Census PR5718-shape helper splits on the PR5907 word: none remain without a mid-word correction (no new κ)

research/p104-pr5718-shape-split-census/README.md

@@ -0,0 +1,87 @@
+# No PR5718-shape helper split remains on the PR5907 P104 word
+
+**Scoped finite certificate; no new κ.** Base: canonical main `19fdb086ea96af9a9f87936a2b888e10af4ed810`.
+The selected record is unchanged.
+
+Matarener's open [PR #5994](https://github.com/CrocSwap/integer-mult-bounds/pull/5994)
+(`research/p104-helper-split-exhaustion`) shows that no PR5599-type helper split remains on the latest conditional
+P104 word, DreamingOfClouds's [PR #5907](https://github.com/CrocSwap/integer-mult-bounds/pull/5907). It names
+splits of the kind in flyingviper's merged [PR #5718](https://github.com/CrocSwap/integer-mult-bounds/pull/5718)
+as the remaining route: different input and output bases, with an output correction. This package tests that
+route on the PR5907 word.
+
+## Result
+
+The split shape of PR5718 (see its `PROOF.md`) is: a helper `p` of a boundary group with charts `(U, V)` is retired
+at a strictly intermediate chart `F` after event `i`; a new independent helper with arbitrary input `z` takes over
+`p`'s continuation (unit injection `b = e_p`); the input functional `c = aP` may use any role whose initial chart is
+zero-dimensional, main inputs included; and the output defect is normalised on roles whose final chart is `V`.
+The census in [shapesplit.py](shapesplit.py) decides exactly over Q, for every helper group, every strictly
+intermediate chart, every cut after an event that touches that chart, and every group helper at the chart, whether
+
+- some combination `a` of the prefix rows at `F` has `a_p ≠ 0` and `aP` in the allowed input support, and
+- the z-direction `d = S e_p` vanishes on every role whose final chart is not `V` (no **leak**), and
+- `a·b = c·d' ≠ 0` for some `d'` that agrees with `d` except on freely corrected `V`-final roles (the **pairing**).
+
+| Word | Input rule | Evaluations | Leak | Pairing fails | Witnesses |
+|---|---|---:|---:|---:|---:|
+| PR5713 source (calibration) | group + U-initial | 8,579 | 3,817 | 2 | **7** |
+| PR5713 source (calibration) | + empty-frame roles | 8,579 | 3,817 | 2 | **7** |
+| PR5907 | group + U-initial | 8,913 | 4,202 | 4 | **0** |
+| PR5907 | + empty-frame roles | 8,913 | 4,206 | 4 | **0** |
+
+**Calibration.** On the PR5713 source word, the census recovers PR5718's own split: cut after event 14330,
+chart 602, helper 708, ranks (2, 7). All 7 witnesses lie on chart 602 and helper 708 (earlier cuts of the same
+meeting).
+
+**PR5907.** No class passes. In 4,206 classes the new helper's z-direction leaks to a role whose final chart is
+not `V`. In the other 4 (chart 549, helper 173, cuts 15974–15988) only the pairing `a_p = d_p c_p` fails. So on
+PR5907, any further PR5718-type split must cancel that leak with a correction in the middle of the word. The
+receipt lists how many leaked roles each class has. 425 classes leak to exactly one role; these are the nearest
+candidates.
+
+PR5718's split itself is a boundary-relaxation witness of the PR5994 census on its source word. So PR5994's
+boundary-support exclusion already rules out PR5718-shape splits on PR5907 when the output defect stays on
+`V`-final roles. This package gives that link an exact calibration and a separate decision procedure for unit
+injection, and it records where the leak goes.
+
+## Scope and limits
+
+- Scalar necessary condition only, for the z-part of the split. The non-z part of the output normalisation, native
+  maps, owned lifetimes, caller, compiler and outer checks are not involved. A witness would still need all of them.
+- Unit injection on one group helper, as in PR5718. Injections along a combination of several fields are not
+  covered.
+- Mid-word corrections, such as `r += q·new` at a later meeting of the new helper with a leaked role, are not
+  modelled. They are the open route, not an exclusion. A direct exact implementation of that relaxation was
+  written but not run to completion, and it is not part of this package.
+
+## Reproduce
+
+Python 3.12, standard library, from the repository root (about 5–30 s):
+
+```sh
+python3.12 -B research/p104-pr5718-shape-split-census/verify.py
+python3.12 -B scripts/research_package.py --package research/p104-pr5718-shape-split-census
+```
+
+Expected marker: `PASS_P104_PR5718_SHAPE_SPLIT_CENSUS`. The verifier authenticates both inputs: the PR5907 word
+`research/p104-helper468-rung-removal/WORD.json.gz` and the PR5713 word read from
+`research/p104-two-boundary-helper-split/inputs/pr5713-source.tar`. It also runs six synthetic controls of the pairing
+decision and compares `RESULT.json` byte for byte.
+
+## Open next questions
+
+- **Leak-1 classes on PR5907.** Can a mid-word correction remove the z-leak of one of the 425 classes that leak to
+  exactly one role outside `V`? Each one that closes adds one zero-paid split per LOCAL. First step: for one such
+  class, list the later meetings of the pivot's chart with the leaked role. Then test whether a correction vector
+  `S_τ e_r` reaches the leaked output coordinate, and check the non-z part of the correction. Blocked by a fast exact
+  span update for the meeting corrections.
+- **Chart 549, helper 173.** The four PR5907 classes without leak fail only the pairing. Does an input role outside
+  the empty-frame rule make `a_p = d_p c_p` solvable? First step: print `A` and `d_p` at cut 15974.
+
+## Credit
+
+PR5994 (Matarener) supplies the census criterion, the pure-subspace construction and the question. PR5718
+(flyingviper) supplies the split shape. PR5713 (Ali Romman) supplies the calibration word. PR5907 (DreamingOfClouds)
+supplies the target word. PR5599 (Ali Romman) supplies the split criterion. The P104 lineage is retained in those
+packages. Nothing of theirs is modified. This package was produced by Nick Petalas. Apache-2.0.

