['physical_events'] if e[0] == 'IDLE'})
+    for e in word['physical_events']:
+        if e[0] == 'IDLE':
+            idle[8*len(e[2])] += 208
+    L.need(idle == physical['whole_idle_jobs'], 'Every whole idle has a native Gaussian and full rank')
+    for term in word['diagonal']:
+        main[1+8*sum(term[1:])] += 104
+    L.need(main == physical['main_targets'], 'Every main target has its full native phase')
+    targets.update(main)
+    L.need(counts['LOCAL'] == 18 and counts['QUERY_SHEAR'] == counts['IDLE'] == 15, 'Complete call census')
+    # Recount by the two path lengths, without using emitted main diagonals.
+    second_t = Counter({r:18*n for r,n in local['helpers'].items()})
+    second_p = Counter({r:18*n for r,n in local['paid'].items()})
+    second_t[145] += 208
+    second_p[1] += 15*104
+    for length in (7,8):
+        for j in range(1,length+1):
+            second_t[1+8*(j+1)] += 208
+            second_p[8*(j+1)] += 208
+    L.need((targets,paid) == (second_t,second_p), 'Independent full invoice')
+    L.need(max(targets) == 145 and max(paid) == 72, 'Maximum recursive ranks')
+    L.need(sum(targets.values()) == 12958 and sum(paid.values()) == 66492, 'Complete field and call counts')
+    L.need(sum(r*n for r,n in targets.items())-sum(r*n for r,n in paid.items()) == 760, 'Complete rank surplus')
+    return targets,paid,counts
+
+
+def run(local,native,word,physical):
+    T,P,counts = assemble(local,native,word,physical)
+    E = L.load(L.ROOT/'research/higher-moment-strictification/verify.py','p104_productive_intervals')
+    other = L.load(L.ROOT/'research/kappa-rebuild/architecture/mixed_target_probe.py','p104_productive_second_intervals')
+    def margin(k):
+        a,b = E.moment(T,1-k), E.moment(P,1-k)
+        return a[0]-b[1],a[1]-b[0]
+    lo,hi,grid = 0,10**12,10**14
+    while hi-lo > 1:
+        m=(lo+hi)//2
+        if margin(Q(m,grid))[0] > 0:
+            lo=m
+        else:
+            hi=m
+    lower,upper = Q(lo,grid),Q(hi,grid)
+    signed = Counter(T)
+    signed.subtract(P)
+    cap = Q('.0034')
+    derivative_upper = Q(0)
+    for rank, count in signed.items():
+        logarithm = E.log_bounds(rank)
+        low = E.mul(E.power(rank, 1-cap), logarithm)[0]
+        high = rank*logarithm[1]
+        derivative_upper -= count*(low if count >= 0 else high)
+    L.need(derivative_upper < 0, 'Unique raw crossing below the retained BIT cap')
+    L.need(margin(lower)[0] > 0 and margin(upper)[1] < 0, 'Strict rational crossing enclosure')
+    L.need(PREVIOUS < KAPPA < TESTED < lower and margin(PREVIOUS)[0] > 0, 'Changed complete bill improves the source claim')
+    t,u,v,c,b = 1-TESTED,Q(1,5),1024,17,18
+    target,paid = E.moment(T,t),E.moment(P,t)
+    tl,th = other.moment(T,TESTED)
+    pl,ph = other.moment(P,TESTED)
+    L.need(tl > ph and max(tl,target[0]) <= min(th,target[1]) and max(pl,paid[0]) <= min(ph,paid[1]), 'Two exact moment engines')
+    alpha = E.divide(paid,target)
+    gamma = E.divide(E.moment(P,t+u),E.mul(E.power(c,u),target))
+    delta = E.divide((Q(sum(T.values())*b),)*2,E.mul(E.power(c,TESTED),target))
+    reserve,decay = Q(1,10**12),Q(39,40)
+    L.need(alpha[1] < 1-reserve and gamma[1] < decay and delta[1] < decay, 'All three charged tail ratios')
+    L.need(decay**128 < Q(1,16), 'Both tail decay blocks')
+    normalized = 1/(1+v*reserve)+Q(4,2**32)
+    L.need(normalized < 1 and c**64 < b**63, 'Full completion, splitting and rounding charges')
+    theta,power = Q(63,64),1024
+    eta = E.scale(E.power(145,-v*TESTED),t)
+    L.need(2*(c**v)**64 <= (145**v)**63 and eta[0] > theta**power, 'Shifted exits and complement capacity')
+    L.need(E.power(145,v*TESTED)[1] < 2**power, 'Compiler initial range')
+    gap = (TESTED-KAPPA)/7
+    L.need(gap.numerator == 1, 'Exact compiler integer grid')
+    step = gap.denominator
+    def wins(j):
+        return (step*j+1)**power < 2**j
+    left,right=1,2
+    while not wins(right):
+        left,right=right,2*right
+    while right-left > 1:
+        m=(left+right)//2
+        if wins(m):
+            right=m
+        else:
+            left=m
+    H=step*right
+    L.need(H > 8*v and wins(right) and not wins(right-1), 'Finite uniform threshold with predecessor rejection')
+    local_routes = (sum(local['paid'].values())+native['helper_normalizers']+native['main_adapters']+4*104+4*local['owned_lifetimes'])*1000
+    L.need(local['real_scalar_allowance']+local_routes < 10**7, 'Every local scalar, route and owned operation is funded')
+    boundary = sum(len(word['boundaries'][side+'_program']) for side in ('left','right'))
+    raw = 18*10**7 + 15*1664 + 32*104*(len(word['physical_events'])+boundary)
+    raw += 32*104*(26+1000)
+    L.need(raw < 10**9, 'Complete nonrecursive raw bound')
+    bit = L.read(L.ROOT/'research/query-thinned-controllers/RESULT.json')['ordinary_BIT']
+    atom = Q(bit['atom'])
+    ordinary=(1-atom)*Q(bit['after_cover'])+atom*Q('.0000384599')
+    admitted=Q(bit['admitted'])
+    L.need(atom > ordinary > admitted > TESTED and atom < 1-ordinary, 'Retained BIT admission and stock')
+    outer_module=L.load(L.ROOT/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py','p104_productive_outer')
+    params={'kappa':KAPPA,'tested_saving':TESTED,'complex_uniform_saving':KAPPA+6*gap,
+            'b':KAPPA+5*gap,'a':KAPPA+4*gap,'q':KAPPA+3*gap,'bit_saving':admitted,
+            'epsilon':1-gap,'beta':1-3*gap,'r0':gap/10,'stop':gap,'layout':gap,'d':gap}
+    outer=outer_module.ledger(params)
+    outer['functional_checks']['actual_new_BIT_stock_sublinear']=params['beta']*(1-atom)
+    L.need(len(outer['strict_checks']) == 54 and len(outer['functional_checks']) == 4, 'Complete outer predicate inventory')
