Mister-Meeseeks · Oct 13, 2026 · Oct 13, 2026 · Oct 13, 2026
diff --git a/research/async-inventory-reconciliation/CLAIM.md b/research/async-inventory-reconciliation/CLAIM.md
@@ -0,0 +1,49 @@
+# Sprint claim: archived asynchronous inventory bound
+
+- Track: research consolidation; assignment seed **95**.
+- OS randomness: `od -An -N4 -tu4 /dev/urandom` returned `2227208895`.
+  This is below `floor(2^32/100)*100 = 4294967200`; reduction modulo 100
+  gives 95 without modulo bias (a value above that cutoff would be redrawn).
+- Exact base: `66849e1475c930fd7732b1a0067ffee7e1e95f60`, freshly cloned
+  and confirmed by `git pull --ff-only`.
+- Candidates, in order: reconcile selected #626 Linux evidence; bind family
+  review decisions to the ledger; reconcile the archived 146-profile
+  asynchronous inventory bound with its source records. Seed `95 % 3 = 2`
+  selects the third; #695 and #704 already cover the first two.
+- Exact scope: the finite profile/width menu and exact dual receipts in
+  `research/experiment-log/negative-searches/async505-inventory-wall/`.
+  Resolve whether its portable replay binds the 146 rows to the archived
+  result files and detects invalid evidence. Check both exact engines.
+- Method: exhaustive comparison of the 146 retained menu entries and their
+  source result files; exact replay; controlled source/receipt mutations.
+  No new allocation, word, timing, or supplier search.
+- Expected deliverable: an offline, reproducible evidence reconciliation
+  checker and a scoped report, with source pins and negative controls.
+- Time box: 35 minutes from 2026-10-13 04:41:33 UTC; finish by 05:16:33 UTC.
+  Orientation ends before 04:48:33; final verification/handoff begins by
+  05:07:48 UTC (the final quarter).
+- Coordination check: GitHub's pinned-issue query returned no issues;
+  refreshed open-PR metadata through #716 showed no matching inventory-wall
+  reconciliation. #630 corrects a different archived E6 screen. No separate
+  reservation issue was opened.
+- Contributor: Alexander Templeton (`azide0x37`), with substantial OpenAI
+  Codex assistance. Original archive, search, and arithmetic authors retain
+  their attribution. Apache-2.0.
+
+## Completed result — 2026-10-13 04:59 UTC
+
+[Verified contribution at commit 7a52e20](https://github.com/azide0x37/integer-mult-bounds/tree/7a52e20d2c16576173b6318947ba5b6095385107/research/async-inventory-reconciliation).
+All 146 source pairs match; both exact receipts reproduce. A removed-rank-one
+charge control exposes a false archived `PASS` under `-O`, with negative margin;
+the companion rejects it and checks source binding with checks active under `-O`.
+It checks 348 inequalities per engine, 12 distinct rejection controls per
+engine, and six historical executions per engine. No new search or κ.
+
+Seven tests pass normally and under optimization. Python 3.10, 3.13 and 3.14
+reports agree; a committed-files-only export also passes from an unrelated
+directory. Archive integrity and selected-result verification pass. Focused
+verification/handoff began at 04:54 UTC, before the planned final-quarter gate.
+The final overlap refresh through #732 found no matching contribution.
+#721 optimizes the central ledger's ZIP reader and #724 audits R/R0 accounting;
+neither overlaps this archived finite-menu/source reconciliation. Main still
+equals the recorded base, and no pinned coordination issue exists.
diff --git a/research/async-inventory-reconciliation/README.md b/research/async-inventory-reconciliation/README.md
@@ -0,0 +1,163 @@
+# Source reconciliation for the archived asynchronous inventory bound
+
+**Research consolidation; no new κ.** All 146 copied profile/width pairs in
+the archived asynchronous inventory certificate agree with their retained
+constructor results. Both original exact receipts reproduce byte-for-byte.
+The companion checker closes a provenance gap and makes its mathematical
+rejections explicit, including under Python optimization.
+
+There is a concrete false-success case in the archived entry point: delete
+every menu word's rank-one charges and run its verifier with `-O`. Both engines
+still emit `PASS_EXACT_FIXED_INVENTORY_FINITE_MENU_DUAL_WALL`, although their
+moment-minus-one lower bound is approximately **−0.30861318239717017**.
+The ordinary, assertion-enabled command correctly rejects that input.
+Changing a menu source path to a nonexistent path also passes with or without
+optimization: the old arithmetic verifier treats provenance fields as inert
+metadata. That second experiment is a missing provenance check, not a
+counterexample to its rational arithmetic.
+
+These are controlled alterations, **not corruption of the committed evidence**.
