diff --git a/research/p104-boundary-reuse/README.md b/research/p104-boundary-reuse/README.md
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+# The tested P104 helper680 split needs more than these three meetings
+
+This combined contribution preserves a legal new contact on [PR5718](https://github.com/CrocSwap/integer-mult-bounds/pull/5718) and the exact obstruction that prevents three specified meetings from completing the proposed helper680 split. **No new κ or universal P104 obstruction is claimed.**
+
+## Main result
+
+For each of three fixed cut encodings (1196, 1199, 1200), on both the original and checked retimed schedules, no ADD/SCALE word at the three specified meetings can preserve the required output. The proof grants arbitrary rational invertible transforms on all 8 or 9 first-meeting fields, arbitrary linear later transforms, and rational terminal normalization. Exact causal propagation forces `X + (ell*w - 1)L = 0`, but the two first-meeting combinations X and L are independent. This removes the earlier coefficient-menu and program-length bounds **inside this specified interface**.
+
+Read the [complete scope and proof](../p104-three-meeting-controllability/README.md) first. Additional owned memory, different cut bases, extra meetings, changed native routes and other consumers remain outside the result. A tensor-span relaxation passes all six cases; the obstruction retains the temporal matrix coupling that this relaxation loses. A singular fake fixes one main output while destroying an independent helper target.
+
+## Constructive calibration and predecessor evidence
+
+The [contact/retiming package](../p104-joint-neutral-search/README.md) supplies two useful positive controls:
+
+- Its generator discovers the published predecessor helper708 cut after another role's MOVE, without being handed that cut, and emits a legal dyadic positive control on all 753 arbitrary columns.
+- Advancing source MOVE16655 of role153 to just after16649 creates a new legal contact at no extra paid or scalar charge. Exact endpoints, frames, lifetimes and inventory are preserved.
+
+The finite two-meeting searches are retained for provenance, with their complete domains and overlapping coverage explicitly recorded. Their millions of failed trials are supporting evidence, not the headline theorem. The registered publication replay regenerates the contact sets, positive controls, legal retiming and invoice, then checks the six exact three-meeting certificates. It authenticates but does not re-enumerate the historical exhaustive search receipts. The optional predecessor `verify.py --full` remains available for that separate task.
+
+## Reproduction
+
+Python 3.12, standard library, from the repository root:
+
+```sh
+python3.12 -B scripts/research_package.py --package research/p104-boundary-reuse
+```
+
+Both normal and optimized registered commands use temporary copies of the frozen packages, compare every original file after replay (ignoring only documented diagnostic timings and compressed-container metadata), and perform exact cross-package predecessor-byte joins. No separate local worktree or network service is needed for scientific replay. [Publication validation](VALIDATION.md) records the actual assembly checks. Original README and validation statements about local-only status remain historical provenance, not current submission status.
+
+The scientific word is pinned to PR5718 `a1534ac45401c9a9c80c07aa65c89e00e33594f8`. Its archive merge is not admission. At the submission base `de5ec2e7a6074068452f45b1a191b5c72832df4a`, selected conditional κ remains .00310045. Frozen sources, contact lists and results retain their exact bytes and attribution. Duplicate vendored predecessor files are intentional immutable copies, checked against the included full predecessor package.
+
+## Significance for researchers
+
+More contacts and favorable information spans do not necessarily compose into a legal temporal program. The contact generator and retiming are reusable construction tools; the exact proof explains why longer local scalar words at these same meetings cannot earn the proposed `18(H4+H5-H9)` target credit. The complete source bill stays 66,348 paid jobs and 12,976 productive fields.
+
+## Open next questions
+
+Reopen only with a named contact/delivery change that defeats the two-direction contradiction, a different cut basis, or an explicit owned-memory contract. Extract its causal transfer before starting a coefficient census and price its full acquisition, delivery, restoration and cleanup against the complete target allowance. No surviving construction or favorable complete bill for these changes is supplied.
+
+Credit [flyingviper](https://github.com/flyingviper)'s [PR5718](https://github.com/CrocSwap/integer-mult-bounds/pull/5718), [Ali Romman](https://github.com/aliromman)'s [PR5713](https://github.com/CrocSwap/integer-mult-bounds/pull/5713) and [PR5708](https://github.com/CrocSwap/integer-mult-bounds/pull/5708), and the full native, helper, controller, compiler and analytic lineage retained in the original notices. Prepared for [zxv](https://github.com/zxv) with substantial OpenAI Codex assistance. Apache-2.0. No full native/outer admission, formal proof-kernel check or independent human theorem acceptance is claimed.
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index 0000000000..f4221d34d1
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+++ b/research/p104-boundary-reuse/SOURCES.json
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+      "path": "research/p104-three-meeting-controllability/results/obstruction.json",
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+      "git_blob": "a2a52b70c14453b455d20fe6a568de4cb002dff5",
+      "sha256": "ecbbddbded939b4018fbc6cfdf99dbfe6693f4dd037c1fd0c4ed0882fd656da2"
+    },
+    {
+      "path": "research/p104-three-meeting-controllability/results/relaxation.json",
+      "usage": "input",
+      "git_blob": "a804909bd8982f544249c6c3c4713ed8160d982c",
+      "sha256": "08798aa22b0cb4ed632858a91cc130d56dd5e694b950e027967288dec662a2d1"
+    },
+    {
+      "path": "research/p104-three-meeting-controllability/vendor/NOTICE",
+      "usage": "input",
+      "git_blob": "f83cecccf587acfa313c8259c0bf6db05d60b52d",
+      "sha256": "c474479a870ae53ae0bcb84f656c2b222380395bbee767ee15e5f9c5b4ce7e79"
+    },
+    {
+      "path": "research/p104-three-meeting-controllability/vendor/README.md",
+      "usage": "input",
+      "git_blob": "a63e2437b0013301e23cc78d2d38c644e3aecde3",
+      "sha256": "8d069d3f2406f2cb0ff9d58f8144c6cf1e28da3ec03741d657c37a117f45d6eb"
+    },
+    {
+      "path": "research/p104-three-meeting-controllability/vendor/SOURCES.json",
+      "usage": "input",
+      "git_blob": "5437d22e1593ab20001a16e768843a29e6259a5d",
+      "sha256": "e6f72350b2d31e655f178a80d3dfb197b06ecf2d81b9e84172b7481c0846e2f1"
+    },
+    {
+      "path": "research/p104-three-meeting-controllability/vendor/emit.py",
+      "usage": "input",
+      "git_blob": "2be45cff8127c327d0771e02b55cdeafa342f727",
+      "sha256": "3cef5005f56f0f391d09175f75698cbdf835a61f0ca7f8439659189ff7bb8ca3"
+    },
+    {
+      "path": "research/p104-three-meeting-controllability/vendor/inputs/controller5718.json",
+      "usage": "input",
+      "git_blob": "cc539db709cf7a6c42872c4380902736ad453af3",
+      "sha256": "a84f6bbd547379597464e56c420cc665f96bc43a9a1351eed4b7cd0fce3cc4b9"
+    },
+    {
+      "path": "research/p104-three-meeting-controllability/vendor/inputs/word5713.json.gz",
+      "usage": "input",
+      "git_blob": "45f6c10bf8a0ad6eb5f6714377a464e274db7dbd",
+      "sha256": "9fd67dd89ed24a644257cd9aef06934ed4c6fbe0441804684a968868f2ef66a8"
+    },
+    {
+      "path": "research/p104-three-meeting-controllability/vendor/inputs/word5718.json.gz",
+      "usage": "input",
+      "git_blob": "4db015aca34ea957dd8b3b4d7ae4fa12b89934f8",
+      "sha256": "cff7196f8b168c4ebf8227185eed98387b66ec5db0179108adfea4045775cc31"
+    },
+    {
+      "path": "research/p104-three-meeting-controllability/vendor/invoice.py",
+      "usage": "input",
+      "git_blob": "d3ee7c701cc230273fa6b458fd080308346c2f1f",
+      "sha256": "d9171336935023fb94d310d782ea00cec1ac60963e137b8766e39d690cbbcca9"
+    },
+    {
+      "path": "research/p104-three-meeting-controllability/vendor/joint.py",
+      "usage": "input",
+      "git_blob": "67ac8368df7e424ef3a491582d2fa45d401fbf32",
+      "sha256": "dd9d055d78f27c1dc663c86efe2d41a8914636bdc47917ebff92882f738831fc"
+    },
+    {
+      "path": "research/p104-three-meeting-controllability/vendor/preflight.py",
+      "usage": "input",
+      "git_blob": "28341deed5b9ded395774316336e4b2a474fca9e",
+      "sha256": "e19cce00813896373826a6ee8ccb3e16f86c95d47bcba5f3b06c90cc2729a8ca"
+    },
+    {
+      "path": "research/p104-three-meeting-controllability/vendor/results/contacts5713.json",
+      "usage": "input",
+      "git_blob": "8c031317e774de596216430dfe66d9df63c191cb",
+      "sha256": "3347f3e4f372189f9a06cb754afdaa6bb812b3a5dc7f1d9d0c16cc00485a73f1"
+    },
+    {
+      "path": "research/p104-three-meeting-controllability/vendor/results/contacts5718.json",
+      "usage": "input",
+      "git_blob": "ee80a3a3b7828e11fcce12b49c5766623d55e564",
+      "sha256": "b799253336add810d04d39512a0641dc4416145de0b121040c8defe6d517cf19"
+    },
+    {
+      "path": "research/p104-three-meeting-controllability/vendor/search.py",
+      "usage": "input",
+      "git_blob": "5d38c521324dbfa761e1e21ae04e1db8cb232458",
+      "sha256": "b94cf3464e67e20ed3b57b28fe355f5a9d35c01c6abb84dabf5ad0c5180face8"
+    },
+    {
+      "path": "research/p104-three-meeting-controllability/verify.py",
+      "usage": "input",
+      "git_blob": "83ea157b24abd26d9b7fe1b178e566962d5064eb",
+      "sha256": "7e6f019f659fc3ed1365fe565e5fc8594429dcbab6ffda95c653be9603a7ecb6"
+    }
+  ]
+}
diff --git a/research/p104-boundary-reuse/TASK.json b/research/p104-boundary-reuse/TASK.json
new file mode 100644
index 0000000000..e66405c4bf
--- /dev/null
+++ b/research/p104-boundary-reuse/TASK.json
@@ -0,0 +1,117 @@
+{
+  "schema_version": 1,
+  "task_id": "p104-side-correction",
+  "priority_revision": 8,
+  "base_commit": "df58e5c53aa4d6e9d581f97e9f81d317cae7f36f",
+  "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": "refined",
+  "actual_scope": "PR5718 helper680 encodings1196/1199/1200, three fixed meetings, original and legally retimed schedules; rational GL first meeting and favorable later transforms.",
+  "scope_change_reason": "Combine the completed source-bound contact construction and stronger three-meeting obstruction; no new search or source retargeting.",
+  "bottleneck_link": "The proposed independent H4+H5 replacement for H9 earns no credit unless the complete scalar endpoints and targets survive.",
+  "budget_minutes": 60,
+  "stop_rule": "Publish the exact scoped obstruction and constructive calibration; do not extend the closed coefficient census.",
+  "outcome": "negative-result",
+  "evidence": "../p104-three-meeting-controllability/results/obstruction.json and the included predecessor controls and invoice.",
+  "author": "zxv",
+  "ai_assistance": "Substantial OpenAI Codex assistance; source work and publication replay, not independent human or formal verification.",
+  "open_questions": [
+    {
+      "question": "Can a changed contact, cut basis or owned-memory boundary defeat the two-direction contradiction within a favorable full bill?",
+      "why_it_matters": "Arbitrary rational ADD/SCALE words at the three specified meetings cannot complete the split.",
+      "first_step": "Extract a concrete changed causal transfer and its complete paid/target invoice before construction.",
+      "blocked_by": "No such changed contract or favorable complete realization is supplied."
+    }
+  ]
+}
diff --git a/research/p104-boundary-reuse/VALIDATION.md b/research/p104-boundary-reuse/VALIDATION.md
new file mode 100644
index 0000000000..3aa4a1a5cb
--- /dev/null
+++ b/research/p104-boundary-reuse/VALIDATION.md
@@ -0,0 +1,19 @@
+# Combined publication validation
+
+2026-10-26; CPython 3.12.8, macOS arm64, standard library. Scientific assembly commit `5da9738d67542585920a6e7677ecc4d55f6d2744`; the later publication commit adds this record only. Canonical main was fetched immediately before submission and remains `de5ec2e7a6074068452f45b1a191b5c72832df4a`.
+
+Passed:
+
+- Registered metadata and exact source pins for `research/p104-boundary-reuse`.
+- Registered normal and optimized replays: source-byte joins; both candidate-generator runs; constructive helper708 control; legal retiming and rejection controls; all six exact causal obstructions and favorable tensor relaxations; unchanged source invoice. The exact final obstruction receipt retains semantic SHA256 `50db363dbaca657f2e43f4f00edd6ef10d667769da9b92bbad30d24d414a955c`.
+- Original file payloads remain semantically identical in temporary replay copies. Only documented diagnostic seconds and compressed-container metadata are excluded from the comparison.
+- `scripts/check_research_commit.py --package research/p104-boundary-reuse`: exact 70-file committed-byte check.
+- Official export and `export_research_package.py check --check-inputs`: all 70 payload files and 65 declared inputs verified.
+- Optimized direct publication replay from that extracted Git-free export with empty PATH; all 71 files including its export manifest stayed byte-identical. The wrapper uses temporary copies, and needs no predecessor checkout or network.
+- `git diff --check` on the contribution.
+
+The optional `--check-source-history` preflight reports that full Git history is required; this checkout is shallow. It is not reported as passed. Every wrapper runtime dependency is nevertheless retained in the committed export and authenticated by its source hashes. Historical source pins and original notices are preserved. The final committed-byte preflight is repeated after adding this record.
+
+The historical exhaustive three-/four-ADD searches were not rerun during assembly. Their frozen receipts are authenticated and their original full replay remains available; the main theorem is instead checked directly by the stronger exact three-meeting proof. No new native, caller, compiler, precision/tape, BIT, outer, Lean, Docker or selected-frontier replay was run. Hosted CI, independent human review and formal-kernel acceptance remain separate.
+
+The original local-only session records are immutable historical evidence; this document and the publication overview describe their combined submission. No new κ or productive credit is claimed.
diff --git a/research/p104-boundary-reuse/VERIFY.json b/research/p104-boundary-reuse/VERIFY.json
new file mode 100644
index 0000000000..7f994eb4f3
--- /dev/null
+++ b/research/p104-boundary-reuse/VERIFY.json
@@ -0,0 +1,96 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/p104-joint-neutral-search/MANIFEST.json",
+    "research/p104-joint-neutral-search/NOTICE",
+    "research/p104-joint-neutral-search/README.md",
+    "research/p104-joint-neutral-search/SOURCES.json",
+    "research/p104-joint-neutral-search/VALIDATION.json",
+    "research/p104-joint-neutral-search/controls.py",
+    "research/p104-joint-neutral-search/emit.py",
+    "research/p104-joint-neutral-search/inputs/controller5718.json",
+    "research/p104-joint-neutral-search/inputs/word5713.json.gz",
+    "research/p104-joint-neutral-search/inputs/word5718.json.gz",
+    "research/p104-joint-neutral-search/invoice.py",
+    "research/p104-joint-neutral-search/joint.py",
+    "research/p104-joint-neutral-search/preflight.py",
+    "research/p104-joint-neutral-search/reachability.py",
+    "research/p104-joint-neutral-search/results/contacts5713.json",
+    "research/p104-joint-neutral-search/results/contacts5718.json",
+    "research/p104-joint-neutral-search/results/controls.json",
+    "research/p104-joint-neutral-search/results/invoice.json",
+    "research/p104-joint-neutral-search/results/joint680-a-fixed.json",
+    "research/p104-joint-neutral-search/results/joint680-b-fixed.json",
+    "research/p104-joint-neutral-search/results/joint680-b-retimed.json",
+    "research/p104-joint-neutral-search/results/joint680-c-fixed.json",
+    "research/p104-joint-neutral-search/results/joint680-c-retimed.json",
+    "research/p104-joint-neutral-search/results/joint680-cut-retimed.json",
+    "research/p104-joint-neutral-search/results/joint680-fixed.json",
+    "research/p104-joint-neutral-search/results/joint680-retimed.json",
+    "research/p104-joint-neutral-search/results/joint695.json",
+    "research/p104-joint-neutral-search/results/positive-word.json.gz",
+    "research/p104-joint-neutral-search/results/positive.json",
+    "research/p104-joint-neutral-search/results/preflight5718.json",
+    "research/p104-joint-neutral-search/results/reach5718.json",
+    "research/p104-joint-neutral-search/results/retimed-word.json.gz",
+    "research/p104-joint-neutral-search/results/two-two680-optimized.json",
+    "research/p104-joint-neutral-search/results/two-two680.json",
+    "research/p104-joint-neutral-search/search.py",
+    "research/p104-joint-neutral-search/two_two.py",
+    "research/p104-joint-neutral-search/verify.py",
+    "research/p104-three-meeting-controllability/MANIFEST.json",
+    "research/p104-three-meeting-controllability/NOTICE",
+    "research/p104-three-meeting-controllability/README.md",
+    "research/p104-three-meeting-controllability/REFRESH.json",
+    "research/p104-three-meeting-controllability/SOURCES.json",
+    "research/p104-three-meeting-controllability/VALIDATION.json",
+    "research/p104-three-meeting-controllability/controls.py",
+    "research/p104-three-meeting-controllability/invoice.py",
+    "research/p104-three-meeting-controllability/obstruction.py",
+    "research/p104-three-meeting-controllability/relax.py",
+    "research/p104-three-meeting-controllability/results/controls.json",
+    "research/p104-three-meeting-controllability/results/invoice.json",
+    "research/p104-three-meeting-controllability/results/obstruction.json",
+    "research/p104-three-meeting-controllability/results/relaxation.json",
+    "research/p104-three-meeting-controllability/vendor/NOTICE",
+    "research/p104-three-meeting-controllability/vendor/README.md",
+    "research/p104-three-meeting-controllability/vendor/SOURCES.json",
+    "research/p104-three-meeting-controllability/vendor/emit.py",
+    "research/p104-three-meeting-controllability/vendor/inputs/controller5718.json",
+    "research/p104-three-meeting-controllability/vendor/inputs/word5713.json.gz",
+    "research/p104-three-meeting-controllability/vendor/inputs/word5718.json.gz",
+    "research/p104-three-meeting-controllability/vendor/invoice.py",
+    "research/p104-three-meeting-controllability/vendor/joint.py",
+    "research/p104-three-meeting-controllability/vendor/preflight.py",
+    "research/p104-three-meeting-controllability/vendor/results/contacts5713.json",
+    "research/p104-three-meeting-controllability/vendor/results/contacts5718.json",
+    "research/p104-three-meeting-controllability/vendor/search.py",
+    "research/p104-three-meeting-controllability/verify.py"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 180,
+      "checks": "Frozen byte joins, regenerated candidate discovery and legal retiming controls, all six rational temporal obstructions, source invoice and negative controls. Historical exhaustive searches are not repeated."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 180,
+      "checks": "Frozen byte joins, regenerated candidate discovery and legal retiming controls, all six rational temporal obstructions, source invoice and negative controls. Historical exhaustive searches are not repeated."
+    }
+  ]
+}
diff --git a/research/p104-boundary-reuse/verify.py b/research/p104-boundary-reuse/verify.py
new file mode 100644
index 0000000000..30c393a2a4
--- /dev/null
+++ b/research/p104-boundary-reuse/verify.py
@@ -0,0 +1,37 @@
+"""Replay combined evidence in temporary copies; retain immutable published bytes."""
+from pathlib import Path
+import gzip, hashlib, json, shutil, subprocess, sys, tempfile
+ROOT=Path(__file__).resolve().parent
+REPO=ROOT.parents[1]
+NAMES=("p104-joint-neutral-search", "p104-three-meeting-controllability")
+def semantic(value):
+    if isinstance(value,dict):return {k:semantic(v) for k,v in value.items() if k!="seconds"}
+    if isinstance(value,list):return [semantic(v) for v in value]
+    return value
+def payload(path):
+    raw=path.read_bytes()
+    if path.name.endswith(".json.gz"):return semantic(json.loads(gzip.decompress(raw)))
+    if path.suffix==".json":return semantic(json.loads(raw))
+    return raw
+source=REPO/"research"/NAMES[0]
+final=REPO/"research"/NAMES[1]
+manifest=json.loads((final/"SOURCES.json").read_text())
+for item in manifest["vendored_predecessor_files"]:
+    left=final/item["path"]
+    right=source/item["path"].removeprefix("vendor/")
+    if left.read_bytes()!=right.read_bytes():raise ValueError("Predecessor byte join: "+str(right))
+# Authenticate every declared input, including wrappers and frozen records.
+for item in json.loads((ROOT/"SOURCES.json").read_text())["files"]:
+    if item["usage"]=="input":
+        if hashlib.sha256((REPO/item["path"]).read_bytes()).hexdigest()!=item["sha256"]:
+            raise ValueError("Pinned input mismatch: "+item["path"])
+with tempfile.TemporaryDirectory(prefix="p104-publication-") as folder:
+    for name in NAMES:
+        src=REPO/"research"/name;dst=Path(folder)/name
+        shutil.copytree(src,dst,ignore=shutil.ignore_patterns("__pycache__","*.pyc"))
+        before={str(p.relative_to(dst)):payload(p) for p in dst.rglob("*") if p.is_file()}
+        flags=["-O"] if sys.flags.optimize else []
+        subprocess.run([sys.executable,*flags,"-B",str(dst/"verify.py")],check=True)
+        after={str(p.relative_to(dst)):payload(p) for p in dst.rglob("*") if p.is_file() and "__pycache__" not in p.parts}
+        if before!=after:raise ValueError("Replay changed proof-relevant contents: "+name)
+print("PASS_P104_BOUNDARY_PUBLICATION: exact obstruction, constructive controls, source joins; no new kappa")
diff --git a/research/p104-joint-neutral-search/MANIFEST.json b/research/p104-joint-neutral-search/MANIFEST.json
new file mode 100644
index 0000000000..64f9ff2090
--- /dev/null
+++ b/research/p104-joint-neutral-search/MANIFEST.json
@@ -0,0 +1,185 @@
+{
+  "schema": "p104-joint-neutral-local-evidence/v1",
+  "files": [
+    {
+      "path": "NOTICE",
+      "hash_type": "raw",
+      "sha256": "c474479a870ae53ae0bcb84f656c2b222380395bbee767ee15e5f9c5b4ce7e79"
+    },
+    {
+      "path": "README.md",
+      "hash_type": "raw",
+      "sha256": "8d069d3f2406f2cb0ff9d58f8144c6cf1e28da3ec03741d657c37a117f45d6eb"
+    },
+    {
+      "path": "SOURCES.json",
+      "hash_type": "raw",
+      "sha256": "e6f72350b2d31e655f178a80d3dfb197b06ecf2d81b9e84172b7481c0846e2f1"
+    },
+    {
+      "path": "VALIDATION.json",
+      "hash_type": "raw",
+      "sha256": "fb62c328470b4a8cb1b520d88030558ffd0e7b0559eb3af853f6067dbb6222d9"
+    },
+    {
+      "path": "controls.py",
+      "hash_type": "raw",
+      "sha256": "2ad7d192bc44fa9543a489fc2d0fc9df9f141a49cdbbb2bb17966fe1fc6dbf8f"
+    },
+    {
+      "path": "emit.py",
+      "hash_type": "raw",
+      "sha256": "3cef5005f56f0f391d09175f75698cbdf835a61f0ca7f8439659189ff7bb8ca3"
+    },
+    {
+      "path": "inputs/controller5718.json",
+      "hash_type": "raw",
+      "sha256": "a84f6bbd547379597464e56c420cc665f96bc43a9a1351eed4b7cd0fce3cc4b9"
+    },
+    {
+      "path": "inputs/word5713.json.gz",
+      "hash_type": "raw",
+      "sha256": "9fd67dd89ed24a644257cd9aef06934ed4c6fbe0441804684a968868f2ef66a8"
+    },
+    {
+      "path": "inputs/word5718.json.gz",
+      "hash_type": "raw",
+      "sha256": "cff7196f8b168c4ebf8227185eed98387b66ec5db0179108adfea4045775cc31"
+    },
+    {
+      "path": "invoice.py",
+      "hash_type": "raw",
+      "sha256": "d9171336935023fb94d310d782ea00cec1ac60963e137b8766e39d690cbbcca9"
+    },
+    {
+      "path": "joint.py",
+      "hash_type": "raw",
+      "sha256": "dd9d055d78f27c1dc663c86efe2d41a8914636bdc47917ebff92882f738831fc"
+    },
+    {
+      "path": "preflight.py",
+      "hash_type": "raw",
+      "sha256": "e19cce00813896373826a6ee8ccb3e16f86c95d47bcba5f3b06c90cc2729a8ca"
+    },
+    {
+      "path": "reachability.py",
+      "hash_type": "raw",
+      "sha256": "006ad9f8b5a0375c9e9480dc12e026a1c0adb480d556f67871c3b0977337cb15"
+    },
+    {
+      "path": "results/contacts5713.json",
+      "hash_type": "json_semantic",
+      "sha256": "bedecd8fc4d67657e04bcae8a9335100aba404924c1bc640d7f486e8769fe0c2"
+    },
+    {
+      "path": "results/contacts5718.json",
+      "hash_type": "json_semantic",
+      "sha256": "e4cb9b7efd885188faefd81f02fd65484404af0aae23d700955ebb2cdc8a693e"
+    },
+    {
+      "path": "results/controls.json",
+      "hash_type": "json_semantic",
+      "sha256": "aa2bd49fdddd3e3ad654fe38c8ce07f57dba18d9cce81ddb7dca805e072ede68"
+    },
+    {
+      "path": "results/invoice.json",
+      "hash_type": "json_semantic",
+      "sha256": "74b358dee3bffcdea1667fcd92eda34daaef17bfb843d5de42ec51c0a5070696"
+    },
+    {
+      "path": "results/joint680-a-fixed.json",
+      "hash_type": "json_semantic",
+      "sha256": "84926fa649d503179d4e72f91f64ffef63e854a19c1799a234d75c8feb30cf05"
+    },
+    {
+      "path": "results/joint680-b-fixed.json",
+      "hash_type": "json_semantic",
+      "sha256": "438b07d27e5eef808aa038fcfc35a2b112cd910081bfa71a7f23878d208085bf"
+    },
+    {
+      "path": "results/joint680-b-retimed.json",
+      "hash_type": "json_semantic",
+      "sha256": "c28f9a243cdae72846280edb57eeb068ca5f494d77c637331d6bd80d0fbb9c6c"
+    },
+    {
+      "path": "results/joint680-c-fixed.json",
+      "hash_type": "json_semantic",
+      "sha256": "c569f4bad2bdfa2a3ef95562aef4a806d43b2b7af14a207eade37e123fe1abf5"
+    },
+    {
+      "path": "results/joint680-c-retimed.json",
+      "hash_type": "json_semantic",
+      "sha256": "4edfbbe30222d88b139a217b7bfda93ad1781861122a5a10d7d4e27cbfa17da3"
+    },
+    {
+      "path": "results/joint680-cut-retimed.json",
+      "hash_type": "json_semantic",
+      "sha256": "eb701f33e3775a2bc8943892230c934ca527102df22904339366a2e7a64b9e22"
+    },
+    {
+      "path": "results/joint680-fixed.json",
+      "hash_type": "json_semantic",
+      "sha256": "b8206f5eab6680c5d0caa367b407b8ffbb0c5e9f799365ade35e225bebaf2b53"
+    },
+    {
+      "path": "results/joint680-retimed.json",
+      "hash_type": "json_semantic",
+      "sha256": "e08b2523aae062a1162178c5d35aba03bedc421f7f0981f8fa51943a2efe5a86"
+    },
+    {
+      "path": "results/joint695.json",
+      "hash_type": "json_semantic",
+      "sha256": "cdf01b7b2acf87de7ea2376d4e9c3b3418c88b83951ea442a4a4bfb01946be8a"
+    },
+    {
+      "path": "results/positive-word.json.gz",
+      "hash_type": "json_gzip_semantic",
+      "sha256": "fa4ea51c2594b2337111fd84b35a13a79ffab6ffbb151362bc16c337701bf563"
+    },
+    {
+      "path": "results/positive.json",
+      "hash_type": "json_semantic",
+      "sha256": "0ecf22bb4c24019bd6885094144b879677030624a178b15d11967c52f6983bcb"
+    },
+    {
+      "path": "results/preflight5718.json",
+      "hash_type": "json_semantic",
+      "sha256": "323fe5b3a77954fc247c00335f73fd8565fbc4325c7dccf2dae617540284ef2d"
+    },
+    {
+      "path": "results/reach5718.json",
+      "hash_type": "json_semantic",
+      "sha256": "a5842aa0ce38d17e4fabfd6a765ed7ac0b5563acd277f344c09553498a5caff9"
+    },
+    {
+      "path": "results/retimed-word.json.gz",
+      "hash_type": "json_gzip_semantic",
+      "sha256": "822955d9a143920af1cf19827bebe4a0b4337edf70267927428151e378f5e1cf"
+    },
+    {
+      "path": "results/two-two680-optimized.json",
+      "hash_type": "json_semantic",
+      "sha256": "02581f82037a0366dd7d317e00b15bed59cbb9e60e7f355e80f427ad87f4d494"
+    },
+    {
+      "path": "results/two-two680.json",
+      "hash_type": "json_semantic",
+      "sha256": "02581f82037a0366dd7d317e00b15bed59cbb9e60e7f355e80f427ad87f4d494"
+    },
+    {
+      "path": "search.py",
+      "hash_type": "raw",
+      "sha256": "b94cf3464e67e20ed3b57b28fe355f5a9d35c01c6abb84dabf5ad0c5180face8"
+    },
+    {
+      "path": "two_two.py",
+      "hash_type": "raw",
+      "sha256": "2c471c996a7b1c5939e47af4654e7af02a083c47e0aac9e7cc67b980fce5c83c"
+    },
+    {
+      "path": "verify.py",
+      "hash_type": "raw",
+      "sha256": "2c273701dc027ade956a2c377ac8ceba2036b6e1a6675e4897f20fbd6572fc0a"
+    }
+  ]
+}
diff --git a/research/p104-joint-neutral-search/NOTICE b/research/p104-joint-neutral-search/NOTICE
new file mode 100644
index 0000000000..f83cecccf5
--- /dev/null
+++ b/research/p104-joint-neutral-search/NOTICE
@@ -0,0 +1,47 @@
+Four paid interior public-basis changes.