+    L.need(all(x > 0 for key in ('strict_checks','functional_checks') for x in outer[key].values()), 'All outer inequalities strict')
+    wrong_cutoff = E.divide((Q(sum(T.values())*21),)*2,E.mul(E.power(20,TESTED),target))
+    L.need(wrong_cutoff[0] > 1, 'Old cutoff fails with this helper inventory')
+    bad=outer_module.ledger(dict(params,bit_saving=Q('.0027')))
+    L.need(any(x <= 0 for x in bad['strict_checks'].values()), 'Insufficient BIT contract rejected')
+    return encode({'kappa':KAPPA,'kappa_decimal':'.00310626335','previous_open_pr5627':PREVIOUS,'gain':KAPPA-PREVIOUS,
+                   'relative_gain_percent':100*(KAPPA/PREVIOUS-1),'raw_root_interval':[lower,upper],
+                   'raw_headroom':[lower-KAPPA,upper-KAPPA],
+                   'raw_ceiling':{'interval':[Q(0),cap],'derivative_upper':derivative_upper},'margin_at_previous':E.display(margin(PREVIOUS)),
+                   'targets':T,'paid':P,'productive_fields':sum(T.values()),'paid_calls':sum(P.values()),
+                   'rank_mass_surplus':760,'full_forward_calls':18,'query_shears':15,'whole_idle_jobs':3120,
+                   'strictification':{'tested':TESTED,'power':v,'cutoff':c,'floor':b,'tail_offset':u,'reserve':reserve,'tail_decay':decay,'tail_block':128,
+                                     'alpha':E.display(alpha),'gamma':E.display(gamma),'delta':E.display(delta),'normalized_paid_upper':normalized},
+                   'compiler':{'theta':theta,'logarithm_power':power,'eta':E.display(eta),'gap':gap,'H':H,'N':'2^'+str(H),
+                               'integer_test_exponent':right,'uniform_saving':params['complex_uniform_saving'],'word_materialized':False},
+                   'nonrecursive':{'local_scalar':local['real_scalar_allowance'],'local_routes':local_routes,
+                                   'raw_scalar_upper':raw,'raw_budget':10**9,'peak_owned_fields':local['peak_owned_fields'],
+                                   'fixed_scalar_growth_bound':'At most 2^(16*26000) before native factors; a declared constant, not an attained norm.',
+                                   'local_paid_rank_mass':local['paid_rank_mass'],
+                                   'tensor_native_growth_bound':'Each rank-r Gaussian has row l1 norm at most 2^(rf); use local_paid_rank_mass for the whole word.'},
+                   'ordinary_BIT':bit,'outer':outer,
+                   'negative_controls':{'old_cutoff':'Rejected by completion-tail ratio greater than one','old_BIT':'Rejected by outer inequalities'}})
diff --git a/research/p104-a2-neutral-cleanup/inputs/pr5644/sources.py b/research/p104-a2-neutral-cleanup/inputs/pr5644/sources.py
new file mode 100644
index 0000000000..ea32e0a120
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/inputs/pr5644/sources.py
@@ -0,0 +1,61 @@
+"""Authenticate the retained PR5627 export before any source import.
+
+Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+The archive checks follow the repository exporter and flyingviper's PR5613.
+"""
+from contextlib import contextmanager
+from hashlib import sha1, sha256
+from pathlib import Path, PurePosixPath
+import importlib.util
+import io
+import json
+import sys
+import tarfile
+import tempfile
+
+HERE = Path(__file__).resolve().parent
+
+
+def need(ok, why):
+    if not ok:
+        raise ValueError(why)
+
+
+def load(path, name):
+    spec = importlib.util.spec_from_file_location(name, path)
+    module = importlib.util.module_from_spec(spec)
+    sys.modules[name] = module
+    spec.loader.exec_module(module)
+    return module
+
+
+@contextmanager
+def sources():
+    pin = json.loads((HERE/'SOURCES.json').read_bytes())['source_export']
+    raw = (HERE/pin['local_path']).read_bytes()
+    need(sha256(raw).hexdigest() == pin['sha256'], 'Exact predecessor archive SHA256')
+    need(sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest() == pin['git_blob'],
+         'Exact retained archive Git blob')
+    with tempfile.TemporaryDirectory(prefix='p104-neutral-source-') as directory:
+        root, names = Path(directory), set()
+        with tarfile.open(fileobj=io.BytesIO(raw), mode='r:') as bundle:
+            for member in bundle.getmembers():
+                path = PurePosixPath(member.name)
+                need(member.isfile() and not path.is_absolute() and '..' not in path.parts
+                     and '\\' not in member.name and ':' not in member.name,
+                     'Regular relative source path')
+                need(member.name not in names, 'Unique source path')
+                names.add(member.name)
+                target = root.joinpath(*path.parts)
+                target.parent.mkdir(parents=True, exist_ok=True)
+                target.write_bytes(bundle.extractfile(member).read())
+        manifest = json.loads((root/'.research-export.json').read_bytes())
+        need(manifest['commit'] == pin['commit'] and manifest['package'] == pin['package']
+             and len(manifest['files']) == pin['files'], 'Exact source commit and inventory')
+        need(names == {'.research-export.json'} | {r['path'] for r in manifest['files']},
+             'No missing or additional source payload')
+        for row in manifest['files']:
+            payload = (root/row['path']).read_bytes()
+            need(len(payload) == row['size'] and sha256(payload).hexdigest() == row['sha256'],
+                 'Authenticated payload: '+row['path'])
+        yield root/pin['package'], root
diff --git a/research/p104-a2-neutral-cleanup/inputs/pr5644/verify.py b/research/p104-a2-neutral-cleanup/inputs/pr5644/verify.py
new file mode 100644
index 0000000000..b8763f22ea
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/inputs/pr5644/verify.py
@@ -0,0 +1,114 @@
+"""Verify the three helper relations and the complete conditional kappa.
