Mister-Meeseeks · Oct 14, 2026 · Oct 14, 2026 · Oct 14, 2026
diff --git a/research/complex-diagonal-child-batches-seed95da/CLAIM.md b/research/complex-diagonal-child-batches-seed95da/CLAIM.md
@@ -0,0 +1,22 @@
+# Coordination claim
+
+Claim posted in the authorized mechanism-coordination thread:
+[Discussion #1167, comment 18920760](https://github.com/CrocSwap/integer-mult-bounds/discussions/1167#discussioncomment-18920760).
+
+- Track: `complex-mechanisms`; accepted seed: `95da2249593d8218c4c1e30f471d675f`.
+- Card: `complex-rank-shape-decoder`, priority revision 3; refined scope `selected-gauge44-diagonal-batch/contiguous-rank1-runs`.
+- Exact base: `0b1cccf86e2f5132ed286a26ef0a681a495740ea`.
+- Object: size-16 diagonal block children from uninterrupted rank-one climbs on distinct output columns in the selected gauge44 provider.
+- Method: source-pinned census in both orientations, exact diagonal multiplication identity, and favorable ceiling screen with all additional interface costs set to zero.
+- Bounded domain: non-overlapping size-16 groups wholly contained in rank-one-only event runs; no reordering, buffering, changed word, or other rank.
+- Nearest predecessor: open PR #1605 / Discussion #1596 on rank-one reblocking thresholds; this package tests cross-column diagonal batching on the exact selected chronology.
+- Expiry: 2026-10-14 10:05 UTC.
+- Outcome: eight groups, 128 rank-one calls; best-case ceiling gain 1.7191%, below 5%. No physical admission or κ claim.
+
+## Result and handoff
+
+The claim was updated with the finding and released at the same Discussion link. The source-pinned
+package was submitted as [PR #1779](https://github.com/CrocSwap/integer-mult-bounds/pull/1779),
+head `1e3128bf642bbaf250b7d6b9639b2bb24b98ce5e`. At the last hosted-status check (2026-10-14
+14:48 UTC), the PR was open and its 61 checks were queued; local registered replay and metadata
+checks passed. Physical input staging and dirty-state restoration remain unimplemented.
diff --git a/research/complex-diagonal-child-batches-seed95da/README.md b/research/complex-diagonal-child-batches-seed95da/README.md
@@ -0,0 +1,94 @@
+# Cross-column diagonal batching has limited chronological coverage
+
+**Scoped construction screen and bounded obstruction. No physical supplier or new κ is claimed.**
+
+## Result
+
+The selected #1094 gauge44 provider has 2,412 rank-one children per orientation. I tested a new
+cross-column mechanism: replace sixteen adjacent rank-one child calls on distinct destination
+columns by one rank-16 child. For input blocks (X_i,Y_i), place them on the diagonals of two
+16-by-16 block matrices. Their product is
+
+\[
+\operatorname{diag}(X_1,\ldots,X_{16})
+\operatorname{diag}(Y_1,\ldots,Y_{16})
+=\operatorname{diag}(X_1Y_1,\ldots,X_{16}Y_{16}).
+\]
+
+The diagonal outputs are exactly the sixteen original rank-one child results; every off-diagonal
+output is zero. This is an exact identity over any associative coefficient ring.
+
+The hash-pinned forward and backward traces each contain exactly eight non-overlapping, uninterrupted
+rank-one batches of size 16: one run of 16 calls and one run of 112 calls, partitioned into seven
+batches. The batches serve 128 of 2,412 rank-one children. No other uninterrupted rank-one run has
+length 16. No event is moved across a scalar, adapter, centre, or other-rank climb.
+
+Replacing those batches preserves the paid rank mass:
+
+| Per-call profile | Rank mass | Exact relaxed ceiling upper endpoint |
+|---|---:|---:|
+| Selected `{1:2412, 2:418, 3:432, 4:142, 5:82, 8:8}` | 5,586 | 0.001690054109089 |
+| Eight ideal rank-16 batches `{1:2284, 2:418, 3:432, 4:142, 5:82, 8:8, 16:8}` | 5,586 | 0.001719107428154 |
+
+The upper endpoint rises by **1.7191%**, below the task's required 5% gate (target 0.001774556814543).
