Research: bound selected-word coordinate frame rails

research/complex-frame-plane-rail-seedca04cc/CLAIM.md

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+# Cycle 15 claim
+
+Track `complex-mechanisms`; seed `ca04ccbf3c8c214a13d9c2452e780d32`;
+`complex-rank-shape-decoder`; priority revision 3; base
+`0b1cccf86e2f5132ed286a26ef0a681a495740ea`; selected-record SHA-256
+`10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32`.
+
+Question: can a single canonical two-coordinate plane be introduced at one
+helper-to-helper addition of the selected PR1094 native local word and propagated
+forward by the inclusion-minimal common-frame closure, with every scalar gate,
+start frame, exact A/B target-level and centre-frame boundary, target endpoint,
+and dirty-helper endpoint fixed? Search all 36
+coordinate two-planes and every helper-to-helper A/B addition. Price every
+induced child rank and reject endpoint changes. The deliverable is the exact
+best profile and fixed-template ceiling over this finite domain, with closure
+and endpoint controls. The 10%-mass-to-rank-9 favorable screen is only 1.04318x;
+this search must cover the whole word to have a chance at the required 5%.
+
+Pinned word is member
+`candidate/strict/global/base/providers/gauge44/FULL-WORD.json.gz` of
+`research/community-frontier1094-audit/selected-replay.tar.gz` (archive SHA-256
+`f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6`, member
+SHA-256 `49596aa4ed4fd36cd4582fd0e8ddeb09fd80370a7d8aea1ede52a135b536d289`);
+its selected profile is `{1:2412, 2:418, 3:432, 4:142, 5:82, 8:8}`.
+
+Relevant predecessors: selected provider PR #1094; PR #699 and
+`complex-sw4-frame8` for isolated B-frame coalescences; PR #1429 for the
+fixed late-block interface optimum; PR #1517 for cross-block communication
+under that interface. Adjacent open PR #1186 provides an exact frame solver
+and delivery-rewrite search for an older PR #1148 joint-entrance k8 word;
+this claim tests a one-plane forced closure on the selected PR1094 word.
+The 2026-10-14 16:23:08 UTC overlap refresh covered all 433 open PRs and 618
+discussions. The later 16:29:05 UTC refresh covered 438 open PRs and 619
+discussions; five text matches were our two claim comments, one
+plane-port discussion thread, and two local background documents. Manual review
+found open PR #1186 (frame solver and delivery rewrites for an older word),
+PR #1825 (paired plane-port decoder on selected labels), and PR #1900 (five
+plane queries for the P111 bit decoder). PRs #1825 and #1900 change the
+coverage contract/decoder; this claim keeps coverage and helper inventory fixed
+and changes only internal frame timing. Discussion claim #18924772 poses the
+plane-port question behind those decoder routes. Nearby #18924220, #1909, and
+#1622 concern a Cartesian input-output grid, tetrad-local masks, and a ten-term
+decoder, respectively.
+
+No scalar operation or helper is added. A surviving schedule is a new paid
+rank distribution only if the exact closure retains all pinned internal and
+terminal interfaces.
+Correction: the initial version of this claim used the older PR699 word and
+was released in comment #18926956 before any package or submission. This
+replacement claim uses the current selected PR1094 word above. It expires
+2026-10-14 17:18:00 UTC.
+
+Interim correction: the first selected-word sweep preserved terminal endpoints
+but did not enforce the exact A/B target-level and centre-frame barrier; the
+independent native audit rejected its best candidate. Those provisional counts
+and profiles are discarded. The search now includes both exact interface
+barriers before any candidate can enter the result.
+
+Final finding: complete coverage of all 90,900 pairs yields 569 no-ops, 89,737
+interface/endpoint conflicts, and 594 valid closures over 13 exact rank
+profiles. The exact maximum ceiling equals the selected baseline bracket and
+does not clear the 5% gate; the best candidate passes the pinned independent
+native audit. Reproduction and the bounded conclusion are packaged at
+`research/complex-frame-plane-rail-seedca04cc/`. No new κ is claimed.

