Audit the composed T488 histogram against literal helper outputs.

research/t488-ownership-invoice/README.md

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+# T488 ownership invoice
+
+**Audit of one published histogram. No new κ.** Selected κ stays
+`0.001672660197076918`.
+
+## Scope and evidence
+
+Original card: `scalar-to-moment`. Scope is **changed**: Discussion #1166
+comment 19022532, question 1, asks for an invoice-level audit of the composed
+T488 package's literal ownership and outputs against its published profile.
+Question 2, the packing-vertex saturation, is already PR #3796 and is not
+repeated here.
+
+Predecessor: PR #3653 (`research/retimed-t488-composition`), publication head
+`607a09ff441c79b215a8127a81f4cc70021d0d9b`, by Rohan Arun / roger-sato, with
+the PR #3633 owner certificate and the PR #3642 retimed words. The arithmetic
+reproduction in PR #3740 explicitly left this ownership invoice open.
+
+The vendored inputs are byte copies of that head:
+
+| File | SHA-256 |
+|---|---|
+| `inputs/checked-base-CANONICAL-WORD.json.gz` | `ba1e3767f52c849c49d7d3852b879d9562265f1f51d15ca40421c51cae0aae6a` |
+| `inputs/checked-extra-CANONICAL-WORD.json.gz` | `f30605f35030460f18b053dbd6031e862bf3c6661141d481d54ffdc1e8d1ad01` |
+| `inputs/PROVIDERS.json` | `d96f2798024ab83edbb8848b62c425992aec182f1f24ef46bb8286dd390618c2` |
+| `inputs/CANDIDATE.json` | `fbdda845beac5bba9baa4b1b8c8f596e98f70b59e1d60ebf4f4d3e8758631bfd` |
+
+These objects are not on canonical main `bb4bccbf42844d2801487450727c2f63e10d1d0f`,
+so they are copied into the package rather than pinned as `base_commit` paths.
+The verifier checks the hashes above.
+
+**Established.** Both retimed canonical words have 408 helpers. For each helper,
+the rank of its final frame minus the rank of its start frame equals that
+provider's literal width, index by index (`gauge44` for the base word, `extra`
+for the other). The two frame tables differ at index 300 only, both of rank 4,
+and that index is not a helper entrance or final frame. The stored local bill
+on both words is `{1:2437, 2:724, 3:226, 4:102, 5:20, 8:8}`. The owner
+certificate's local bill and both provider `actual_paid_profile` maps are
+`{1:2439, 2:726, 3:224, 4:102, 5:20, 8:8}`. The per-call delta is
+`-2` rank 1, `-2` rank 2, `+2` rank 3, and its rank mass is 0.
+
+With `4392 = 9 * 488` calls, the certificate profile plus `4392` times that
+delta is exactly the published histogram
+
+```text
+{1:10817496, 2:3179808, 3:1024434, 4:447984, 5:94794, 8:35136, 48:186782}
+```
+
+The idle residual, `profile - calls * local`, is the same before and after the
+delta: `{1:114192, 3:31842, 5:6954, 48:186782}`. Rank mass stays
+`65088 * 488 = 31762944`. The published physical count `437757` equals
+`896 * 488 + 509`. Placed helper width per call is `3279`, a different ledger
+from the local child bill.
+
+**Not established.** The 1,791,936 literal rows were not regenerated, and this
+package does not import `owners/run.py` or `independent_literal.py`. The
+predecessor profile is the certificate value. The stored `local_profile` field
+is cross-checked, not re-derived by a gate climb. No native admission, no
+moment bracket, and no selected-frontier change.
+
+## Reproduce
+
+From the repository root, Python 3.12, standard library only:
+
+```sh
+python3 scripts/research_package.py --package research/t488-ownership-invoice --check-only
+python3.12 -B scripts/research_package.py --package research/t488-ownership-invoice
+```
+
+Expected marker: `PASS_T488_OWNERSHIP_INVOICE` with `rows_regenerated=false`
+and `no_new_kappa=true`. One incremented helper width and one incremented
+published count are rejected in memory.
+
+## Open next questions
+
+1. Sum residual capacities from a fresh `FILL.json.gz` and compare them with
+   `{1:114192, 3:31842, 5:6954, 48:186782}` without reading `CANDIDATE.profile`.
+   That closes the certificate-versus-rows gap. The blocker is the
+   several-minute integral-network expander in PR #3653.
+2. Climb the canonical gate frames, including warps and centre charges, and
+   compare the resulting child histogram with the stored local bill. Helper
+   output widths do not determine that bill. The blocker is that the canonical
+   encoding is not the borrow-word schedule already checked by the local proof.
+
+## Credit
+
+PR #3633 supplies the T488 owner certificate. PR #3642 supplies the retimed
+words. PR #3653 publishes the composed profile and its own owner replay.
+PR #3740 records the open invoice question, and PR #3796 closes the separate
+saturation question. Prepared by unpaidmoon with substantial Cursor Grok
+assistance. Apache-2.0.