+This is already the most favorable screen: every new operand-copy, source-access, frame, interface,
+hosting, output-storage, precision, and dirty-restoration charge is set to zero. The physical child
+would expose 256 input slots per side and 256 output slots per batch, although only sixteen diagonal
+inputs and outputs are useful. Its actual gathering and restoration contract has not been realized
+or priced. Since the free-interface profile misses the declared gate, this chronology-constrained
+family is stopped before physical rewriting.
+
+This result does not rule out batching nonconsecutive children with stored operands, changing the
+word or template, or using another block size. It supplies no supplier admission, κ, or selected-record
+change.
+
+## Source and overlap
+
+The provider member is
+`candidate/strict/global/base/providers/gauge44/LOCAL-PROGRAMS.json.gz` in
+[`selected-replay.tar.gz`](../community-frontier1094-audit/selected-replay.tar.gz), archive SHA-256
+`f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6` and member SHA-256
+`241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a`. The selected-record SHA-256
+is `10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32`; all live pins are listed
+in [SOURCES.json](SOURCES.json).
+
+Nearest predecessor work is Arham Tahir's [PR #1605](https://github.com/CrocSwap/integer-mult-bounds/pull/1605)
+(head `488f2ecf1835c6d813e96543656dddf0062fdc9a`)
+and Josie Elliston's [Discussion #1596](https://github.com/CrocSwap/integer-mult-bounds/discussions/1596),
+which derive rank-one reblocking budgets and leave chronological physical batching open. Navinor's
+[Discussion #1659](https://github.com/CrocSwap/integer-mult-bounds/discussions/1659) and [PR #1686](https://github.com/CrocSwap/integer-mult-bounds/pull/1686)
+settle same-word per-column frame assignments. The present test changes the interface by batching
+across sixteen distinct destination columns through a diagonal rank-16 child; it does not improve a
+per-column frame assignment. The exact diagonal identity is elementary, while its physical input,
+output, and restoration realization remains open.
+
+## Reproduce
+
+From the repository root, Python 3.12 and the standard library are sufficient:
+
+```sh
+python3 scripts/research_package.py --package research/complex-diagonal-child-batches-seed95da --check-only
+python3.12 scripts/research_package.py --package research/complex-diagonal-child-batches-seed95da
+```
+
+The verifier checks both event orientations, every admissible contiguous batch, the unchanged rank
+mass, the exact diagonal product identity, the rational ceiling bracket, and failure controls for
+off-diagonal support, duplicate destinations, and wrong-rank events.
+
+## Open next questions
+
+Can nonconsecutive rank-one children be buffered into diagonal rank-16 batches with a fully charged
+source, copy, frame, hosting, output, and arbitrary-dirty restoration schedule? This matters because
+the available contiguous batches cover too little rank-one payload to pass the 5% screen. A feasible
+first step is to pin operand-ready/use windows for the selected word and solve the resulting disjoint
+16-way interval packing problem. The blocker is that the current local event trace records child
+columns and frame changes, not a realized multi-column dirty-state memory contract.
+
+## Credit
+
+Credit Sagar Thakrar / PR1012 for the retained coverage identity, Douglas Colkitt / PR1240 for the
+local-word ceiling model, Arham Tahir / PR1605 and Josie Elliston / Discussion #1596 for rank-one
+reblocking budgets, Navinor / Discussion #1659 and PR1686 for same-word frame screens, and the
+selected Rohan Arun / Jeremy Kothe / Hao Yan construction lineage. Prepared by Jose Manuel
+(@jmbarrancoml) with substantial OpenAI Codex assistance in source analysis, proof, code, and prose.