+The archive's documented command does not enable optimization. Its original
+sources, manifests, reports, and claims are preserved without modification.
+
+## Reproduce
+
+From the repository root, with UV and Python 3.10 or later available:
+
+```sh
+uv run --offline python -B research/async-inventory-reconciliation/verify.py
+```
+
+Expected:
+
+```text
+PASS_ASYNC_INVENTORY_RECONCILIATION 146 source rows, 696 dual inequalities, 24 rejection controls, 12 historical replays
+```
+
+The command uses the standard library and requires no network or solver. It
+compares its deterministic report with [RESULT.json](RESULT.json). Every
+historical subprocess writes to a fresh temporary directory. The same command
+with `python -I -O -B` checks that the companion's rejection conditions survive
+optimization. `--write /absolute/new-report.json` saves a report to a fresh
+path instead of comparing it with the committed result.
+
+Local validation on macOS used Python 3.10.21, 3.13.15, and 3.14.7; reports
+agreed, including isolated optimized runs. Seven focused tests pass normally
+and under optimization:
+
+```sh
+uv run --offline python -I -B research/async-inventory-reconciliation/test_reconciliation.py
+uv run --offline python -I -O -B research/async-inventory-reconciliation/test_reconciliation.py
+```
+
+The original archive integrity check and the selected-record/source-inventory
+check also pass. No repository-wide supplier rebuild was run: this additive
+package changes neither construction sources nor selected certificates.
+Hosted CI and the full mathematical theorem remain separate from these checks.
+
+## Evidence chain and completed coverage
+
+The exact base is `66849e1475c930fd7732b1a0067ffee7e1e95f60`.
+[SOURCE-PINS.json](SOURCE-PINS.json) pins the original verifier, both arithmetic
+engines, copied menu, two exact receipts, explanatory records, and the archive
+manifest. That manifest supplies hashes for every resolved constructor result;
+the companion checks both the manifest's own pin and those actual file bytes.
+The inventory-bound archive was introduced by commit
+`01ad6ae33543b4df9732e7399a21f115d5cf94fd`. The subsequent research integration
+records PR477 at `a5b588d7f16be383ec80e6c5adaa1a75049cb758`, with scope limited
+to archive integrity/navigation rather than historical mathematical replay.
+
+| Source family | Rows checked | Retained status |
+|---|---:|---|
+| `complex501-selective-gauges` | 65 | `PASS_LOCAL_CONSTRUCTOR_ONLY` |
+| `complex501-kernel-gauge-trades` | 78 | `PASS_LOCAL_CONSTRUCTOR_ONLY` |
+| `async505-retimed-new-kernels` | 3 | `PASS_LOCAL_CONSTRUCTOR_ONLY` |
+
+The last three menu labels add `retimed-` to their source labels; the aliases
+are explicit. The first 143 source reports call their width histogram
+`width_counts`, while the last three call it `widths`. All numerical entries
+agree exactly after this field-name mapping. Every row contains 560 helpers.
+There is no new constructor replay or physical admission of these 146 words.
+
+The fixed model has ambient dimension 73, 7,680 live families, 72 complete
+invocations, widths `{5,7,8,9}`, and capacities with multiplicities
+`{8:5760,16:3840,32:3840,48:3840}`. At
+`b = 1373311441205186394131 / 10^24`, the independently enumerated multiplicity
+tuples give 4, 14, 77, and 253 legal patterns for those capacities: **348 per
+engine**, including empty patterns. This enumeration differs from the archived
+verifier's recursive enumeration of nondecreasing width lists.
+
+For each engine, the checker evaluates all dual inequalities, all 146 reduced
+word costs, the minimum, its exact bound and strict margin, and the retained
+six-step outer recurrence. Both margins remain positive (approximately
+`3.1131651758e-26` and `3.1123866414e-26`); `baseline` is the unique minimum.
+The exact rational margins are retained in RESULT.json. This corroborates the
+historical obstruction at its original endpoint; it does not improve it.
+
+## Why these checks imply the scoped obstruction
+
+Let `c(r)` be the moment numerator for a paid remainder of rank `r`, including
+the inherited `10^-16 * 32*m^2` rank-one fallback charge per paid child, and
+let `c(0)=0`. The pinned engines give outward rational bounds on these costs.
+For each available capacity `r` and every fitting helper pattern `p`, the
+companion checks
+
+```text
+alpha[r] + sum(beta[w] for w in p) <= lower(c(r - sum(p))).
+```
+
+Summing over all capacity bins bounds the remainder cost below by the
+inventory's alpha contribution plus the total helper beta contribution.