+
+Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+"""
+import argparse
+from copy import deepcopy
+import gzip
+import json
+from pathlib import Path
+import sys
+import tempfile
+
+sys.dont_write_bytecode = True
+HERE = Path(__file__).resolve().parent
+sys.path.insert(0, str(HERE))
+from sources import sources, load, need
+import construct
+
+
+def rejected(action):
+    try:
+        action()
+    except ValueError as error:
+        return str(error)
+    raise ValueError('An invalid certificate was accepted')
+
+
+def run():
+    witnesses = json.loads((HERE/'WITNESS.json').read_bytes())
+    with sources() as (parent, root):
+        L = load(parent/'local.py', 'local')
+        source = L.read(parent/'WORD.json.gz')
+        old = L.replay(source)
+        word, changes, local = construct.construct(source, witnesses, L)
+        columns = L.reverse_columns(word)
+        need((local['public_inputs'],local['owned_fields'],local['owned_lifetimes'],local['peak_owned_fields']) ==
+             (743,9,11,2), 'All independent inputs and owned lifetimes')
+        print('PASS three exact relations, unchanged targets and all 565504 matrix entries', flush=True)
+        native = L.native(word)
+        C = load(root/'research/p104-productive-controller/caller.py', 'neutral_caller')
+        caller = C.construct()
+        need(caller == L.read(root/'research/p104-productive-controller/CONTROLLER.json'), 'Exact retained controller')
+        physical = C.physical(caller, word)
+        print('PASS all native phases and the full physical caller', flush=True)
+        original_price = (parent/'pricing.py').read_text()
+        edits = [
+            ("Q('.00310440546'), Q('.003104405465')", "Q('.00310626335'), Q('.003106263355')"),
+            ("PREVIOUS = Q('.00308595')", "PREVIOUS = Q('.00310440546')"),
+            ('== 66546', '== 66492'),
+            ("'kappa_decimal':'.00310440546'", "'kappa_decimal':'.00310626335'"),
+            ('previous_open_pr5601', 'previous_open_pr5627')]
+        for before, after in edits:
+            need(original_price.count(before) == 1, 'One declared price substitution')
+            original_price = original_price.replace(before, after)
+        need((HERE/'pricing.py').read_text() == original_price, 'Only declared price changes')
+        P = load(HERE/'pricing.py', 'neutral_price')
+        costs = P.run(local, native, caller, physical)
+        controls = C.controls(caller)
+        bad = deepcopy(witnesses[0])
+        key = next(iter(bad['cancel']))
+        bad['cancel'][key] = str(L.Q(bad['cancel'][key])+1)
+        controls['false_cancellation'] = rejected(lambda: construct.relation(source, bad, L))
+        bad = deepcopy(witnesses[0])
+        bad['cut'] += 1
+        controls['wrong_cut'] = rejected(lambda: construct.relation(source, bad, L))
+        bad = deepcopy(word)
+        bad['program'].pop(0)
+        controls['missing_input_basis'] = rejected(lambda: L.replay(bad))
+        bad = deepcopy(word)
+        bad['program'].pop(max(i for i,e in enumerate(bad['program']) if e[0] == 'CLEAR'))
+        controls['missing_owned_erasure'] = rejected(lambda: L.replay(bad))
+        bad = deepcopy(local)
+        bad['helpers'][1] += 1
+        controls['extra_target_credit'] = rejected(lambda: P.assemble(bad,native,caller,physical))
+        bad = deepcopy(local)
+        bad['paid'][1] -= 1
+        controls['unpaid_query'] = rejected(lambda: P.assemble(bad,native,caller,physical))
+        result = dict(status='PASS_P104_NEUTRAL_HELPER_KAPPA_00310626335',
+                      source_commit='ed4dc88a09a7d201971f6603b8c2074e95dd9c32',
+                      authenticated_source_files=36, changes=changes,
+                      local_paid_delta={1:-3,5:-3,6:3}, local_helper_delta={},
+                      source_local=old, local=local, separate_columns=columns,
+                      native=native, physical_caller=physical, complete_cost=costs,
+                      negative_controls=controls,
+                      limits=['The five selected framework assumptions and helper-endpoint contract remain.',
+                              'The enormous uniform word and complete rounded multiplier are not materialized.',
+                              'These author checks are not independent scientific review or a proof-kernel theorem.',
+                              'The improvement is small. No large gain or global optimum is established.'])