+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.
+No subagents.
+
+The following exact notice is retained from PR5660.
+
+New helper-subspace construction, proof and replay:
+Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+The same assistant performed the construction and author-side checks.
+
+Retained contributions:
+flyingviper: PR5605 shared relay, PR5612 delayed relay, and the PR5608/PR5613
+relay/split compositions.
+Scratch-net: PR5606 prepared-helper identities and target debit.
+Pierre-Loic Doulcet (hexapode): PR5565 commuting-contact construction, used as the exact source.
+Ali Romman: PR5602 fixed boundary relations, PR5601 three-contact frame
+change, PR5580 contact step,
+and PR5544/5545 complete P104 caller.
+Joel Pulikkan (GamingPuzzled): PR5569 priced helper handoff.
+DreamingOfClouds: PR5561 free helper endpoints and PR5568 search tools.
+thu-nmrc: PR5551 contact improvements.
+Gareth Davidson (bitplane): PR2305 source composition.
+David Arias: PR2152 coalesced P104 word.
+Cinna Davis: PR2219 private reuse and the controller lineage.
+Jacob Alan Sussman: productive mixed-target recursion.
+zxv and Cao Yifan: exact intervals, compiler and native/pricing lineage.
+GamingPuzzled: PR5472 successor handoff, a predecessor to the split concept.
+The retained source notices preserve earlier geometry, BIT and analytic credit.
+
+The elementary rank-one basis identity is not claimed as a new general
+linear-algebra theorem. The contribution is its explicit independent-target
+use on this P104 word and the complete conditional kappa improvement.
+
+New contribution: Ali Romman, with substantial OpenAI Codex assistance.
+The four-gate source-version rewrite composes zxv PR5643 and Ali Romman PR5644.
+The A2 method retains Chris R/Clear1nsight PR3998 and ToikY PR4019 credit.
+The compensated triangle method retains Cinna Davis PR4692 credit.
+No subagents were used for this contribution. Apache-2.0.
+
+Concurrent PR5650 by zxv publishes the PR5643/PR5644 composition. PR5651 by
+Ali Romman corroborates it. This package credits that released composition
+and contributes the further four-gate placement.
+
+New work: distributed scalar updates on an unobserved public field interval, the exact witness and complete conditional price. Prepared for Ali Romman with substantial OpenAI Codex assistance. No subagents. Apache-2.0. The source archive retains all predecessor notices.
+
+Two-boundary main-assisted helper split and early cleanup: flyingviper with substantial
+OpenAI Codex assistance, including independent AI review agents. Apache-2.0.
diff --git a/research/p104-joint-neutral-search/README.md b/research/p104-joint-neutral-search/README.md
new file mode 100644
index 0000000000..a63e2437b0
--- /dev/null
+++ b/research/p104-joint-neutral-search/README.md
@@ -0,0 +1,200 @@
+# A legal new P104 contact does not finish the bounded helper680 split
+
+**Local-only checked experiment; no new κ and no universal obstruction.**
+Canonical main was freshly fetched as `df0137efd35e11b4445734bf612bdd4c7ebc330c`,
+with priority revision7 and selected conditional κ `.00310045` unchanged.
+The source is pending [PR5718](https://github.com/CrocSwap/integer-mult-bounds/pull/5718)
+at `a1534ac45401c9a9c80c07aa65c89e00e33594f8`, claiming `.00311024570`.
+Its inherited native, ownership, compiler, precision/tape and analytic assumptions
+remain. This package does not independently admit that claim.
+
+The experiment changes an actual route schedule: source event16655,
+`MOVE 153,659,164`, is advanced to just after event16649. No intervening
+instruction touches153. This creates a contact between153,685 and the fresh
+continuation of680 before680 leaves frame164. Exact replay on every one of753
+arbitrary source input columns verifies the retimed word, all frames, owned
+lifetimes, target inventory and unchanged complete local paid/scalar bill.
+This is a source-preserving change in transport timing, not a new frame itinerary.
+
+## Checked result
+
+1. **The candidate generator discovers the known positive.** It examines both
+   departure and arrival groups after every role's MOVE. On PR5713 it finds
+   the PR5718 cut at14330, pivot708, `708 +=154/2`, without being given that cut.
+   There are1,880 compatible cut encodings on PR5713 and1,871 on PR5718;
+   1,554 and1,546, respectively, are triggered by another role's MOVE.
+   Counts include distinct encodings and repeated equivalent cut states.
+2. **An exact emitted positive control passes.** The generic constructor
+   implements the discovered708 split using literal dyadic ADD/SCALE operations,
+   every arbitrary input, legal frames and owned INIT/COPY/CLEAR rules. It has
+   the published paid/target profile. Its deliberately unsimplified terminal
+   normalizer costs225,210 local scalar units, versus221,474 in the published
+   PR5718 word. This is a recovered predecessor construction, not a new gain.
+3. **Endpoint tests precede expansion.** All1,867 tested successor encodings
+   fail cleanup using terminal frame groups alone; four440 encodings were
+   excluded rather than revisited. A favorable temporal-span relaxation on
+   all123 non-440 cuts with at most three endpoint-response fields rejects
+   one:695 at13644. It grants unlimited frame-local memory and allows every
+   MOVE to carry the entire available source-frame span. The required output159
+   remains outside the span, with exact remainder `2 e700 + 2 e701` in the
+   receipt's elimination basis. This is a scoped rational span failure, not a
+   claimed universal separating functional. The other122 survive this relaxation.
+4. **The three-ADD domain has no survivor.** Three concrete680 cut encodings,
+   at13920 and13922, were tested on the original and retimed schedules. Each
+   permits zero, one or two ADDs at the cut and zero or one at the later meeting.
+   All4,887,150 literal program pairs fail. Two cuts at13922 are triggered by
+   another helper's MOVE. The first steps are unrestricted: temporary errors,
+   reads from the retired field and movement of corrections between roles are
+   allowed. There is no greedy requirement to remove an error immediately.
+5. **The four-ADD extension also fails.** For the13920 cut on the retimed word,
+   zero, one or two ADDs at each of the two meetings give43,430,473 literal
+   program pairs. All fail an exact necessary condition on main output153.
+   The second meeting has949 distinct full three-field response matrices and276
+   distinct effects on153; these are exact deduplications of all1,333 second
+   sequences. The driver evaluates30,919,369 distinct-matrix pairs. Six exact
+   rational input-coordinate probes already reject every pair, so no modular
+   discovery or unpriced rational inverse is counted as an implementation.
+
+An initial unsorted larger temporal-span run was interrupted without a result.
+Only the completed123-cut run is evidence. Three exploratory shorter runs
+(4,477,17,329 and49,321 cases) are retained separately; they are not added to
+an allegedly disjoint coverage total. The four-ADD domain overlaps the
+three-ADD cases. A failed candidate does not receive target credit.
+
+## Exact bounded model
+
+The prefix/suffix generator uses exact `Fraction` arithmetic, all public and
+arbitrary dirty-owned entry columns, source frame containment and the actual
+scalar word. It tests cuts `a=e_p+q e_s`. If purity determines q, that exact
+value must be dyadic; when both rows are pure, the finite menu is
+`q in {-2,-1,-1/2,1/2,1,2}`, together with the unmodified pivot.
+It requires `c_p=beta_p=c beta=1`, with every nonzero coordinate of c and beta
+at the pivot's initial frame. `beta=E^-1 S e_p` includes the actual main shear.
+These sufficient conditions do not exhaust all helper boundary bases.
+
+The three selected cut encodings are:
+
+| Index | Source cut | Trigger | Cut operation | Input functional c |
+| --- | ---: | ---: | --- | --- |
+|1196|13920|680|identity|`e680`|
+|1199|13922|681|`680 -=679`|`e680-e679`|
+|1200|13922|681|`680 +=682`|`e680`|
+
+Each has suffix response `e126+e153+e680` and split ranks5+4.
+The first meeting uses exactly roles`[680,753,679,682,685,686]` at frame1049.
+Roles outside that list retain their literal original operations. Here753
+is the exploration label for the new independent input; emitted words shift
+owned labels and use public index744 instead. On the original schedule the
+second meeting is after16651 at frame164, with roles`[685,753]`.
+On the retimed schedule it is after16652, with roles`[153,685,753]`.
+Every ADD has distinct source/destination and coefficient from the six-value
+menu above. Zero-length sequences and cancelling/inverse sequences are included.
+The four-ADD domain uses the1196 cut and the retimed second meeting.
+
+The suffix response to a first ADD is propagated through the literal word.
+Every second source uses the state changed by all first ADDs. An exact
+low-rank endpoint update is checked against a separate literal suffix walk
+on every coefficient. Terminal normalization is granted favorably whenever
+rational row spaces match. A proposed survivor would still require an emitted
+dyadic-unit factorization, full endpoint and ownership replay, ordinary cost,
+native/caller compatibility and complete pricing. No new candidate reaches
+that stage here.
+
+Resource bounds are explicit: at most six first-meeting roles, three second-
+meeting roles, two ADDs per meeting and six possible coefficients. The three-
+ADD driver caps each run at1,250,000 program pairs; all six completed. The
+four-ADD driver caps at50,000,000 matrix pairs and completes below that cap.
+It is a finite alphabet result. Longer programs, a third meeting, SCALEs in
+intermediate programs, multi-source cut bases and genuinely different native
+routes remain outside it.
+
+## Complete signed invoice and ordinary work
+
+`results/invoice.json` reconstructs the whole18-call source invoice from the
+checked local bill and pinned literal controller. It has66,348 paid jobs,
+12,976 productive fields and rank surplus760. The source local paid bill is
+
+```
+2184 H1 + 459 H2 + 495 H3 + 92 H4 + 159 H5 + 22 H6 + 15 H7.
+```
+
+The source local helper target bill is
+
+```
+2 H1 + 5 H2 + 91 H4 + 6 H5 + 6 H7 + 15 H8 + 411 H9.
+```
+
+The unrealized680 proposal has `Delta paid=0`,
+`Delta targets=18(H4+H5-H9)` and therefore
+`Delta(paid-targets)=18(H9-H4-H5)<0` for every`0<t<1`, `Hr=r^t`.
+Both the retired old input and the new arbitrary input are credited only
+if their complete targets are preserved. The route retiming adds zero paid
+jobs and zero scalar operations; source scalar work remains221,474.
+Input basis plus retirement costs16,32 and24 scalar units for the three cuts;
+four menu ADDs cost at most40 additional units. Terminal normalization,
+new-helper allocation/routes/cleanup and compiler/outer obligations are
+**unknown and unrun**, because every candidate fails before those modules exist.
+They are not priced at zero. The favorable signed invoice is an allowance,
+not an emitted construction or a κ claim.
+
+## Reproduction and evidence
+
+Python3.14.5 standard library on macOS; source bytes and Git blobs are in
+`SOURCES.json`. No Lean, Docker, full native, compiler, outer or selected cold
+replay was run. The source and retimed scalar/frame checks cover all753
+arbitrary input columns, owned peak2 and11 owned lifetimes. The emitted known
+positive covers753 columns after adding one fresh public input to PR5713.
+The complete serial `--full` replay passed. Normal and optimized controls and
+the complete four-ADD receipts agree. Controls reject an illegal retiming across a write, a wrong source frame,
+a non-dyadic ADD, unearned old H9 credit, a missing retirement and wrong-order
+multi-meeting operations. A separate two-meeting fixture and real-P104
+changed-state formula check pass.
+
+From the repository root:
+
+```sh
+python3 -B research/p104-joint-neutral-search/verify.py
+python3 -O -B research/p104-joint-neutral-search/controls.py
+python3 -B research/p104-joint-neutral-search/verify.py --full
+```
+
+The quick verifier checks frozen receipt integrity, regenerates both contact
+sets, and runs the constructive/negative controls and complete invoice.
+`--full` additionally reruns the1867-cut terminal screen,123-cut temporal
+relaxation, six declared three-ADD searches and the four-ADD search, serially.
+Expect roughly8 minutes for full replay on the recorded host. Search timings
+are diagnostic and excluded from semantic receipt comparisons.
+
+## Open next questions
+
+- A different transport contact is still needed for695 before more scalar
+  search: the favorable fixed-itinerary span already fails. This package does
+  not revisit helper440 or the known PR5440 native-letter mismatch.
+- For680, first test a favorable controllability model with a **third** actual
+  meeting, after15468 at frame1075 with479/527/continuation680. That introduces
+  source rows absent from the two tested meetings. Preserve the same complete
+  invoice and reject by exact availability before enumerating longer words.
+  This is a distinct finite question; no success is forecast.
+- The optional cross-call paid-answer span discriminator was not run. It still
+  needs versioned physical query maps at caller events0 and3, actual stage
+  routes and native operators, and retention/read/transport/cleanup charges.
+  Input-row continuity and distinct query identities do not answer it. A new
+  session should bind one such output rather than enlarge a duplicate census.
+
+## Significance for researchers
+
+The predecessor generator really did omit useful contact classes: the new
+one discovers the published positive at another role's MOVE. A legal retiming
+also creates a new contact at no recursive charge. Neither fact implies a
+new independent split. This experiment explicitly explores temporary correction
+redistribution and still fails in its two-meeting domain, while preserving
+longer and physically different routes as open questions.
+
+Credit [flyingviper](https://github.com/flyingviper)'s PR5718,
+[Ali Romman](https://github.com/aliromman)'s PR5713/5708 and the complete
+predecessor P104/native/controller/compiler lineage retained in`NOTICE`.
+The frozen earlier information-reuse and multi-meeting investigations are
+listed in`SOURCES.json` and remain unchanged. Prepared for
+[zxv](https://github.com/zxv) with substantial OpenAI Codex assistance; no
+subagents. The linear algebra and temporal identities are standard.
+Apache-2.0. No public post, PR, merge or selected-frontier change was made.
diff --git a/research/p104-joint-neutral-search/SOURCES.json b/research/p104-joint-neutral-search/SOURCES.json
new file mode 100644
index 0000000000..5437d22e15
--- /dev/null
+++ b/research/p104-joint-neutral-search/SOURCES.json
@@ -0,0 +1,41 @@
+{
+  "repository": "https://github.com/CrocSwap/integer-mult-bounds",
+  "canonical_main": "df0137efd35e11b4445734bf612bdd4c7ebc330c",
+  "priority_revision": 7,
+  "selected_kappa": ".00310045",
+  "pending_source_kappa": ".00311024570",
+  "source_status": "pending author claim; no selected frontier update",
+  "sources": [
+    {
+      "path": "inputs/word5713.json.gz",
+      "sha256": "9fd67dd89ed24a644257cd9aef06934ed4c6fbe0441804684a968868f2ef66a8",
+      "commit": "a5348f7143f95fe0046b92b96172e30763c7d731",
+      "repository_path": "research/p104-temporal-updates/WORD.json.gz",
+      "git_blob": "45f6c10bf8a0ad6eb5f6714377a464e274db7dbd"
+    },
+    {
+      "path": "inputs/word5718.json.gz",
+      "sha256": "cff7196f8b168c4ebf8227185eed98387b66ec5db0179108adfea4045775cc31",
+      "commit": "a1534ac45401c9a9c80c07aa65c89e00e33594f8",
+      "repository_path": "research/p104-two-boundary-helper-split/WORD.json.gz",
+      "git_blob": "4db015aca34ea957dd8b3b4d7ae4fa12b89934f8"
+    },
+    {
+      "path": "inputs/controller5718.json",
+      "sha256": "a84f6bbd547379597464e56c420cc665f96bc43a9a1351eed4b7cd0fce3cc4b9",
+      "commit": "a1534ac45401c9a9c80c07aa65c89e00e33594f8",
+      "repository_path": "research/p104-productive-controller/CONTROLLER.json",
+      "git_blob": "cc539db709cf7a6c42872c4380902736ad453af3"
+    }
+  ],
+  "environment": {
+    "python": "3.14.5 (main, May 10 2026, 10:21:34) [Clang 21.0.0 (clang-2100.0.123.102)]",
+    "platform": "macOS-26.5.1-arm64-arm-64bit-Mach-O"
+  },
+  "predecessor_local_reports": [
+    "/private/tmp/integer-mult-information-reuse/research/information-reuse-screen/README.md",
+    "/private/tmp/integer-mult-information-reuse/research/p104-multimeeting-repair/README.md",
+    "/tmp/luna-inforeuse-controller/cross_local_input_ledger.md",
+    "/tmp/luna-inforeuse-bit/FINDING.md"
+  ]
+}
diff --git a/research/p104-joint-neutral-search/VALIDATION.json b/research/p104-joint-neutral-search/VALIDATION.json
new file mode 100644
index 0000000000..ce03eabca6
--- /dev/null
+++ b/research/p104-joint-neutral-search/VALIDATION.json
@@ -0,0 +1,23 @@
+{
+  "status": "PASS_LOCAL_FINITE_REPLAY",
+  "checked_at_utc": "2026-10-26T15:21:16Z",
+  "canonical_main": "df0137efd35e11b4445734bf612bdd4c7ebc330c",
+  "selected_kappa": ".00310045",
+  "source_head": "a1534ac45401c9a9c80c07aa65c89e00e33594f8",
+  "source_pending_kappa": ".00311024570",
+  "full_replay": "python3 -B research/p104-joint-neutral-search/verify.py --full",
+  "full_replay_passed": true,
+  "normal_optimized_controls_passed": true,
+  "normal_optimized_four_ADD_receipts_equal": true,
+  "pinned_git_blob_comparison": "all three input files match exact pinned blobs",
+  "three_ADD_program_pairs": 4887150,
+  "four_ADD_program_pairs": 43430473,
+  "new_survivors": 0,
+  "new_kappa": false,
+  "unrun": [
+    "new native/caller/compiler/outer admission: no surviving construction",
+    "cross-call paid-answer span discriminator",
+    "Lean/Docker/selected cold replay"
+  ],
+  "scope": "finite rational scalar/route timing domain under retained native/frame interpretation; no universal obstruction or whole multiplication theorem"
+}
diff --git a/research/p104-joint-neutral-search/controls.py b/research/p104-joint-neutral-search/controls.py
new file mode 100644
index 0000000000..8b5cb2032b
--- /dev/null
+++ b/research/p104-joint-neutral-search/controls.py
@@ -0,0 +1,72 @@
+"""Exact discovery, emitted-word, changed-state and custody controls."""
+from emit import *
+from reachability import reach_test
+import tempfile
+
+def rejected(fn,label):
+ try:fn()
+ except ValueError:return label
+ raise ValueError('accepted mutation: '+label)
+
+def main():
+ w=load('word5718.json.gz');base=audit(w)
+ # A legal existing MOVE is advanced across events that do not touch role153.
+ route=retime(w,16655,16649);shift=audit(route);need(base==shift,'retimed exact endpoint/invoice/ordinary match')
+ (HERE/'results/retimed-word.json.gz').write_bytes(gzip.compress(json.dumps(route,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+ tests=[rejected(lambda:retime(w,16655,15829),'retiming across a source write')]
+ bad=deepcopy(route);bad['program'][16650][2]=3;tests.append(rejected(lambda:audit(bad),'wrong retimed source frame'))
+ bad=deepcopy(w);bad['program'][0][-2]='1/3';tests.append(rejected(lambda:audit(bad),'non-dyadic ADD'))
+ # Reconstruct the published positive from a cut the generator actually found.
+ old=load('word5713.json.gz');cuts=json.loads((HERE/'results/contacts5713.json').read_text())['cuts'];c=next(c for c in cuts if c['cut']==14330 and c['pivot']==708 and c['a']=={'708':'1','154':'1/2'})
+ for k in ('a','c','h0','d','beta'):c[k]=unrow(c[k])
+ positive=construct(old,c);pos=audit(positive)
+ wrong=deepcopy(positive);wrong['final'][708]=127;tests.append(rejected(lambda:audit(wrong),'unearned retired H9 target'))
+ wrong=deepcopy(positive);wrong['program'].remove(['ADD',708,154,'1/2',602]);tests.append(rejected(lambda:audit(wrong),'missing retirement ADD'))
+ # Two same-frame meetings. The second read must see the changed first state.
+ toy=dict(public=3,owned_fields=0,live=[],ports=[],frames=[[],[1],[1,2]],initial=[1,1,1],final=[2,2,2],program=[['ADD',1,0,'1',1],['ADD',2,1,'1',1],['MOVE',0,1,2,False],['MOVE',1,1,2,False],['MOVE',2,1,2,False],['ADD',2,1,'-1',2],['ADD',1,0,'-1',2]])
+ need(audit(toy)['columns']==3,'two-meeting fixture')
+ wrong=deepcopy(toy);wrong['program'][-2],wrong['program'][-1]=wrong['program'][-1],wrong['program'][-2]
+ tests.append(rejected(lambda:audit(wrong),'wrong-order changed-state fixture'))
+ # Response formula for two inserted ADDs agrees on every coefficient with literal execution.
+ # Base toy contains only the legal movements; extras are at the two actual frames.
+ bare=deepcopy(toy);bare['program']=[e for e in bare['program'] if e[0]=='MOVE']
+ R=[{r:Q(1)} for r in range(3)];R[1]={1:Q(1)};first_src=dict(R[0]);add(R[1],first_src,Q(1));later_src=dict(R[1]);add(R[2],later_src,Q(2))
+ expected=[{0:Q(1)},{1:Q(1),0:Q(1)},{2:Q(1),1:Q(2),0:Q(2)}];need(R==expected,'changed-state two ADD formula')
+ stale=[{0:Q(1)},{1:Q(1),0:Q(1)},{2:Q(1),1:Q(2)}];need(stale!=R,'stale source must differ')
+ # On an actual retimed P104 word, compare the low-rank update formula against a literal suffix.
+ cc=json.loads((HERE/'results/contacts5718.json').read_text())['cuts'][1196]
+ for key in ('a','c','h0','d','beta'):cc[key]=unrow(cc[key])
+ first,second=13920,16652;pivot=680;fresh=753
+ snap=raw(route,cc,{first,second});one=snap[first][0];two=snap[second][0]
+ s1=dict(one[pivot]);D1=responses(route,pivot,first,[685])[685];D2=responses(route,pivot,second,[153])[153];mid=responses(route,pivot,first,[685],second)[685]
+ s2=dict(two[685]);add(s2,s1,mid.get(685,0));need(s2!=two[685],'actual second source must change')
+ predicted,_,*_=endpoints(route,cc)
+ for r,a in D1.items():add(predicted[r],s1,a)
+ for r,a in D2.items():add(predicted[r],s2,a)
+ literal=[dict(z) for z in one];add(literal[685],literal[pivot],Q(1))
+ for i in range(first+1,len(route['program'])):
+  apply(literal,renamed(route['program'][i],pivot,fresh))
+  if i==second:add(literal[153],literal[685],Q(1))
+ need(literal==predicted,'actual P104 response formula all coefficients')
+ # Four ADDs include a second source changed earlier in the same meeting.
+ local1=[dict(z) for z in one];local2=[dict(z) for z in two];predicted,_,*_=endpoints(route,cc)
+ seq1=[(685,680,Q(1)),(685,753,Q(-1,2))];seq2=[(153,685,Q(-2)),(685,753,Q(1,2))]
+ for r,s,a in seq1:
+  src=dict(local1[s]);add(local1[r],src,a);endresponse=responses(route,pivot,first,[r])[r];mresponse=responses(route,pivot,first,[r],second)[r]
+  for t,b in endresponse.items():add(predicted[t],src,a*b)
+  for t,b in mresponse.items():add(local2[t],src,a*b)
+ for r,s,a in seq2:
+  src=dict(local2[s]);add(local2[r],src,a);endresponse=responses(route,pivot,second,[r])[r]
+  for t,b in endresponse.items():add(predicted[t],src,a*b)
+ literal=[dict(z) for z in one]
+ for r,s,a in seq1:add(literal[r],literal[s],a)
+ for i in range(first+1,len(route['program'])):
+  apply(literal,renamed(route['program'][i],pivot,fresh))
+  if i==second:
+   for r,s,a in seq2:add(literal[r],literal[s],a)
+ need(literal==predicted,'actual P104 four-step response formula all coefficients')
+ payload=(HERE/'inputs/word5718.json.gz').read_bytes();corrupt=bytearray(payload);corrupt[-1]^=1
+ need(hashlib.sha256(corrupt).hexdigest()!=PINS['word5718.json.gz'],'source corruption must reject')
+ out=dict(status='PASS',source=base,retimed=shift,known_positive=pos,negative_controls=tests,two_meeting_fixture=True,changed_source_formula=True,actual_P104_two_step_formula_all_columns=True,source_corruption_rejected=True,actual_P104_four_step_formula_all_columns=True)
+ (HERE/'results/controls.json').write_text(json.dumps(fmt(out),indent=2)+'\n');print(json.dumps(fmt(out)))
+if __name__=='__main__':main()
diff --git a/research/p104-joint-neutral-search/emit.py b/research/p104-joint-neutral-search/emit.py
new file mode 100644
index 0000000000..2be45cff81
--- /dev/null
+++ b/research/p104-joint-neutral-search/emit.py
@@ -0,0 +1,114 @@
+"""Emit and independently replay dyadic words; no modular implementation claims."""
+from joint import *
+
+def scalar_cost(e):
+ if e[0]=='MOVE':return 0
+ if e[0] in ('INIT','CLEAR'):return 2
+ q=Q(e[-2]);a,b=abs(q.numerator),q.denominator
+ return 2*(abs(a.bit_length()-b.bit_length())+(q<0)) if e[0]=='SCALE' else 2*(2+a.bit_length()+a.bit_count()+b.bit_length()-1)
+
+def audit(w):
+ n=w['public'];N=n+w['owned_fields'];rows=[{r:Q(1)} for r in range(N)];ch=w['initial']+[None]*w['owned_fields'];fs=[span(x) for x in w['frames']];active=set();unwritten=set();paid=Counter();peak=life=0
+ for i,e in enumerate(w['program']):
+  op,r=e[:2];need(0<=r<N,'role index')
+  if op=='INIT':
+   need(r>=n and ch[r] is None,'owned INIT');ch[r]=e[2];active.add(r);unwritten.add(r);peak=max(peak,len(active));life+=1
+  elif op=='CLEAR':need(r in active and ch[r]==e[2],'owned CLEAR');ch[r]=None;active.remove(r);unwritten.discard(r)
+  elif op=='MOVE':
+   need(ch[r]==e[2] and e[4]==(r in active),'MOVE source/ownership')
+   need(fs[e[3]]<fs[e[2]] if e[4] else fs[e[2]]<fs[e[3]],'MOVE containment')
+   ch[r]=e[3];paid[abs(len(w['frames'][e[2]])-len(w['frames'][e[3]]))]+=1
+  else:
+   need(ch[r]==e[-1],'scalar destination frame');q=Q(e[-2]);a,b=abs(q.numerator),q.denominator
+   need(q and b&(b-1)==0 and abs(q)+1<2**16,'dyadic scalar coefficient')
+   if op=='SCALE':need(a&(a-1)==0,'SCALE dyadic unit')
+   else:
+    need(e[2]!=r and 0<=e[2]<N and ch[e[2]]==e[-1],'scalar source frame')
+    if op=='COPY':need(r in unwritten,'owned first COPY')
+   unwritten.discard(r)
+  apply(rows,e)
+ need(not active and ch[:n]==w['final'],'final frame/ownership')
+ for r,row in enumerate(rows):
+  target={r:Q(1)} if r<n else {}
+  if r-112 in w['live']:target[r-112]=Q(1)
+  need(row==target,'endpoint '+str(r))
+ main=set(w['live'])|{r+112 for r in w['live']}
+ targets=Counter(len(w['frames'][w['final'][r]])-len(w['frames'][w['initial'][r]]) for r in range(n) if r not in main)
+ return dict(columns=N,paid=dict(paid),targets=dict(targets),scalar=sum(map(scalar_cost,w['program'])),owned_peak=peak,owned_lifetimes=life)
+
+def normalize_group(rows,desired,roles,frame):
+ # Reduce actual and desired matrices by identical canonical row elimination.
+ # If inversions are not dyadic units the emitter stops, even if Q rowspaces agree.
+ def reduce(vals):
+  vals={r:dict(vals[r]) for r in roles};ops=[];used=[]
+  for col in sorted(set().union(*(set(v) for v in vals.values()))):
+   possible=[r for r in roles if r not in used and vals[r].get(col)]
+   if not possible:continue
+   r=possible[0];q=vals[r][col]
+   if q!=1:
+    inv=1/q;need(abs(inv.numerator)&(abs(inv.numerator)-1)==0 and inv.denominator&(inv.denominator-1)==0,'non-unit pivot')
+    vals[r]=scale(vals[r],inv);ops.append(['SCALE',r,str(inv),frame])
+   for s in roles:
+    if s!=r and vals[s].get(col):
+     q=-vals[s][col];need(q.denominator&(q.denominator-1)==0,'non-dyadic elimination')
+     add(vals[s],vals[r],q);ops.append(['ADD',s,r,str(q),frame])
+   used.append(r)
+  return vals,used,ops
+ va,ua,oa=reduce(rows);vd,ud,od=reduce(desired)
+ # Matching pivot rows may require permutation. Emit swaps as three ADDs and a sign.