research/t488-ownership-invoice/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "bb4bccbf42844d2801487450727c2f63e10d1d0f",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5",
+      "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0"
+    }
+  ]
+}

research/t488-ownership-invoice/TASK.json

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+{
+  "schema_version": 1,
+  "task_id": "scalar-to-moment",
+  "priority_revision": 6,
+  "base_commit": "bb4bccbf42844d2801487450727c2f63e10d1d0f",
+  "original_card": {
+    "id": "scalar-to-moment",
+    "question": "Can one known scalar simplification be converted into an actual paid-profile improvement?",
+    "starting_points": [
+      "research/r439-bsection-stars-seed01/README.md",
+      "certificates/selected-result.json"
+    ],
+    "methods": [
+      "Derive the changed legal frame itinerary and exact child histogram.",
+      "Prove a scoped obstruction showing why that scalar gain cannot change the paid contract."
+    ],
+    "acceptance_gate": "An unchanged histogram is not a kappa gain; record any separate runtime or proof benefit explicitly.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "research/r439-bsection-stars-seed01/verify.py"
+      ],
+      "expected": "PASS_R439_BSECTION_STARS",
+      "inspect": "Observe that the positive control improves scalar counts while retaining the paid histogram.",
+      "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Choose one simplification and derive the complete changed frame itinerary, or prove why it cannot change the histogram.",
+    "bottleneck_link": "A legal change to the histogram, not addition count alone, is the bridge to an exponent gain.",
+    "allowed_variations": [
+      "One existing scalar simplification and one proposed frame-path change."
+    ],
+    "scope_change_triggers": [
+      "Submitting only another scalar count as completion of a paid-profile task."
+    ],
+    "overlap_terms": [
+      "scalar simplification",
+      "paid profile",
+      "R439"
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Audit the PR #3653 composed T488 published child histogram against the predecessor owner certificate and the literal helper output widths of both retimed canonical words.",
+  "scope_change_reason": "Discussion #1166 comment 19022532 question 1 asks for an invoice of an already published composition. This is not a new scalar simplification and does not claim a paid-profile improvement.",
+  "bottleneck_link": "The composed histogram is the paid profile that would enter a moment. Confirming it is the owner invoice plus a mass-zero local delta says the retiming did not create a new child histogram beyond that repricing. No new kappa.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop after the published histogram, idle residual and both helper-width lists agree, or at the first mismatch. Do not regenerate the integral-network journal or rerun admission.",
+  "outcome": "partial",
+  "evidence": "verify.py recomputes helper output widths from frame ranks and the composed histogram from the owner certificate plus the local-bill delta.",
+  "author": "unpaidmoon",
+  "ai_assistance": "Substantial Cursor Grok assistance for the audit, verifier and notes.",
+  "open_questions": [
+    {
+      "question": "Does a fresh sum of the 1791936 literal owner rows reproduce the idle residual {1:114192, 3:31842, 5:6954, 48:186782} without reading CANDIDATE.profile?",
+      "why_it_matters": "This audit treats the predecessor certificate profile as the owner invoice. A drifted certificate would still pass the arithmetic split.",
+      "first_step": "Run owners/upstream/portable_expand.py from PR #3653 at 607a09ff into a fresh directory and sum residual capacities from FILL.json.gz.",
+      "blocked_by": "The expander is a several-minute integral-network reconstruction and is outside this package's bounded check."
+    },
+    {
+      "question": "Does the stored canonical local_profile equal the child histogram obtained by climbing the canonical gate frames, including warps and centre charges?",
+      "why_it_matters": "The composed histogram multiplies the stored local bill. Helper output widths do not determine that bill.",
+      "first_step": "Resolve each canonical gate's frame index and apply the monotone climb used for the borrow-word local proof.",
+      "blocked_by": "The canonical encoding is not the borrow-word schedule, and this package does not replay that climb."
+    }
+  ]
+}

research/t488-ownership-invoice/VERIFY.json

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+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 60,
+      "checks": "Published T488 histogram equals the predecessor owner profile plus 4392 times the local delta; both helper output-width lists match the provider widths; one-width and one-count controls fail closed."
+    }
+  ]
+}