+        return P.encode(result), word
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--write', action='store_true')
+    args = parser.parse_args()
+    with tempfile.TemporaryDirectory(prefix='p104-neutral-bytecode-') as cache:
+        sys.pycache_prefix = cache
+        result, word = run()
+    for name, value in (('RESULT.json', result), ('WORD.json.gz', word)):
+        path = HERE/name
+        if args.write:
+            raw = (json.dumps(value,sort_keys=True,indent=None if name.endswith('.gz') else 2)+'\n').encode()
+            path.write_bytes(gzip.compress(raw,mtime=0) if name.endswith('.gz') else raw)
+        else:
+            raw = path.read_bytes()
+            need(json.loads(gzip.decompress(raw) if name.endswith('.gz') else raw) == value,
+                 'Exact saved artifact: '+name)
+    print(result['status'])
+    print(json.dumps({k:result['complete_cost'][k] for k in
+                     ('kappa_decimal','gain','raw_root_interval','productive_fields','paid_calls')},sort_keys=True))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/p104-a2-neutral-cleanup/invoices/COMPARISON.json b/research/p104-a2-neutral-cleanup/invoices/COMPARISON.json
new file mode 100644
index 0000000000..827cce01bf
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/invoices/COMPARISON.json
@@ -0,0 +1,89 @@
+{
+  "assurance": {
+    "contract": "Exact matching user declarations; mathematical applicability is not verified.",
+    "inconclusive": "Mixed hinge signs do not establish a power-moment crossing or failure.",
+    "input_binding": "SHA-256 identifies the exact input bytes read, when loaded by this CLI.",
+    "scope": "Histogram arithmetic only. Histogram correctness, circuit legality, ownership, phases, precision, supplier admission and compiler endpoints are not validated."
+  },
+  "classification": "uniformly_better",
+  "contract": {
+    "ambient_rank": 145,
+    "boundary": "Complete PR5627-derived p16/a7 caller before the same mixed-target compiler",
+    "model": "mixed-target-unnormalized-power-v1",
+    "rank_semantics": "H_r costs r^(1-C); debit surrendered productive fields"
+  },
+  "delta_paid": {
+    "2": 18,
+    "3": -18,
+    "5": -18,
+    "6": 18
+  },
+  "delta_targets": {},
+  "hinges": [
+    {
+      "rank": 0,
+      "value": 0
+    },
+    {
+      "rank": 2,
+      "value": 0
+    },
+    {
+      "rank": 3,
+      "value": -18
+    },
+    {
+      "rank": 5,
+      "value": -18
+    },
+    {
+      "rank": 6,
+      "value": 0
+    }
+  ],
+  "inputs": {
+    "new": {
+      "bytes": 815,
+      "path": "research/p104-a2-neutral-cleanup/invoices/common.json",
+      "sha256": "586c720e8a8125b9d4a528e82e7fcf0ea9324b6c3a6384e3e25eb4bcb2a526ae"
+    },
+    "old": {
+      "bytes": 815,
+      "path": "research/p104-a2-neutral-cleanup/invoices/pr5644.json",
+      "sha256": "b44cf8cb4ba5f241e43f656917035b2691d99858bc729d37d01cbf14f1e243ec"
+    }
+  },
+  "method_credit": "Classical concave order/majorization; mightyOil's t16-moment-order-audit and its retained predecessors. No new theorem claim.",
+  "power_moment": {
+    "exponent": "0 < t < 1",
+    "new_minus_old_sign": "strictly_negative",
+    "tariff": "r^t"
+  },
+  "quantity": "(new paid - new targets) - (old paid - old targets)",
+  "rank_mass": {
+    "delta": {
+      "paid": 0,
+      "paid_minus_targets": 0,
+      "targets": 0
+    },
+    "new": {
+      "paid": 240764,
+      "paid_minus_targets": -760,
+      "targets": 241524
+    },
+    "old": {
+      "paid": 240764,
+      "paid_minus_targets": -760,
+      "targets": 241524
+    }
+  },
+  "schema": "integer-mult-recursive-invoice-comparison/v1",
+  "signed_net_delta": {
+    "2": 18,
+    "3": -18,
+    "5": -18,
+    "6": 18
+  },
+  "tariff_class": "increasing concave f on nonnegative ranks, with f(0)=0",
+  "uniform_order": "weak; some concave tariffs can give equality"
+}
diff --git a/research/p104-a2-neutral-cleanup/invoices/common.json b/research/p104-a2-neutral-cleanup/invoices/common.json
new file mode 100644
index 0000000000..e49e4c624a
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/invoices/common.json
@@ -0,0 +1,44 @@
+{
+  "schema": "integer-mult-recursive-invoice/v1",
+  "contract": {
+    "model": "mixed-target-unnormalized-power-v1",
+    "rank_semantics": "H_r costs r^(1-C); debit surrendered productive fields",
+    "ambient_rank": 145,
+    "boundary": "Complete PR5627-derived p16/a7 caller before the same mixed-target compiler"
+  },
+  "paid": {
+    "1": 41106,
+    "16": 416,
+    "2": 8226,
+    "24": 416,
+    "3": 8874,
+    "32": 416,
+    "4": 1638,
+    "40": 416,
+    "48": 416,
+    "5": 2862,
+    "56": 416,
+    "6": 396,
+    "64": 416,
+    "7": 270,
+    "72": 208
+  },
+  "targets": {
+    "1": 36,
+    "145": 208,
+    "17": 416,
+    "2": 72,
+    "25": 416,
+    "33": 416,
+    "4": 1638,
+    "41": 416,
+    "49": 416,
+    "5": 108,
+    "57": 416,
+    "65": 416,
+    "7": 90,
+    "73": 208,
+    "8": 288,
+    "9": 7398
+  }
+}
diff --git a/research/p104-a2-neutral-cleanup/invoices/pr5644.json b/research/p104-a2-neutral-cleanup/invoices/pr5644.json
new file mode 100644
index 0000000000..612d39d1c4
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/invoices/pr5644.json
@@ -0,0 +1,44 @@
+{
+  "schema": "integer-mult-recursive-invoice/v1",
+  "contract": {
+    "model": "mixed-target-unnormalized-power-v1",
+    "rank_semantics": "H_r costs r^(1-C); debit surrendered productive fields",
+    "ambient_rank": 145,
+    "boundary": "Complete PR5627-derived p16/a7 caller before the same mixed-target compiler"
+  },
+  "paid": {
+    "1": 41106,
+    "16": 416,
+    "2": 8208,
+    "24": 416,
+    "3": 8892,
+    "32": 416,
+    "4": 1638,
+    "40": 416,
+    "48": 416,
+    "5": 2880,
+    "56": 416,
+    "6": 378,
+    "64": 416,
+    "7": 270,
+    "72": 208
+  },
+  "targets": {
+    "1": 36,
+    "145": 208,
+    "17": 416,
+    "2": 72,
+    "25": 416,
+    "33": 416,
+    "4": 1638,
+    "41": 416,
+    "49": 416,
+    "5": 108,
+    "57": 416,
+    "65": 416,
+    "7": 90,
+    "73": 208,
+    "8": 288,
+    "9": 7398
+  }
+}
diff --git a/research/p104-a2-neutral-cleanup/pricing.py b/research/p104-a2-neutral-cleanup/pricing.py
new file mode 100644
index 0000000000..3bd475205b
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/pricing.py
@@ -0,0 +1,174 @@
+"""Complete mixed-target price, compiler and outer transfer.