+ need(len(ua)==len(roles)==len(ud),'full group rank')
+ for src,dst in zip(ua,ud):
+  if src==dst:continue
+  # In current normalized va, move row with same canonical functional to target slot.
+  holder=next(r for r in roles if va[r]==vd[dst])
+  if holder==dst:continue
+  oa.extend([['ADD',dst,holder,'1',frame],['ADD',holder,dst,'-1',frame],['ADD',dst,holder,'1',frame],['SCALE',holder,'-1',frame]])
+  va[dst],va[holder]=va[holder],va[dst]
+ need(va==vd,'canonical same-rowspace')
+ inv=[]
+ for e in reversed(od):
+  x=list(e);x[-2]=str(1/Q(e[-2]) if e[0]=='SCALE' else -Q(e[-2]));inv.append(x)
+ return oa+inv
+
+def construct(w,c,extra=()):
+ n=w['public'];N=n+w['owned_fields'];p=c['pivot'];out=deepcopy(w);out['public']=n+1;out['initial']=w['initial']+[c['frame']];out['final']=w['final']+[w['final'][p]];out['final'][p]=c['frame']
+ k0=dict(c['c']);add(k0,{p:Q(1)},-1);program=[];u=w['initial'][p]
+ for r,q in sorted(k0.items()):program.append(['ADD',p,r,str(-q),u])
+ for r,q in sorted(c['beta'].items()):
+  if r!=p:program.append(['ADD',r,p,str(q),u])
+ def ren(r,i):
+  if r>=n:return r+1
+  if i>c['cut'] and r==p:return n
+  return r
+ extras=defaultdict(list)
+ for i,e in extra:extras[i].append(e)
+ for i,orig in enumerate(w['program']):
+  e=list(orig);e[1]=ren(e[1],i)
+  if e[0] in ('ADD','COPY'):e[2]=ren(e[2],i)
+  program.append(e)
+  if i==c['cut']:
+   for r,q in c['a'].items():
+    if r!=p:program.append(['ADD',p,r,str(q),c['frame']])
+  for e0 in extras[i]:
+   e=list(e0);e[1]=n if e[1]==N else e[1]+(e[1]>=n)
+   if e[0] in ('ADD','COPY'):e[2]=n if e[2]==N else e[2]+(e[2]>=n)
+   program.append(e)
+ out['program']=program
+ rows=[{r:Q(1)} for r in range(N+1)]
+ for e in program:apply(rows,e)
+ desired=[{r:Q(1)} if r<n+1 else {} for r in range(N+1)]
+ for r in w['live']:desired[r+112][r]=Q(1)
+ groups=defaultdict(list)
+ for r,f in enumerate(out['final']):groups[f].append(r)
+ for f,roles in groups.items():
+  if any(rows[r]!=desired[r] for r in roles):
+   ops=normalize_group(rows,desired,roles,f);program.extend(ops)
+   for e in ops:apply(rows,e)
+ out['schema']='p104-joint-neutral-search/1';return out
+
+def main():
+ w=load('word5713.json.gz');cuts=json.loads((HERE/'results/contacts5713.json').read_text())['cuts'];c=next(c for c in cuts if c['cut']==14330 and c['pivot']==708 and c['a']=={'708':'1','154':'1/2'})
+ for k in ('a','c','h0','d','beta'):c[k]=unrow(c[k])
+ out=construct(w,c);receipt=audit(out);receipt.update(source_sha256=PINS['word5713.json.gz'],cut=c['cut'],pivot=c['pivot'],status='positive_control_emitted_exact_dyadic_word')
+ (HERE/'results/positive-word.json.gz').write_bytes(gzip.compress(json.dumps(out,sort_keys=True,separators=(',',':')).encode(),mtime=0));(HERE/'results/positive.json').write_text(json.dumps(fmt(receipt),indent=2)+'\n');print(receipt)
+if __name__=='__main__':main()
diff --git a/research/p104-joint-neutral-search/inputs/controller5718.json b/research/p104-joint-neutral-search/inputs/controller5718.json
new file mode 100644
index 0000000000..cc539db709
--- /dev/null
+++ b/research/p104-joint-neutral-search/inputs/controller5718.json
@@ -0,0 +1,5480 @@
+{
+  "ambient_rank": 145,
+  "boundaries": {
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+    13,
+    15,
+    17,
+    19,
+    21,
+    23,
+    25,
+    27,
+    29,
+    31
+  ]
+}
diff --git a/research/p104-joint-neutral-search/inputs/word5713.json.gz b/research/p104-joint-neutral-search/inputs/word5713.json.gz
new file mode 100644
index 0000000000..45f6c10bf8
Binary files /dev/null and b/research/p104-joint-neutral-search/inputs/word5713.json.gz differ
diff --git a/research/p104-joint-neutral-search/inputs/word5718.json.gz b/research/p104-joint-neutral-search/inputs/word5718.json.gz
new file mode 100644
index 0000000000..4db015aca3
Binary files /dev/null and b/research/p104-joint-neutral-search/inputs/word5718.json.gz differ
diff --git a/research/p104-joint-neutral-search/invoice.py b/research/p104-joint-neutral-search/invoice.py
new file mode 100644
index 0000000000..d3ee7c701c
--- /dev/null
+++ b/research/p104-joint-neutral-search/invoice.py
@@ -0,0 +1,21 @@
+"""Complete signed paid/target invoices and declared ordinary obligations."""
+from emit import *
+
+def whole(local,controller):
+ paid=Counter();targets=Counter()
+ for e in controller['physical_events']:
+  if e[0]=='LOCAL':paid.update(local['paid']);targets.update(local['targets'])
+  elif e[0]=='QUERY_SHEAR':paid[1]+=104
+  elif e[0]=='IDLE':paid[8*len(e[2])]+=208
+ for term in controller['diagonal']:targets[1+8*sum(term[1:])]+=104
+ return dict(paid=dict(sorted(paid.items())),targets=dict(sorted(targets.items())))
+
+def main():
+ controls=json.loads((HERE/'results/controls.json').read_text());local={k:{int(r):v for r,v in controls['source'][k].items()} for k in ('paid','targets')}
+ controller=json.loads((HERE/'inputs/controller5718.json').read_text());need(hashlib.sha256((HERE/'inputs/controller5718.json').read_bytes()).hexdigest()=='a84f6bbd547379597464e56c420cc665f96bc43a9a1351eed4b7cd0fce3cc4b9','controller source hash')
+ base=whole(local,controller);need(sum(base['paid'].values())==66348 and sum(base['targets'].values())==12976,'complete baseline counts')
+ proposed=deepcopy(base);proposed['targets'][9]-=18;proposed['targets'][4]+=18;proposed['targets'][5]+=18
+ need(sum(r*n for r,n in base['targets'].items())-sum(r*n for r,n in base['paid'].items())==760,'complete rank surplus')
+ out=dict(source_sha256=PINS['word5718.json.gz'],base=base,unrealized_680_split=proposed,delta_paid={},delta_targets={4:18,5:18,9:-18},signed_delta_paid_minus_targets={4:-18,5:-18,9:18},proof='18*(9^t-4^t-5^t)<0 for 0<t<1 by strict subadditivity; no surviving endpoint implements this proposed invoice',ordinary=dict(source_local_scalar=controls['source']['scalar'],retiming_added_scalar=0,retiming_added_paid_moves=0,input_and_retirement_scalar_by_cut={1196:16,1199:32,1200:24},four_ADD_upper=40,terminal_normalization='unknown: no candidate passes even the favorable rational endpoint test',new_helper_routes_allocation_cleanup='unknown: no candidate emitted',compiler_and_outer='unrun: no survivor'),kappa_status='NO_NEW_KAPPA; selected .00310045; source pending PR5718 claims .00311024570')
+ (HERE/'results/invoice.json').write_text(json.dumps(fmt(out),indent=2)+'\n');print(dict(paid=sum(base['paid'].values()),targets=sum(base['targets'].values()),rank_surplus=760,source_scalar=controls['source']['scalar'],delta_targets=out['delta_targets']))
+if __name__=='__main__':main()
diff --git a/research/p104-joint-neutral-search/joint.py b/research/p104-joint-neutral-search/joint.py
new file mode 100644
index 0000000000..67ac8368df
--- /dev/null
+++ b/research/p104-joint-neutral-search/joint.py
@@ -0,0 +1,113 @@
+"""Finite exact neutral ADD search with one existing MOVE retimed inside a touch gap.
+
+State keeps every input coefficient. Up to two ADDs at first meeting, one at
+second, and a favorable terminal normalization test. No monotone repair filter.
+"""
+from preflight import *
+from copy import deepcopy
+
+def renamed(e,p,fresh):
+ e=list(e)
+ if e[1]==p:e[1]=fresh
+ if e[0] in ('ADD','COPY') and e[2]==p:e[2]=fresh
+ return e
+
+def raw(w,c,sites):
+ n=w['public'];N=n+w['owned_fields'];p=c['pivot'];fresh=N
+ _,_,k,_,_=endpoints(w,c)
+ rows=[{r:Q(1)} for r in range(N)]+[{}];ch=w['initial']+[None]*w['owned_fields']+[c['frame']]
+ for r in range(N):
+  add(rows[r],k,c['beta'].get(r,0))
+  if r==p:add(rows[r],{p:Q(1)},-1)
+ saved={}
+ for i,orig in enumerate(w['program']):
+  e=renamed(orig,p,fresh) if i>c['cut'] else orig
+  apply(rows,e);charts_step(ch,e)
+  if i==c['cut']:rows[p]={p:Q(1)};rows[fresh]={fresh:Q(1)};ch[p]=ch[fresh]=c['frame']
+  if i in sites:saved[i]=([dict(z) for z in rows],list(ch))
+ return saved
+
+def responses(w,p,site,roles,stop=None):
+ N=w['public']+w['owned_fields'];fresh=N;cols=[{r:Q(1)} for r in range(N+1)]
+ end=len(w['program']) if stop is None else stop+1
+ for orig in reversed(w['program'][site+1:end]):
+  e=renamed(orig,p,fresh);op,r=e[:2]
+  if op in ('INIT','CLEAR'):cols[r]={}
+  elif op=='SCALE':cols[r]=scale(cols[r],Q(e[-2]))
+  elif op!='MOVE':
+   add(cols[e[2]],cols[r],Q(e[-2]))
+   if op=='COPY':cols[r]={}
+ return {r:cols[r] for r in roles}
+
+def terminal_groups(w,c):
+ N=w['public']+w['owned_fields'];p=c['pivot'];ch=w['final']+[None]*w['owned_fields']+[w['final'][p]];ch[p]=c['frame'];groups=defaultdict(list)
+ for r,f in enumerate(ch):
+  if f is not None:groups[f].append(r)
+ return groups
+
+def groups_check(base,desired,groups,updates,fast=None):
+ for f,roles in groups.items():
+  if fast is not None and f not in fast:continue
+  changed={}
+  for d,s,a in updates:
+   for r,v in d.items():
+    if r in roles:
+     if r not in changed:changed[r]=dict(base[r])
+     add(changed[r],s,a*v)
+  if not changed:actual=lambda r:base[r]
+  else:actual=lambda r:changed.get(r,base[r])
+  if all(actual(r)==desired[r] for r in roles):continue
+  b=basis(actual(r) for r in roles)
+  if any(rem(desired[r],b) for r in roles):return False
+ return True
+
+def actions(roles):
+ return [(r,s,a) for r in roles for s in roles if r!=s for a in (Q(-2),Q(-1),Q(-1,2),Q(1,2),Q(1),Q(2))]
+
+def run(w,c,first,second,first_frame,second_frame,depth=1,cap=30000,first_roles=None,second_roles=None):
+ saved=raw(w,c,{first,second});R1,C1=saved[first];R2,C2=saved[second]
+ g1=[r for r,f in enumerate(C1) if f==first_frame];g2=[r for r,f in enumerate(C2) if f==second_frame]
+ if first_roles is not None:need(set(first_roles)<=set(g1),'first role frame');g1=first_roles
+ if second_roles is not None:need(set(second_roles)<=set(g2),'second role frame');g2=second_roles
+ need(len(g1)<=6 and len(g2)<=6,'bounded meeting size')
+ groups=terminal_groups(w,c);base,desired,*_=endpoints(w,c)
+ bad=[f for f,roles in groups.items() if not groups_check(base,desired,{f:roles},[])]
+ D1=responses(w,c['pivot'],first,g1);D2=responses(w,c['pivot'],second,g2);mid=responses(w,c['pivot'],first,g1,second)
+ a1=actions(g1);a2=[None]+actions(g2);tested=0;passfast=0;survivors=[];neutral=0
+ # a fixed input list is the complete stated domain at each meeting.
+ seqs=[()] + [(a,) for a in a1]
+ if depth==2:seqs +=[(a,b) for a in a1 for b in a1]
+ for seq in seqs:
+  local={r:dict(R1[r]) for r in g1};up=[];midrows={r:dict(R2[r]) for r in g2}
+  for r,s,a in seq:
+   src=dict(local[s]);add(local[r],src,a);up.append((D1[r],src,a))
+   for v,b in mid[r].items():
+    if v in midrows:add(midrows[v],src,a*b)
+  if seq and not groups_check(base,desired,groups,up,fast=bad):neutral+=1
+  for action in a2:
+   if tested>=cap:return dict(tested=tested,cap=cap,truncated=True,groups=[g1,g2],first_sequences=len(seqs),neutral_first_sequences=neutral,fast_survivors=passfast,survivors=survivors)
+   updates=list(up)
+   if action:
+    r,s,a=action;updates.append((D2[r],midrows[s],a))
+   tested+=1
+   if not groups_check(base,desired,groups,updates,fast=bad):continue
+   passfast+=1
+   if groups_check(base,desired,groups,updates):
+    survivors.append(dict(first=seq,second=action));print('SURVIVOR',fmt(survivors[-1]),flush=True)
+ return dict(tested=tested,cap=cap,truncated=False,groups=[g1,g2],first_sequences=len(seqs),neutral_first_sequences=neutral,fast_survivors=passfast,survivors=survivors)
+
+def retime(w,index,after):
+ e=w['program'][index];need(e[0]=='MOVE' and not e[4],'public MOVE only');r=e[1]
+ lo,hi=sorted((index,after));between=w['program'][lo+1:hi+1] if after>index else w['program'][lo+1:hi]
+ need(all(x[1]!=r and not(x[0] in ('ADD','COPY') and x[2]==r) for x in between),'retiming crosses a role touch')
+ out=deepcopy(w);p=out['program'];move=p.pop(index);at=after if after>index else after+1;p.insert(at,move)
+ return out
+
+def main():
+ ap=argparse.ArgumentParser();ap.add_argument('--index',type=int,default=350);ap.add_argument('--first',type=int,default=13644);ap.add_argument('--second',type=int,default=16800);ap.add_argument('--first-frame',type=int,default=597);ap.add_argument('--second-frame',type=int,default=170);ap.add_argument('--depth',type=int,default=1);ap.add_argument('--cap',type=int,default=30000);ap.add_argument('--first-roles');ap.add_argument('--second-roles');ap.add_argument('--move',type=int);ap.add_argument('--after',type=int);ap.add_argument('--out',default='joint695.json');a=ap.parse_args()
+ w=load('word5718.json.gz');c=json.loads((HERE/'results/contacts5718.json').read_text())['cuts'][a.index]
+ for k in ('a','c','h0','d','beta'):c[k]=unrow(c[k])
+ if a.move is not None:w=retime(w,a.move,a.after)
+ t=time.monotonic();result=run(w,c,a.first,a.second,a.first_frame,a.second_frame,a.depth,a.cap,[int(v) for v in a.first_roles.split(',')] if a.first_roles else None,[int(v) for v in a.second_roles.split(',')] if a.second_roles else None);result.update(source_sha256=PINS['word5718.json.gz'],index=a.index,cut=c['cut'],pivot=c['pivot'],meetings=[a.first,a.second],frames=[a.first_frame,a.second_frame],depth=a.depth,route=dict(move=a.move,after=a.after),seconds=time.monotonic()-t)
+ (HERE/'results'/a.out).write_text(json.dumps(fmt(result),indent=2)+'\n');print(json.dumps(fmt(result)),flush=True)
+if __name__=='__main__':main()
diff --git a/research/p104-joint-neutral-search/preflight.py b/research/p104-joint-neutral-search/preflight.py
new file mode 100644
index 0000000000..28341deed5
--- /dev/null
+++ b/research/p104-joint-neutral-search/preflight.py
@@ -0,0 +1,91 @@
+"""Exact favorable endpoint availability, before scalar program search."""
+from search import *
+
+def basis(rows):
+ out={}
+ for row in rows:
+  z=dict(row)
+  while z:
+   j=min(z)
+   if j not in out:
+    out[j]=scale(z,1/z[j]);break
+   add(z,out[j],-z[j])
+ return out
+
+def rem(row,b):
+ z=dict(row)
+ while z and min(z) in b:add(z,b[min(z)],-z[min(z)])
+ return z
+
+def endpoints(w,c):
+ n=w['public'];N=n+w['owned_fields'];p=c['pivot'];fresh=N
+ k={p:Q(2)};add(k,c['c'],-1)
+ q=dict(c['h0']);add(q,k,sum(v*c['beta'].get(j,0) for j,v in q.items()));add(q,{p:Q(1)},-c['h0'].get(p,0))
+ eta=dict(k);add(eta,q,-1);eta[fresh]=Q(1)
+ rows=[{r:Q(1)} if r<n else {} for r in range(N)]+[{fresh:Q(1)}]
+ for r in w['live']:rows[r+112][r]=Q(1)
+ desired=[dict(z) for z in rows]
+ for r,v in c['d'].items():
+  if r!=p:add(rows[r],eta,v)
+ rows[p]={p:Q(1)};rows[fresh]=dict(eta)
+ return rows,desired,k,q,eta
+
+def terminal_test(w,c):
+ rows,desired,*_=endpoints(w,c);n=w['public'];N=n+w['owned_fields'];p=c['pivot']
+ ch=w['final']+[None]*w['owned_fields']+[w['final'][p]];ch[p]=c['frame']
+ groups=defaultdict(list)
+ for r,f in enumerate(ch):
+  if f is not None:groups[f].append(r)
+ failed=[]
+ for f,roles in groups.items():
+  if all(rows[r]==desired[r] for r in roles):continue
+  b=basis(rows[r] for r in roles)
+  for r in roles:
+   z=rem(desired[r],b)
+   if z:failed.append(dict(role=r,frame=f,remainder=z))
+ return failed
+
+def closed_tests(w,c,prefix,ch,last_inbound):
+ n=w['public'];N=n+w['owned_fields'];p=c['pivot'];fresh=N
+ _,desired,k,q,eta=endpoints(w,c)
+ def rightB(row):
+  out=dict(row);add(out,k,sum(v*c['beta'].get(j,0) for j,v in row.items()));add(out,{p:Q(1)},-row.get(p,0));return out
+ defects=set(c['d'])-{p};defects.add(fresh)
+ groups=defaultdict(list)
+ for r in defects:
+  f=w['final'][p if r==fresh else r]
+  if last_inbound.get(f,-1)<=c['cut']:groups[f].append(r)
+ failed=[]
+ for f,targets in groups.items():
+  vals=[rightB(prefix[r]) for r,g in enumerate(ch) if g==f and r!=p]
+  if ch[p]==f:vals.append({fresh:Q(1)})
+  if c['frame']==f:vals.append({p:Q(1)})
+  b=basis(vals)
+  for r in targets:
+   z=rem(desired[r],b)
+   if z:failed.append(dict(role=r,frame=f,remainder=z))
+ return failed
+
+def main():
+ ap=argparse.ArgumentParser();ap.add_argument('--word',default='word5718.json.gz');ap.add_argument('--contacts',default='contacts5718.json');ap.add_argument('--out',default='preflight5718.json');a=ap.parse_args()
+ w=load(a.word);d=json.loads((HERE/'results'/a.contacts).read_text());need(d['source_sha256']==PINS[a.word],'source join')
+ cuts=d['cuts']
+ for c in cuts:
+  for k in ('a','c','h0','d','beta'):c[k]=unrow(c[k])
+ by=defaultdict(list)
+ for j,c in enumerate(cuts):by[c['cut']].append(j)
+ last={e[3]:i for i,e in enumerate(w['program']) if e[0]=='MOVE'}
+ n=w['public'];N=n+w['owned_fields'];rows=[{r:Q(1)} for r in range(N)];ch=w['initial']+[None]*w['owned_fields'];out=[];counts=Counter()
+ for i,e in enumerate(w['program']):
+  apply(rows,e);charts_step(ch,e)
+  for j in by[i]:
+   c=cuts[j]
+   # This explicitly omits the commissioned known-closed helper440 contract.
+   if c['pivot']==440:counts['excluded_fixed440']+=1;continue
+   fail=closed_tests(w,c,rows,ch,last);terminal=terminal_test(w,c)
+   counts['tested']+=1;counts['closed_rejects']+=bool(fail);counts['terminal_rejects']+=bool(terminal)
+   out.append(dict(index=j,cut=c['cut'],pivot=c['pivot'],trigger=c['trigger'],ranks=c['ranks'],defects=len(c['d']),closed_failed=fail,terminal_failed=terminal))
+ (HERE/'results'/a.out).write_text(json.dumps(fmt(dict(source_sha256=PINS[a.word],counts=dict(counts),results=out)),indent=2)+'\n')
+ print(dict(counts),flush=True)
+ print('terminal survivors',[(s['index'],s['cut'],s['pivot'],s['defects']) for s in out if not s['terminal_failed']][:60],flush=True)
+if __name__=='__main__':main()
diff --git a/research/p104-joint-neutral-search/reachability.py b/research/p104-joint-neutral-search/reachability.py
new file mode 100644
index 0000000000..e679085854
--- /dev/null
+++ b/research/p104-joint-neutral-search/reachability.py
@@ -0,0 +1,49 @@
+"""Favorable temporal span propagation, granting free mixing and unlimited retention.
+
+A MOVE may convey the entire source frame span, a relaxation of its one-field
+capacity. Every legal scalar sequence on this fixed itinerary is contained.
+"""
+from preflight import *
+
+def reach_test(w,c,prefix,ch,program=None):
+ n=w['public'];N=n+w['owned_fields'];p=c['pivot'];fresh=N
+ _,desired,k,q,eta=endpoints(w,c)
+ reach=defaultdict(int)
+ for r,f in enumerate(ch):
+  if f is not None:reach[f]|=1<<r
+ # Old p is retired, and its continuation is the new independent input.
+ reach[ch[p]]&=~(1<<p);reach[c['frame']]|=(1<<p)|(1<<fresh)
+ for e in (program or w['program'])[c['cut']+1:]:
+  if e[0]=='MOVE':reach[e[3]]|=reach[e[2]]
+ actual=[]
+ for r,row in enumerate(prefix):
+  z=dict(row);add(z,k,sum(v*c['beta'].get(j,0) for j,v in row.items()));add(z,{p:Q(1)},-row.get(p,0));actual.append(z)
+ actual[p]={p:Q(1)};actual.append({fresh:Q(1)})
+ grouped=defaultdict(list)
+ for r in (set(c['d'])-{p})|{fresh}:
+  f=w['final'][p if r==fresh else r];grouped[f].append(r)
+ fails=[];ranks={}
+ for f,targets in grouped.items():
+  mask=reach[f];b=basis(sorted((actual[r] for r in range(N+1) if mask>>r&1),key=len));ranks[f]=len(b)
+  for r in targets:
+   z=rem(desired[r],b)
+   if z:fails.append(dict(role=r,frame=f,remainder=z,available_rank=len(b)))
+ return fails,ranks
+
+def main():
+ ap=argparse.ArgumentParser();ap.add_argument('--word',default='word5718.json.gz');ap.add_argument('--contacts',default='contacts5718.json');ap.add_argument('--out',default='reach5718.json');ap.add_argument('--max-defects',type=int,default=3);a=ap.parse_args()
+ w=load(a.word);d=json.loads((HERE/'results'/a.contacts).read_text());need(d['source_sha256']==PINS[a.word],'source join');cuts=d['cuts'];by=defaultdict(list)
+ for j,c in enumerate(cuts):
+  if c['pivot']==440 or len(c['d'])>a.max_defects:continue
+  for k in ('a','c','h0','d','beta'):c[k]=unrow(c[k])
+  by[c['cut']].append((j,c))
+ N=w['public']+w['owned_fields'];rows=[{r:Q(1)} for r in range(N)];ch=w['initial']+[None]*w['owned_fields'];out=[]
+ for i,e in enumerate(w['program']):
+  apply(rows,e);charts_step(ch,e)
+  for j,c in by[i]:
+   fails,ranks=reach_test(w,c,rows,ch);out.append(dict(index=j,cut=i,pivot=c['pivot'],trigger=c['trigger'],defects=len(c['d']),failed=fails,ranks=ranks))
+   if len(out)%20==0: print(dict(completed=len(out),rejected=sum(bool(s['failed']) for s in out)),flush=True)
+ (HERE/'results'/a.out).write_text(json.dumps(fmt(dict(source_sha256=PINS[a.word],max_defects=a.max_defects,results=out)),indent=2)+'\n')
+ print(dict(tested=len(out),rejected=sum(bool(s['failed']) for s in out),survivors=sum(not s['failed'] for s in out)),flush=True)
+ print([(s['index'],s['cut'],s['pivot'],s['defects']) for s in out if not s['failed']][:80],flush=True)
+if __name__=='__main__':main()
diff --git a/research/p104-joint-neutral-search/results/contacts5713.json b/research/p104-joint-neutral-search/results/contacts5713.json
new file mode 100644
index 0000000000..8c031317e7
--- /dev/null
+++ b/research/p104-joint-neutral-search/results/contacts5713.json
@@ -0,0 +1,273546 @@
+{
+  "source_sha256": "9fd67dd89ed24a644257cd9aef06934ed4c6fbe0441804684a968868f2ef66a8",
+  "domain": "after every MOVE, departure and arrival groups; a=e_p+q e_s, q chosen for purity or +/-1/2,+/-1,+/-2",
+  "stats": {
+    "helper_contact_contexts": 6008,
+    "prefix_candidates": 2012,
+    "compatible_bases": 1880,
+    "other_role_candidates": 1554
+  },
+  "cuts": [
+    {
+      "cut": 9598,
+      "pivot": 224,
+      "frame": 0,
+      "a": {
+        "224": "1"
+      },
+      "c": {
+        "224": "1",
+        "225": "-1",
+        "227": "1"
+      },
+      "h0": {
+        "224": "1",
+        "225": "-1",
+        "227": "1"
+      },
+      "ranks": [
+        1,
+        8
+      ],
+      "trigger": 224,
+      "d": {
+        "188": "1",
+        "224": "1",
+        "173": "-1/2",
+        "166": "-1/2",
+        "214": "-1/2",
+        "213": "-1/2",
+        "167": "-1/2",
+        "212": "-1/2",
+        "168": "-1/2",
+        "124": "-1/2",
+        "143": "-1/2",
+        "126": "1/2",
+        "151": "-1/2",
+        "117": "-1/2",
+        "181": "-1/2",
+        "180": "-1/2",
+        "116": "-1/2",
+        "179": "-1/2",
+        "192": "-1/2",
+        "200": "-1/2"
+      },
+      "beta": {
+        "188": "1",
+        "224": "1",
+        "173": "-1/2",
+        "166": "-1/2",
+        "214": "-1/2",
+        "213": "-1/2",
+        "167": "-1/2",
+        "212": "-1/2",
+        "168": "-1/2",
+        "124": "-1/2",
+        "143": "-1/2",
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diff --git a/research/p104-joint-neutral-search/results/contacts5718.json b/research/p104-joint-neutral-search/results/contacts5718.json
new file mode 100644
index 0000000000..ee80a3a3b7
--- /dev/null
+++ b/research/p104-joint-neutral-search/results/contacts5718.json
@@ -0,0 +1,271798 @@
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+}
diff --git a/research/p104-joint-neutral-search/results/controls.json b/research/p104-joint-neutral-search/results/controls.json
new file mode 100644
index 0000000000..2de861ecd2
--- /dev/null
+++ b/research/p104-joint-neutral-search/results/controls.json
@@ -0,0 +1,88 @@
+{
+  "status": "PASS",
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+    "paid": {
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+      "2": 459,
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+      "4": 92,
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+  "two_meeting_fixture": true,
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+  "actual_P104_two_step_formula_all_columns": true,
+  "source_corruption_rejected": true,
+  "actual_P104_four_step_formula_all_columns": true
+}
diff --git a/research/p104-joint-neutral-search/results/invoice.json b/research/p104-joint-neutral-search/results/invoice.json
new file mode 100644
index 0000000000..ab4ac839e9
--- /dev/null
+++ b/research/p104-joint-neutral-search/results/invoice.json
@@ -0,0 +1,104 @@
+{
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+  "base": {
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+      "64": 416,
+      "72": 208
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+      "65": 416,
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+      "145": 208
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+    "5": 18,
+    "9": -18
+  },
+  "signed_delta_paid_minus_targets": {
+    "4": -18,
+    "5": -18,
+    "9": 18
+  },
+  "proof": "18*(9^t-4^t-5^t)<0 for 0<t<1 by strict subadditivity; no surviving endpoint implements this proposed invoice",
+  "ordinary": {
+    "source_local_scalar": 221474,
+    "retiming_added_scalar": 0,
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+    "four_ADD_upper": 40,
+    "terminal_normalization": "unknown: no candidate passes even the favorable rational endpoint test",
+    "new_helper_routes_allocation_cleanup": "unknown: no candidate emitted",
+    "compiler_and_outer": "unrun: no survivor"
+  },
+  "kappa_status": "NO_NEW_KAPPA; selected .00310045; source pending PR5718 claims .00311024570"
+}
diff --git a/research/p104-joint-neutral-search/results/joint680-a-fixed.json b/research/p104-joint-neutral-search/results/joint680-a-fixed.json
new file mode 100644
index 0000000000..4901e57579
--- /dev/null
+++ b/research/p104-joint-neutral-search/results/joint680-a-fixed.json
@@ -0,0 +1,41 @@
+{
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diff --git a/research/p104-joint-neutral-search/results/joint680-b-fixed.json b/research/p104-joint-neutral-search/results/joint680-b-fixed.json
new file mode 100644
index 0000000000..66eafd5f54
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+++ b/research/p104-joint-neutral-search/results/joint680-b-fixed.json
@@ -0,0 +1,41 @@
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diff --git a/research/p104-joint-neutral-search/results/joint680-b-retimed.json b/research/p104-joint-neutral-search/results/joint680-b-retimed.json
new file mode 100644
index 0000000000..874bbbc76a
--- /dev/null
+++ b/research/p104-joint-neutral-search/results/joint680-b-retimed.json
@@ -0,0 +1,42 @@
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diff --git a/research/p104-joint-neutral-search/results/joint680-c-fixed.json b/research/p104-joint-neutral-search/results/joint680-c-fixed.json
new file mode 100644
index 0000000000..db874c2adc
--- /dev/null
+++ b/research/p104-joint-neutral-search/results/joint680-c-fixed.json
@@ -0,0 +1,41 @@
+{
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diff --git a/research/p104-joint-neutral-search/results/joint680-c-retimed.json b/research/p104-joint-neutral-search/results/joint680-c-retimed.json
new file mode 100644
index 0000000000..df37be6b63
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+++ b/research/p104-joint-neutral-search/results/joint680-c-retimed.json
@@ -0,0 +1,42 @@
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diff --git a/research/p104-joint-neutral-search/results/joint680-cut-retimed.json b/research/p104-joint-neutral-search/results/joint680-cut-retimed.json
new file mode 100644
index 0000000000..d726523836
--- /dev/null
+++ b/research/p104-joint-neutral-search/results/joint680-cut-retimed.json
@@ -0,0 +1,42 @@
+{
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diff --git a/research/p104-joint-neutral-search/results/joint680-fixed.json b/research/p104-joint-neutral-search/results/joint680-fixed.json
new file mode 100644
index 0000000000..2b7f0ba385
--- /dev/null
+++ b/research/p104-joint-neutral-search/results/joint680-fixed.json
@@ -0,0 +1,38 @@
+{
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diff --git a/research/p104-joint-neutral-search/results/joint680-retimed.json b/research/p104-joint-neutral-search/results/joint680-retimed.json
new file mode 100644
index 0000000000..dc6edcea7c
--- /dev/null
+++ b/research/p104-joint-neutral-search/results/joint680-retimed.json
@@ -0,0 +1,39 @@
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diff --git a/research/p104-joint-neutral-search/results/joint695.json b/research/p104-joint-neutral-search/results/joint695.json
new file mode 100644
index 0000000000..bde5b25c66
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+++ b/research/p104-joint-neutral-search/results/joint695.json
@@ -0,0 +1,41 @@
+{
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diff --git a/research/p104-joint-neutral-search/results/positive-word.json.gz b/research/p104-joint-neutral-search/results/positive-word.json.gz
new file mode 100644
index 0000000000..0bf5a563f7
Binary files /dev/null and b/research/p104-joint-neutral-search/results/positive-word.json.gz differ
diff --git a/research/p104-joint-neutral-search/results/positive.json b/research/p104-joint-neutral-search/results/positive.json
new file mode 100644
index 0000000000..5f29d5f839
--- /dev/null
+++ b/research/p104-joint-neutral-search/results/positive.json
@@ -0,0 +1,28 @@
+{
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+  "status": "positive_control_emitted_exact_dyadic_word"
+}
diff --git a/research/p104-joint-neutral-search/results/preflight5718.json b/research/p104-joint-neutral-search/results/preflight5718.json
new file mode 100644
index 0000000000..fc27839a34
--- /dev/null
+++ b/research/p104-joint-neutral-search/results/preflight5718.json
@@ -0,0 +1,258041 @@
+{
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+}
diff --git a/research/p104-joint-neutral-search/results/retimed-word.json.gz b/research/p104-joint-neutral-search/results/retimed-word.json.gz
new file mode 100644
index 0000000000..b5377e0091
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diff --git a/research/p104-joint-neutral-search/results/two-two680-optimized.json b/research/p104-joint-neutral-search/results/two-two680-optimized.json
new file mode 100644
index 0000000000..d754d8d5ff
--- /dev/null
+++ b/research/p104-joint-neutral-search/results/two-two680-optimized.json
@@ -0,0 +1,35 @@
+{
+  "first_sequences": 32581,
+  "second_sequences": 1333,
+  "literal_program_pairs": 43430473,
+  "second_distinct_matrices": 949,
+  "second_critical_effects": 276,
+  "matrix_pairs": 30919369,
+  "probe_pass": 0,
+  "critical_row_pass": 0,
+  "survivors": [],
+  "critical": 153,
+  "groups": [
+    [
+      680,
+      753,
+      679,
+      682,
+      685,
+      686
+    ],
+    [
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+    ]
+  ],
+  "source_sha256": "cff7196f8b168c4ebf8227185eed98387b66ec5db0179108adfea4045775cc31",
+  "cut": 13920,
+  "pivot": 680,
+  "route": {
+    "move": 16655,
+    "after": 16649
+  },
+  "seconds": 57.95915158302523
+}
diff --git a/research/p104-joint-neutral-search/results/two-two680.json b/research/p104-joint-neutral-search/results/two-two680.json
new file mode 100644
index 0000000000..8b0588cccf
--- /dev/null
+++ b/research/p104-joint-neutral-search/results/two-two680.json
@@ -0,0 +1,35 @@
+{
+  "first_sequences": 32581,
+  "second_sequences": 1333,
+  "literal_program_pairs": 43430473,
+  "second_distinct_matrices": 949,
+  "second_critical_effects": 276,
+  "matrix_pairs": 30919369,
+  "probe_pass": 0,
+  "critical_row_pass": 0,
+  "survivors": [],
+  "critical": 153,
+  "groups": [
+    [
+      680,
+      753,
+      679,
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+      685,
+      686
+    ],
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+      753
+    ]
+  ],
+  "source_sha256": "cff7196f8b168c4ebf8227185eed98387b66ec5db0179108adfea4045775cc31",
+  "cut": 13920,
+  "pivot": 680,
+  "route": {
+    "move": 16655,
+    "after": 16649
+  },
+  "seconds": 58.29730762494728
+}
diff --git a/research/p104-joint-neutral-search/search.py b/research/p104-joint-neutral-search/search.py
new file mode 100644
index 0000000000..5d38c52132
--- /dev/null
+++ b/research/p104-joint-neutral-search/search.py
@@ -0,0 +1,101 @@
+"""Exact dyadic contact generation and bounded joint route/scalar exploration."""