research/complex-frame-plane-rail-seedca04cc/NATIVE-AUDIT.json

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+{
+  "status": "PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES",
+  "input_file": "BEST-WORD.json.gz",
+  "content_sha256": "35dba4d11d0bafe1a2f3a19290a850a681f8c2de1b29ec4fe6516ece5791c428",
+  "compressed_sha256": "13a8e666069311175608b83768bb0b377f43805c7677c33ccc9b944f2e3cdae0",
+  "parent_center_interface": null,
+  "v": 112,
+  "h": 9,
+  "R": 480,
+  "entering": 192,
+  "lowends": 78,
+  "coldends": 48,
+  "compensation_gates": 7208,
+  "local_profile": {
+    "1": 2412,
+    "2": 418,
+    "3": 432,
+    "4": 142,
+    "5": 82,
+    "8": 8
+  },
+  "width_inventory": {
+    "4": 56,
+    "5": 32,
+    "7": 30,
+    "8": 122,
+    "9": 240
+  },
+  "checked_columns": 704,
+  "elapsed_seconds": 0.9026521999985562,
+  "scope": "Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing."
+}

research/complex-frame-plane-rail-seedca04cc/PROOF.md

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+# Finite closure and ceiling argument
+
+## Claim
+
+For the pinned selected PR1094 local word, the 36 coordinate subspaces `P = span(e_i,e_j)` and each eligible helper-helper A/B gate have been exhaustively considered as a one-time plane injection followed by least common-frame propagation. Among closures preserving the original exact A/B target-level and centre-frame interfaces and all final endpoints, the best paid profile has exactly the selected baseline profile. Thus this mechanism, in this finite domain and under the fixed-template model, gives no ceiling improvement, in particular not the catalogue's required 5% improvement.
+
+The claim is about this word and this family of frame schedules only.
+
+## Least closure and cost
+
+The replay constructs an ordered list of events from the selected word. It includes scalar gates in A and B, then inserts the exact target-level and centre-frame constraints at their A/B boundary, followed by cleanup events and every final target or helper endpoint. Each event records its original output frame `F` and the incoming frames of its participating registers.
+
+After injecting `P` at a selected helper-helper gate, any later gate reached by an active register must place both gate operands in a common output frame that contains the original `F` and `P`. The least such frame is `span(F,P)`. The enumerator assigns exactly that frame, updates both participants, and keeps propagation active precisely when the augmented output still has a new dimension beyond `F`. If a target-level, centre-frame, or final endpoint does not already contain `P`, the schedule is rejected. This is a direct monotone event replay: it neither skips an induced climb nor adds a frame dimension not forced by the seeded plane and gate.
+
+At each changed event, the script replaces the original per-register climb ranks by the exact new ranks `dim(span(F,P)) - dim(incoming_frame)`, including both gate operands. The original chain profile is decomposed into these gate/interface/endpoint climbs and a checked fixed remainder of eight rank-8 units. The new chain profile is added back to that fixed remainder. It verifies that total paid rank mass is conserved when the same exact endpoints are retained.
+
+## Exhaustion and controls
+
+There are `binom(9,2)=36` coordinate planes and 2,525 eligible helper-helper additions in A/B, so the enumerated domain has 90,900 plane/gate pairs. There are 90,331 non-noop pairs. Of these, 89,737 violate an exact internal interface or final endpoint; 56,830 of the rejections occur at an internal target-level or centre-frame barrier. The remaining 594 closures are priced. They realize 13 distinct profiles. A saved negative-control witness injects `[1,2]` at event 0 and reaches register 60's exact centre frame at event 3563, which does not contain `[1,2]`; this pair must be rejected.
+
+The profile search uses the exact interval arithmetic in pinned `complex-local-word-ceiling/ceiling.py` for the 5%-above-baseline gate and for each surviving profile's ceiling. The floating bisection in `search.py` only chooses which closure to serialize; the exact ceiling intervals over all 13 profiles independently certify that the selected profile is the maximum and strictly separate it from the other 12. The best profile is the original profile, and its exact ceiling bracket equals the exact baseline bracket. Its lower endpoint is `1690054109/10^12`; the largest other-profile upper endpoint is `1690012017/10^12`, leaving a strict gap of `42092/10^12`.
+
+## Independent native check
+
+`BEST-WORD.json.gz` serializes the best closure while retaining the selected scalar program. The pinned `gauge44-slots/independent/audit_local.py` independently checks the exact scalar map in both orientations, all literal frame chains, centre levels, dyadic units, entrance-zero response, wrapper exclusion, and final helper row/column cones. Its receipt records the same paid profile and selected dimensions. The verifier also changes the candidate's claimed rank-1 paid count by one and requires the native auditor to reject it with `paid profile mismatch`.
+
+This native audit is local evidence for the candidate. It is not global owner admission, full supplier reproving, or an exponent reprice. The no-improvement conclusion follows only from the bounded exact profile enumeration and the pinned fixed-template ceiling model.