+New material is Apache-2.0; frozen source archives and licenses are unchanged.
diff --git a/research/complex-diagonal-child-batches-seed95da/SOURCES.json b/research/complex-diagonal-child-batches-seed95da/SOURCES.json
@@ -0,0 +1,42 @@
+{
+  "schema_version": 1,
+  "base_commit": "0b1cccf86e2f5132ed286a26ef0a681a495740ea",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "input",
+      "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11",
+      "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "06c96f5579bb67ed1b86d334e78fbed7da6945f1",
+      "sha256": "6686ad58f1fbdbc87134a78901b60fd53a20d3984355e91defbbebc9e9fa8075"
+    },
+    {
+      "path": "research/community-frontier1094-audit/SELECTED-SOURCE.json",
+      "usage": "input",
+      "git_blob": "6a75493790b4eff9c4a98051ef8b01d6aad0d5a8",
+      "sha256": "79b3de5db3dbcb9829789ba58e9e45758926031e2a7d80667a08429d369be53b"
+    },
+    {
+      "path": "research/community-frontier1094-audit/selected-replay.tar.gz",
+      "usage": "input",
+      "git_blob": "c24daf067f9c543421d89ca2eeaa4eb78a57fb6f",
+      "sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6"
+    },
+    {
+      "path": "research/complex-local-word-ceiling/RESULT.json",
+      "usage": "input",
+      "git_blob": "77f55043a679dd722330f1e2499863e36376d9f9",
+      "sha256": "d91d6c46509875abf1f61de67c2609656d3dc685451299f83caa6f922493692d"
+    },
+    {
+      "path": "research/complex-local-word-ceiling/ceiling.py",
+      "usage": "input",
+      "git_blob": "6c0f54527d879396f689523bfde19928a9b6157c",
+      "sha256": "86a1432870b3b21d8454106ec9162fddc0471472d9214c590a1420f2426cedfc"
+    }
+  ]
+}
diff --git a/research/complex-diagonal-child-batches-seed95da/TASK.json b/research/complex-diagonal-child-batches-seed95da/TASK.json
@@ -0,0 +1,83 @@
+{
+  "schema_version": 1,
+  "task_id": "complex-rank-shape-decoder",
+  "track": "complex-mechanisms",
+  "research_seed": "95da2249593d8218c4c1e30f471d675f",
+  "priority_revision": 3,
+  "catalogue_sha256": "6686ad58f1fbdbc87134a78901b60fd53a20d3984355e91defbbebc9e9fa8075",
+  "base_commit": "0b1cccf86e2f5132ed286a26ef0a681a495740ea",
+  "selected_record_sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32",
+  "predecessors": [
+    {
+      "reference": "CrocSwap/integer-mult-bounds#1605",
+      "head": "488f2ecf1835c6d813e96543656dddf0062fdc9a",
+      "relationship": "Rank-one reblocking cost thresholds; this package adds an exact chronological cross-column diagonal-batch census."
+    },
+    {
+      "reference": "CrocSwap/integer-mult-bounds#1094",
+      "head": "0fc329d0bec93ca7cd288eaea1295172e8789810",
+      "relationship": "Selected provider construction and source lineage, retained through the pinned main-branch source archive."
+    }
+  ],
+  "claim_url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1167#discussioncomment-18920760",
+  "original_card": {
+    "id": "complex-rank-shape-decoder",
+    "question": "Can a decoder deliver the local paid mass in fewer, larger-rank children (block frame climbs instead of rank-1 to rank-3 steps)?",
+    "starting_points": [
+      "research/complex-local-word-ceiling/README.md",
+      "research/complex-decoder-field-extension-seed44/README.md",
+      "research/complex-frame-pair-decoders/README.md"
+    ],
+    "methods": [
+      "Find one exact small decoding identity whose frame path climbs in blocks, and price its complete per-call profile.",
+      "Bound the best effective child rank achievable for one fixed support alphabet, including copies, frames and restoration."
+    ],
+    "acceptance_gate": "A per-call local profile, with all copied information, frames and restoration counted, whose ceiling exceeds the selected word's by at least 5%; masked or overcomplete supports must change an assumption of the eight-term all-pairs bound.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "research/complex-local-word-ceiling/verify.py"
+      ],
+      "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING",
+      "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.",
+      "scope": "Positive control and planning budget only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin. Ideal budget: rank-16 delivery is 2.31x (levers.py).",
+    "bottleneck_link": "Rank-1 children are about half of recursive cost; the selected word's effective child rank is about 3.9. Larger-rank delivery lowers recursive cost per unit of paid mass.",
+    "allowed_variations": [
+      "One masked, overcomplete or block decoder family with exact labels and supports.",
+      "A scoped lower bound on effective rank for one alphabet.",
+      "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope."