+from fractions import Fraction as Q
+from collections import defaultdict, Counter
+from pathlib import Path
+import argparse, gzip, hashlib, json, time
+HERE=Path(__file__).resolve().parent
+PINS={'word5713.json.gz':'9fd67dd89ed24a644257cd9aef06934ed4c6fbe0441804684a968868f2ef66a8','word5718.json.gz':'cff7196f8b168c4ebf8227185eed98387b66ec5db0179108adfea4045775cc31'}
+def need(x,msg):
+ if not x: raise ValueError(msg)
+def add(a,b,q=Q(1)):
+ for k,v in tuple(b.items()):
+  z=a.get(k,0)+q*v
+  if z:a[k]=z
+  else:a.pop(k,None)
+def scale(a,q):return {k:v*q for k,v in a.items() if v*q}
+def apply(rows,e):
+ op,r=e[:2]
+ if op=='MOVE':return
+ if op in ('INIT','CLEAR'):rows[r]={}
+ elif op=='SCALE':rows[r]=scale(rows[r],Q(e[-2]))
+ else:
+  s=e[2];a=dict(rows[s])
+  if op=='COPY':rows[r]={}
+  add(rows[r],a,Q(e[-2]))
+def charts_step(ch,e):
+ if e[0]=='MOVE':ch[e[1]]=e[3]
+ elif e[0] in ('INIT','CLEAR'):ch[e[1]]=e[2] if e[0]=='INIT' else None
+def span(xs):
+ s={0}
+ for x in xs:s|={v^x for v in tuple(s)}
+ return s
+def load(name):
+ p=HERE/'inputs'/name;b=p.read_bytes();need(hashlib.sha256(b).hexdigest()==PINS[name],'source hash')
+ return json.loads(gzip.decompress(b))
+def fmt(x):
+ if isinstance(x,dict):return {str(k):fmt(v) for k,v in x.items()}
+ if isinstance(x,(tuple,list)):return [fmt(v) for v in x]
+ if isinstance(x,Q):return str(x)
+ return x
+def unrow(x):return {int(k):Q(v) for k,v in x.items()}
+def generate(w):
+ n=w['public'];N=n+w['owned_fields'];main=set(w['live'])|{r+112 for r in w['live']}
+ fs=[span(b) for b in w['frames']];rows=[{r:Q(1)} for r in range(N)];ch=w['initial']+[None]*(N-n);at=defaultdict(set)
+ for r,f in enumerate(ch):at[f].add(r)
+ stats=Counter();by=defaultdict(list)
+ # Every MOVE changes contact at both departure and arrival. No input-column-zero assumption.
+ for i,e in enumerate(w['program']):
+  if e[0]=='MOVE':
+   _,m,old,f,_=e;at[old].remove(m);at[f].add(m);ch[m]=f
+   for frame in sorted({old,f}):
+    for p in sorted(at[frame]):
+     if p>=n or p in main:continue
+     u,v=w['initial'][p],w['final'][p]
+     if not fs[u]<fs[frame]<fs[v]:continue
+     stats['helper_contact_contexts']+=1
+     outside={k:x for k,x in rows[p].items() if k>=n or w['initial'][k]!=u}
+     options=[(None,Q(0))] if not outside else []
+     for s in sorted(at[frame]-{p}):
+      out={k:x for k,x in rows[s].items() if k>=n or w['initial'][k]!=u}
+      if not out:
+       if not outside:
+        options.extend((s,q) for q in (Q(-2),Q(-1),Q(-1,2),Q(1,2),Q(1),Q(2)))
+       continue
+      k=min(out);q=-outside.get(k,0)/out[k]
+      if q and all(outside.get(j,0)+q*out.get(j,0)==0 for j in outside.keys()|out.keys()):options.append((s,q))
+     for s,q in options:
+      if q.denominator&(q.denominator-1):continue
+      c=dict(rows[p]);a={p:Q(1)}
+      if s is not None:add(c,rows[s],q);a[s]=q
+      if c.get(p)!=1:continue
+      stats['prefix_candidates']+=1
+      by[i].append(dict(cut=i,pivot=p,frame=frame,a=a,c=c,h0=dict(rows[p]),ranks=[len(w['frames'][frame])-len(w['frames'][u]),len(w['frames'][v])-len(w['frames'][frame])],trigger=m))
+  else:
+   if e[0] in ('INIT','CLEAR'):
+    r=e[1];at[ch[r]].remove(r);charts_step(ch,e);at[ch[r]].add(r)
+   apply(rows,e)
+ cols=[{r:Q(1)} for r in range(N)];keep=[]
+ for i in range(len(w['program'])-1,-1,-1):
+  for s in by.pop(i,[]):
+   p=s['pivot'];u=w['initial'][p];d=cols[p];beta=dict(d)
+   for r in w['live']:
+    if r in d:beta[r+112]=beta.get(r+112,0)-d[r]
+   beta={k:v for k,v in beta.items() if v}
+   if beta.get(p)!=1 or any(k>=n or w['initial'][k]!=u for k in beta):continue
+   if sum(x*beta.get(k,0) for k,x in s['c'].items())!=1:continue
+   s.update(d=dict(d),beta=beta);keep.append(s)
+  e=w['program'][i];op,r=e[:2]
+  if op in ('INIT','CLEAR'):cols[r]={}
+  elif op=='SCALE':cols[r]=scale(cols[r],Q(e[-2]))
+  elif op!='MOVE':
+   add(cols[e[2]],cols[r],Q(e[-2]))
+   if op=='COPY':cols[r]={}
+ stats['compatible_bases']=len(keep);stats['other_role_candidates']=sum(s['trigger']!=s['pivot'] for s in keep)
+ # Exact identical cut state dedup across consecutive MOVE triggers is left visible in raw counts.
+ return sorted(keep,key=lambda s:(s['cut'],s['pivot'],tuple(s['a'].items()))),dict(stats)
+def main():
+ ap=argparse.ArgumentParser();ap.add_argument('--word',default='word5718.json.gz');ap.add_argument('--out',default='contacts5718.json');a=ap.parse_args()
+ t=time.monotonic();w=load(a.word);cuts,stats=generate(w);out=dict(source_sha256=PINS[a.word],domain='after every MOVE, departure and arrival groups; a=e_p+q e_s, q chosen for purity or +/-1/2,+/-1,+/-2',stats=stats,cuts=cuts)
+ (HERE/'results'/a.out).write_text(json.dumps(fmt(out),indent=2)+'\n');print(json.dumps(dict(stats=stats,seconds=time.monotonic()-t)),flush=True)
+ if a.word=='word5713.json.gz':need(any(c['cut']==14330 and c['pivot']==708 and c['a']=={708:Q(1),154:Q(1,2)} for c in cuts),'generator must DISCOVER PR5718 control')
+if __name__=='__main__':main()
diff --git a/research/p104-joint-neutral-search/two_two.py b/research/p104-joint-neutral-search/two_two.py
new file mode 100644
index 0000000000..82b91a7edf
--- /dev/null
+++ b/research/p104-joint-neutral-search/two_two.py
@@ -0,0 +1,65 @@
+"""Exact 2+2 ADD domain, deduplicating second-meeting response rows.
+
+Every literal ADD sequence is represented. Probes are exact Q functionals;
+passing probes triggers the complete coefficient and terminal-group tests.
+"""
+from joint import *
+
+def run22(w,c,first,second,roles,second_frame,cap=50000000):
+ snap=raw(w,c,{first,second});R1=snap[first][0];R2,ch=snap[second];g2=[r for r,f in enumerate(ch) if f==second_frame]
+ need(len(g2)<=3,'second meeting bound');need(all(snap[first][1][r]==c['frame'] for r in roles),'first coframe')
+ base,desired,*_=endpoints(w,c);groups=terminal_groups(w,c)
+ bad=[f for f,rs in groups.items() if not groups_check(base,desired,{f:rs},[])];need(len(bad)==1 and len(groups[bad[0]])==1,'single critical endpoint frame')
+ critical=groups[bad[0]][0];want=desired[critical]
+ D1=responses(w,c['pivot'],first,roles);D2=responses(w,c['pivot'],second,g2);mid=responses(w,c['pivot'],first,roles,second)
+ A=actions(roles);B=actions(g2);seq1=[()]+[(a,) for a in A]+[(a,b) for a in A for b in A];seq2=[()]+[(a,) for a in B]+[(a,b) for a in B for b in B]
+ # Each K entry is an actual same-frame two-ADD endpoint correction matrix.
+ matrices={}
+ for seq in seq2:
+  rows={r:{r:Q(1)} for r in g2}
+  for r,s,a in seq:add(rows[r],rows[s],a)
+  key=tuple(tuple(rows[r].get(s,0)-Q(r==s) for s in g2) for r in g2)
+  matrices.setdefault(key,seq)
+ effects=defaultdict(list)
+ for matrix,seq in matrices.items():
+  coeff=tuple(sum(D2[r].get(critical,0)*matrix[j][i] for j,r in enumerate(g2)) for i,s in enumerate(g2))
+  effects[coeff].append((matrix,seq))
+ probes=[c['pivot'],w['public']+w['owned_fields'],685,679,682,686]
+ # First sequence provenance and integer multiplicities remain in seq counts.
+ tested=0;probe_pass=0;row_pass=0;survivors=[];seen=set();first_unique=0
+ for ix,seq in enumerate(seq1):
+  loc={r:dict(R1[r]) for r in roles};up=[];rows2={r:dict(R2[r]) for r in g2};end=dict(base[critical])
+  for r,s,a in seq:
+   src=dict(loc[s]);add(loc[r],src,a);up.append((D1[r],src,a));add(end,src,a*D1[r].get(critical,0))
+   for t in g2:add(rows2[t],src,a*mid[r].get(t,0))
+  signature=(tuple(sorted(end.items())),tuple(tuple(sorted(rows2[r].items())) for r in g2),tuple((tuple(sorted(d.items())),tuple(sorted(s.items())),a) for d,s,a in up))
+  # Do not dedup first paths: distinct endpoint updates outside the critical row matter.
+  first_unique+=1
+  for coeff,cases in effects.items():
+   tested+=sum(1 for _ in cases)
+   if tested>cap:raise ValueError('explicit unique-matrix resource cap exceeded')
+   if any(end.get(j,0)+sum(a*rows2[r].get(j,0) for r,a in zip(g2,coeff)) for j in probes if j not in want):continue
+   probe_pass+=len(cases);target=dict(end)
+   for r,a in zip(g2,coeff):add(target,rows2[r],a)
+   if set(target)!=set(want):continue
+   pivot=min(want);ratio=target[pivot]/want[pivot]
+   if not ratio or any(target[j]!=ratio*v for j,v in want.items()):continue
+   row_pass+=len(cases)
+   for matrix,seq2w in cases:
+    updates=list(up)
+    for j,r in enumerate(g2):
+     source={}
+     for i,s in enumerate(g2):add(source,rows2[s],matrix[j][i])
+     if source:updates.append((D2[r],source,Q(1)))
+    if groups_check(base,desired,groups,updates):
+     survivors.append(dict(first=seq,second=seq2w));print('SURVIVOR',fmt(survivors[-1]),flush=True)
+  if ix and ix%5000==0:print(dict(first_sequences=ix,total=len(seq1),survivors=len(survivors)),flush=True)
+ return dict(first_sequences=len(seq1),second_sequences=len(seq2),literal_program_pairs=len(seq1)*len(seq2),second_distinct_matrices=len(matrices),second_critical_effects=len(effects),matrix_pairs=tested,probe_pass=probe_pass,critical_row_pass=row_pass,survivors=survivors,critical=critical,groups=[roles,g2])
+
+def main():
+ ap=argparse.ArgumentParser();ap.add_argument('--index',type=int,default=1196);ap.add_argument('--out',default='two-two680.json');a=ap.parse_args()
+ w=retime(load('word5718.json.gz'),16655,16649);c=json.loads((HERE/'results/contacts5718.json').read_text())['cuts'][a.index]
+ for k in ('a','c','h0','d','beta'):c[k]=unrow(c[k])
+ t=time.monotonic();out=run22(w,c,c['cut'],16652,[680,753,679,682,685,686],164);out.update(source_sha256=PINS['word5718.json.gz'],cut=c['cut'],pivot=c['pivot'],route=dict(move=16655,after=16649),seconds=time.monotonic()-t)
+ (HERE/'results'/a.out).write_text(json.dumps(fmt(out),indent=2)+'\n');print(json.dumps(fmt(out)))
+if __name__=='__main__':main()
diff --git a/research/p104-joint-neutral-search/verify.py b/research/p104-joint-neutral-search/verify.py
new file mode 100644
index 0000000000..62f049a62a
--- /dev/null
+++ b/research/p104-joint-neutral-search/verify.py
@@ -0,0 +1,48 @@
+"""Reproduce this finite local package, with expensive searches only under --full."""
+from pathlib import Path
+import argparse, gzip, hashlib, json, subprocess, sys, time
+HERE=Path(__file__).resolve().parent
+
+def need(ok,msg):
+ if not ok:raise ValueError(msg)
+def semantic(x):
+ if isinstance(x,dict):return {k:semantic(v) for k,v in x.items() if k!='seconds'}
+ if isinstance(x,list):return [semantic(v) for v in x]
+ return x
+
+def run(script,args=(),receipt=None):
+ expected=semantic(json.loads((HERE/'results'/receipt).read_text())) if receipt else None
+ p=subprocess.run([sys.executable,'-B',str(HERE/script),*args],text=True,capture_output=True)
+ need(p.returncode==0,script+' failed:\n'+p.stdout+'\n'+p.stderr)
+ if receipt:need(semantic(json.loads((HERE/'results'/receipt).read_text()))==expected,'semantic receipt changed: '+receipt)
+ print('PASS',script,*args,flush=True)
+
+def main():
+ ap=argparse.ArgumentParser();ap.add_argument('--full',action='store_true');a=ap.parse_args()
+ manifest=json.loads((HERE/'MANIFEST.json').read_text())
+ for row in manifest['files']:
+  data=(HERE/row['path']).read_bytes()
+  if row['hash_type']=='json_semantic':data=json.dumps(semantic(json.loads(data)),sort_keys=True,separators=(',',':')).encode()
+  elif row['hash_type']=='json_gzip_semantic':data=json.dumps(semantic(json.loads(gzip.decompress(data))),sort_keys=True,separators=(',',':')).encode()
+  else:need(row['hash_type']=='raw','unknown hash type')
+  need(hashlib.sha256(data).hexdigest()==row['sha256'],'changed frozen file '+row['path'])
+ for name,result in [('word5713.json.gz','contacts5713.json'),('word5718.json.gz','contacts5718.json')]:run('search.py',['--word',name,'--out',result],result)
+ run('controls.py',receipt='controls.json');run('invoice.py',receipt='invoice.json')
+ counts=[]
+ for label in ('a','b','c'):
+  for route in ('fixed','retimed'):
+   file='joint680-'+label+'-'+route+'.json' if label!='a' or route=='fixed' else 'joint680-cut-retimed.json'
+   d=json.loads((HERE/'results'/file).read_text());need(not d['truncated'] and not d['survivors'],'completed negative receipt');counts.append(d['tested'])
+ need(sum(counts)==4887150,'complete three-ADD coverage')
+ two=json.loads((HERE/'results/two-two680.json').read_text());need(two['literal_program_pairs']==43430473 and two['matrix_pairs']==30919369 and two['probe_pass']==0 and not two['survivors'],'complete four-ADD coverage')
+ if a.full:
+  run('preflight.py',receipt='preflight5718.json');run('reachability.py',receipt='reach5718.json')
+  for index,first,label in [(1196,13920,'a'),(1199,13922,'b'),(1200,13922,'c')]:
+   for route in ('fixed','retimed'):
+    file='joint680-'+label+'-'+route+'.json' if label!='a' or route=='fixed' else 'joint680-cut-retimed.json'
+    args=['--index',str(index),'--first',str(first),'--second',str(16651 if route=='fixed' else 16652),'--first-frame','1049','--second-frame','164','--first-roles','680,753,679,682,685,686','--depth','2','--cap','1250000','--out',file]
+    if route=='retimed':args+=['--move','16655','--after','16649']
+    run('joint.py',args,file)
+  run('two_two.py',receipt='two-two680.json')
+ print(json.dumps(dict(status='PASS',full=a.full,three_ADD_program_pairs=sum(counts),four_ADD_program_pairs=two['literal_program_pairs'],new_kappa=False)))
+if __name__=='__main__':main()
diff --git a/research/p104-three-meeting-controllability/MANIFEST.json b/research/p104-three-meeting-controllability/MANIFEST.json
new file mode 100644
index 0000000000..e5d84848e1
--- /dev/null
+++ b/research/p104-three-meeting-controllability/MANIFEST.json
@@ -0,0 +1,31 @@
+{
+  "schema": "p104-three-meeting-controllability/1",
+  "files": {
+    "NOTICE": "0b59c350392ec496e80dbd603707dc3fdd7ab60c2738a6362307ac88cb967939",
+    "README.md": "b64f88e7e3dd3cee3aa2a385b6c07dd7e5a3b91e757e1e8cfc93c8fc531df738",
+    "REFRESH.json": "439d389aa6c3f4efc9613dd87362b676c1e3990a681dcb6c684bb9a39e293e5f",
+    "SOURCES.json": "ea456f6e89e827052f83eefe2cf65cac1d544d0a106ba80d785650bd4556f2b4",
+    "controls.py": "59c1ef13bf7a35bded1c3ff5db1f1c6174835f4c7c2930b55c4294181a75b568",
+    "invoice.py": "326fbef0f5630b4326daa63789ac7db3968b7d4249dd4218229b0e8fb8218bdc",
+    "obstruction.py": "98a542c0035bdcc90a7a1a63d9458144f7d506ea5b8de36d0dd1f2a5834c19ca",
+    "relax.py": "d188aaf30d214421aed9434bd5f4225cdfe28de9fb922ce8022e0e60939659ed",
+    "results/controls.json": "4d1e97ece48c2afbb42371132bc5ed3f9c5fb6ddb17e626f3a7829a12958d06a",
+    "results/invoice.json": "5ca7dd44c608f268cad8b96244beee8db7944b4d67664a1197b18de0bc178a3a",
+    "results/obstruction.json": "ecbbddbded939b4018fbc6cfdf99dbfe6693f4dd037c1fd0c4ed0882fd656da2",
+    "results/relaxation.json": "08798aa22b0cb4ed632858a91cc130d56dd5e694b950e027967288dec662a2d1",
+    "vendor/NOTICE": "c474479a870ae53ae0bcb84f656c2b222380395bbee767ee15e5f9c5b4ce7e79",
+    "vendor/README.md": "8d069d3f2406f2cb0ff9d58f8144c6cf1e28da3ec03741d657c37a117f45d6eb",
+    "vendor/SOURCES.json": "e6f72350b2d31e655f178a80d3dfb197b06ecf2d81b9e84172b7481c0846e2f1",
+    "vendor/emit.py": "3cef5005f56f0f391d09175f75698cbdf835a61f0ca7f8439659189ff7bb8ca3",
+    "vendor/inputs/controller5718.json": "a84f6bbd547379597464e56c420cc665f96bc43a9a1351eed4b7cd0fce3cc4b9",
+    "vendor/inputs/word5713.json.gz": "9fd67dd89ed24a644257cd9aef06934ed4c6fbe0441804684a968868f2ef66a8",
+    "vendor/inputs/word5718.json.gz": "cff7196f8b168c4ebf8227185eed98387b66ec5db0179108adfea4045775cc31",
+    "vendor/invoice.py": "d9171336935023fb94d310d782ea00cec1ac60963e137b8766e39d690cbbcca9",
+    "vendor/joint.py": "dd9d055d78f27c1dc663c86efe2d41a8914636bdc47917ebff92882f738831fc",
+    "vendor/preflight.py": "e19cce00813896373826a6ee8ccb3e16f86c95d47bcba5f3b06c90cc2729a8ca",
+    "vendor/results/contacts5713.json": "3347f3e4f372189f9a06cb754afdaa6bb812b3a5dc7f1d9d0c16cc00485a73f1",
+    "vendor/results/contacts5718.json": "b799253336add810d04d39512a0641dc4416145de0b121040c8defe6d517cf19",
+    "vendor/search.py": "b94cf3464e67e20ed3b57b28fe355f5a9d35c01c6abb84dabf5ad0c5180face8",
+    "verify.py": "7e6f019f659fc3ed1365fe565e5fc8594429dcbab6ffda95c653be9603a7ecb6"
+  }
+}
diff --git a/research/p104-three-meeting-controllability/NOTICE b/research/p104-three-meeting-controllability/NOTICE
new file mode 100644
index 0000000000..f2bff9de93
--- /dev/null
+++ b/research/p104-three-meeting-controllability/NOTICE
@@ -0,0 +1 @@
+Apache-2.0. Prepared for zxv (https://github.com/zxv) with substantial OpenAI Codex assistance. No subagents. New exact scoped three-meeting controllability analysis. Preserve all source notices in vendor/NOTICE, which credits the complete P104/native/controller/compiler lineage. Vendored predecessor files are unchanged from commit 1f51164a1dba5b9cb7639d3b760d2a0660931f63. No full theorem or new kappa is claimed.
diff --git a/research/p104-three-meeting-controllability/README.md b/research/p104-three-meeting-controllability/README.md
new file mode 100644
index 0000000000..ab6d2bf3b4
--- /dev/null
+++ b/research/p104-three-meeting-controllability/README.md
@@ -0,0 +1,218 @@
+# The three specified helper680 meetings cannot realize the split with invertible local scalar transforms
+
+**Local-only exact scoped obstruction; no new κ.** The added meeting at
+event15468 really supplies new source rows, but does not finish this split.
+For each of the three predecessor encodings, any number of ADD/SCALE operations
+at the three specified meetings fails, even when their coefficients are arbitrary
+rationals. This closes a changed three-meeting interface, rather than extending
+the predecessor's finite two-meeting coefficient census.
+
+The scientific source remains [PR5718](https://github.com/CrocSwap/integer-mult-bounds/pull/5718)
+at `a1534ac45401c9a9c80c07aa65c89e00e33594f8`, claiming conditional κ
+`.00311024570`. It was merged as an archive on October26; merging does not
+admit its claim. Canonical main was refreshed to
+`de5ec2e7a6074068452f45b1a191b5c72832df4a`, priority revision8. The selected
+conditional κ remains `.00310045`, with the five retained framework assumptions.
+Current selection, review and reproduction are resolved through
+`certificates/selected-result.json`; the selected cold replay was not run here.
+
+## Exact scope
+
+The input basis, retirement and cut are the three encodings1196,1199,1200 in
+the frozen predecessor contact list. The first cut is after13920 or13922 at
+frame1049. We allow a full invertible rational linear transform on **all** fields
+then sharing that frame:8 fields at13920,9 at13922. This includes the retired680,
+fresh continuation z, and the fields omitted from the predecessor's six-role
+search. The intermediate meeting is after15468, frame1075, roles479/527/z.