research/p104-pr5718-shape-split-census/SOURCES.json

@@ -0,0 +1,30 @@
+{
+  "schema_version": 1,
+  "base_commit": "19fdb086ea96af9a9f87936a2b888e10af4ed810",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "581f8d87008354eb5b869f7ed9de1317ad837ce8",
+      "sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec",
+      "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81"
+    },
+    {
+      "path": "research/p104-helper468-rung-removal/WORD.json.gz",
+      "usage": "input",
+      "git_blob": "7ffe7b500b02b9d0de49a85ec53e36004f1a411f",
+      "sha256": "b69a9cb3a26d4f40aa7ad14f814b188fe16a782999f6f56292538e447d67b284"
+    },
+    {
+      "path": "research/p104-two-boundary-helper-split/inputs/pr5713-source.tar",
+      "usage": "input",
+      "git_blob": "ec8f4bccaca147bc80cec078147fb95bc515036e",
+      "sha256": "c4d8d0bcd6231eb4539a76d66b0dbd465313cbc50d279ca974a55fecb935d544"
+    }
+  ]
+}

research/p104-pr5718-shape-split-census/TASK.json

@@ -0,0 +1,123 @@
+{
+  "schema_version": 1,
+  "task_id": "p104-side-correction",
+  "priority_revision": 8,
+  "base_commit": "19fdb086ea96af9a9f87936a2b888e10af4ed810",
+  "original_card": {
+    "id": "p104-side-correction",
+    "question": "Can joint helper bases and a legal causal split improve the complete P104 productive/paid invoice?",
+    "starting_points": [
+      "docs/research/current-priorities.md",
+      "docs/research/research-family-status.md",
+      "certificates/selected-result.json",
+      "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md",
+      "research/p104-helper-subspace-splits/README.md",
+      "research/dyadic-helper-channel-capacity/README.md"
+    ],
+    "methods": [
+      "Construct and independently check one source-bound instance of the stated first experiment.",
+      "Seek an exact counterexample or target-specific complete-budget obstruction to that same proposed change."
+    ],
+    "acceptance_gate": "An exact arbitrary-input identity, source/target frame availability and restoration at the chosen cut, plus the complete channel+correction+idle/hosting bill or an explicit favorable bound. The native channel alone is not a supplier. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_selected_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read revision 8, the selected review and live exact-source handoffs. Then follow this card's bounded first_experiment.",
+      "scope": "Source-bound orientation only, not a supplier replay or theorem proof."
+    },
+    "first_experiment": "Start with the selected #5599 emitted word and review pending #5718 distinct input/output bases plus #5717/#5719 coverage before claiming work. Pick one uncovered source word, helper group and cut region. Prove the arbitrary-input relation and legal entry/exit corrections, then compare full target and paid profiles. Reject if completion, owned lifetimes or consumer costs repay the gain. A static pairing rank alone is not a physical split.",
+    "bottleneck_link": "Judge the actual current supplier contract and complete signed target/paid bill; frozen-profile ceilings require an applicability proof.",
+    "allowed_variations": [
+      "One exact source head, helper/cut region or quantified proposition and changed hypothesis; check live handoffs first. Different seeds are not different scopes."
+    ],
+    "scope_change_triggers": [
+      "Changing source head, helper/cut domain, operation alphabet or caller boundary without recording the new scope.",
+      "Treating an archived proposal or local numerical pass as complete supplier admission."
+    ],
+    "overlap_terms": [
+      "P104",
+      "helper basis",
+      "helper split",
+      "5718",
+      "dyadic capacity"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #4133: literal-slot defect",
+        "evidence": "research/p104-literal-slot-defect/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "88666f1dee93fbd85b31fd5d6f91a219e111b5f4",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4136: uniform commutation gap",
+        "evidence": "research/p104-uniform-commutation-gap/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "281ce601a8be9db470de630759179c23e1dfaa88",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4140: uniform encoding gap",
+        "evidence": "research/p104-uniform-encoding-gap/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "de25c6525aa866962309df5d107b32d55e6e5628",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4153: source-chart shortcut exhausts its optimistic allowance",