+
+The interval and compiler bounds follow zxv and Cao Yifan. The productive
+recursion is by Jacob Alan Sussman. The controller is by Cinna Davis.
+Adapted from Ali Romman's PR5544/5545 for the two coupled contact changes.
+Successor choices were prepared for thu-nmrc with OpenAI Codex assistance.
+Helper-subspace targets were added by Ali Romman with OpenAI Codex assistance.
+The source commuting-contact construction is by Pierre-Loic Doulcet (hexapode) in PR5565.
+The source coupled-frame change is by Ali Romman with OpenAI Codex in PR5601.
+Five fixed boundary relations are from Ali Romman's PR5602.
+The shared and delayed relays are from flyingviper's PR5605 and PR5612. The preparation is from
+Scratch-net's PR5606. Their costs and target debit are included.
+Ali Romman's complete caller/price proof and all predecessor credit are retained.
+Apache-2.0.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+import local as L
+
+KAPPA, TESTED = Q('.00310644468'), Q('.003106444685')
+PREVIOUS = Q('.00310626335')
+
+
+def encode(x):
+    if isinstance(x,Q):
+        return str(x)
+    if isinstance(x,dict):
+        return {str(k):encode(v) for k,v in x.items()}
+    if isinstance(x,(list,tuple)):
+        return [encode(v) for v in x]
+    return x
+
+
+def assemble(local, native, word, physical):
+    paid, targets = Counter(), Counter()
+    counts = Counter()
+    L.need(local['helpers'] == native['helpers'], 'Every productive helper has a native target')
+    for e in word['physical_events']:
+        counts[e[0]] += 1
+        if e[0] == 'LOCAL':
+            L.need(e[3] is False, 'Every source invocation is forward')
+            paid.update(local['paid'])
+            targets.update(local['helpers'])
+        elif e[0] == 'QUERY_SHEAR':
+            paid[1] += 104
+        elif e[0] == 'IDLE':
+            paid[8*len(e[2])] += 208
+    main = Counter()
+    idle = Counter({8*len(e[2]):0 for e in word['physical_events'] if e[0] == 'IDLE'})
+    for e in word['physical_events']:
+        if e[0] == 'IDLE':
+            idle[8*len(e[2])] += 208
+    L.need(idle == physical['whole_idle_jobs'], 'Every whole idle has a native Gaussian and full rank')
+    for term in word['diagonal']:
+        main[1+8*sum(term[1:])] += 104
+    L.need(main == physical['main_targets'], 'Every main target has its full native phase')
+    targets.update(main)
+    L.need(counts['LOCAL'] == 18 and counts['QUERY_SHEAR'] == counts['IDLE'] == 15, 'Complete call census')
+    # Recount by the two path lengths, without using emitted main diagonals.
+    second_t = Counter({r:18*n for r,n in local['helpers'].items()})
+    second_p = Counter({r:18*n for r,n in local['paid'].items()})
+    second_t[145] += 208
+    second_p[1] += 15*104
+    for length in (7,8):
+        for j in range(1,length+1):
+            second_t[1+8*(j+1)] += 208
+            second_p[8*(j+1)] += 208
+    L.need((targets,paid) == (second_t,second_p), 'Independent full invoice')
+    L.need(max(targets) == 145 and max(paid) == 72, 'Maximum recursive ranks')
+    L.need(sum(targets.values()) == 12958 and sum(paid.values()) == 66492, 'Complete field and call counts')
+    L.need(sum(r*n for r,n in targets.items())-sum(r*n for r,n in paid.items()) == 760, 'Complete rank surplus')
+    return targets,paid,counts
+
+
+def run(local,native,word,physical):
+    T,P,counts = assemble(local,native,word,physical)
+    E = L.load(L.ROOT/'research/higher-moment-strictification/verify.py','p104_productive_intervals')
+    other = L.load(L.ROOT/'research/kappa-rebuild/architecture/mixed_target_probe.py','p104_productive_second_intervals')
+    def margin(k):
+        a,b = E.moment(T,1-k), E.moment(P,1-k)
+        return a[0]-b[1],a[1]-b[0]
+    lo,hi,grid = 0,10**12,10**14
+    while hi-lo > 1:
+        m=(lo+hi)//2
+        if margin(Q(m,grid))[0] > 0:
+            lo=m
+        else:
+            hi=m
+    lower,upper = Q(lo,grid),Q(hi,grid)
+    signed = Counter(T)
+    signed.subtract(P)
+    cap = Q('.0034')
+    derivative_upper = Q(0)
+    for rank, count in signed.items():
+        logarithm = E.log_bounds(rank)
+        low = E.mul(E.power(rank, 1-cap), logarithm)[0]
+        high = rank*logarithm[1]
+        derivative_upper -= count*(low if count >= 0 else high)
+    L.need(derivative_upper < 0, 'Unique raw crossing below the retained BIT cap')
+    L.need(margin(lower)[0] > 0 and margin(upper)[1] < 0, 'Strict rational crossing enclosure')
+    L.need(PREVIOUS < KAPPA < TESTED < lower and margin(PREVIOUS)[0] > 0, 'Changed complete bill improves the source claim')
+    t,u,v,c,b = 1-TESTED,Q(1,5),1024,17,18
+    target,paid = E.moment(T,t),E.moment(P,t)
+    tl,th = other.moment(T,TESTED)
+    pl,ph = other.moment(P,TESTED)
+    L.need(tl > ph and max(tl,target[0]) <= min(th,target[1]) and max(pl,paid[0]) <= min(ph,paid[1]), 'Two exact moment engines')
+    alpha = E.divide(paid,target)
+    gamma = E.divide(E.moment(P,t+u),E.mul(E.power(c,u),target))
+    delta = E.divide((Q(sum(T.values())*b),)*2,E.mul(E.power(c,TESTED),target))
+    reserve,decay = Q(1,10**12),Q(39,40)
+    L.need(alpha[1] < 1-reserve and gamma[1] < decay and delta[1] < decay, 'All three charged tail ratios')
+    L.need(decay**128 < Q(1,16), 'Both tail decay blocks')