+The last meeting is after16651 on the source schedule, frame164, roles685/z,
+or after16652 on the checked retiming, with roles153/685/z.
+
+Here z has exploration label753. An emitted new public input would use index744
+and shift owned labels, as the inherited constructor does.
+
+At the first meeting we require a GL map on its resident fields. Every finite
+ADD and nonzero SCALE word on these fields has that property, including neutral,
+nonmonotone, long and non-dyadic words. At later meetings we grant arbitrary
+linear transforms, including singular maps. We also grant arbitrary rational
+terminal normalization within each actual final frame. Thus this is a **necessary
+relaxation of the specified ADD/SCALE construction domain**, not a sufficient
+constructible class or a physical implementation.
+
+Outside these meetings the literal source word is fixed. The sole alternative
+schedule is the predecessor's independently rechecked advancement of source
+MOVE16655 (`153,659→164`) to just after16649. All753 source columns, frames,
+owned lifetimes and bills agree. Other schedules, other cut bases, additional
+meetings, new native queries, and extra retained/transported owned fields are
+outside the obstruction. In particular, an effective singular first transform
+implemented with additional owned storage is not covered merely by calling it
+a local scalar transform. Its complete custody, restoration and costs need a
+new model.
+
+## Controllability certificate
+
+Let `a_r` be the row in first-meeting field r after its arbitrary invertible
+transform. The rows `a_r` are independent. Exact formal-row propagation through
+the source gives two independent combinations:
+
+| Encodings | X | L |
+| --- | --- | --- |
+|1196, cut13920|`a_z`|`a_z-a682+a683-a684-a686`|
+|1199/1200, cut13922|`a_z+a682`|`a_z+a683-a684-a686`|
+
+The two coefficient rows have rank2 before and after every invertible first
+transform. Full coefficient receipts are in `results/obstruction.json`.
+
+At the second meeting the actual continuation is `L+A`, while479 and527
+contain fixed source rows A and B. The first transform does not change A or B.
+We therefore grant the new continuation
+
+```
+Q = w L + a A + b B
+```
+
+with arbitrary rational w,a,b. Changed479/527 have no propagation into the last
+meeting or final output153. At that last meeting the two helper rows are
+
+```
+z   = C + Q
+685 = (C - Q)/2,       C = a685 + C0.
+```
+
+The row N in153 is unaffected by either earlier transform. The exact endpoint
+before the last transform is `t + X - L - A + Q`, where
+`t=e153+e41` is the required main target. Granting arbitrary last-meeting
+transformations further relaxes its possible endpoint to
+
+```
+t + X - L - A + k C + ell Q + g N.
+```
+
+On the original schedule153 is not a last-meeting source; granting N anyway
+only enlarges that model. All identities use the **changed** earlier rows,
+not stale baseline rows. Formal propagation checks every coefficient, and
+noncommuting literal dyadic fixtures independently check the three-stage identity.
+
+Output153 is the sole final field at frame164, so terminal normalization can
+only multiply its row: the displayed expression must equal `lambda*t`.
+The frozen rows have these successive private-coordinate probes:
+
+- N has coefficient−1 at input44; A, B, C0, t and first-meeting rows have none.
+  Thus g=0.
+- Input153 then forces lambda=1.
+- C0 has coefficient1/2 at input22; A, B, t and first-meeting rows have none.
+  Thus k=0.
+- Input479 forces `ell*a=1`; input527 forces `ell*b=0`.
+
+The remaining first-meeting equation is
+
+```
+X + (ell*w - 1) L = 0.
+```
+
+This contradicts the rank2 certificate for X,L. No length or coefficient search
+is needed. The checker establishes these identities for all three encodings
+on both schedules, using8 or9 independent first rows and5 independent external
+directions. The contradiction already uses one required main endpoint; dropping
+other independent-output constraints only makes the relaxation more favorable.
+
+## Why a broader span test was insufficient
+
+`relax.py` first grants independent correction tensors at each meeting, with
+source spaces enlarged by every earlier meeting that can reach it. Their ranks
+are8/10/11 or8/10/12 at cut13920, and9/11/12 or9/11/13 at cut13922. The exact
+linear membership equations are consistent in all six cases. Each retimed case
+even has a frozen rational witness with all independent final target rowspaces
+and full ranks in this overly permissive model. Such a tensor witness need not
+factor into temporally compatible local matrices. The source-bound identity
+above retains that missing coupling and rejects the physical ADD/SCALE domain.
+No witness from this relaxed model is counted as a construction.
+
+## Controls and invoice
+
+The emitted predecessor positive, helper708 on PR5713, passes the exact scalar,
+frame, ownership and target audit on all753 arbitrary columns. Its generic
+normalizer costs225,210 scalar units, versus the published source221,474;
+this is an inherited positive control, not a new improvement.
+
+Controls reject wrong chronology, inaccessible source153 at the intermediate
+meeting, a wrong frame, a legal-frame ADD corrupting the new independent target,
+and an illegal retiming across a role touch. A deliberately singular first map
+can satisfy output153, but loses independent input683 even when every final
+frame is pooled. This explains why discarding an independent target cannot
+evade the certificate. A separate control checks linear quotient reduction.
+
+`results/invoice.json` reconstructs the literal whole18-call source:66,348 paid
+jobs,12,976 productive fields and rank surplus760. The local paid bill is
+
+```
+2184 H1 + 459 H2 + 495 H3 + 92 H4 + 159 H5 + 22 H6 + 15 H7.
+```
+
+The proposed allowance remains `Delta paid=0` and
+`Delta targets=18(H4+H5-H9)`. It is favorable for every `0<t<1`, but **no new
+target credit is earned**. Source local scalar cost is221,474; the retiming
+adds zero. Input basis plus retirement would cost16/32/24 scalar units for
+the three cuts. No new local program, terminal normalizer, new-helper allocation
+and route schedule, cleanup or recursive bridge was implemented. Their unknown
+costs are not zero. No complete caller, native-phase, compiler, ordinary-admission,
+precision/tape, BIT compatibility or outer replay was run for a new construction,
+because no construction survives the necessary scalar test.
+
+## Reproduction
+
+The package is self-contained, uses the Python standard library, and preserves
+the predecessor files unchanged under `vendor/`. `SOURCES.json` pins their exact
+bytes and Git provenance. `MANIFEST.json` covers the complete package; receipt
+comparison is semantic JSON, without compressed-container regeneration.
+
+From this worktree root:
+
+```sh
+python3 -B research/p104-three-meeting-controllability/verify.py
+python3 -O -B research/p104-three-meeting-controllability/verify.py
+```
+
+Both commands replay the full six-case tensor relaxation, all six exact
+obstructions, the known constructive positive, rejection controls, changed-state
+fixtures and complete invoice. They require no Git, network or absolute
+predecessor path. `VALIDATION.json` records actual environments and results.
+This is exact rational source analysis, without formal-kernel or independent
+human acceptance.
+
+## Open next questions
+
+**Expansion decision: stop the three specified meetings.** Longer ADD/SCALE
+words, SCALEs and larger coefficients at these meetings cannot fix this class.
+This does not establish an obstruction for helper680 with arbitrary topology.
+
+The smallest changed-interface question is whether one additional actual
+contact can supply a second independent first-meeting combination, or can
+change the protected singleton153 endpoint. Begin by extracting its causal
+transfer and testing whether the rank2 contradiction still follows; do not
+restart a coefficient census. Any added paid bridge must be compared with the
+entire18(H4+H5−H9) target allowance before construction. Additional owned memory
+needs explicit lifetime, delivery, restore and erasure rules. No next construction
+round is justified solely by this handoff.
+
+Cross-call paid-answer reconstruction belongs to the separately assigned chat
+and was not investigated here. No helper440 cache search, helper695 fixed-route
+search or PR5440 native mismatch replay was performed.
+
+## Significance for researchers
+
+The added intermediate meeting passes crude availability tests but still cannot
+separate two independent temporal source combinations using this interface.
+The exact obstruction removes both coefficient and program-length limits from
+the earlier failure while keeping its physical source, cuts and final target
+fixed. A useful next question must change information delivery or the boundary,
+rather than enlarge the same scalar alphabet.
+
+Credit [flyingviper](https://github.com/flyingviper)'s PR5718,
+[Ali Romman](https://github.com/AliRomman)'s PR5713/5708 and all retained native,
+helper, controller, compiler and analytic authors in `vendor/NOTICE`.
+The local predecessor is commit `1f51164a1dba5b9cb7639d3b760d2a0660931f63`,
+`research/p104-joint-neutral-search`; its earlier information-reuse and
+multi-meeting reports are credited in `SOURCES.json`. Prepared for
+[zxv](https://github.com/zxv) with substantial OpenAI Codex assistance, without
+subagents. Elementary linear algebra and tensor propagation are standard.
+Apache-2.0. No public post, PR, merge, closure or selected-frontier edit was made.
diff --git a/research/p104-three-meeting-controllability/REFRESH.json b/research/p104-three-meeting-controllability/REFRESH.json
new file mode 100644
index 0000000000..4c13bf1813
--- /dev/null
+++ b/research/p104-three-meeting-controllability/REFRESH.json
@@ -0,0 +1,43 @@
+{
+  "canonical_main": "de5ec2e7a6074068452f45b1a191b5c72832df4a",
+  "priority_revision": 8,
+  "selected_kappa": "0.00310045",
+  "selected_record_sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5",
+  "live_overlap": {
+    "searched_at": "2026-10-26T15:57:28.560105+00:00",
+    "remote": {
+      "open_prs": {
+        "fetched_at": "2026-10-26T15:56:12.961969+00:00",
+        "complete_pagination": true,
+        "records": 310
+      },
+      "discussions": {
+        "fetched_at": "2026-10-26T15:57:28.160324+00:00",
+        "complete_pagination": true,
+        "records": 5104
+      }
+    },
+    "local": {
+      "head": "de5ec2e7a6074068452f45b1a191b5c72832df4a",
+      "records": 0,
+      "head_records": 7845,
+      "complete_head_inventory": false
+    },
+    "matches_total": 488,
+    "warnings": [
+      "local: 7845 HEAD note paths were not searched; inspect coverage.local.unsearched_head_paths in --json output and materialize relevant notes before treating a lack of matches as evidence."
+    ]
+  },
+  "live_relevant_threads": [
+    1163,
+    1166,
+    5125,
+    5600,
+    5645,
+    5748
+  ],
+  "coverage_limits": "No arbitrary historical diffs, unpublished work or complete local package inventory. No novelty claim.",
+  "final_fetch_main": "de5ec2e7a6074068452f45b1a191b5c72832df4a",
+  "source_pr_merged_at": "2026-10-26T15:22:41Z",
+  "first_checkout_failures": "Missing partial-clone blobs, then insufficient disk for full tree. Managed worktree created with an empty bootstrap tree and switched to the refreshed base with sparse paths. No shared working files changed."
+}
diff --git a/research/p104-three-meeting-controllability/SOURCES.json b/research/p104-three-meeting-controllability/SOURCES.json
new file mode 100644
index 0000000000..9d7fd3f19b
--- /dev/null
+++ b/research/p104-three-meeting-controllability/SOURCES.json
@@ -0,0 +1,108 @@
+{
+  "repository": "https://github.com/CrocSwap/integer-mult-bounds",
+  "canonical_main": "de5ec2e7a6074068452f45b1a191b5c72832df4a",
+  "priority_revision": 8,
+  "selected_kappa": "0.00310045",
+  "source_pr": 5718,
+  "source_head": "a1534ac45401c9a9c80c07aa65c89e00e33594f8",
+  "source_claim": "0.00311024570",
+  "source_status": "merged/archive; not selected",
+  "word5718_sha256": "cff7196f8b168c4ebf8227185eed98387b66ec5db0179108adfea4045775cc31",
+  "vendored_predecessor_files": [
+    {
+      "path": "vendor/NOTICE",
+      "sha256": "c474479a870ae53ae0bcb84f656c2b222380395bbee767ee15e5f9c5b4ce7e79",
+      "git_blob": "f83cecccf587acfa313c8259c0bf6db05d60b52d",
+      "predecessor_commit": "1f51164a1dba5b9cb7639d3b760d2a0660931f63",
+      "repository_path": "research/p104-joint-neutral-search/NOTICE"
+    },
+    {
+      "path": "vendor/README.md",
+      "sha256": "8d069d3f2406f2cb0ff9d58f8144c6cf1e28da3ec03741d657c37a117f45d6eb",
+      "git_blob": "a63e2437b0013301e23cc78d2d38c644e3aecde3",
+      "predecessor_commit": "1f51164a1dba5b9cb7639d3b760d2a0660931f63",
+      "repository_path": "research/p104-joint-neutral-search/README.md"
+    },
+    {
+      "path": "vendor/SOURCES.json",
+      "sha256": "e6f72350b2d31e655f178a80d3dfb197b06ecf2d81b9e84172b7481c0846e2f1",
+      "git_blob": "5437d22e1593ab20001a16e768843a29e6259a5d",
+      "predecessor_commit": "1f51164a1dba5b9cb7639d3b760d2a0660931f63",
+      "repository_path": "research/p104-joint-neutral-search/SOURCES.json"
+    },
+    {
+      "path": "vendor/emit.py",
+      "sha256": "3cef5005f56f0f391d09175f75698cbdf835a61f0ca7f8439659189ff7bb8ca3",
+      "git_blob": "2be45cff8127c327d0771e02b55cdeafa342f727",
+      "predecessor_commit": "1f51164a1dba5b9cb7639d3b760d2a0660931f63",
+      "repository_path": "research/p104-joint-neutral-search/emit.py"
+    },
+    {
+      "path": "vendor/inputs/controller5718.json",
+      "sha256": "a84f6bbd547379597464e56c420cc665f96bc43a9a1351eed4b7cd0fce3cc4b9",
+      "git_blob": "cc539db709cf7a6c42872c4380902736ad453af3",
+      "predecessor_commit": "1f51164a1dba5b9cb7639d3b760d2a0660931f63",
+      "repository_path": "research/p104-joint-neutral-search/inputs/controller5718.json"
+    },
+    {
+      "path": "vendor/inputs/word5713.json.gz",
+      "sha256": "9fd67dd89ed24a644257cd9aef06934ed4c6fbe0441804684a968868f2ef66a8",
+      "git_blob": "45f6c10bf8a0ad6eb5f6714377a464e274db7dbd",
+      "predecessor_commit": "1f51164a1dba5b9cb7639d3b760d2a0660931f63",
+      "repository_path": "research/p104-joint-neutral-search/inputs/word5713.json.gz"
+    },
+    {
+      "path": "vendor/inputs/word5718.json.gz",
+      "sha256": "cff7196f8b168c4ebf8227185eed98387b66ec5db0179108adfea4045775cc31",
+      "git_blob": "4db015aca34ea957dd8b3b4d7ae4fa12b89934f8",
+      "predecessor_commit": "1f51164a1dba5b9cb7639d3b760d2a0660931f63",
+      "repository_path": "research/p104-joint-neutral-search/inputs/word5718.json.gz"
+    },
+    {
+      "path": "vendor/invoice.py",
+      "sha256": "d9171336935023fb94d310d782ea00cec1ac60963e137b8766e39d690cbbcca9",
+      "git_blob": "d3ee7c701cc230273fa6b458fd080308346c2f1f",
+      "predecessor_commit": "1f51164a1dba5b9cb7639d3b760d2a0660931f63",
+      "repository_path": "research/p104-joint-neutral-search/invoice.py"
+    },
+    {
+      "path": "vendor/joint.py",
+      "sha256": "dd9d055d78f27c1dc663c86efe2d41a8914636bdc47917ebff92882f738831fc",
+      "git_blob": "67ac8368df7e424ef3a491582d2fa45d401fbf32",
+      "predecessor_commit": "1f51164a1dba5b9cb7639d3b760d2a0660931f63",
+      "repository_path": "research/p104-joint-neutral-search/joint.py"
+    },
+    {
+      "path": "vendor/preflight.py",
+      "sha256": "e19cce00813896373826a6ee8ccb3e16f86c95d47bcba5f3b06c90cc2729a8ca",
+      "git_blob": "28341deed5b9ded395774316336e4b2a474fca9e",
+      "predecessor_commit": "1f51164a1dba5b9cb7639d3b760d2a0660931f63",
+      "repository_path": "research/p104-joint-neutral-search/preflight.py"
+    },
+    {
+      "path": "vendor/results/contacts5713.json",
+      "sha256": "3347f3e4f372189f9a06cb754afdaa6bb812b3a5dc7f1d9d0c16cc00485a73f1",
+      "git_blob": "8c031317e774de596216430dfe66d9df63c191cb",
+      "predecessor_commit": "1f51164a1dba5b9cb7639d3b760d2a0660931f63",
+      "repository_path": "research/p104-joint-neutral-search/results/contacts5713.json"
+    },
+    {
+      "path": "vendor/results/contacts5718.json",
+      "sha256": "b799253336add810d04d39512a0641dc4416145de0b121040c8defe6d517cf19",
+      "git_blob": "ee80a3a3b7828e11fcce12b49c5766623d55e564",
+      "predecessor_commit": "1f51164a1dba5b9cb7639d3b760d2a0660931f63",
+      "repository_path": "research/p104-joint-neutral-search/results/contacts5718.json"
+    },
+    {
+      "path": "vendor/search.py",
+      "sha256": "b94cf3464e67e20ed3b57b28fe355f5a9d35c01c6abb84dabf5ad0c5180face8",
+      "git_blob": "5d38c521324dbfa761e1e21ae04e1db8cb232458",
+      "predecessor_commit": "1f51164a1dba5b9cb7639d3b760d2a0660931f63",
+      "repository_path": "research/p104-joint-neutral-search/search.py"
+    }
+  ],
+  "earlier_reports": [
+    "/private/tmp/integer-mult-information-reuse/research/information-reuse-screen/README.md",
+    "/private/tmp/integer-mult-information-reuse/research/p104-multimeeting-repair/README.md"
+  ]
+}
diff --git a/research/p104-three-meeting-controllability/VALIDATION.json b/research/p104-three-meeting-controllability/VALIDATION.json
new file mode 100644
index 0000000000..9e02fc9b3f
--- /dev/null
+++ b/research/p104-three-meeting-controllability/VALIDATION.json
@@ -0,0 +1,81 @@
+{
+  "status": "PASS",
+  "python": "3.14.5 (main, May 10 2026, 10:21:34) [Clang 21.0.0 (clang-2100.0.123.102)]",
+  "executable": "/opt/homebrew/opt/python@3.14/bin/python3.14",
+  "platform": "macOS-26.5.1-arm64-arm-64bit-Mach-O",
+  "runs": [
+    {
+      "command": [
+        "/opt/homebrew/opt/python@3.14/bin/python3.14",
+        "-B",
+        "/Users/temp/.codex/worktrees/helper680-three-meeting/integer-mult-bounds/research/p104-three-meeting-controllability/verify.py"
+      ],
+      "seconds": 12.629082917002961,
+      "result": {
+        "constructive_positive": true,
+        "exact_obstructions": 6,
+        "new_kappa": false,
+        "paid_jobs": 66348,
+        "productive_fields": 12976,
+        "rejection_controls": true,
+        "relaxation_cases": 6,
+        "semantic_sha256": "50db363dbaca657f2e43f4f00edd6ef10d667769da9b92bbad30d24d414a955c",
+        "source_columns": 753,
+        "source_corruption_rejected": true,
+        "status": "PASS"
+      }
+    },
+    {
+      "command": [
+        "/opt/homebrew/opt/python@3.14/bin/python3.14",
+        "-O",
+        "-B",
+        "/Users/temp/.codex/worktrees/helper680-three-meeting/integer-mult-bounds/research/p104-three-meeting-controllability/verify.py"
+      ],
+      "seconds": 13.481343541992828,
+      "result": {
+        "constructive_positive": true,
+        "exact_obstructions": 6,
+        "new_kappa": false,
+        "paid_jobs": 66348,
+        "productive_fields": 12976,
+        "rejection_controls": true,
+        "relaxation_cases": 6,
+        "semantic_sha256": "50db363dbaca657f2e43f4f00edd6ef10d667769da9b92bbad30d24d414a955c",
+        "source_columns": 753,
+        "source_corruption_rejected": true,
+        "status": "PASS"
+      }
+    },
+    {
+      "command": [
+        "python3",
+        "-O",
+        "-B",
+        "<Git-free copy>/verify.py"
+      ],
+      "seconds": 13.034390249988064,
+      "result": {
+        "constructive_positive": true,
+        "exact_obstructions": 6,
+        "new_kappa": false,
+        "paid_jobs": 66348,
+        "productive_fields": 12976,
+        "rejection_controls": true,
+        "relaxation_cases": 6,
+        "semantic_sha256": "50db363dbaca657f2e43f4f00edd6ef10d667769da9b92bbad30d24d414a955c",
+        "source_columns": 753,
+        "source_corruption_rejected": true,
+        "status": "PASS"
+      }
+    }
+  ],
+  "scope": "Exact scalar/source-bound obstruction; inherited native assumptions remain; no native/caller/compiler/outer/Lean/Docker replay",
+  "framework_assumptions": [
+    "native_all_columns",
+    "owned_erasure",
+    "compiler",
+    "precision_tape",
+    "analytic_recovery"
+  ]
+}
diff --git a/research/p104-three-meeting-controllability/controls.py b/research/p104-three-meeting-controllability/controls.py
new file mode 100644
index 0000000000..b8d2c35b2c
--- /dev/null
+++ b/research/p104-three-meeting-controllability/controls.py
@@ -0,0 +1,78 @@
+"""Constructive positive and semantic rejection controls for the exact model."""
+from obstruction import *
+
+def reject(fn,label,contains=None):
+ try:fn()
+ except ValueError as e:
+  need(contains is None or contains in str(e),'wrong rejection: '+label+': '+str(e))
+  return dict(control=label,reason=str(e))
+ raise ValueError('mutation accepted: '+label)
+
+def run():
+ w,c,ts,fs,snap,roles=case(1196,True)
+ source=audit(load('word5718.json.gz'));retimed=audit(w)
+ need(source==retimed,'route retiming preserves all endpoints, costs, frames and ownership')
+ old=load('word5713.json.gz')
+ pc=next(c for c in json.loads((HERE/'results/contacts5713.json').read_text())['cuts']
+         if c['cut']==14330 and c['pivot']==708 and c['a']=={'708':'1','154':'1/2'})
+ for k in ('a','c','h0','d','beta'):pc[k]=unrow(pc[k])
+ positive=construct(old,pc);pos=audit(positive)
+ need(pos['paid']==source['paid'] and pos['targets']==source['targets'],'known positive published recursive profile')
+ rejected=[]
+ rejected.append(reject(lambda:relaxation(w,c,[ts[1],ts[0],ts[2]],fs,snap,roles),'wrong meeting chronology','chronology'))
+ badroles=deepcopy(roles);badroles[1].append(153)
+ rejected.append(reject(lambda:relaxation(w,c,ts,fs,snap,badroles),'inaccessible source at intermediate meeting','source/frame'))
+ badframes=list(fs);badframes[1]=164
+ rejected.append(reject(lambda:relaxation(w,c,ts,badframes,snap,roles),'wrong intermediate frame','source/frame'))
+ bad=deepcopy(positive);bad['program'].append(['ADD',old['public'],682,'1',127])
+ rejected.append(reject(lambda:audit(bad),'independent new target changed at a legal frame','endpoint '+str(old['public'])))
+ rejected.append(reject(lambda:retime(load('word5718.json.gz'),16655,15829),'route retiming across a write','role touch'))
+ # A singular first map can fool the singleton-output condition. Its dropped
+ # original e683 cannot be recovered anywhere, even after ignoring all frames.
+ rows=[dict(z) for z in snap[ts[0]][0]]
+ rows[683]=sumrows(rows,{682:Q(1),684:Q(1),686:Q(1)})
+ localrank=len(basis(rows[r] for r in roles[0]));need(localrank==len(roles[0])-1,'singular first map')
+ walk(w,c,rows,ts[0],ts[1]);rows[753]=dict(rows[479])
+ walk(w,c,rows,ts[1],len(w['program'])-1)
+ desired=endpoints(w,c)[1]
+ need(rows[153]==desired[153],'rank-loss fake passes singleton153')
+ missing=project({683:Q(1)},basis(rows));need(bool(missing),'rank-loss fake loses independent target683')
+ # Nonlinear temporal cross terms must use the actually changed second state.
+ literal=[dict(z) for z in snap[ts[0]][0]]
+ add(literal[753],literal[685],Q(1))
+ walk(w,c,literal,ts[0],ts[1]);changed=dict(literal[753]);stale=snap[ts[1]][0][753]
+ need(changed!=stale,'second source really changed')
+ want=dict(stale);add(want,snap[ts[0]][0][685],Q(1))
+ need(changed==want,'changed temporal source exact all coefficients')
+ need(changed!=stale,'stale-state rejection')
+ # Canonical quotient must remain linear even with a missing low pivot.
+ qb=basis([{2:Q(1),3:Q(1)}]);a={1:Q(1),2:Q(1)};b={1:Q(-1)}
+ lhs=dict(a);add(lhs,b);lhs=project(lhs,qb);rhs=project(a,qb);add(rhs,project(b,qb))
+ need(lhs==rhs,'linear quotient control')
+ # Literal changed-state replay independently checks the universal endpoint
+ # identity with several noncommuting dyadic shears at each actual meeting.
+ imports=[]
+ for idx in (1196,1199,1200):
+  ww,cc,tt,ff,ss,rr=case(idx,True);cert=certify(idx,True)
+  literal=[dict(z) for z in ss[tt[0]][0]]
+  for a,b in zip(rr[0],rr[0][1:]):add(literal[a],literal[b],Q(-1,2))
+  X=sumrows(literal,cert['X']);L=sumrows(literal,cert['L'])
+  walk(ww,cc,literal,tt[0],tt[1]);A=dict(literal[479])
+  add(literal[753],literal[479],Q(2));add(literal[527],literal[753],Q(-1,2));add(literal[753],literal[527],Q(1))
+  Qrow=dict(literal[753]);walk(ww,cc,literal,tt[1],tt[2])
+  before=[dict(z) for z in literal]
+  add(literal[153],literal[685],Q(1));add(literal[685],literal[753],Q(-1,2));add(literal[753],literal[153],Q(2))
+  predicted=dict(cert['target153']);add(predicted,X);add(predicted,L,-1);add(predicted,A,-1);add(predicted,Qrow)
+  for r,d in responses(ww,680,tt[2],rr[2]).items():
+   delta=dict(literal[r]);add(delta,before[r],-1);add(predicted,delta,d.get(153,Q(0)))
+  walk(ww,cc,literal,tt[2],len(ww['program'])-1)
+  need(predicted==literal[153],'three-meeting literal changed-state identity')
+  imports.append(idx)
+ return dict(status='PASS',source=source,retimed=retimed,known_positive=pos,
+             rejection_controls=rejected,rank_loss_control=dict(first_rank=localrank,
+             output153_passes=True,independent_target683_missing=missing),
+             changed_second_source_all_coefficients=True,linear_quotient=True,
+             literal_three_meeting_identity_all_columns=imports)
+
+if __name__=='__main__':
+ out=run();(ROOT/'results/controls.json').write_text(json.dumps(fmt(out),indent=2)+'\n');print(json.dumps(fmt(out)))
diff --git a/research/p104-three-meeting-controllability/invoice.py b/research/p104-three-meeting-controllability/invoice.py
new file mode 100644
index 0000000000..b3926dc84d
--- /dev/null
+++ b/research/p104-three-meeting-controllability/invoice.py
@@ -0,0 +1,27 @@
+"""Exact complete baseline invoice; unrealized target allowance is not earned."""
+from relax import *
+import importlib.util
+spec=importlib.util.spec_from_file_location('predecessor_invoice',ROOT/'vendor/invoice.py')
+prior=importlib.util.module_from_spec(spec);spec.loader.exec_module(prior)
+
+def run():
+ w=load('word5718.json.gz');local=audit(w)
+ controller=json.loads((HERE/'inputs/controller5718.json').read_text())
+ whole=prior.whole(local,controller)
+ need(sum(whole['paid'].values())==66348 and sum(whole['targets'].values())==12976,'complete source inventory')
+ surplus=sum(r*n for r,n in whole['targets'].items())-sum(r*n for r,n in whole['paid'].items())
+ need(surplus==760,'rank surplus')
+ return dict(source_local=local,complete_source=whole,rank_surplus=surplus,local_calls=18,
+             prospective_delta_paid={},prospective_delta_targets={4:18,5:18,9:-18},
+             prospective_signed_delta='18*(9^t-4^t-5^t)<0 for 0<t<1',
+             earned_delta_targets={},kappa_status='NO_NEW_KAPPA',selected_kappa='0.00310045',
+             source_claim='0.00311024570; PR5718 archived/merged, not selected',
+             ordinary=dict(source_local_scalar=local['scalar'],retiming_added=0,
+             input_basis_and_retirement={1196:16,1199:32,1200:24},
+             new_local_program='none: exact obstruction',terminal_normalization='unimplemented; not priced at zero',
+             new_helper_routes_allocation_cleanup='unimplemented; not priced at zero',
+             additional_recursive_bridge='none constructed; not priced at zero',
+             compiler_caller_outer='unrun: no complete local survivor'))
+
+if __name__=='__main__':
+ out=run();(ROOT/'results/invoice.json').write_text(json.dumps(fmt(out),indent=2)+'\n');print(json.dumps(fmt(out)))
diff --git a/research/p104-three-meeting-controllability/obstruction.py b/research/p104-three-meeting-controllability/obstruction.py
new file mode 100644
index 0000000000..f34875034a
--- /dev/null
+++ b/research/p104-three-meeting-controllability/obstruction.py
@@ -0,0 +1,89 @@
+"""Source-bound three-meeting obstruction, exact rational arithmetic only.
+
+The first meeting allows any GL_m(Q) map on EVERY public field at its frame.