+    ],
+    "scope_change_triggers": [
+      "Repacking idle remainders of an unchanged word (covered by the packing ceiling).",
+      "Repeating the eight-term all-pairs search inside its proved scope."
+    ],
+    "overlap_terms": [
+      "rank shape",
+      "block climb",
+      "masked decoder",
+      "overcomplete",
+      "effective rank"
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "On the selected #1094 gauge44 provider, census size-16 diagonal rank-16 batches drawn only from uninterrupted rank-one child runs on distinct destination columns, in both orientations; price the exact transformed local profile with all additional interface costs optimistically set to zero.",
+  "scope_change_reason": "The broad rank-shape card is refined away from the heavily covered same-column frame-retiming and eight-term masked-decoder families. This changes the child interface: one rank-16 diagonal block child serves sixteen rank-one children across distinct output columns. The bounded experiment stops if even the zero-additional-cost profile misses the 5% ceiling gate.",
+  "bottleneck_link": "Rank-one children are a large share of the selected local recursive mass. A rank-16 child can lower the moment per unit of preserved rank mass, so a valid cross-column batch could improve the binding complex-side ceiling.",
+  "budget_minutes": 60,
+  "stop_rule": "Restrict to non-overlapping size-16 batches wholly contained in uninterrupted rank-one climb runs in the hash-pinned selected provider, ignoring only explicit phase markers. Grant all new copying, source, frame, interface, hosting, output-storage, precision and restoration costs zero for the ceiling screen. Stop without physical rewriting if the resulting exact ceiling is below 1.05 times the selected local-word ceiling; do not expand into nonconsecutive buffering or a different word in this cycle.",
+  "outcome": "negative-result",
+  "evidence": "Both source orientations have 2,412 rank-one climbs and exactly eight admissible size-16 batches, serving 128 climbs. The mass-preserving ideal profile {1:2284, 2:418, 3:432, 4:142, 5:82, 8:8, 16:8} has exact rational ceiling upper endpoint 1719107428154/10^15, 1.7191% above the baseline 1690054109089/10^15 and below the 5% target. The 16-way diagonal block identity is exact. Every additional physical interface charge is waived in this favorable screen; no physical admission, new supplier, or kappa is claimed.",
+  "author": "Jose Manuel (@jmbarrancoml)",
+  "ai_assistance": "Substantial OpenAI Codex assistance in source analysis, mathematical formulation, exact verifier, package construction, and writing; no subagents.",
+  "open_questions": [
+    {
+      "question": "Can nonconsecutive rank-one children be buffered into diagonal rank-16 batches with a fully charged source, copy, frame, hosting, output, and arbitrary-dirty restoration schedule?",
+      "why_it_matters": "The eight contiguous batches cover too little rank-one payload to pass the 5% ceiling screen; a larger packing would be needed before the new interface could affect the binding supplier materially.",
+      "first_step": "Pin operand-ready/use windows from the selected local word, then solve a disjoint 16-way interval packing problem and price one emitted batch end to end.",
+      "blocked_by": "The pinned local event trace records columns and frame changes but does not specify a multi-column dirty-state memory layout, operand lifetimes, or the restoration contract for an M16 child."
+    }
+  ]
+}
diff --git a/research/complex-diagonal-child-batches-seed95da/VERIFY.json b/research/complex-diagonal-child-batches-seed95da/VERIFY.json
@@ -0,0 +1,24 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "certificates/selected-result.json",
+    "research/community-frontier1094-audit/SELECTED-SOURCE.json",
+    "research/community-frontier1094-audit/selected-replay.tar.gz",
+    "research/complex-local-word-ceiling/RESULT.json",
+    "research/complex-local-word-ceiling/ceiling.py"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Archive/member pins; exact rank-one event profiles in both orientations; all maximum disjoint size-16 uninterrupted batch windows; direct-sum diagonal product identity; mass-preserving candidate profile; certified baseline and candidate ceiling brackets; five-percent rejection and three mathematical/source negative controls."
+    }
+  ]
+}