+For each whole-word menu choice, the checker adds its local paid profile
+cost to its helper beta contribution. Therefore even a fractional mixture
+of 72 menu choices pays at least 72 times the smallest reduced word cost.
+Dividing their sum by `m*live` gives the independently recounted bound.
+Its value is strictly above one at the rejected endpoint. The nonnegative
+moment terms increase with the saving, so this fixed model cannot certify
+that endpoint or a larger one. Discarding chronology, distinct-call owner
+constraints, and integrality only enlarges this model.
+
+The retained outer recurrence is checked separately, with its original
+eta, beta, initial value, six steps, and rounding grid. No other outer
+assembly is excluded. This derivation inherits the interval engines and
+fallback law; the companion is not a third implementation of transcendental
+enclosures or a formal proof of the general multiplication theorem.
+
+## Negative controls and historical discrepancy
+
+Twelve distinct controls run against each engine: nonexistent source,
+changed paid profile, changed widths, omitted row, duplicate source,
+boolean in place of an integer count, raised capacity dual, raised width
+dual, wrong input digest, changed bound, changed outer grid, and deleted
+rank-one charges. All 24 checks reject. In particular, the deleted-charge
+control reaches the mathematical `bound > 1` check independently of source
+binding. The original entry point is also replayed on unchanged inputs and
+the two counterexample inputs, both normally and under `-O`, for both
+engines (12 subprocesses). All four unchanged receipts match the committed
+bytes; the altered-input behavior is recorded separately in RESULT.json.
+
+This is finite evidence reconciliation. It does not establish the physical
+legality of every menu entry, validate an LP solver's completeness, extend
+the fixed word menu, or certify all-size compilation, common-label/mutable
+basis realization, hosting, precision/tape/exact recovery, or analytic
+transfer. No new κ and no failure of the selected #626/#543 construction
+is claimed. The selected record and `upstream/` are unchanged.
+
+## Attribution and coordination
+
+Rohan Arun supplied the archive, source searches, inventory-dual construction,
+and portable certificate, with the AI-assistance disclosure retained in the
+original records. Credit remains with the PR501/502 retiming authors, PR505
+whole-owner construction, PR496 pooling, PR484 gauges/kernel, DreamingOfClouds
+and preceding suppliers. The arithmetic is the pinned PR361/Mercator engine
+and Douglas Colkitt's independent base-two cross-check inherited through that
+chain. Colkitt's integration records explicitly separated archive integrity
+from mathematical replay.
+
+This companion was prepared by Alexander Templeton (`azide0x37`) with
+substantial OpenAI Codex assistance, under Apache-2.0. It is not independent
+human peer review. [CLAIM.md](CLAIM.md) records seed 95, the three candidate
+tasks, base, overlap checks, bounded coverage, and timing. No new search was
+run. PR695 concerns selected Linux evidence, PR704 concerns the central review
+ledger, and PR630 corrects a different E6 archive screen; this contribution
+depends on none of those pending changes.
diff --git a/research/async-inventory-reconciliation/RESULT.json b/research/async-inventory-reconciliation/RESULT.json
@@ -0,0 +1,182 @@
+{
+  "status": "PASS_ASYNC_INVENTORY_RECONCILIATION",
+  "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+  "assignment_seed": 95,
+  "source_rows_checked": 146,
+  "source_prefix_counts": {
+    "async505-retimed-new-kernels": 3,
+    "complex501-kernel-gauge-trades": 78,
+    "complex501-selective-gauges": 65
+  },
+  "source_status": "PASS_LOCAL_CONSTRUCTOR_ONLY",
+  "label_aliases": {
+    "retimed-COMPONENT": "COMPONENT",
+    "retimed-JOINT-47": "JOINT-47",
+    "retimed-JOINT-51": "JOINT-51"
+  },
+  "source_bindings_sha256": "7b4f4a5995b9e668c78abf3f7216d67824da698243e1213b1c5c96e4043c0b58",
+  "source_pins_sha256": "dbce44c5fba3fe56e7666a495a6e8c731d23854fb0bbd3ad8ddd39fcf9fdafe8",
+  "arithmetic": [
+    {
+      "method": "mercator",
+      "patterns_by_capacity": {
+        "8": 4,
+        "16": 14,
+        "32": 77,
+        "48": 253
+      },
+      "strict_margin": "268578454740576800274273094905340548951671997/8627182933488204734293444827846281815563886215212983193953155279749120",
+      "minimizing_labels": [
+        "baseline"
+      ],
+      "next_kappa": "68571402169121/50000000000000000"
+    },
+    {
+      "method": "base-two",
+      "patterns_by_capacity": {
+        "8": 4,
+        "16": 14,
+        "32": 77,
+        "48": 253
+      },