+Later meetings are further relaxed to arbitrary linear transforms. The final
+normalizer may be arbitrary rational within each actual final frame.
+"""
+from relax import *
+
+def sumrows(rows,weights):
+ out={}
+ for r,q in weights.items():add(out,rows[r],q)
+ return out
+
+def walk(w,c,rows,start,stop):
+ for e in w['program'][start+1:stop+1]:apply(rows,renamed(e,c['pivot'],len(rows)-1))
+
+def certify(index,retimed):
+ w,c,ts,fs,snap,roles=case(index,retimed);t1,t2,t3=ts
+ R1=snap[t1][0];S=basis(R1[r] for r in roles[0])
+ need(len(S)==len(roles[0]),'independent first-meeting source rows')
+ # Independent formal rows represent arbitrary transformed first-meeting rows.
+ formal={r:{2000+r:Q(1)} for r in roles[0]}
+ rows=[dict(z) for z in R1]
+ for r,z in formal.items():rows[r]=dict(z)
+ walk(w,c,rows,t1,t2)
+ A=dict(rows[479]);B=dict(rows[527])
+ L=responses(w,680,t1,roles[0],t2)
+ l={r:v.get(753,Q(0)) for r,v in L.items() if v.get(753)}
+ lrow=sumrows(formal,l);want=dict(A);add(want,lrow)
+ need(rows[753]==want,'second continuation = A+L')
+ need(not (set(A)|set(B))&set().union(*(set(v) for v in formal.values())),'A/B independent of first transform')
+ # A replaced second continuation Q carries the CHANGED first-meeting state.
+ # Other second destinations have no transfer into the third meeting or output153.
+ d2=responses(w,680,t2,roles[1]);mid2=responses(w,680,t2,roles[1],t3)
+ for r in (479,527):
+  need(153 not in d2[r] and not set(mid2[r])&set(roles[2]),'unused second outputs cannot repair153')
+ rows[753]={3000:Q(1)}
+ walk(w,c,rows,t2,t3)
+ C=dict(rows[753]);add(C,{3000:Q(1)},-1)
+ want=scale(C,Q(1,2));add(want,{3000:Q(1)},Q(-1,2))
+ need(rows[685]==want,'third rows = (C-Q)/2, C+Q')
+ N=dict(rows[153]);need(not set(N)&set().union(*(set(v) for v in formal.values())),'third153 unaffected by first transform')
+ cweights={r:C.get(2000+r,Q(0)) for r in roles[0] if C.get(2000+r)}
+ C0=dict(C);add(C0,sumrows(formal,cweights),-1)
+ need(cweights=={685:Q(1)},'C = changed first685 + C0')
+ # Propagate the formal rows to the endpoint, retaining Q as a free symbol.
+ walk(w,c,rows,t3,len(w['program'])-1)
+ target=endpoints(w,c)[1][153]
+ end=rows[153];x={r:end.get(2000+r,Q(0))+l.get(r,Q(0)) for r in roles[0]}
+ x={r:q for r,q in x.items() if q}
+ X=sumrows(formal,x)
+ want=dict(target);add(want,X);add(want,lrow,-1);add(want,A,-1);add(want,{3000:Q(1)})
+ need(end==want,'exact final153 = target+X-L-A+Q')
+ d3=responses(w,680,t3,roles[2])
+ # Any later transform affects153 by a linear combination of N,C,Q.
+ # The relaxed model grants all three coefficients independently.
+ need(all(not set(snap[t3][0][r])&{680} for r in roles[2]),'third source sanity')
+ need(terminal_groups(w,c)[164]==[153],'actual final153 singleton')
+ # t,S,A,B,C0,N are independent. More specifically, N has private44,
+ # C0 private22, A private479, B private527, target private153.
+ external=[target,A,B,C0,N]
+ ranks=[len(S)]
+ sb=dict(S)
+ for v in external:
+  sb=basis(list(sb.values())+[v]);ranks.append(len(sb))
+ need(ranks==list(range(len(S),len(S)+6)),'external independent directions')
+ need(len(basis([x,l]))==2,'X and L independent coefficient combinations')
+ # These linear functionals successively force g=0, lambda=1, k=0,
+ # l*a=1, l*b=0 in target+X-L-A+k*C+l*(w*L+a*A+b*B)+g*N=lambda*target.
+ probes={44:dict(N=N.get(44,0),C0=C0.get(44,0),A=A.get(44,0),B=B.get(44,0),target=target.get(44,0)),
+         153:dict(N=N.get(153,0),C0=C0.get(153,0),A=A.get(153,0),B=B.get(153,0),target=target.get(153,0)),
+         22:dict(C0=C0.get(22,0),A=A.get(22,0),B=B.get(22,0)),
+         479:dict(A=A.get(479,0),B=B.get(479,0)),527:dict(A=A.get(527,0),B=B.get(527,0))}
+ need(probes[44]==dict(N=Q(-1),C0=0,A=0,B=0,target=0),'private44 probe')
+ need(probes[153]['target']==1 and all(probes[153][k]==0 for k in ('C0','A','B')),'target153 probe')
+ need(probes[22]==dict(C0=Q(1,2),A=0,B=0),'private22 probe')
+ need(probes[479]==dict(A=Q(1),B=0) and probes[527]==dict(A=0,B=Q(1)),'A/B probes')
+ # Then X+(l*w-1)L=0 contradicts independence under any GL_m first map.
+ return dict(index=index,retimed=retimed,sites=ts,frames=fs,roles=roles,first_rank=len(S),X=x,L=l,
+             coefficient_pair_rank=2,external_ranks=ranks,A=A,B=B,C0=C0,N=N,target153=target,probes=probes,
+             endpoint_identity='target153 + X - L - A + k*C + ell*Q + g*N; Q=w*L+a*A+b*B; C=first685+C0',
+             forced_equations=['g=0','lambda=1','k=0','ell*a=1','ell*b=0','X+(ell*w-1)*L=0'],
+             status='NO_GL_FIRST_MEETING_SOLUTION',all_input_coefficients_checked=True)
+
+def main():
+ out=[certify(i,r) for i in (1196,1199,1200) for r in (False,True)]
+ (ROOT/'results/obstruction.json').write_text(json.dumps(fmt(out),indent=2)+'\n')
+ print(json.dumps(fmt([{k:v for k,v in r.items() if k in ('index','retimed','sites','first_rank','X','L','coefficient_pair_rank','external_ranks','status')} for r in out])),flush=True)
+if __name__=='__main__':main()
diff --git a/research/p104-three-meeting-controllability/relax.py b/research/p104-three-meeting-controllability/relax.py
new file mode 100644
index 0000000000..56c8247cae
--- /dev/null
+++ b/research/p104-three-meeting-controllability/relax.py
@@ -0,0 +1,131 @@
+"""Exact, necessary (not sufficient) causal tensor relaxation over Q.
+
+At meeting j, each local destination gets an independent arbitrary injection
+from a source space Vj. Vj contains its baseline rows and the source spaces of
+earlier meetings with a nonzero literal transfer into this meeting. This grants
+more memory and independent control than an actual invertible local program.
+Endpoint rows must belong to their desired final frame's target rowspace.
+We also test rank after quotienting unchanged same-frame output rows.
+"""
+from pathlib import Path
+import sys
+ROOT=Path(__file__).resolve().parent
+sys.path.insert(0,str(ROOT/'vendor'))
+from emit import *
+
+def project(row,b):
+ """Linear canonical quotient; unlike early-exit membership remainder."""
+ z=dict(row)
+ for p,v in sorted(b.items()):
+  if p in z:add(z,v,-z[p])
+ return z
+
+def case(index=1196,retimed=True):
+ w=load('word5718.json.gz')
+ if retimed:w=retime(w,16655,16649)
+ c=json.loads((HERE/'results/contacts5718.json').read_text())['cuts'][index]
+ for k in ('a','c','h0','d','beta'):c[k]=unrow(c[k])
+ sites=[c['cut'],15468,16652 if retimed else 16651]
+ frames=[1049,1075,164]
+ snap=raw(w,c,set(sites))
+ roles=[[r for r,f in enumerate(snap[t][1]) if f==frame] for t,frame in zip(sites,frames)]
+ return w,c,sites,frames,snap,roles
+
+def equations_solve(equations,n):
+ """Return affine solution x_j = constant + sum a_jk free_k, or failure."""
+ b={}
+ for row,rhs in equations:
+  z=dict(row);v=rhs
+  while z:
+   p=min(z)
+   if p not in b:
+    a=z[p];z=scale(z,1/a);v/=a;b[p]=(z,v);break
+   a=z[p];add(z,b[p][0],-a);v-=a*b[p][1]
+  if not z and v:return None
+ free=sorted(set(range(n))-set(b));aff={j:{j:Q(1)} for j in free};const={j:Q(0) for j in free}
+ for p,(z,rhs) in sorted(b.items(),reverse=True):
+  a={};v=rhs
+  for j,q in z.items():
+   if j==p:continue
+   add(a,aff[j],-q);v-=q*const[j]
+  aff[p]=a;const[p]=v
+ return const,aff,free
+
+def relaxation(w,c,sites,frames,snap,roles):
+ need(sites==sorted(sites) and len(set(sites))==len(sites),'chronology')
+ for t,f,rs in zip(sites,frames,roles):
+  need(all(snap[t][1][r]==f for r in rs),'meeting source/frame')
+ base,desired,*_=endpoints(w,c);groups=terminal_groups(w,c)
+ outframe={r:f for f,rs in groups.items() for r in rs}
+ Vs=[];Ds=[];gen=[];edges=[]
+ for j,(t,rs) in enumerate(zip(sites,roles)):
+  src=[dict(snap[t][0][r]) for r in rs]
+  for i in range(j):
+   tr=responses(w,c['pivot'],sites[i],roles[i],t)
+   if any(set(tr[d])&set(rs) for d in roles[i]):
+    src.extend(Vs[i]);edges.append([i,j])
+  V=list(basis(src).values());Vs.append(V)
+  D=responses(w,c['pivot'],t,rs);Ds.append(D)
+  for d in rs:
+   for v in V:gen.append((j,d,D[d],v))
+ affected=sorted(set(c['d'])|{len(base)-1}|set().union(*(set(d) for _,_,d,_ in gen)))
+ desired_b={f:basis(desired[r] for r in rs) for f,rs in groups.items()}
+ eq=defaultdict(dict);rhs={}
+ for r in affected:
+  if r not in outframe:continue
+  f=outframe[r];z=project(base[r],desired_b[f])
+  for col,v in z.items():rhs[r,col]=-v
+ for k,(_,_,d,v) in enumerate(gen):
+  for r,a in d.items():
+   if r not in outframe:continue
+   z=project(v,desired_b[outframe[r]])
+   for col,b in z.items():eq[r,col][k]=a*b
+ allkeys=sorted(set(eq)|set(rhs));sol=equations_solve([(eq[k],rhs.get(k,Q(0))) for k in allkeys],len(gen))
+ result=dict(source_ranks=list(map(len,Vs)),source_edges=edges,roles=roles,sites=sites,frames=frames,generators=len(gen),equations=len(allkeys),consistent=sol is not None,affected=affected)
+ if sol is None:return result,None
+ const,aff,free=sol;rows={r:dict(base[r]) for r in affected};coeff={r:{} for r in affected}
+ for key in allkeys:
+  need(sum(q*const[j] for j,q in eq[key].items())==rhs.get(key,Q(0)),'affine particular solution')
+  for k in free:need(sum(q*aff[j].get(k,0) for j,q in eq[key].items())==0,'affine nullspace')
+ for k,(_,_,d,v) in enumerate(gen):
+  for r,a in d.items():
+   add(rows[r],v,a*const[k])
+   for j,b in aff[k].items():
+    coeff[r].setdefault(j,{})
+    add(coeff[r][j],v,a*b)
+ ranks=[]
+ for f,rs in groups.items():
+  changed=[r for r in rs if r in affected]
+  if not changed:continue
+  fixed=basis(desired[r] for r in rs if r not in affected)
+  available=[project(rows[r],fixed) for r in changed]
+  available += [project(v,fixed) for r in changed for v in coeff[r].values()]
+  rk=len(basis(available))
+  ranks.append(dict(frame=f,roles=changed,required=len(changed),favorable_union_rank=rk,rank_obstruction=rk<len(changed)))
+ result.update(free_parameters=len(free),rank_tests=ranks)
+ # A point here is only a witness for this overly permissive tensor model.
+ # It is NOT a compatible sequence of physical local matrices.
+ for seed in range(1,4):
+  values={j:Q((j*seed+seed)%11-5) for j in free}
+  sample={r:dict(rows[r]) for r in affected}
+  for r in affected:
+   for j,v in coeff[r].items():add(sample[r],v,values[j])
+  ok=True
+  for f,rs in groups.items():
+   vals=[sample.get(r,base[r]) for r in rs]
+   if len(basis(vals))!=len(rs) or any(project(v,desired_b[f]) for v in vals):ok=False;break
+  if ok:
+   result['relaxed_full_independent_target_witness']=dict(seed=seed,free_values=values)
+   break
+ else:result['relaxed_full_independent_target_witness']=None
+ return result,(gen,sol,rows,coeff)
+
+def main():
+ out=[]
+ for idx in (1196,1199,1200):
+  for rt in (False,True):
+   w,c,sites,frames,snap,roles=case(idx,rt)
+   r,_=relaxation(w,c,sites,frames,snap,roles);r.update(index=idx,retimed=rt)
+   out.append(r);print(json.dumps(fmt(r)),flush=True)
+ (ROOT/'results/relaxation.json').write_text(json.dumps(fmt(out),indent=2)+'\n')
+if __name__=='__main__':main()
diff --git a/research/p104-three-meeting-controllability/results/controls.json b/research/p104-three-meeting-controllability/results/controls.json
new file mode 100644
index 0000000000..0774d7f92c
--- /dev/null
+++ b/research/p104-three-meeting-controllability/results/controls.json
@@ -0,0 +1,111 @@
+{
+  "status": "PASS",
+  "source": {
+    "columns": 753,
+    "paid": {
+      "1": 2184,
+      "2": 459,
+      "5": 159,
+      "4": 92,
+      "3": 495,
+      "7": 15,
+      "6": 22
+    },
+    "targets": {
+      "9": 411,
+      "2": 5,
+      "8": 15,
+      "4": 91,
+      "5": 6,
+      "7": 6,
+      "1": 2
+    },
+    "scalar": 221474,
+    "owned_peak": 2,
+    "owned_lifetimes": 11
+  },
+  "retimed": {
+    "columns": 753,
+    "paid": {
+      "1": 2184,
+      "2": 459,
+      "5": 159,
+      "4": 92,
+      "3": 495,
+      "7": 15,
+      "6": 22
+    },
+    "targets": {
+      "9": 411,
+      "2": 5,
+      "8": 15,
+      "4": 91,
+      "5": 6,
+      "7": 6,
+      "1": 2
+    },
+    "scalar": 221474,
+    "owned_peak": 2,
+    "owned_lifetimes": 11
+  },
+  "known_positive": {
+    "columns": 753,
+    "paid": {
+      "1": 2184,
+      "2": 459,
+      "5": 159,
+      "4": 92,
+      "3": 495,
+      "7": 15,
+      "6": 22
+    },
+    "targets": {
+      "9": 411,
+      "2": 5,
+      "8": 15,
+      "4": 91,
+      "5": 6,
+      "7": 6,
+      "1": 2
+    },
+    "scalar": 225210,
+    "owned_peak": 2,
+    "owned_lifetimes": 11
+  },
+  "rejection_controls": [
+    {
+      "control": "wrong meeting chronology",
+      "reason": "chronology"
+    },
+    {
+      "control": "inaccessible source at intermediate meeting",
+      "reason": "meeting source/frame"
+    },
+    {
+      "control": "wrong intermediate frame",
+      "reason": "meeting source/frame"
+    },
+    {
+      "control": "independent new target changed at a legal frame",
+      "reason": "endpoint 743"
+    },
+    {
+      "control": "route retiming across a write",
+      "reason": "retiming crosses a role touch"
+    }
+  ],
+  "rank_loss_control": {
+    "first_rank": 7,
+    "output153_passes": true,
+    "independent_target683_missing": {
+      "683": "1"
+    }
+  },
+  "changed_second_source_all_coefficients": true,
+  "linear_quotient": true,
+  "literal_three_meeting_identity_all_columns": [
+    1196,
+    1199,
+    1200
+  ]
+}
diff --git a/research/p104-three-meeting-controllability/results/invoice.json b/research/p104-three-meeting-controllability/results/invoice.json
new file mode 100644
index 0000000000..0367736147
--- /dev/null
+++ b/research/p104-three-meeting-controllability/results/invoice.json
@@ -0,0 +1,90 @@
+{
+  "source_local": {
+    "columns": 753,
+    "paid": {
+      "1": 2184,
+      "2": 459,
+      "5": 159,
+      "4": 92,
+      "3": 495,
+      "7": 15,
+      "6": 22
+    },
+    "targets": {
+      "9": 411,
+      "2": 5,
+      "8": 15,
+      "4": 91,
+      "5": 6,
+      "7": 6,
+      "1": 2
+    },
+    "scalar": 221474,
+    "owned_peak": 2,
+    "owned_lifetimes": 11
+  },
+  "complete_source": {
+    "paid": {
+      "1": 40872,
+      "2": 8262,
+      "3": 8910,
+      "4": 1656,
+      "5": 2862,
+      "6": 396,
+      "7": 270,
+      "16": 416,
+      "24": 416,
+      "32": 416,
+      "40": 416,
+      "48": 416,
+      "56": 416,
+      "64": 416,
+      "72": 208
+    },
+    "targets": {
+      "1": 36,
+      "2": 90,
+      "4": 1638,
+      "5": 108,
+      "7": 108,
+      "8": 270,
+      "9": 7398,
+      "17": 416,
+      "25": 416,
+      "33": 416,
+      "41": 416,
+      "49": 416,
+      "57": 416,
+      "65": 416,
+      "73": 208,
+      "145": 208
+    }
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+  "selected_kappa": "0.00310045",
+  "source_claim": "0.00311024570; PR5718 archived/merged, not selected",
+  "ordinary": {
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+    "retiming_added": 0,
+    "input_basis_and_retirement": {
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+    "new_local_program": "none: exact obstruction",
+    "terminal_normalization": "unimplemented; not priced at zero",
+    "new_helper_routes_allocation_cleanup": "unimplemented; not priced at zero",
+    "additional_recursive_bridge": "none constructed; not priced at zero",
+    "compiler_caller_outer": "unrun: no complete local survivor"
+  }
+}
diff --git a/research/p104-three-meeting-controllability/results/obstruction.json b/research/p104-three-meeting-controllability/results/obstruction.json
new file mode 100644
index 0000000000..a2a52b70c1
--- /dev/null
+++ b/research/p104-three-meeting-controllability/results/obstruction.json
@@ -0,0 +1,1947 @@
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+        "roles": [
+          127
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 164,
+        "roles": [
+          153
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 165,
+        "roles": [
+          154
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 175,
+        "roles": [
+          164
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 226,
+        "roles": [
+          218
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 1049,
+        "roles": [
+          680
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      }
+    ],
+    "relaxed_full_independent_target_witness": null,
+    "index": 1199,
+    "retimed": false
+  },
+  {
+    "source_ranks": [
+      9,
+      11,
+      13
+    ],
+    "source_edges": [
+      [
+        0,
+        1
+      ],
+      [
+        0,
+        2
+      ],
+      [
+        1,
+        2
+      ]
+    ],
+    "roles": [
+      [
+        679,
+        680,
+        681,
+        682,
+        683,
+        684,
+        685,
+        686,
+        753
+      ],
+      [
+        479,
+        527,
+        753
+      ],
+      [
+        153,
+        685,
+        753
+      ]
+    ],
+    "sites": [
+      13922,
+      15468,
+      16652
+    ],
+    "frames": [
+      1049,
+      1075,
+      164
+    ],
+    "generators": 153,
+    "equations": 288,
+    "consistent": true,
+    "affected": [
+      126,
+      127,
+      153,
+      154,
+      164,
+      218,
+      479,
+      527,
+      679,
+      680,
+      681,
+      682,
+      683,
+      684,
+      685,
+      686,
+      753
+    ],
+    "free_parameters": 94,
+    "rank_tests": [
+      {
+        "frame": 127,
+        "roles": [
+          126,
+          479,
+          527,
+          679,
+          681,
+          682,
+          683,
+          684,
+          685,
+          686,
+          753
+        ],
+        "required": 11,
+        "favorable_union_rank": 11,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 141,
+        "roles": [
+          127
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 164,
+        "roles": [
+          153
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 165,
+        "roles": [
+          154
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 175,
+        "roles": [
+          164
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 226,
+        "roles": [
+          218
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 1049,
+        "roles": [
+          680
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      }
+    ],
+    "relaxed_full_independent_target_witness": {
+      "seed": 1,
+      "free_values": {
+        "10": "-5",
+        "36": "-1",
+        "38": "1",
+        "39": "2",
+        "40": "3",
+        "41": "4",
+        "42": "5",
+        "43": "-5",
+        "44": "-4",
+        "45": "-3",
+        "47": "-1",
+        "48": "0",
+        "49": "1",
+        "50": "2",
+        "51": "3",
+        "52": "4",
+        "53": "5",
+        "54": "-5",
+        "56": "-3",
+        "57": "-2",
+        "58": "-1",
+        "59": "0",
+        "60": "1",
+        "61": "2",
+        "62": "3",
+        "63": "4",
+        "65": "-5",
+        "66": "-4",
+        "67": "-3",
+        "68": "-2",
+        "69": "-1",
+        "70": "0",
+        "71": "1",
+        "72": "2",
+        "74": "4",
+        "75": "5",
+        "76": "-5",
+        "77": "-4",
+        "78": "-3",
+        "79": "-2",
+        "80": "-1",
+        "92": "0",
+        "93": "1",
+        "94": "2",
+        "95": "3",
+        "97": "5",
+        "98": "-5",
+        "99": "-4",
+        "100": "-3",
+        "101": "-2",
+        "102": "-1",
+        "105": "2",
+        "106": "3",
+        "107": "4",
+        "108": "5",
+        "109": "-5",
+        "110": "-4",
+        "111": "-3",
+        "112": "-2",
+        "113": "-1",
+        "116": "2",
+        "117": "3",
+        "119": "5",
+        "120": "-5",
+        "121": "-4",
+        "122": "-3",
+        "123": "-2",
+        "124": "-1",
+        "125": "0",
+        "126": "1",
+        "128": "3",
+        "129": "4",
+        "130": "5",
+        "131": "-5",
+        "132": "-4",
+        "133": "-3",
+        "134": "-2",
+        "135": "-1",
+        "136": "0",
+        "137": "1",
+        "138": "2",
+        "139": "3",
+        "141": "5",
+        "142": "-5",
+        "143": "-4",
+        "144": "-3",
+        "145": "-2",
+        "146": "-1",
+        "147": "0",
+        "148": "1",
+        "149": "2",
+        "150": "3",
+        "151": "4",
+        "152": "5"
+      }
+    },
+    "index": 1199,
+    "retimed": true
+  },
+  {
+    "source_ranks": [
+      9,
+      11,
+      12
+    ],
+    "source_edges": [
+      [
+        0,
+        1
+      ],
+      [
+        0,
+        2
+      ],
+      [
+        1,
+        2
+      ]
+    ],
+    "roles": [
+      [
+        679,
+        680,
+        681,
+        682,
+        683,
+        684,
+        685,
+        686,
+        753
+      ],
+      [
+        479,
+        527,
+        753
+      ],
+      [
+        685,
+        753
+      ]
+    ],
+    "sites": [
+      13922,
+      15468,
+      16651
+    ],
+    "frames": [
+      1049,
+      1075,
+      164
+    ],
+    "generators": 138,
+    "equations": 136,
+    "consistent": true,
+    "affected": [
+      126,
+      127,
+      153,
+      154,
+      164,
+      218,
+      479,
+      527,
+      679,
+      680,
+      681,
+      682,
+      683,
+      684,
+      685,
+      686,
+      753
+    ],
+    "free_parameters": 83,
+    "rank_tests": [
+      {
+        "frame": 127,
+        "roles": [
+          126,
+          479,
+          527,
+          679,
+          681,
+          682,
+          683,
+          684,
+          685,
+          686,
+          753
+        ],
+        "required": 11,
+        "favorable_union_rank": 11,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 141,
+        "roles": [
+          127
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 164,
+        "roles": [
+          153
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 165,
+        "roles": [
+          154
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 175,
+        "roles": [
+          164
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 226,
+        "roles": [
+          218
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 1049,
+        "roles": [
+          680
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      }
+    ],
+    "relaxed_full_independent_target_witness": null,
+    "index": 1200,
+    "retimed": false
+  },
+  {
+    "source_ranks": [
+      9,
+      11,
+      13
+    ],
+    "source_edges": [
+      [
+        0,
+        1
+      ],
+      [
+        0,
+        2
+      ],
+      [
+        1,
+        2
+      ]
+    ],
+    "roles": [
+      [
+        679,
+        680,
+        681,
+        682,
+        683,
+        684,
+        685,
+        686,
+        753
+      ],
+      [
+        479,
+        527,
+        753
+      ],
+      [
+        153,
+        685,
+        753
+      ]
+    ],
+    "sites": [
+      13922,
+      15468,
+      16652
+    ],
+    "frames": [
+      1049,
+      1075,
+      164
+    ],
+    "generators": 153,
+    "equations": 288,
+    "consistent": true,
+    "affected": [
+      126,
+      127,
+      153,
+      154,
+      164,
+      218,
+      479,
+      527,
+      679,
+      680,
+      681,
+      682,
+      683,
+      684,
+      685,
+      686,
+      753
+    ],
+    "free_parameters": 94,
+    "rank_tests": [
+      {
+        "frame": 127,
+        "roles": [
+          126,
+          479,
+          527,
+          679,
+          681,
+          682,
+          683,
+          684,
+          685,
+          686,
+          753
+        ],
+        "required": 11,
+        "favorable_union_rank": 11,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 141,
+        "roles": [
+          127
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 164,
+        "roles": [
+          153
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 165,
+        "roles": [
+          154
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 175,
+        "roles": [
+          164
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 226,
+        "roles": [
+          218
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      },
+      {
+        "frame": 1049,
+        "roles": [
+          680
+        ],
+        "required": 1,
+        "favorable_union_rank": 1,
+        "rank_obstruction": false
+      }
+    ],
+    "relaxed_full_independent_target_witness": {
+      "seed": 1,
+      "free_values": {
+        "10": "-5",
+        "36": "-1",
+        "38": "1",
+        "39": "2",
+        "40": "3",
+        "41": "4",
+        "42": "5",
+        "43": "-5",
+        "44": "-4",
+        "45": "-3",
+        "47": "-1",
+        "48": "0",
+        "49": "1",
+        "50": "2",
+        "51": "3",
+        "52": "4",
+        "53": "5",
+        "54": "-5",
+        "56": "-3",
+        "57": "-2",
+        "58": "-1",
+        "59": "0",
+        "60": "1",
+        "61": "2",
+        "62": "3",
+        "63": "4",
+        "65": "-5",
+        "66": "-4",
+        "67": "-3",
+        "68": "-2",
+        "69": "-1",
+        "70": "0",
+        "71": "1",
+        "72": "2",
+        "74": "4",
+        "75": "5",
+        "76": "-5",
+        "77": "-4",
+        "78": "-3",
+        "79": "-2",
+        "80": "-1",
+        "92": "0",
+        "93": "1",
+        "94": "2",
+        "95": "3",
+        "97": "5",
+        "98": "-5",
+        "99": "-4",
+        "100": "-3",
+        "101": "-2",
+        "102": "-1",
+        "105": "2",
+        "106": "3",
+        "107": "4",
+        "108": "5",
+        "109": "-5",
+        "110": "-4",
+        "111": "-3",
+        "112": "-2",
+        "113": "-1",
+        "116": "2",
+        "117": "3",
+        "119": "5",
+        "120": "-5",
+        "121": "-4",
+        "122": "-3",
+        "123": "-2",
+        "124": "-1",
+        "125": "0",
+        "126": "1",
+        "128": "3",
+        "129": "4",
+        "130": "5",
+        "131": "-5",
+        "132": "-4",
+        "133": "-3",
+        "134": "-2",
+        "135": "-1",
+        "136": "0",
+        "137": "1",
+        "138": "2",
+        "139": "3",
+        "141": "5",
+        "142": "-5",
+        "143": "-4",
+        "144": "-3",
+        "145": "-2",
+        "146": "-1",
+        "147": "0",
+        "148": "1",
+        "149": "2",
+        "150": "3",
+        "151": "4",
+        "152": "5"
+      }
+    },
+    "index": 1200,
+    "retimed": true
+  }
+]
diff --git a/research/p104-three-meeting-controllability/vendor/NOTICE b/research/p104-three-meeting-controllability/vendor/NOTICE
new file mode 100644
index 0000000000..f83cecccf5
--- /dev/null
+++ b/research/p104-three-meeting-controllability/vendor/NOTICE
@@ -0,0 +1,47 @@
+Four paid interior public-basis changes.
+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.
+No subagents.
+
+The following exact notice is retained from PR5660.
+
+New helper-subspace construction, proof and replay:
+Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+The same assistant performed the construction and author-side checks.
+
+Retained contributions:
+flyingviper: PR5605 shared relay, PR5612 delayed relay, and the PR5608/PR5613
+relay/split compositions.
+Scratch-net: PR5606 prepared-helper identities and target debit.
+Pierre-Loic Doulcet (hexapode): PR5565 commuting-contact construction, used as the exact source.
+Ali Romman: PR5602 fixed boundary relations, PR5601 three-contact frame
+change, PR5580 contact step,
+and PR5544/5545 complete P104 caller.
+Joel Pulikkan (GamingPuzzled): PR5569 priced helper handoff.