+        "evidence": "research/p104-source-chart-shortcut/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "9123241fea53df77e51ffe30d9aca1625d4bf3a8",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4154: fiber-tag seam mismatch",
+        "evidence": "research/p104-fiber-tag-seam/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "4ffcdaee5d6255a9cea1fe53a5424435068089d0",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "Selected PR5599: complete helper-subspace construction and independent caller replay; five framework assumptions remain.",
+        "evidence": "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md",
+        "remaining": "The next experiment must identify uncovered source-specific work. Successor archive intake does not transfer this admission.",
+        "status": "reviewed",
+        "source_commit": "09dd0965711ca7eeb169057a420abab1c9052137",
+        "selected_record_sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5"
+      }
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Exact scalar census, on the PR5907 P104 word, of helper splits with the shape of PR5718: a helper retired at a strictly intermediate chart with a unit injection of a new independent helper, an input functional on group, U-initial or empty-frame-initial roles, and output normalisation only on roles whose final chart is V. Calibrated on the PR5713 source word, where it recovers PR5718's own split.",
+  "scope_change_reason": "The card asks for a complete legal split with its invoice. PR5994 excluded PR5599-type splits on PR5907 and named PR5718-type splits as the remaining route; this package tests that route's scalar necessary condition and locates where a mid-word correction would be needed, without building a supplier.",
+  "bottleneck_link": "Complex currently binds the selected assembly; a zero-paid helper split adds H_r+H_s-H_(r+s) per LOCAL to the productive side. This census says which split shapes remain possible on the latest conditional P104 word.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop at one exact census with calibration; do not build or price a split.",
+  "outcome": "completed",
+  "evidence": "verify.py: pinned inputs; calibration recovers PR5718's split (cut 14330, chart 602, helper 708) among 7 witnesses on PR5713, all at chart 602 and helper 708; PR5907 has 0 witnesses under both input rules (4,206 leak and 4 pairing classes under the empty-frame rule); 6 synthetic decision controls; RESULT.json compared byte-for-byte.",
+  "author": "Nick Petalas",
+  "ai_assistance": "Independent human and formal proof-kernel review are unclaimed.",
+  "open_questions": [
+    {
+      "question": "Can a mid-word correction remove the z-leak of one of the 425 PR5907 classes whose leak reaches exactly one role outside V?",
+      "why_it_matters": "These are the only PR5718-type candidates on PR5907; each one that closes adds one zero-paid split per LOCAL.",
+      "first_step": "For a leak-1 class, list the later meetings of the pivot's chart with the leaked role and test whether S_tau e_r reaches the leaked output coordinate; then check the non-z part of the correction.",
+      "blocked_by": "A fast exact span maintenance for the meeting corrections; a direct Fraction implementation took more than ten minutes per word."
+    },
+    {
+      "question": "Do the four PR5907 pairing failures at chart 549 (helper 173) survive a changed input functional outside the empty-frame rule?",
+      "why_it_matters": "They are the only PR5907 classes with no output leak; only the pairing a_p = d_p c_p fails.",
+      "first_step": "Print A and d_p for cut 15974 and test which extra input role would make a_p = d_p c_p solvable.",
+      "blocked_by": "None."
+    }
+  ]
+}

research/p104-pr5718-shape-split-census/VERIFY.json

@@ -0,0 +1,21 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/p104-helper468-rung-removal/WORD.json.gz",
+    "research/p104-two-boundary-helper-split/inputs/pr5713-source.tar"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 300,
+      "checks": "Authenticate the PR5907 word and the PR5713 source archive; exact census of PR5718-shape helper splits under group+U-initial and empty-frame input rules on both words; calibration recovers PR5718's split at cut 14330, chart 602, helper 708 on PR5713; zero witnesses on PR5907; six synthetic pairing-decision controls; RESULT.json compared byte-for-byte."
+    }
+  ]
+}