research/complex-frame-plane-rail-seedca04cc/README.md

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+# Coordinate-plane temporal frame rail (seed `ca04ccbf`)
+
+**Outcome: scoped negative result. No new conditional bound or supplier admission is claimed.**
+
+## Question and result
+
+The selected PR1094 word has local paid profile `{1:2412, 2:418, 3:432, 4:142, 5:82, 8:8}`. This experiment changed frame timing: inject one coordinate two-plane at one helper-to-helper addition, then propagate the least common-frame closure through later gates. It held the scalar program, helper inventory, start frames, exact A/B target-level and centre-frame interfaces, and all final target and dirty-helper endpoints fixed. Every induced climb was priced at its actual rank.
+
+The complete domain is 36 coordinate two-planes by 2,525 eligible seed gates (90,900 pairs). The exact result is 569 no-ops, 89,737 endpoint or internal-interface conflicts, and 594 valid schedules over 13 distinct rank profiles. None reaches the task's 5% ceiling improvement. The highest profile is exactly the baseline profile, with ceiling bracket `[1690054109/10^12, 169005411/10^11]`. Its lower endpoint exceeds the largest other profile's upper endpoint, `1690012017/10^12`, by `42092/10^12`. The best candidate word passes the pinned independent exact native audit.
+
+This closes only the coordinate-plane, single-injection subfamily on this exact word. The first exploratory sweep omitted internal A/B interface barriers and its candidate failed the native audit; that sweep was discarded. The packaged rerun includes both exact target-level and centre-frame barriers, and the counterexample control exercises a centre-frame conflict. No global κ, asymptotic improvement, or general impossibility statement follows.
+
+The selected result is resolved from `certificates/selected-result.json`; source identity and base commit `0b1cccf86e2f5132ed286a26ef0a681a495740ea` are pinned in [SOURCES.json](SOURCES.json). The actual word is member `candidate/strict/global/base/providers/gauge44/FULL-WORD.json.gz` of the pinned selected replay archive, not the historical PR699 word.
+
+## Reproduce
+
+From the repository root:
+
+```sh
+python3 scripts/research_package.py --package research/complex-frame-plane-rail-seedca04cc --check-only
+python3.12 scripts/research_package.py --package research/complex-frame-plane-rail-seedca04cc
+```
+
+The registered replay reruns all 90,900 cases, compares the exact evidence, audits the committed candidate, and verifies that corrupting its claimed paid histogram is rejected. It needs no third-party packages. On systems without Python 3.12, run `python3 -B research/complex-frame-plane-rail-seedca04cc/verify.py` directly; the package metadata check still requires 3.12 for the repository's generic replay.
+
+## Proof and cost accounting
+
+See [PROOF.md](PROOF.md) for the closure invariant, completeness of the finite enumerator, exact interval comparison, and limits. All state and arithmetic needed for the claim are in `SEARCH.json`, `BEST-WORD.json.gz`, and `NATIVE-AUDIT.json`.
+
+## Open next questions
+
+Can a non-coordinate two-dimensional subspace of `F2^9` beat the selected ceiling under the same one-gate closure and exact interface constraints? There are 43,435 such subspaces in total. The first useful step is to compute the automorphism group preserving the pinned gate supports and interfaces, then quotient this Grassmannian before screening representatives. This run does not cover that domain.
+
+## Predecessors and credit
+
+The source is the selected complex provider associated with PR #1094. PR #699 and `research/complex-sw4-frame8` provide historical frame-coalescence context; PR #1429 studies a fixed late-block rank optimum; PR #1517 studies a cross-block floor under that interface. Adjacent open PR #1186 supplies an exact frame solver and delivery-rewrite search for an older PR #1148 word. Open PR #1825 investigates a paired plane-port decoder on selected E8 labels, while PR #1900 studies five plane queries for the P111 bit decoder. Those constructions change the coverage contract or decoder. This package instead tests forced coordinate-plane propagation on the selected PR1094 word with its coverage, helper inventory, and exact interfaces fixed. Source-specific notices remain with their pinned files. New research artifacts are Apache-2.0. OpenAI Codex autonomously designed, implemented, and packaged this experiment; see [TASK.json](TASK.json) for disclosure.