+DreamingOfClouds: PR5561 free helper endpoints and PR5568 search tools.
+thu-nmrc: PR5551 contact improvements.
+Gareth Davidson (bitplane): PR2305 source composition.
+David Arias: PR2152 coalesced P104 word.
+Cinna Davis: PR2219 private reuse and the controller lineage.
+Jacob Alan Sussman: productive mixed-target recursion.
+zxv and Cao Yifan: exact intervals, compiler and native/pricing lineage.
+GamingPuzzled: PR5472 successor handoff, a predecessor to the split concept.
+The retained source notices preserve earlier geometry, BIT and analytic credit.
+
+The elementary rank-one basis identity is not claimed as a new general
+linear-algebra theorem. The contribution is its explicit independent-target
+use on this P104 word and the complete conditional kappa improvement.
+
+New contribution: Ali Romman, with substantial OpenAI Codex assistance.
+The four-gate source-version rewrite composes zxv PR5643 and Ali Romman PR5644.
+The A2 method retains Chris R/Clear1nsight PR3998 and ToikY PR4019 credit.
+The compensated triangle method retains Cinna Davis PR4692 credit.
+No subagents were used for this contribution. Apache-2.0.
+
+Concurrent PR5650 by zxv publishes the PR5643/PR5644 composition. PR5651 by
+Ali Romman corroborates it. This package credits that released composition
+and contributes the further four-gate placement.
+
+New work: distributed scalar updates on an unobserved public field interval, the exact witness and complete conditional price. Prepared for Ali Romman with substantial OpenAI Codex assistance. No subagents. Apache-2.0. The source archive retains all predecessor notices.
+
+Two-boundary main-assisted helper split and early cleanup: flyingviper with substantial
+OpenAI Codex assistance, including independent AI review agents. Apache-2.0.
diff --git a/research/p104-three-meeting-controllability/vendor/README.md b/research/p104-three-meeting-controllability/vendor/README.md
new file mode 100644
index 0000000000..a63e2437b0
--- /dev/null
+++ b/research/p104-three-meeting-controllability/vendor/README.md
@@ -0,0 +1,200 @@
+# A legal new P104 contact does not finish the bounded helper680 split
+
+**Local-only checked experiment; no new κ and no universal obstruction.**
+Canonical main was freshly fetched as `df0137efd35e11b4445734bf612bdd4c7ebc330c`,
+with priority revision7 and selected conditional κ `.00310045` unchanged.
+The source is pending [PR5718](https://github.com/CrocSwap/integer-mult-bounds/pull/5718)
+at `a1534ac45401c9a9c80c07aa65c89e00e33594f8`, claiming `.00311024570`.
+Its inherited native, ownership, compiler, precision/tape and analytic assumptions
+remain. This package does not independently admit that claim.
+
+The experiment changes an actual route schedule: source event16655,
+`MOVE 153,659,164`, is advanced to just after event16649. No intervening
+instruction touches153. This creates a contact between153,685 and the fresh
+continuation of680 before680 leaves frame164. Exact replay on every one of753
+arbitrary source input columns verifies the retimed word, all frames, owned
+lifetimes, target inventory and unchanged complete local paid/scalar bill.
+This is a source-preserving change in transport timing, not a new frame itinerary.
+
+## Checked result
+
+1. **The candidate generator discovers the known positive.** It examines both
+   departure and arrival groups after every role's MOVE. On PR5713 it finds
+   the PR5718 cut at14330, pivot708, `708 +=154/2`, without being given that cut.
+   There are1,880 compatible cut encodings on PR5713 and1,871 on PR5718;
+   1,554 and1,546, respectively, are triggered by another role's MOVE.
+   Counts include distinct encodings and repeated equivalent cut states.
+2. **An exact emitted positive control passes.** The generic constructor
+   implements the discovered708 split using literal dyadic ADD/SCALE operations,
+   every arbitrary input, legal frames and owned INIT/COPY/CLEAR rules. It has
+   the published paid/target profile. Its deliberately unsimplified terminal
+   normalizer costs225,210 local scalar units, versus221,474 in the published
+   PR5718 word. This is a recovered predecessor construction, not a new gain.
+3. **Endpoint tests precede expansion.** All1,867 tested successor encodings
+   fail cleanup using terminal frame groups alone; four440 encodings were
+   excluded rather than revisited. A favorable temporal-span relaxation on
+   all123 non-440 cuts with at most three endpoint-response fields rejects
+   one:695 at13644. It grants unlimited frame-local memory and allows every
+   MOVE to carry the entire available source-frame span. The required output159
+   remains outside the span, with exact remainder `2 e700 + 2 e701` in the
+   receipt's elimination basis. This is a scoped rational span failure, not a
+   claimed universal separating functional. The other122 survive this relaxation.
+4. **The three-ADD domain has no survivor.** Three concrete680 cut encodings,
+   at13920 and13922, were tested on the original and retimed schedules. Each
+   permits zero, one or two ADDs at the cut and zero or one at the later meeting.
+   All4,887,150 literal program pairs fail. Two cuts at13922 are triggered by
+   another helper's MOVE. The first steps are unrestricted: temporary errors,
+   reads from the retired field and movement of corrections between roles are
+   allowed. There is no greedy requirement to remove an error immediately.
+5. **The four-ADD extension also fails.** For the13920 cut on the retimed word,
+   zero, one or two ADDs at each of the two meetings give43,430,473 literal
+   program pairs. All fail an exact necessary condition on main output153.
+   The second meeting has949 distinct full three-field response matrices and276
+   distinct effects on153; these are exact deduplications of all1,333 second
+   sequences. The driver evaluates30,919,369 distinct-matrix pairs. Six exact
+   rational input-coordinate probes already reject every pair, so no modular
+   discovery or unpriced rational inverse is counted as an implementation.
+
+An initial unsorted larger temporal-span run was interrupted without a result.
+Only the completed123-cut run is evidence. Three exploratory shorter runs
+(4,477,17,329 and49,321 cases) are retained separately; they are not added to
+an allegedly disjoint coverage total. The four-ADD domain overlaps the
+three-ADD cases. A failed candidate does not receive target credit.
+
+## Exact bounded model
+
+The prefix/suffix generator uses exact `Fraction` arithmetic, all public and
+arbitrary dirty-owned entry columns, source frame containment and the actual
+scalar word. It tests cuts `a=e_p+q e_s`. If purity determines q, that exact
+value must be dyadic; when both rows are pure, the finite menu is
+`q in {-2,-1,-1/2,1/2,1,2}`, together with the unmodified pivot.
+It requires `c_p=beta_p=c beta=1`, with every nonzero coordinate of c and beta
+at the pivot's initial frame. `beta=E^-1 S e_p` includes the actual main shear.
+These sufficient conditions do not exhaust all helper boundary bases.
+
+The three selected cut encodings are:
+
+| Index | Source cut | Trigger | Cut operation | Input functional c |
+| --- | ---: | ---: | --- | --- |
+|1196|13920|680|identity|`e680`|
+|1199|13922|681|`680 -=679`|`e680-e679`|
+|1200|13922|681|`680 +=682`|`e680`|
+
+Each has suffix response `e126+e153+e680` and split ranks5+4.
+The first meeting uses exactly roles`[680,753,679,682,685,686]` at frame1049.
+Roles outside that list retain their literal original operations. Here753
+is the exploration label for the new independent input; emitted words shift
+owned labels and use public index744 instead. On the original schedule the
+second meeting is after16651 at frame164, with roles`[685,753]`.
+On the retimed schedule it is after16652, with roles`[153,685,753]`.
+Every ADD has distinct source/destination and coefficient from the six-value
+menu above. Zero-length sequences and cancelling/inverse sequences are included.
+The four-ADD domain uses the1196 cut and the retimed second meeting.
+
+The suffix response to a first ADD is propagated through the literal word.
+Every second source uses the state changed by all first ADDs. An exact
+low-rank endpoint update is checked against a separate literal suffix walk
+on every coefficient. Terminal normalization is granted favorably whenever
+rational row spaces match. A proposed survivor would still require an emitted
+dyadic-unit factorization, full endpoint and ownership replay, ordinary cost,
+native/caller compatibility and complete pricing. No new candidate reaches
+that stage here.
+
+Resource bounds are explicit: at most six first-meeting roles, three second-
+meeting roles, two ADDs per meeting and six possible coefficients. The three-
+ADD driver caps each run at1,250,000 program pairs; all six completed. The
+four-ADD driver caps at50,000,000 matrix pairs and completes below that cap.
+It is a finite alphabet result. Longer programs, a third meeting, SCALEs in
+intermediate programs, multi-source cut bases and genuinely different native
+routes remain outside it.
+
+## Complete signed invoice and ordinary work
+
+`results/invoice.json` reconstructs the whole18-call source invoice from the
+checked local bill and pinned literal controller. It has66,348 paid jobs,
+12,976 productive fields and rank surplus760. The source local paid bill is
+
+```
+2184 H1 + 459 H2 + 495 H3 + 92 H4 + 159 H5 + 22 H6 + 15 H7.
+```
+
+The source local helper target bill is
+
+```
+2 H1 + 5 H2 + 91 H4 + 6 H5 + 6 H7 + 15 H8 + 411 H9.
+```
+
+The unrealized680 proposal has `Delta paid=0`,
+`Delta targets=18(H4+H5-H9)` and therefore
+`Delta(paid-targets)=18(H9-H4-H5)<0` for every`0<t<1`, `Hr=r^t`.
+Both the retired old input and the new arbitrary input are credited only
+if their complete targets are preserved. The route retiming adds zero paid
+jobs and zero scalar operations; source scalar work remains221,474.
+Input basis plus retirement costs16,32 and24 scalar units for the three cuts;
+four menu ADDs cost at most40 additional units. Terminal normalization,
+new-helper allocation/routes/cleanup and compiler/outer obligations are
+**unknown and unrun**, because every candidate fails before those modules exist.
+They are not priced at zero. The favorable signed invoice is an allowance,
+not an emitted construction or a κ claim.
+
+## Reproduction and evidence
+
+Python3.14.5 standard library on macOS; source bytes and Git blobs are in
+`SOURCES.json`. No Lean, Docker, full native, compiler, outer or selected cold
+replay was run. The source and retimed scalar/frame checks cover all753
+arbitrary input columns, owned peak2 and11 owned lifetimes. The emitted known
+positive covers753 columns after adding one fresh public input to PR5713.
+The complete serial `--full` replay passed. Normal and optimized controls and
+the complete four-ADD receipts agree. Controls reject an illegal retiming across a write, a wrong source frame,
+a non-dyadic ADD, unearned old H9 credit, a missing retirement and wrong-order
+multi-meeting operations. A separate two-meeting fixture and real-P104
+changed-state formula check pass.
+
+From the repository root:
+
+```sh
+python3 -B research/p104-joint-neutral-search/verify.py
+python3 -O -B research/p104-joint-neutral-search/controls.py
+python3 -B research/p104-joint-neutral-search/verify.py --full
+```
+
+The quick verifier checks frozen receipt integrity, regenerates both contact
+sets, and runs the constructive/negative controls and complete invoice.
+`--full` additionally reruns the1867-cut terminal screen,123-cut temporal
+relaxation, six declared three-ADD searches and the four-ADD search, serially.
+Expect roughly8 minutes for full replay on the recorded host. Search timings
+are diagnostic and excluded from semantic receipt comparisons.
+
+## Open next questions
+
+- A different transport contact is still needed for695 before more scalar
+  search: the favorable fixed-itinerary span already fails. This package does
+  not revisit helper440 or the known PR5440 native-letter mismatch.
+- For680, first test a favorable controllability model with a **third** actual
+  meeting, after15468 at frame1075 with479/527/continuation680. That introduces
+  source rows absent from the two tested meetings. Preserve the same complete
+  invoice and reject by exact availability before enumerating longer words.
+  This is a distinct finite question; no success is forecast.
+- The optional cross-call paid-answer span discriminator was not run. It still
+  needs versioned physical query maps at caller events0 and3, actual stage
+  routes and native operators, and retention/read/transport/cleanup charges.
+  Input-row continuity and distinct query identities do not answer it. A new
+  session should bind one such output rather than enlarge a duplicate census.
+
+## Significance for researchers
+
+The predecessor generator really did omit useful contact classes: the new
+one discovers the published positive at another role's MOVE. A legal retiming
+also creates a new contact at no recursive charge. Neither fact implies a
+new independent split. This experiment explicitly explores temporary correction
+redistribution and still fails in its two-meeting domain, while preserving
+longer and physically different routes as open questions.
+
+Credit [flyingviper](https://github.com/flyingviper)'s PR5718,
+[Ali Romman](https://github.com/aliromman)'s PR5713/5708 and the complete
+predecessor P104/native/controller/compiler lineage retained in`NOTICE`.
+The frozen earlier information-reuse and multi-meeting investigations are
+listed in`SOURCES.json` and remain unchanged. Prepared for
+[zxv](https://github.com/zxv) with substantial OpenAI Codex assistance; no
+subagents. The linear algebra and temporal identities are standard.
+Apache-2.0. No public post, PR, merge or selected-frontier change was made.
diff --git a/research/p104-three-meeting-controllability/vendor/SOURCES.json b/research/p104-three-meeting-controllability/vendor/SOURCES.json
new file mode 100644
index 0000000000..5437d22e15
--- /dev/null
+++ b/research/p104-three-meeting-controllability/vendor/SOURCES.json
@@ -0,0 +1,41 @@
+{
+  "repository": "https://github.com/CrocSwap/integer-mult-bounds",
+  "canonical_main": "df0137efd35e11b4445734bf612bdd4c7ebc330c",
+  "priority_revision": 7,
+  "selected_kappa": ".00310045",
+  "pending_source_kappa": ".00311024570",
+  "source_status": "pending author claim; no selected frontier update",
+  "sources": [
+    {
+      "path": "inputs/word5713.json.gz",
+      "sha256": "9fd67dd89ed24a644257cd9aef06934ed4c6fbe0441804684a968868f2ef66a8",
+      "commit": "a5348f7143f95fe0046b92b96172e30763c7d731",
+      "repository_path": "research/p104-temporal-updates/WORD.json.gz",
+      "git_blob": "45f6c10bf8a0ad6eb5f6714377a464e274db7dbd"
+    },
+    {
+      "path": "inputs/word5718.json.gz",
+      "sha256": "cff7196f8b168c4ebf8227185eed98387b66ec5db0179108adfea4045775cc31",
+      "commit": "a1534ac45401c9a9c80c07aa65c89e00e33594f8",
+      "repository_path": "research/p104-two-boundary-helper-split/WORD.json.gz",
+      "git_blob": "4db015aca34ea957dd8b3b4d7ae4fa12b89934f8"
+    },
+    {
+      "path": "inputs/controller5718.json",
+      "sha256": "a84f6bbd547379597464e56c420cc665f96bc43a9a1351eed4b7cd0fce3cc4b9",
+      "commit": "a1534ac45401c9a9c80c07aa65c89e00e33594f8",
+      "repository_path": "research/p104-productive-controller/CONTROLLER.json",
+      "git_blob": "cc539db709cf7a6c42872c4380902736ad453af3"
+    }
+  ],
+  "environment": {
+    "python": "3.14.5 (main, May 10 2026, 10:21:34) [Clang 21.0.0 (clang-2100.0.123.102)]",
+    "platform": "macOS-26.5.1-arm64-arm-64bit-Mach-O"
+  },
+  "predecessor_local_reports": [
+    "/private/tmp/integer-mult-information-reuse/research/information-reuse-screen/README.md",
+    "/private/tmp/integer-mult-information-reuse/research/p104-multimeeting-repair/README.md",
+    "/tmp/luna-inforeuse-controller/cross_local_input_ledger.md",
+    "/tmp/luna-inforeuse-bit/FINDING.md"
+  ]
+}
diff --git a/research/p104-three-meeting-controllability/vendor/emit.py b/research/p104-three-meeting-controllability/vendor/emit.py
new file mode 100644
index 0000000000..2be45cff81
--- /dev/null
+++ b/research/p104-three-meeting-controllability/vendor/emit.py
@@ -0,0 +1,114 @@
+"""Emit and independently replay dyadic words; no modular implementation claims."""
+from joint import *
+
+def scalar_cost(e):
+ if e[0]=='MOVE':return 0
+ if e[0] in ('INIT','CLEAR'):return 2
+ q=Q(e[-2]);a,b=abs(q.numerator),q.denominator
+ return 2*(abs(a.bit_length()-b.bit_length())+(q<0)) if e[0]=='SCALE' else 2*(2+a.bit_length()+a.bit_count()+b.bit_length()-1)
+
+def audit(w):
+ n=w['public'];N=n+w['owned_fields'];rows=[{r:Q(1)} for r in range(N)];ch=w['initial']+[None]*w['owned_fields'];fs=[span(x) for x in w['frames']];active=set();unwritten=set();paid=Counter();peak=life=0
+ for i,e in enumerate(w['program']):
+  op,r=e[:2];need(0<=r<N,'role index')
+  if op=='INIT':
+   need(r>=n and ch[r] is None,'owned INIT');ch[r]=e[2];active.add(r);unwritten.add(r);peak=max(peak,len(active));life+=1
+  elif op=='CLEAR':need(r in active and ch[r]==e[2],'owned CLEAR');ch[r]=None;active.remove(r);unwritten.discard(r)
+  elif op=='MOVE':
+   need(ch[r]==e[2] and e[4]==(r in active),'MOVE source/ownership')
+   need(fs[e[3]]<fs[e[2]] if e[4] else fs[e[2]]<fs[e[3]],'MOVE containment')
+   ch[r]=e[3];paid[abs(len(w['frames'][e[2]])-len(w['frames'][e[3]]))]+=1
+  else:
+   need(ch[r]==e[-1],'scalar destination frame');q=Q(e[-2]);a,b=abs(q.numerator),q.denominator
+   need(q and b&(b-1)==0 and abs(q)+1<2**16,'dyadic scalar coefficient')
+   if op=='SCALE':need(a&(a-1)==0,'SCALE dyadic unit')
+   else:
+    need(e[2]!=r and 0<=e[2]<N and ch[e[2]]==e[-1],'scalar source frame')
+    if op=='COPY':need(r in unwritten,'owned first COPY')
+   unwritten.discard(r)
+  apply(rows,e)
+ need(not active and ch[:n]==w['final'],'final frame/ownership')
+ for r,row in enumerate(rows):
+  target={r:Q(1)} if r<n else {}
+  if r-112 in w['live']:target[r-112]=Q(1)
+  need(row==target,'endpoint '+str(r))
+ main=set(w['live'])|{r+112 for r in w['live']}
+ targets=Counter(len(w['frames'][w['final'][r]])-len(w['frames'][w['initial'][r]]) for r in range(n) if r not in main)
+ return dict(columns=N,paid=dict(paid),targets=dict(targets),scalar=sum(map(scalar_cost,w['program'])),owned_peak=peak,owned_lifetimes=life)
+
+def normalize_group(rows,desired,roles,frame):
+ # Reduce actual and desired matrices by identical canonical row elimination.
+ # If inversions are not dyadic units the emitter stops, even if Q rowspaces agree.
+ def reduce(vals):
+  vals={r:dict(vals[r]) for r in roles};ops=[];used=[]
+  for col in sorted(set().union(*(set(v) for v in vals.values()))):
+   possible=[r for r in roles if r not in used and vals[r].get(col)]
+   if not possible:continue
+   r=possible[0];q=vals[r][col]
+   if q!=1:
+    inv=1/q;need(abs(inv.numerator)&(abs(inv.numerator)-1)==0 and inv.denominator&(inv.denominator-1)==0,'non-unit pivot')
+    vals[r]=scale(vals[r],inv);ops.append(['SCALE',r,str(inv),frame])
+   for s in roles:
+    if s!=r and vals[s].get(col):
+     q=-vals[s][col];need(q.denominator&(q.denominator-1)==0,'non-dyadic elimination')
+     add(vals[s],vals[r],q);ops.append(['ADD',s,r,str(q),frame])
+   used.append(r)
+  return vals,used,ops
+ va,ua,oa=reduce(rows);vd,ud,od=reduce(desired)
+ # Matching pivot rows may require permutation. Emit swaps as three ADDs and a sign.
+ need(len(ua)==len(roles)==len(ud),'full group rank')
+ for src,dst in zip(ua,ud):
+  if src==dst:continue
+  # In current normalized va, move row with same canonical functional to target slot.
+  holder=next(r for r in roles if va[r]==vd[dst])
+  if holder==dst:continue
+  oa.extend([['ADD',dst,holder,'1',frame],['ADD',holder,dst,'-1',frame],['ADD',dst,holder,'1',frame],['SCALE',holder,'-1',frame]])
+  va[dst],va[holder]=va[holder],va[dst]
+ need(va==vd,'canonical same-rowspace')
+ inv=[]
+ for e in reversed(od):
+  x=list(e);x[-2]=str(1/Q(e[-2]) if e[0]=='SCALE' else -Q(e[-2]));inv.append(x)
+ return oa+inv
+
+def construct(w,c,extra=()):
+ n=w['public'];N=n+w['owned_fields'];p=c['pivot'];out=deepcopy(w);out['public']=n+1;out['initial']=w['initial']+[c['frame']];out['final']=w['final']+[w['final'][p]];out['final'][p]=c['frame']
+ k0=dict(c['c']);add(k0,{p:Q(1)},-1);program=[];u=w['initial'][p]
+ for r,q in sorted(k0.items()):program.append(['ADD',p,r,str(-q),u])
+ for r,q in sorted(c['beta'].items()):
+  if r!=p:program.append(['ADD',r,p,str(q),u])
+ def ren(r,i):
+  if r>=n:return r+1
+  if i>c['cut'] and r==p:return n
+  return r
+ extras=defaultdict(list)
+ for i,e in extra:extras[i].append(e)
+ for i,orig in enumerate(w['program']):
+  e=list(orig);e[1]=ren(e[1],i)
+  if e[0] in ('ADD','COPY'):e[2]=ren(e[2],i)
+  program.append(e)
+  if i==c['cut']:
+   for r,q in c['a'].items():
+    if r!=p:program.append(['ADD',p,r,str(q),c['frame']])
+  for e0 in extras[i]:
+   e=list(e0);e[1]=n if e[1]==N else e[1]+(e[1]>=n)
+   if e[0] in ('ADD','COPY'):e[2]=n if e[2]==N else e[2]+(e[2]>=n)
+   program.append(e)
+ out['program']=program
+ rows=[{r:Q(1)} for r in range(N+1)]
+ for e in program:apply(rows,e)
+ desired=[{r:Q(1)} if r<n+1 else {} for r in range(N+1)]
+ for r in w['live']:desired[r+112][r]=Q(1)
+ groups=defaultdict(list)
+ for r,f in enumerate(out['final']):groups[f].append(r)
+ for f,roles in groups.items():
+  if any(rows[r]!=desired[r] for r in roles):
+   ops=normalize_group(rows,desired,roles,f);program.extend(ops)
+   for e in ops:apply(rows,e)
+ out['schema']='p104-joint-neutral-search/1';return out
+
+def main():
+ w=load('word5713.json.gz');cuts=json.loads((HERE/'results/contacts5713.json').read_text())['cuts'];c=next(c for c in cuts if c['cut']==14330 and c['pivot']==708 and c['a']=={'708':'1','154':'1/2'})
+ for k in ('a','c','h0','d','beta'):c[k]=unrow(c[k])
+ out=construct(w,c);receipt=audit(out);receipt.update(source_sha256=PINS['word5713.json.gz'],cut=c['cut'],pivot=c['pivot'],status='positive_control_emitted_exact_dyadic_word')
+ (HERE/'results/positive-word.json.gz').write_bytes(gzip.compress(json.dumps(out,sort_keys=True,separators=(',',':')).encode(),mtime=0));(HERE/'results/positive.json').write_text(json.dumps(fmt(receipt),indent=2)+'\n');print(receipt)
+if __name__=='__main__':main()
diff --git a/research/p104-three-meeting-controllability/vendor/inputs/controller5718.json b/research/p104-three-meeting-controllability/vendor/inputs/controller5718.json
new file mode 100644
index 0000000000..cc539db709
--- /dev/null
+++ b/research/p104-three-meeting-controllability/vendor/inputs/controller5718.json
@@ -0,0 +1,5480 @@
+{
+  "ambient_rank": 145,
+  "boundaries": {
+    "left": [
+      [
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+    [
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+    ],
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+    ],
+    [
+      "SIGNED_SWAP",
+      2,
+      3
+    ],
+    [
+      "SIGNED_SWAP",
+      4,
+      5
+    ],
+    [
+      "SIGNED_SWAP",
+      6,
+      7
+    ],
+    [
+      "SIGNED_SWAP",
+      8,
+      9
+    ],
+    [
+      "SIGNED_SWAP",
+      10,
+      11
+    ],
+    [
+      "SIGNED_SWAP",
+      12,
+      13
+    ],
+    [
+      "SIGNED_SWAP",
+      14,
+      15
+    ],
+    [
+      "SIGNED_SWAP",
+      16,
+      17
+    ],
+    [
+      "SIGNED_SWAP",
+      18,
+      19
+    ],
+    [
+      "SIGNED_SWAP",
+      20,
+      21
+    ],
+    [
+      "SIGNED_SWAP",
+      22,
+      23
+    ],
+    [
+      "SIGNED_SWAP",
+      24,
+      25
+    ],
+    [
+      "SIGNED_SWAP",
+      26,
+      27
+    ],
+    [
+      "SIGNED_SWAP",
+      28,
+      29
+    ],
+    [
+      "SIGNED_SWAP",
+      30,
+      31
+    ]
+  ],
+  "prefix_pairs": 7,
+  "wrapper_sites": [
+    1,
+    3,
+    5,
+    7,
+    9,
+    11,
+    13,
+    15,
+    17,
+    19,
+    21,
+    23,
+    25,
+    27,
+    29,
+    31
+  ]
+}
diff --git a/research/p104-three-meeting-controllability/vendor/inputs/word5713.json.gz b/research/p104-three-meeting-controllability/vendor/inputs/word5713.json.gz
new file mode 100644
index 0000000000..45f6c10bf8
Binary files /dev/null and b/research/p104-three-meeting-controllability/vendor/inputs/word5713.json.gz differ
diff --git a/research/p104-three-meeting-controllability/vendor/inputs/word5718.json.gz b/research/p104-three-meeting-controllability/vendor/inputs/word5718.json.gz
new file mode 100644
index 0000000000..4db015aca3
Binary files /dev/null and b/research/p104-three-meeting-controllability/vendor/inputs/word5718.json.gz differ
diff --git a/research/p104-three-meeting-controllability/vendor/invoice.py b/research/p104-three-meeting-controllability/vendor/invoice.py
new file mode 100644
index 0000000000..d3ee7c701c
--- /dev/null
+++ b/research/p104-three-meeting-controllability/vendor/invoice.py
@@ -0,0 +1,21 @@
+"""Complete signed paid/target invoices and declared ordinary obligations."""
+from emit import *
+
+def whole(local,controller):
+ paid=Counter();targets=Counter()
+ for e in controller['physical_events']:
+  if e[0]=='LOCAL':paid.update(local['paid']);targets.update(local['targets'])
+  elif e[0]=='QUERY_SHEAR':paid[1]+=104
+  elif e[0]=='IDLE':paid[8*len(e[2])]+=208
+ for term in controller['diagonal']:targets[1+8*sum(term[1:])]+=104
+ return dict(paid=dict(sorted(paid.items())),targets=dict(sorted(targets.items())))
+
+def main():
+ controls=json.loads((HERE/'results/controls.json').read_text());local={k:{int(r):v for r,v in controls['source'][k].items()} for k in ('paid','targets')}
+ controller=json.loads((HERE/'inputs/controller5718.json').read_text());need(hashlib.sha256((HERE/'inputs/controller5718.json').read_bytes()).hexdigest()=='a84f6bbd547379597464e56c420cc665f96bc43a9a1351eed4b7cd0fce3cc4b9','controller source hash')
+ base=whole(local,controller);need(sum(base['paid'].values())==66348 and sum(base['targets'].values())==12976,'complete baseline counts')
+ proposed=deepcopy(base);proposed['targets'][9]-=18;proposed['targets'][4]+=18;proposed['targets'][5]+=18
+ need(sum(r*n for r,n in base['targets'].items())-sum(r*n for r,n in base['paid'].items())==760,'complete rank surplus')
+ out=dict(source_sha256=PINS['word5718.json.gz'],base=base,unrealized_680_split=proposed,delta_paid={},delta_targets={4:18,5:18,9:-18},signed_delta_paid_minus_targets={4:-18,5:-18,9:18},proof='18*(9^t-4^t-5^t)<0 for 0<t<1 by strict subadditivity; no surviving endpoint implements this proposed invoice',ordinary=dict(source_local_scalar=controls['source']['scalar'],retiming_added_scalar=0,retiming_added_paid_moves=0,input_and_retirement_scalar_by_cut={1196:16,1199:32,1200:24},four_ADD_upper=40,terminal_normalization='unknown: no candidate passes even the favorable rational endpoint test',new_helper_routes_allocation_cleanup='unknown: no candidate emitted',compiler_and_outer='unrun: no survivor'),kappa_status='NO_NEW_KAPPA; selected .00310045; source pending PR5718 claims .00311024570')
+ (HERE/'results/invoice.json').write_text(json.dumps(fmt(out),indent=2)+'\n');print(dict(paid=sum(base['paid'].values()),targets=sum(base['targets'].values()),rank_surplus=760,source_scalar=controls['source']['scalar'],delta_targets=out['delta_targets']))
+if __name__=='__main__':main()
diff --git a/research/p104-three-meeting-controllability/vendor/joint.py b/research/p104-three-meeting-controllability/vendor/joint.py
new file mode 100644
index 0000000000..67ac8368df
--- /dev/null
+++ b/research/p104-three-meeting-controllability/vendor/joint.py
@@ -0,0 +1,113 @@
+"""Finite exact neutral ADD search with one existing MOVE retimed inside a touch gap.