+    normalized = 1/(1+v*reserve)+Q(4,2**32)
+    L.need(normalized < 1 and c**64 < b**63, 'Full completion, splitting and rounding charges')
+    theta,power = Q(63,64),1024
+    eta = E.scale(E.power(145,-v*TESTED),t)
+    L.need(2*(c**v)**64 <= (145**v)**63 and eta[0] > theta**power, 'Shifted exits and complement capacity')
+    L.need(E.power(145,v*TESTED)[1] < 2**power, 'Compiler initial range')
+    gap = (TESTED-KAPPA)/7
+    L.need(gap.numerator == 1, 'Exact compiler integer grid')
+    step = gap.denominator
+    def wins(j):
+        return (step*j+1)**power < 2**j
+    left,right=1,2
+    while not wins(right):
+        left,right=right,2*right
+    while right-left > 1:
+        m=(left+right)//2
+        if wins(m):
+            right=m
+        else:
+            left=m
+    H=step*right
+    L.need(H > 8*v and wins(right) and not wins(right-1), 'Finite uniform threshold with predecessor rejection')
+    local_routes = (sum(local['paid'].values())+native['helper_normalizers']+native['main_adapters']+4*104+4*local['owned_lifetimes'])*1000
+    L.need(local['real_scalar_allowance']+local_routes < 10**7, 'Every local scalar, route and owned operation is funded')
+    boundary = sum(len(word['boundaries'][side+'_program']) for side in ('left','right'))
+    raw = 18*10**7 + 15*1664 + 32*104*(len(word['physical_events'])+boundary)
+    raw += 32*104*(26+1000)
+    L.need(raw < 10**9, 'Complete nonrecursive raw bound')
+    bit = L.read(L.ROOT/'research/query-thinned-controllers/RESULT.json')['ordinary_BIT']
+    atom = Q(bit['atom'])
+    ordinary=(1-atom)*Q(bit['after_cover'])+atom*Q('.0000384599')
+    admitted=Q(bit['admitted'])
+    L.need(atom > ordinary > admitted > TESTED and atom < 1-ordinary, 'Retained BIT admission and stock')
+    outer_module=L.load(L.ROOT/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py','p104_productive_outer')
+    params={'kappa':KAPPA,'tested_saving':TESTED,'complex_uniform_saving':KAPPA+6*gap,
+            'b':KAPPA+5*gap,'a':KAPPA+4*gap,'q':KAPPA+3*gap,'bit_saving':admitted,
+            'epsilon':1-gap,'beta':1-3*gap,'r0':gap/10,'stop':gap,'layout':gap,'d':gap}
+    outer=outer_module.ledger(params)
+    outer['functional_checks']['actual_new_BIT_stock_sublinear']=params['beta']*(1-atom)
+    L.need(len(outer['strict_checks']) == 54 and len(outer['functional_checks']) == 4, 'Complete outer predicate inventory')
+    L.need(all(x > 0 for key in ('strict_checks','functional_checks') for x in outer[key].values()), 'All outer inequalities strict')
+    wrong_cutoff = E.divide((Q(sum(T.values())*21),)*2,E.mul(E.power(20,TESTED),target))
+    L.need(wrong_cutoff[0] > 1, 'Old cutoff fails with this helper inventory')
+    bad=outer_module.ledger(dict(params,bit_saving=Q('.0027')))
+    L.need(any(x <= 0 for x in bad['strict_checks'].values()), 'Insufficient BIT contract rejected')
+    return encode({'kappa':KAPPA,'kappa_decimal':'.00310644468','previous_open_pr5627':PREVIOUS,'gain':KAPPA-PREVIOUS,
+                   'relative_gain_percent':100*(KAPPA/PREVIOUS-1),'raw_root_interval':[lower,upper],
+                   'raw_headroom':[lower-KAPPA,upper-KAPPA],
+                   'raw_ceiling':{'interval':[Q(0),cap],'derivative_upper':derivative_upper},'margin_at_previous':E.display(margin(PREVIOUS)),
+                   'targets':T,'paid':P,'productive_fields':sum(T.values()),'paid_calls':sum(P.values()),
+                   'rank_mass_surplus':760,'full_forward_calls':18,'query_shears':15,'whole_idle_jobs':3120,
+                   'strictification':{'tested':TESTED,'power':v,'cutoff':c,'floor':b,'tail_offset':u,'reserve':reserve,'tail_decay':decay,'tail_block':128,
+                                     'alpha':E.display(alpha),'gamma':E.display(gamma),'delta':E.display(delta),'normalized_paid_upper':normalized},
+                   'compiler':{'theta':theta,'logarithm_power':power,'eta':E.display(eta),'gap':gap,'H':H,'N':'2^'+str(H),
+                               'integer_test_exponent':right,'uniform_saving':params['complex_uniform_saving'],'word_materialized':False},
+                   'nonrecursive':{'local_scalar':local['real_scalar_allowance'],'local_routes':local_routes,
+                                   'raw_scalar_upper':raw,'raw_budget':10**9,'peak_owned_fields':local['peak_owned_fields'],
+                                   'fixed_scalar_growth_bound':'At most 2^(16*26000) before native factors; a declared constant, not an attained norm.',
+                                   'local_paid_rank_mass':local['paid_rank_mass'],
+                                   'tensor_native_growth_bound':'Each rank-r Gaussian has row l1 norm at most 2^(rf); use local_paid_rank_mass for the whole word.'},
+                   'ordinary_BIT':bit,'outer':outer,
+                   'negative_controls':{'old_cutoff':'Rejected by completion-tail ratio greater than one','old_BIT':'Rejected by outer inequalities'}})
diff --git a/research/p104-a2-neutral-cleanup/verify.py b/research/p104-a2-neutral-cleanup/verify.py
new file mode 100644
index 0000000000..eb74ae34f0
--- /dev/null
+++ b/research/p104-a2-neutral-cleanup/verify.py
@@ -0,0 +1,139 @@
+"""Full exact PR5643/PR5644 composition replay.