+      "strict_margin": "9959637252396207064063/320000000000000000000000000000000000000000000000",
+      "minimizing_labels": [
+        "baseline"
+      ],
+      "next_kappa": "68571402169121/50000000000000000"
+    }
+  ],
+  "rejection_controls": {
+    "mercator": [
+      "missing_source",
+      "changed_profile",
+      "changed_widths",
+      "truncated_menu",
+      "duplicate_source",
+      "boolean_count",
+      "raise_capacity_dual",
+      "raise_width_dual",
+      "wrong_input_digest",
+      "changed_bound",
+      "changed_outer_grid",
+      "removed_rank1_charges"
+    ],
+    "base-two": [
+      "missing_source",
+      "changed_profile",
+      "changed_widths",
+      "truncated_menu",
+      "duplicate_source",
+      "boolean_count",
+      "raise_capacity_dual",
+      "raise_width_dual",
+      "wrong_input_digest",
+      "changed_bound",
+      "changed_outer_grid",
+      "removed_rank1_charges"
+    ]
+  },
+  "historical_replays": {
+    "mercator": [
+      {
+        "case": "unchanged",
+        "optimized": false,
+        "exit_code": 0,
+        "emitted_pass": true,
+        "strict_margin": "268578454740576800274273094905340548951671997/8627182933488204734293444827846281815563886215212983193953155279749120",
+        "strict_margin_positive": true
+      },
+      {
+        "case": "unchanged",
+        "optimized": true,
+        "exit_code": 0,
+        "emitted_pass": true,
+        "strict_margin": "268578454740576800274273094905340548951671997/8627182933488204734293444827846281815563886215212983193953155279749120",
+        "strict_margin_positive": true
+      },
+      {
+        "case": "wrong_source",
+        "optimized": false,
+        "exit_code": 0,
+        "emitted_pass": true,
+        "strict_margin": "268578454740576800274273094905340548951671997/8627182933488204734293444827846281815563886215212983193953155279749120",
+        "strict_margin_positive": true
+      },
+      {
+        "case": "wrong_source",
+        "optimized": true,
+        "exit_code": 0,
+        "emitted_pass": true,
+        "strict_margin": "268578454740576800274273094905340548951671997/8627182933488204734293444827846281815563886215212983193953155279749120",
+        "strict_margin_positive": true
+      },
+      {
+        "case": "removed_rank1_charges",
+        "optimized": false,
+        "exit_code": 1,
+        "emitted_pass": false,
+        "strict_margin": null,
+        "strict_margin_positive": null
+      },
+      {
+        "case": "removed_rank1_charges",
+        "optimized": true,
+        "exit_code": 0,
+        "emitted_pass": true,
+        "strict_margin": "-26624623802263490289339900959937751459305964823568614158441723030443153/86271829334882047342934448278462818155638862152129831939531552797491200",
+        "strict_margin_positive": false
+      }
+    ],
+    "base-two": [
+      {
+        "case": "unchanged",
+        "optimized": false,
+        "exit_code": 0,
+        "emitted_pass": true,
+        "strict_margin": "9959637252396207064063/320000000000000000000000000000000000000000000000",
+        "strict_margin_positive": true
+      },
+      {
+        "case": "unchanged",
+        "optimized": true,
+        "exit_code": 0,
+        "emitted_pass": true,
+        "strict_margin": "9959637252396207064063/320000000000000000000000000000000000000000000000",
+        "strict_margin_positive": true
+      },
+      {
+        "case": "wrong_source",
+        "optimized": false,
+        "exit_code": 0,
+        "emitted_pass": true,
+        "strict_margin": "9959637252396207064063/320000000000000000000000000000000000000000000000",
+        "strict_margin_positive": true
+      },
+      {
+        "case": "wrong_source",
+        "optimized": true,
+        "exit_code": 0,
+        "emitted_pass": true,
+        "strict_margin": "9959637252396207064063/320000000000000000000000000000000000000000000000",
+        "strict_margin_positive": true
+      },
+      {
+        "case": "removed_rank1_charges",
+        "optimized": false,
+        "exit_code": 1,
+        "emitted_pass": false,
+        "strict_margin": null,
+        "strict_margin_positive": null
+      },
+      {
+        "case": "removed_rank1_charges",
+        "optimized": true,
+        "exit_code": 0,
+        "emitted_pass": true,
+        "strict_margin": "-197512436734188915780845901548704348049546930551/640000000000000000000000000000000000000000000000",
+        "strict_margin_positive": false
+      }
+    ]
+  },
+  "scope": "Pinned historical profile/width reports and two exact finite-menu dual receipts. Uses inherited interval engines. No new search, supplier admission, kappa, independent interval implementation, or full multiplication theorem."
+}