+
+State keeps every input coefficient. Up to two ADDs at first meeting, one at
+second, and a favorable terminal normalization test. No monotone repair filter.
+"""
+from preflight import *
+from copy import deepcopy
+
+def renamed(e,p,fresh):
+ e=list(e)
+ if e[1]==p:e[1]=fresh
+ if e[0] in ('ADD','COPY') and e[2]==p:e[2]=fresh
+ return e
+
+def raw(w,c,sites):
+ n=w['public'];N=n+w['owned_fields'];p=c['pivot'];fresh=N
+ _,_,k,_,_=endpoints(w,c)
+ rows=[{r:Q(1)} for r in range(N)]+[{}];ch=w['initial']+[None]*w['owned_fields']+[c['frame']]
+ for r in range(N):
+  add(rows[r],k,c['beta'].get(r,0))
+  if r==p:add(rows[r],{p:Q(1)},-1)
+ saved={}
+ for i,orig in enumerate(w['program']):
+  e=renamed(orig,p,fresh) if i>c['cut'] else orig
+  apply(rows,e);charts_step(ch,e)
+  if i==c['cut']:rows[p]={p:Q(1)};rows[fresh]={fresh:Q(1)};ch[p]=ch[fresh]=c['frame']
+  if i in sites:saved[i]=([dict(z) for z in rows],list(ch))
+ return saved
+
+def responses(w,p,site,roles,stop=None):
+ N=w['public']+w['owned_fields'];fresh=N;cols=[{r:Q(1)} for r in range(N+1)]
+ end=len(w['program']) if stop is None else stop+1
+ for orig in reversed(w['program'][site+1:end]):
+  e=renamed(orig,p,fresh);op,r=e[:2]
+  if op in ('INIT','CLEAR'):cols[r]={}
+  elif op=='SCALE':cols[r]=scale(cols[r],Q(e[-2]))
+  elif op!='MOVE':
+   add(cols[e[2]],cols[r],Q(e[-2]))
+   if op=='COPY':cols[r]={}
+ return {r:cols[r] for r in roles}
+
+def terminal_groups(w,c):
+ N=w['public']+w['owned_fields'];p=c['pivot'];ch=w['final']+[None]*w['owned_fields']+[w['final'][p]];ch[p]=c['frame'];groups=defaultdict(list)
+ for r,f in enumerate(ch):
+  if f is not None:groups[f].append(r)
+ return groups
+
+def groups_check(base,desired,groups,updates,fast=None):
+ for f,roles in groups.items():
+  if fast is not None and f not in fast:continue
+  changed={}
+  for d,s,a in updates:
+   for r,v in d.items():
+    if r in roles:
+     if r not in changed:changed[r]=dict(base[r])
+     add(changed[r],s,a*v)
+  if not changed:actual=lambda r:base[r]
+  else:actual=lambda r:changed.get(r,base[r])
+  if all(actual(r)==desired[r] for r in roles):continue
+  b=basis(actual(r) for r in roles)
+  if any(rem(desired[r],b) for r in roles):return False
+ return True
+
+def actions(roles):
+ return [(r,s,a) for r in roles for s in roles if r!=s for a in (Q(-2),Q(-1),Q(-1,2),Q(1,2),Q(1),Q(2))]
+
+def run(w,c,first,second,first_frame,second_frame,depth=1,cap=30000,first_roles=None,second_roles=None):
+ saved=raw(w,c,{first,second});R1,C1=saved[first];R2,C2=saved[second]
+ g1=[r for r,f in enumerate(C1) if f==first_frame];g2=[r for r,f in enumerate(C2) if f==second_frame]
+ if first_roles is not None:need(set(first_roles)<=set(g1),'first role frame');g1=first_roles
+ if second_roles is not None:need(set(second_roles)<=set(g2),'second role frame');g2=second_roles
+ need(len(g1)<=6 and len(g2)<=6,'bounded meeting size')
+ groups=terminal_groups(w,c);base,desired,*_=endpoints(w,c)
+ bad=[f for f,roles in groups.items() if not groups_check(base,desired,{f:roles},[])]
+ D1=responses(w,c['pivot'],first,g1);D2=responses(w,c['pivot'],second,g2);mid=responses(w,c['pivot'],first,g1,second)
+ a1=actions(g1);a2=[None]+actions(g2);tested=0;passfast=0;survivors=[];neutral=0
+ # a fixed input list is the complete stated domain at each meeting.
+ seqs=[()] + [(a,) for a in a1]
+ if depth==2:seqs +=[(a,b) for a in a1 for b in a1]
+ for seq in seqs:
+  local={r:dict(R1[r]) for r in g1};up=[];midrows={r:dict(R2[r]) for r in g2}
+  for r,s,a in seq:
+   src=dict(local[s]);add(local[r],src,a);up.append((D1[r],src,a))
+   for v,b in mid[r].items():
+    if v in midrows:add(midrows[v],src,a*b)
+  if seq and not groups_check(base,desired,groups,up,fast=bad):neutral+=1
+  for action in a2:
+   if tested>=cap:return dict(tested=tested,cap=cap,truncated=True,groups=[g1,g2],first_sequences=len(seqs),neutral_first_sequences=neutral,fast_survivors=passfast,survivors=survivors)
+   updates=list(up)
+   if action:
+    r,s,a=action;updates.append((D2[r],midrows[s],a))
+   tested+=1
+   if not groups_check(base,desired,groups,updates,fast=bad):continue
+   passfast+=1
+   if groups_check(base,desired,groups,updates):
+    survivors.append(dict(first=seq,second=action));print('SURVIVOR',fmt(survivors[-1]),flush=True)
+ return dict(tested=tested,cap=cap,truncated=False,groups=[g1,g2],first_sequences=len(seqs),neutral_first_sequences=neutral,fast_survivors=passfast,survivors=survivors)
+
+def retime(w,index,after):
+ e=w['program'][index];need(e[0]=='MOVE' and not e[4],'public MOVE only');r=e[1]
+ lo,hi=sorted((index,after));between=w['program'][lo+1:hi+1] if after>index else w['program'][lo+1:hi]
+ need(all(x[1]!=r and not(x[0] in ('ADD','COPY') and x[2]==r) for x in between),'retiming crosses a role touch')
+ out=deepcopy(w);p=out['program'];move=p.pop(index);at=after if after>index else after+1;p.insert(at,move)
+ return out
+
+def main():
+ ap=argparse.ArgumentParser();ap.add_argument('--index',type=int,default=350);ap.add_argument('--first',type=int,default=13644);ap.add_argument('--second',type=int,default=16800);ap.add_argument('--first-frame',type=int,default=597);ap.add_argument('--second-frame',type=int,default=170);ap.add_argument('--depth',type=int,default=1);ap.add_argument('--cap',type=int,default=30000);ap.add_argument('--first-roles');ap.add_argument('--second-roles');ap.add_argument('--move',type=int);ap.add_argument('--after',type=int);ap.add_argument('--out',default='joint695.json');a=ap.parse_args()
+ w=load('word5718.json.gz');c=json.loads((HERE/'results/contacts5718.json').read_text())['cuts'][a.index]
+ for k in ('a','c','h0','d','beta'):c[k]=unrow(c[k])
+ if a.move is not None:w=retime(w,a.move,a.after)
+ t=time.monotonic();result=run(w,c,a.first,a.second,a.first_frame,a.second_frame,a.depth,a.cap,[int(v) for v in a.first_roles.split(',')] if a.first_roles else None,[int(v) for v in a.second_roles.split(',')] if a.second_roles else None);result.update(source_sha256=PINS['word5718.json.gz'],index=a.index,cut=c['cut'],pivot=c['pivot'],meetings=[a.first,a.second],frames=[a.first_frame,a.second_frame],depth=a.depth,route=dict(move=a.move,after=a.after),seconds=time.monotonic()-t)
+ (HERE/'results'/a.out).write_text(json.dumps(fmt(result),indent=2)+'\n');print(json.dumps(fmt(result)),flush=True)
+if __name__=='__main__':main()
diff --git a/research/p104-three-meeting-controllability/vendor/preflight.py b/research/p104-three-meeting-controllability/vendor/preflight.py
new file mode 100644
index 0000000000..28341deed5
--- /dev/null
+++ b/research/p104-three-meeting-controllability/vendor/preflight.py
@@ -0,0 +1,91 @@
+"""Exact favorable endpoint availability, before scalar program search."""
+from search import *
+
+def basis(rows):
+ out={}
+ for row in rows:
+  z=dict(row)
+  while z:
+   j=min(z)
+   if j not in out:
+    out[j]=scale(z,1/z[j]);break
+   add(z,out[j],-z[j])
+ return out
+
+def rem(row,b):
+ z=dict(row)
+ while z and min(z) in b:add(z,b[min(z)],-z[min(z)])
+ return z
+
+def endpoints(w,c):
+ n=w['public'];N=n+w['owned_fields'];p=c['pivot'];fresh=N
+ k={p:Q(2)};add(k,c['c'],-1)
+ q=dict(c['h0']);add(q,k,sum(v*c['beta'].get(j,0) for j,v in q.items()));add(q,{p:Q(1)},-c['h0'].get(p,0))
+ eta=dict(k);add(eta,q,-1);eta[fresh]=Q(1)
+ rows=[{r:Q(1)} if r<n else {} for r in range(N)]+[{fresh:Q(1)}]
+ for r in w['live']:rows[r+112][r]=Q(1)
+ desired=[dict(z) for z in rows]
+ for r,v in c['d'].items():
+  if r!=p:add(rows[r],eta,v)
+ rows[p]={p:Q(1)};rows[fresh]=dict(eta)
+ return rows,desired,k,q,eta
+
+def terminal_test(w,c):
+ rows,desired,*_=endpoints(w,c);n=w['public'];N=n+w['owned_fields'];p=c['pivot']
+ ch=w['final']+[None]*w['owned_fields']+[w['final'][p]];ch[p]=c['frame']
+ groups=defaultdict(list)
+ for r,f in enumerate(ch):
+  if f is not None:groups[f].append(r)
+ failed=[]
+ for f,roles in groups.items():
+  if all(rows[r]==desired[r] for r in roles):continue
+  b=basis(rows[r] for r in roles)
+  for r in roles:
+   z=rem(desired[r],b)
+   if z:failed.append(dict(role=r,frame=f,remainder=z))
+ return failed
+
+def closed_tests(w,c,prefix,ch,last_inbound):
+ n=w['public'];N=n+w['owned_fields'];p=c['pivot'];fresh=N
+ _,desired,k,q,eta=endpoints(w,c)
+ def rightB(row):
+  out=dict(row);add(out,k,sum(v*c['beta'].get(j,0) for j,v in row.items()));add(out,{p:Q(1)},-row.get(p,0));return out
+ defects=set(c['d'])-{p};defects.add(fresh)
+ groups=defaultdict(list)
+ for r in defects:
+  f=w['final'][p if r==fresh else r]
+  if last_inbound.get(f,-1)<=c['cut']:groups[f].append(r)
+ failed=[]
+ for f,targets in groups.items():
+  vals=[rightB(prefix[r]) for r,g in enumerate(ch) if g==f and r!=p]
+  if ch[p]==f:vals.append({fresh:Q(1)})
+  if c['frame']==f:vals.append({p:Q(1)})
+  b=basis(vals)
+  for r in targets:
+   z=rem(desired[r],b)
+   if z:failed.append(dict(role=r,frame=f,remainder=z))
+ return failed
+
+def main():
+ ap=argparse.ArgumentParser();ap.add_argument('--word',default='word5718.json.gz');ap.add_argument('--contacts',default='contacts5718.json');ap.add_argument('--out',default='preflight5718.json');a=ap.parse_args()
+ w=load(a.word);d=json.loads((HERE/'results'/a.contacts).read_text());need(d['source_sha256']==PINS[a.word],'source join')
+ cuts=d['cuts']
+ for c in cuts:
+  for k in ('a','c','h0','d','beta'):c[k]=unrow(c[k])
+ by=defaultdict(list)
+ for j,c in enumerate(cuts):by[c['cut']].append(j)
+ last={e[3]:i for i,e in enumerate(w['program']) if e[0]=='MOVE'}
+ n=w['public'];N=n+w['owned_fields'];rows=[{r:Q(1)} for r in range(N)];ch=w['initial']+[None]*w['owned_fields'];out=[];counts=Counter()
+ for i,e in enumerate(w['program']):
+  apply(rows,e);charts_step(ch,e)
+  for j in by[i]:
+   c=cuts[j]
+   # This explicitly omits the commissioned known-closed helper440 contract.
+   if c['pivot']==440:counts['excluded_fixed440']+=1;continue
+   fail=closed_tests(w,c,rows,ch,last);terminal=terminal_test(w,c)
+   counts['tested']+=1;counts['closed_rejects']+=bool(fail);counts['terminal_rejects']+=bool(terminal)
+   out.append(dict(index=j,cut=c['cut'],pivot=c['pivot'],trigger=c['trigger'],ranks=c['ranks'],defects=len(c['d']),closed_failed=fail,terminal_failed=terminal))
+ (HERE/'results'/a.out).write_text(json.dumps(fmt(dict(source_sha256=PINS[a.word],counts=dict(counts),results=out)),indent=2)+'\n')
+ print(dict(counts),flush=True)
+ print('terminal survivors',[(s['index'],s['cut'],s['pivot'],s['defects']) for s in out if not s['terminal_failed']][:60],flush=True)
+if __name__=='__main__':main()
diff --git a/research/p104-three-meeting-controllability/vendor/results/contacts5713.json b/research/p104-three-meeting-controllability/vendor/results/contacts5713.json
new file mode 100644
index 0000000000..8c031317e7
--- /dev/null
+++ b/research/p104-three-meeting-controllability/vendor/results/contacts5713.json
@@ -0,0 +1,273546 @@
+{
+  "source_sha256": "9fd67dd89ed24a644257cd9aef06934ed4c6fbe0441804684a968868f2ef66a8",
+  "domain": "after every MOVE, departure and arrival groups; a=e_p+q e_s, q chosen for purity or +/-1/2,+/-1,+/-2",
+  "stats": {
+    "helper_contact_contexts": 6008,
+    "prefix_candidates": 2012,
+    "compatible_bases": 1880,
+    "other_role_candidates": 1554
+  },
+  "cuts": [
+    {
+      "cut": 9598,
+      "pivot": 224,
+      "frame": 0,
+      "a": {
+        "224": "1"
+      },
+      "c": {
+        "224": "1",
+        "225": "-1",
+        "227": "1"
+      },
+      "h0": {
+        "224": "1",
+        "225": "-1",
+        "227": "1"
+      },
+      "ranks": [
+        1,
+        8
+      ],
+      "trigger": 224,
+      "d": {
+        "188": "1",
+        "224": "1",
+        "173": "-1/2",
+        "166": "-1/2",
+        "214": "-1/2",
+        "213": "-1/2",
+        "167": "-1/2",
+        "212": "-1/2",
+        "168": "-1/2",
+        "124": "-1/2",
+        "143": "-1/2",
+        "126": "1/2",
+        "151": "-1/2",
+        "117": "-1/2",
+        "181": "-1/2",
+        "180": "-1/2",
+        "116": "-1/2",
+        "179": "-1/2",
+        "192": "-1/2",
+        "200": "-1/2"
+      },
+      "beta": {
+        "188": "1",
+        "224": "1",
+        "173": "-1/2",
+        "166": "-1/2",
+        "214": "-1/2",
+        "213": "-1/2",
+        "167": "-1/2",
+        "212": "-1/2",
+        "168": "-1/2",
+        "124": "-1/2",
+        "143": "-1/2",
+        "126": "1/2",
+        "151": "-1/2",
+        "117": "-1/2",
+        "181": "-1/2",
+        "180": "-1/2",
+        "116": "-1/2",
+        "179": "-1/2",
+        "192": "-1/2",
+        "200": "-1/2"
+      }
+    },
+    {
+      "cut": 9600,
+      "pivot": 224,
+      "frame": 0,
+      "a": {
+        "224": "1",
+        "0": "-1"
+      },
+      "c": {
+        "224": "1",
+        "225": "-1",
+        "227": "1"
+      },
+      "h0": {
+        "224": "1",
+        "225": "-1",
+        "227": "1",
+        "0": "1"
+      },
+      "ranks": [
+        1,
+        8
+      ],
+      "trigger": 225,
+      "d": {
+        "188": "1",
+        "224": "1",
+        "173": "-1/2",
+        "166": "-1/2",
+        "214": "-1/2",
+        "213": "-1/2",
+        "167": "-1/2",
+        "212": "-1/2",
+        "168": "-1/2",
+        "124": "-1/2",
+        "143": "-1/2",
+        "126": "1/2",
+        "151": "-1/2",
+        "117": "-1/2",
+        "181": "-1/2",
+        "180": "-1/2",
+        "116": "-1/2",
+        "179": "-1/2",
+        "192": "-1/2",
+        "200": "-1/2"
+      },
+      "beta": {
+        "188": "1",
+        "224": "1",
+        "173": "-1/2",
+        "166": "-1/2",
+        "214": "-1/2",
+        "213": "-1/2",
+        "167": "-1/2",
+        "212": "-1/2",
+        "168": "-1/2",
+        "124": "-1/2",
+        "143": "-1/2",
+        "126": "1/2",
+        "151": "-1/2",
+        "117": "-1/2",
+        "181": "-1/2",
+        "180": "-1/2",
+        "116": "-1/2",
+        "179": "-1/2",
+        "192": "-1/2",
+        "200": "-1/2"
+      }
+    },
+    {
+      "cut": 9604,
+      "pivot": 228,
+      "frame": 81,
+      "a": {
+        "228": "1"
+      },
+      "c": {
+        "228": "1",
+        "225": "1",
+        "227": "-1"
+      },
+      "h0": {
+        "228": "1",
+        "225": "1",
+        "227": "-1"
+      },
+      "ranks": [
+        1,
+        8
+      ],
+      "trigger": 228,
+      "d": {
+        "228": "1",
+        "146": "-1/2",
+        "220": "-1/2",
+        "135": "-1/2",
+        "219": "-1/2",
+        "136": "-1/2",
+        "157": "-1/2",
+        "147": "-1/2",
+        "134": "-1/2",
+        "221": "-1/2",
+        "176": "-1/2",
+        "180": "1/2",
+        "177": "-1/2",
+        "181": "1/2",
+        "209": "-1/2",
+        "116": "1/2",
+        "208": "-1/2",
+        "117": "1/2",
+        "207": "-1/2",
+        "200": "1/2",
+        "120": "-1/2",
+        "178": "-1/2",
+        "192": "1/2",
+        "138": "-1/2",
+        "179": "1/2",
+        "154": "-1/2",
+        "217": "-1/2",
+        "153": "-1/2",
+        "218": "-1/2",
+        "139": "-1/2",
+        "112": "1/2",
+        "190": "1/2",
+        "211": "1/2",
+        "128": "-1/2",
+        "156": "-1/2",
+        "199": "1/2",
+        "127": "1/2",
+        "165": "1/2",
+        "164": "1/2",
+        "125": "1/2",
+        "163": "1/2",
+        "193": "-1/2",
+        "204": "1/2",
+        "119": "1/2",
+        "169": "-1/2",
+        "155": "-1/2",
+        "216": "-1/2",
+        "142": "-1/2",
+        "172": "-1/2",
+        "171": "-1/2",
+        "141": "-1/2",
+        "170": "-1/2",
+        "140": "-1/2",
+        "205": "-1/2",
+        "198": "-1/2"
+      },
+      "beta": {
+        "228": "1",
+        "146": "-1/2",
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diff --git a/research/p104-three-meeting-controllability/vendor/results/contacts5718.json b/research/p104-three-meeting-controllability/vendor/results/contacts5718.json
new file mode 100644
index 0000000000..ee80a3a3b7
--- /dev/null
+++ b/research/p104-three-meeting-controllability/vendor/results/contacts5718.json
@@ -0,0 +1,271798 @@
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+}
diff --git a/research/p104-three-meeting-controllability/vendor/search.py b/research/p104-three-meeting-controllability/vendor/search.py
new file mode 100644
index 0000000000..5d38c52132
--- /dev/null
+++ b/research/p104-three-meeting-controllability/vendor/search.py
@@ -0,0 +1,101 @@
+"""Exact dyadic contact generation and bounded joint route/scalar exploration."""
+from fractions import Fraction as Q
+from collections import defaultdict, Counter
+from pathlib import Path
+import argparse, gzip, hashlib, json, time
+HERE=Path(__file__).resolve().parent
+PINS={'word5713.json.gz':'9fd67dd89ed24a644257cd9aef06934ed4c6fbe0441804684a968868f2ef66a8','word5718.json.gz':'cff7196f8b168c4ebf8227185eed98387b66ec5db0179108adfea4045775cc31'}
+def need(x,msg):
+ if not x: raise ValueError(msg)
+def add(a,b,q=Q(1)):
+ for k,v in tuple(b.items()):
+  z=a.get(k,0)+q*v
+  if z:a[k]=z
+  else:a.pop(k,None)
+def scale(a,q):return {k:v*q for k,v in a.items() if v*q}
+def apply(rows,e):
+ op,r=e[:2]
+ if op=='MOVE':return
+ if op in ('INIT','CLEAR'):rows[r]={}
+ elif op=='SCALE':rows[r]=scale(rows[r],Q(e[-2]))
+ else:
+  s=e[2];a=dict(rows[s])
+  if op=='COPY':rows[r]={}
+  add(rows[r],a,Q(e[-2]))
+def charts_step(ch,e):
+ if e[0]=='MOVE':ch[e[1]]=e[3]
+ elif e[0] in ('INIT','CLEAR'):ch[e[1]]=e[2] if e[0]=='INIT' else None
+def span(xs):
+ s={0}
+ for x in xs:s|={v^x for v in tuple(s)}
+ return s
+def load(name):
+ p=HERE/'inputs'/name;b=p.read_bytes();need(hashlib.sha256(b).hexdigest()==PINS[name],'source hash')
+ return json.loads(gzip.decompress(b))
+def fmt(x):
+ if isinstance(x,dict):return {str(k):fmt(v) for k,v in x.items()}
+ if isinstance(x,(tuple,list)):return [fmt(v) for v in x]
+ if isinstance(x,Q):return str(x)
+ return x
+def unrow(x):return {int(k):Q(v) for k,v in x.items()}
+def generate(w):
+ n=w['public'];N=n+w['owned_fields'];main=set(w['live'])|{r+112 for r in w['live']}
+ fs=[span(b) for b in w['frames']];rows=[{r:Q(1)} for r in range(N)];ch=w['initial']+[None]*(N-n);at=defaultdict(set)
+ for r,f in enumerate(ch):at[f].add(r)
+ stats=Counter();by=defaultdict(list)
+ # Every MOVE changes contact at both departure and arrival. No input-column-zero assumption.
+ for i,e in enumerate(w['program']):
+  if e[0]=='MOVE':
+   _,m,old,f,_=e;at[old].remove(m);at[f].add(m);ch[m]=f
+   for frame in sorted({old,f}):
+    for p in sorted(at[frame]):
+     if p>=n or p in main:continue
+     u,v=w['initial'][p],w['final'][p]
+     if not fs[u]<fs[frame]<fs[v]:continue
+     stats['helper_contact_contexts']+=1
+     outside={k:x for k,x in rows[p].items() if k>=n or w['initial'][k]!=u}
+     options=[(None,Q(0))] if not outside else []
+     for s in sorted(at[frame]-{p}):
+      out={k:x for k,x in rows[s].items() if k>=n or w['initial'][k]!=u}
+      if not out:
+       if not outside:
+        options.extend((s,q) for q in (Q(-2),Q(-1),Q(-1,2),Q(1,2),Q(1),Q(2)))
+       continue
+      k=min(out);q=-outside.get(k,0)/out[k]
+      if q and all(outside.get(j,0)+q*out.get(j,0)==0 for j in outside.keys()|out.keys()):options.append((s,q))
+     for s,q in options:
+      if q.denominator&(q.denominator-1):continue
+      c=dict(rows[p]);a={p:Q(1)}
+      if s is not None:add(c,rows[s],q);a[s]=q
+      if c.get(p)!=1:continue
+      stats['prefix_candidates']+=1
+      by[i].append(dict(cut=i,pivot=p,frame=frame,a=a,c=c,h0=dict(rows[p]),ranks=[len(w['frames'][frame])-len(w['frames'][u]),len(w['frames'][v])-len(w['frames'][frame])],trigger=m))
+  else:
+   if e[0] in ('INIT','CLEAR'):
+    r=e[1];at[ch[r]].remove(r);charts_step(ch,e);at[ch[r]].add(r)
+   apply(rows,e)
+ cols=[{r:Q(1)} for r in range(N)];keep=[]
+ for i in range(len(w['program'])-1,-1,-1):
+  for s in by.pop(i,[]):
+   p=s['pivot'];u=w['initial'][p];d=cols[p];beta=dict(d)
+   for r in w['live']:
+    if r in d:beta[r+112]=beta.get(r+112,0)-d[r]
+   beta={k:v for k,v in beta.items() if v}
+   if beta.get(p)!=1 or any(k>=n or w['initial'][k]!=u for k in beta):continue
+   if sum(x*beta.get(k,0) for k,x in s['c'].items())!=1:continue
+   s.update(d=dict(d),beta=beta);keep.append(s)
+  e=w['program'][i];op,r=e[:2]
+  if op in ('INIT','CLEAR'):cols[r]={}
+  elif op=='SCALE':cols[r]=scale(cols[r],Q(e[-2]))
+  elif op!='MOVE':
+   add(cols[e[2]],cols[r],Q(e[-2]))
+   if op=='COPY':cols[r]={}
+ stats['compatible_bases']=len(keep);stats['other_role_candidates']=sum(s['trigger']!=s['pivot'] for s in keep)
+ # Exact identical cut state dedup across consecutive MOVE triggers is left visible in raw counts.
+ return sorted(keep,key=lambda s:(s['cut'],s['pivot'],tuple(s['a'].items()))),dict(stats)
+def main():
+ ap=argparse.ArgumentParser();ap.add_argument('--word',default='word5718.json.gz');ap.add_argument('--out',default='contacts5718.json');a=ap.parse_args()
+ t=time.monotonic();w=load(a.word);cuts,stats=generate(w);out=dict(source_sha256=PINS[a.word],domain='after every MOVE, departure and arrival groups; a=e_p+q e_s, q chosen for purity or +/-1/2,+/-1,+/-2',stats=stats,cuts=cuts)
+ (HERE/'results'/a.out).write_text(json.dumps(fmt(out),indent=2)+'\n');print(json.dumps(dict(stats=stats,seconds=time.monotonic()-t)),flush=True)
+ if a.word=='word5713.json.gz':need(any(c['cut']==14330 and c['pivot']==708 and c['a']=={708:Q(1),154:Q(1,2)} for c in cuts),'generator must DISCOVER PR5718 control')
+if __name__=='__main__':main()
diff --git a/research/p104-three-meeting-controllability/verify.py b/research/p104-three-meeting-controllability/verify.py
new file mode 100644
index 0000000000..83ea157b24
--- /dev/null
+++ b/research/p104-three-meeting-controllability/verify.py
@@ -0,0 +1,42 @@
+"""Read-only, Git-free, full exact replay of this scoped research package."""
+from pathlib import Path
+import hashlib,json
+ROOT=Path(__file__).resolve().parent
+
+def need(condition,message):
+ if not condition:raise ValueError(message)
+
+def check_hash(data,expected):
+ need(hashlib.sha256(data).hexdigest()==expected,'source or package byte corruption')
+
+def main():
+ manifest=json.loads((ROOT/'MANIFEST.json').read_text())
+ for name,sha in manifest['files'].items():check_hash((ROOT/name).read_bytes(),sha)
+ sources=json.loads((ROOT/'SOURCES.json').read_text())
+ for s in sources['vendored_predecessor_files']:
+  data=(ROOT/s['path']).read_bytes();check_hash(data,s['sha256'])
+  need(hashlib.sha1(b'blob '+str(len(data)).encode()+b'\0'+data).hexdigest()==s['git_blob'],'predecessor Git blob')
+ # A corrupt immutable source must fail before any scientific interpretation.
+ data=(ROOT/'vendor/inputs/word5718.json.gz').read_bytes();bad=bytearray(data);bad[-1]^=1
+ try:check_hash(bad,sources['word5718_sha256'])
+ except ValueError:pass
+ else:raise ValueError('source corruption accepted')
+ from obstruction import certify
+ from relax import case,relaxation,fmt
+ import sys
+ sys.path.insert(0,str(ROOT))
+ import controls,invoice
+ obs=[certify(i,r) for i in (1196,1199,1200) for r in (False,True)]
+ relax=[]
+ for i in (1196,1199,1200):
+  for rt in (False,True):
+   w,c,ts,fs,snap,roles=case(i,rt);r,_=relaxation(w,c,ts,fs,snap,roles);r.update(index=i,retimed=rt);relax.append(r)
+ payload={'obstruction':obs,'relaxation':relax,'controls':controls.run(),'invoice':invoice.run()}
+ for name,value in payload.items():
+  need(fmt(value)==json.loads((ROOT/'results'/f'{name}.json').read_text()),'receipt mismatch '+name)
+ semantic=hashlib.sha256(json.dumps(fmt(payload),sort_keys=True,separators=(',',':')).encode()).hexdigest()
+ print(json.dumps(dict(status='PASS',exact_obstructions=6,relaxation_cases=6,
+                      constructive_positive=True,rejection_controls=True,source_corruption_rejected=True,
+                      source_columns=753,paid_jobs=66348,productive_fields=12976,new_kappa=False,
+                      semantic_sha256=semantic),sort_keys=True))
+if __name__=='__main__':main()