+
+Prepared for zxv with substantial OpenAI Codex assistance; Apache-2.0.
+Ali Romman's cleanup constructor/checker and all P104, native, controller,
+compiler, BIT and analytic notices remain. The A2 identity retains its earlier
+Chris R/Clear1nsight, ToikY and scoped-audit attribution.
+"""
+from pathlib import Path
+from collections import Counter
+from copy import deepcopy
+from hashlib import sha256,sha1
+import argparse,gzip,importlib.util,json,sys,tempfile
+sys.dont_write_bytecode=True
+HERE=Path(__file__).resolve().parent
+A2=HERE/'inputs/pr5643'
+CLEANUP=HERE/'inputs/pr5644'
+REPLAY_SOURCES_SHA256='a2b96619a65cfdd99d6651d65626793f27e6a7fbc13e97f01d66b7634817fc92'
+A2_PAYLOAD='c7545eab4e1394ba942a7ac8e4d70860d172cabda151a559fd566478aa38204b'
+COMPOSED_PAYLOAD='42fe73e3240340aa185aab3cf976f8f6b783603b4d5513345519a260c1253d4a'
+
+def need(ok,why):
+ if not ok:raise ValueError(why)
+def load(path,name):
+ s=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(s);sys.modules[name]=m;s.loader.exec_module(m);return m
+def read(path):
+ raw=path.read_bytes();return json.loads(gzip.decompress(raw)if path.suffix=='.gz'else raw)
+def blob(raw):return sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest()
+def check_bytes(raw,row):
+ need(len(raw)==row['size'] and sha256(raw).hexdigest()==row['sha256'],'Exact retained source SHA256 '+row.get('path',row.get('local_path','')))
+ if 'git_blob'in row:need(blob(raw)==row['git_blob'],'Exact retained source Git blob')
+def authenticate():
+ raw=(HERE/'REPLAY-SOURCES.json').read_bytes()
+ need(sha256(raw).hexdigest()==REPLAY_SOURCES_SHA256,'Frozen exact retained source inventory')
+ pins=json.loads(raw)
+ need(pins['sources']=={'pr5643':'a3ff5c628bfc8825553d62d913f3e91f75d6825f','pr5644':'c5871955d89bf73506fd68b0a5bf1cf2b3153c02'},'Exact submitted source heads')
+ for row in pins['files']:check_bytes((HERE/row['local_path']).read_bytes(),row)
+ need(sha256(gzip.decompress((A2/'WORD.json.gz').read_bytes())).hexdigest()==A2_PAYLOAD,'Exact submitted A2 candidate payload')
+ return pins
+
+def changes(a,b):
+ d=Counter(a);d.subtract(b);return{r:c for r,c in d.items()if c}
+def reject(f):
+ try:f()
+ except ValueError as e:return str(e)
+ raise ValueError('Malformed composition control accepted')
+def make_word(L,C):
+ A=load(A2/'construct.py','retained_a2_construct')
+ a2_payload,_=A.construct()
+ need(a2_payload==gzip.decompress((A2/'WORD.json.gz').read_bytes()),'Exact PR5643 regeneration')
+ a2,source=json.loads(a2_payload),read(A2/'inputs/pr5627-WORD.json.gz')
+ witnesses=read(CLEANUP/'WITNESS.json')
+ cleaned,_,_=C.construct(source,witnesses,L)
+ need(cleaned==read(CLEANUP/'WORD.json.gz'),'Exact PR5644 reconstruction')
+ word,receipts,local=C.construct(a2,witnesses,L)
+ word['schema']='p104-a2-helper-cleanup-composition/1'
+ payload=json.dumps(word,separators=(',',':')).encode()
+ need(sha256(payload).hexdigest()==COMPOSED_PAYLOAD,'Entire composed candidate payload')
+ need(gzip.decompress((HERE/'WORD.json.gz').read_bytes())==payload,'Saved composed payload')
+ old={name:L.replay(w)for name,w in [('pr5627',source),('pr5643',a2),('pr5644',cleaned)]}
+ need(changes(local['paid'],old['pr5644']['paid'])=={2:1,3:-1,5:-1,6:1},'A2 paid exchange survives all cleanup edits')
+ need(changes(local['paid'],old['pr5643']['paid'])=={1:-3,5:-3,6:3},'Three cleanup paid exchanges survive A2')
+ need(all(local['helpers']==x['helpers']for x in old.values()),'Every target retained against all sources')
+ need(all(word[k]==a2[k]for k in ('public','owned_fields','initial','final','ports','live','frames')),'All endpoint/native boundary inventories retained')
+ need(C.owned_events(word)==C.owned_events(a2),'All owned instructions and order retained')
+ need(local['real_scalar_allowance']==220220,'All additional ordinary work included')
+ return word,receipts,local,old,witnesses
+
+def run(quick=False):
+ authenticate()
+ S=load(CLEANUP/'sources.py','composition_framework_sources')
+ L=load(A2/'inputs/pr5627-local.py','local')
+ C=load(CLEANUP/'construct.py','retained_cleanup')
+ word,receipts,local,old,witnesses=make_word(L,C)
+ print('PASS actual common word: all arbitrary-input rows, frames, fixed boundaries and full local paid-target delta',flush=True)
+ if quick:return {'status':'PASS_P104_COMPOSITION_QUICK'}
+ with S.sources()as(prior,framework):
+  L.ROOT=framework
+  foundation=[]
+  need((prior/'local.py').read_bytes()==(A2/'inputs/pr5627-local.py').read_bytes(),'Identical exported PR5627 local checker')
+  for row in read(prior/'SOURCES.json')['files']:
+   path=framework/row['path']
+   if path.is_file():
+    need(sha256(path.read_bytes()).hexdigest()==row['sha256'],'Exact scientific foundation '+row['path']);foundation.append(row['path'])
+  need(len(foundation)==19,'Complete retained manifest rows available in exact export')
+  transpose=L.reverse_columns(word)
+  print('PASS every dense transpose column',transpose['columns'],flush=True)
+  native=L.native(word)
+  print('PASS every native map and exact phase',native['distinct_maps'],flush=True)
+  caller_module=load(framework/'research/p104-productive-controller/caller.py','composed_caller')
+  caller=caller_module.construct()
+  need(caller==read(framework/'research/p104-productive-controller/CONTROLLER.json'),'Exact retained complete caller')
+  physical=caller_module.physical(caller,word)
+  print('PASS full composed physical caller',flush=True)
+  original=(CLEANUP/'pricing.py').read_text()
+  edits=[("Q('.00310626335'), Q('.003106263355')","Q('.00310644468'), Q('.003106444685')"),("PREVIOUS = Q('.00310440546')","PREVIOUS = Q('.00310626335')"),("'kappa_decimal':'.00310626335'","'kappa_decimal':'.00310644468'")]
+  for before,after in edits:
+   need(original.count(before)==1,'One literal price adaptation');original=original.replace(before,after)
+  need((HERE/'pricing.py').read_text()==original,'No changed mathematical pricing predicate')
+  P=load(HERE/'pricing.py','composed_price')
+  price=P.run(local,native,caller,physical)
+  print('PASS two exact moment engines, compiler, BIT stock and all58 outer conditions',price['raw_root_interval'],flush=True)
+  controls=caller_module.controls(caller)
+  bad=deepcopy(witnesses[0]);key=next(iter(bad['cancel']));bad['cancel'][key]=str(L.Q(bad['cancel'][key])+1)
+  controls['false_cleanup_cancellation']=reject(lambda:C.relation(read(A2/'WORD.json.gz'),bad,L))
+  bad=deepcopy(witnesses[0]);bad['cut']+=1
+  controls['wrong_cleanup_cut']=reject(lambda:C.relation(read(A2/'WORD.json.gz'),bad,L))
+  bad=deepcopy(word);bad['program'].pop(0)
+  controls['missing_input_basis']=reject(lambda:L.replay(bad))
+  gate=['ADD',340,715,'-4',396]
+  bad=deepcopy(word);need(bad['program'].count(gate)==1,'Unique A2 correction');bad['program'].remove(gate)
+  controls['missing_A2_correction']=reject(lambda:L.replay(bad))
+  bad=deepcopy(word);i=bad['program'].index(gate);bad['program'][i][-1]=825
+  controls['wrong_A2_contact_frame']=reject(lambda:L.replay(bad))
+  bad=deepcopy(word);bad['program'].pop(max(i for i,e in enumerate(bad['program'])if e[0]=='CLEAR'))
+  controls['missing_owned_erasure']=reject(lambda:L.replay(bad))
+  bad=deepcopy(local);bad['helpers'][1]+=1
+  controls['extra_target_credit']=reject(lambda:P.assemble(bad,native,caller,physical))
+  bad=deepcopy(local);bad['paid'][1]-=1
+  controls['unpaid_query']=reject(lambda:P.assemble(bad,native,caller,physical))
+  bad=deepcopy(local);bad['paid'][2]+=1;bad['paid'][3]-=1
+  controls['undercharged_A2_child']=reject(lambda:P.assemble(bad,native,caller,physical))
+  # Byte-mutation controls use temporary bytes; immutable source files are never changed.
+  for row in read(HERE/'REPLAY-SOURCES.json')['files']:
+   raw=(HERE/row['local_path']).read_bytes()
+   if raw:
+    controls['source_byte_mutation_'+row['local_path']]=reject(lambda raw=raw,row=row:check_bytes(bytes([raw[0]^1])+raw[1:],row))
+  result=P.encode({'status':'PASS_P104_COMPOSED_KAPPA_00310644468','sources':{'pr5643':'a3ff5c628bfc8825553d62d913f3e91f75d6825f','pr5644':'c5871955d89bf73506fd68b0a5bf1cf2b3153c02'},'foundation_files':foundation,'local':local,'previous_local':old,'cleanup_changes':receipts,'delta_vs_pr5627':changes(local['paid'],old['pr5627']['paid']),'delta_vs_pr5643':changes(local['paid'],old['pr5643']['paid']),'delta_vs_pr5644':changes(local['paid'],old['pr5644']['paid']),'target_delta':{},'transpose':transpose,'native':native,'physical':physical,'complete_cost':price,'controls':controls,'candidate_payload_sha256':COMPOSED_PAYLOAD})
+ return result
+
+def main():
+ ap=argparse.ArgumentParser(description=__doc__);ap.add_argument('--quick',action='store_true');ap.add_argument('--write',action='store_true');args=ap.parse_args()
+ with tempfile.TemporaryDirectory(prefix='p104-compose-bytecode-')as cache:
+  sys.pycache_prefix=cache;result=run(args.quick)
+ if not args.quick:
+  target=HERE/'FULL-RESULT.json'
+  if args.write:target.write_text(json.dumps(result,sort_keys=True,indent=2)+'\n')
+  else:need(read(target)==result,'Exact saved complete composition receipt')
+ print(result['status'],flush=True)
+if __name__=='__main__':main()