Certify zero four-shear headroom in twelve PR4470 receiver windows (no new kappa)

research/four-shear-window-ceilings/README.md

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+# Four-shear ceilings for twelve receiver windows
+
+**All twelve windows have certified zero headroom at C=0.00302015. No new kappa.** Assignment B independently covers every word of at most four unit shears on the same three persistent fields and fixed boundaries used by fork PR15. Even a favourable geometric relaxation cannot improve their paid moment. [RESULT.json](RESULT.json) retains the exact source-bound receipt; [VALIDATION.md](VALIDATION.md) records the passing hosted replay.
+
+## Complete alphabet and scope
+
+The twelve generators are y_i += sign*y_j for i != j and sign in {-1,1}. Every word of lengths zero through four is enumerated, including cancellations: 22,621 words. For each of the four sign choices exactly 84 words have the required exact integer 3 by 3 receiver endpoint, comprising two length-two, two length-three and eighty length-four words. No heuristic pruning or floating-point equality is used.
+
+The source has 128 eligible adjacent pairs. Only the explicitly bounded first twelve are tested; all are in phase B. Each has all 84 matching words admitted by the dimension screen. Ten windows have one relaxed paid profile, and the two at indices 10575 and 10579 have four. Every profile's directed gain upper bound is nonpositive; the best is exactly zero. The original path is included, so the optimistic ceiling is attained by the incumbent. This does not cover the other 116 windows or joint changes to overlapping windows.
+
+## Why the relaxation is a valid ceiling
+
+For each endpoint-matching word, propagate mandatory lower subspaces forward. At a contact of fields i,j, every legal common frame contains the sum of their current lower bounds; update both to that sum. Propagate permissible upper subspaces backwards from the fixed exits, replacing both operands' bounds by their intersection. Induction gives L_j contained in F_j contained in U_j for every actual monotone path. If L_j is not contained in U_j, the word is impossible under this contract.
+
+For surviving words, enumerate every integer contact dimension between dim(L_j) and dim(U_j), nondecreasing along each operand's path and bounded by its fixed terminal dimension. Charge each positive entrance/intermediate gap and every remaining exit gap. The sum of charged ranks equals total terminal-minus-entrance rank mass. Forgetting simultaneous incidence constraints can add profiles, never remove a legal one. Thus minimum relaxed paid moment is a lower bound on legal cost, and old cost minus that lower bound is an upper bound on possible gain.
+
+All distinct relaxed profiles are retained. Directed rational intervals bound signed old-minus-new costs, with identical profiles treated as exact equality. The independent power method uses binary-reduced logarithms and an alternating expansion of r*exp(-C log r). Optimistic positive profiles would not establish a construction; here none exists. Individual window gains must never be summed across overlapping operations or shared resources.
+
+## Reproduction and independence
+
+Python 3.12, standard library only:
+
+```sh
+python -B scripts/research_package.py --package research/four-shear-window-ceilings
+python -I -O -B research/four-shear-window-ceilings/verify.py --self-test
+```
+
+The registered source-bound replay passed on CPython 3.12.15, including normal verification, optimised controls and preservation of committed inputs. Seven source files are pinned by Git blob and SHA256. The inherited constructor emits candidate data only; no predecessor proof engine or PR15 acceptance routine is imported. Window extraction, scalar enumeration, relaxation and interval arithmetic are separately implemented. Normal replay compares the full retained receipt without rewriting it. Exact small-domain controls include 68 actual geometric paths plus exit-charge, incompatible-exit and equality checks.
+
+## Task and overlap
+
+Canonical base f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc, priority revision 7; PR4470 source b9a13c1673e0e9697de410de16e8bbf3207a7363. TASK.json records the refined independent-moment assignment. PR4121 uses older T360 sources; #4091's fixed-inventory ceiling is not transferred outside its hypotheses. PR4529/4532/4533 concern compiler gates and ranks. Searches were targeted, not exhaustive overlap pagination or proof of novelty. The historical baseline helper was not run. No selected record or frozen input changed.
+
+## Open next questions
+
+Do not reseed this exact domain. A useful next experiment must change the length cap, coefficient alphabet, adjacency, owned-field allowance or producer/consumer boundary explicitly and reprice the complete contract. Another window is outside the certificate but should have a concrete structural reason for investigation. Physical lowering, full native correctness and consumer transfer remain necessary for any later positive candidate. TASK.json records the next question and blockers.
+
+## Credit
+
+Credit zxv's receiver-sharing and productive-helper work, Cinna Davis's PR4470, Jacob Alan Sussman, GamingPuzzled's earlier finite census and the retained native/Clifford/geometry/outer contributors. Prepared for Chris R / Clear1nsight with substantial OpenAI assistance, Apache-2.0. Separate implementations in one session do not imply separately launched agents, independent human review or formal acceptance.

research/four-shear-window-ceilings/RECEIPT-COMPARISON.md

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+# Canonical JSON receipt adapter
+
+The fresh scientific result uses integer rank keys in Python dictionaries; JSON object keys are strings. The original direct main function compares those Python objects before normalisation, so it cannot verify an otherwise identical stored result. The registered entry point is now replay.py, which authenticates the unchanged scientific engine at blob 804451f1b6a420d32cb2f4bc660c23550021badb, executes run() with every source and mathematical check, and compares every field in canonical JSON form. It never invokes the --write authoring path or changes RESULT.json.
+
+Only object order and JSON's required string key representation are normalised. No value is rounded or omitted. Arrays remain ordered and encoded boolean/integer and integer/float values remain distinct. Six controls reject changed counts, types, array order and missing/extra fields in normal and optimised modes. Use the registered command or replay.py for the stored receipt; the original --self-test remains valid. This adapter preserves scientific evidence rather than changing acceptance predicates.

research/four-shear-window-ceilings/RESULT.json

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+{"controls":{"actual_small_paths_checked":68,"enumerated_words_per_sign_case":22621,"exact_equality_control":true,"exit_charge_control":true,"incompatible_exit_control":true,"word_counts":{"(-1, -1)":84,"(-1, 1)":84,"(1, -1)":84,"(1, 1)":84}},"excluded_window_count":12,"new_kappa":false,"not_covered":["geometric attainability of relaxed profiles","nonadjacent or larger windows","joint overlapping rewrites","physical native admission","global ceiling or new kappa"],"scale":1000000000000000000,"schema":"four-shear-window-ceilings/v1","source_head":"b9a13c1673e0e9697de410de16e8bbf3207a7363","status":"PASS_FINITE_ALPHABET_CEILINGS","tested_saving":"60403/20000000","tested_windows":12,"total_eligible_windows":128,"windows":[{"certified_no_strict_gain":true,"coefficients":[-1,1],"compatible_words":84,"exit_dimensions":[0,2,0],"index":10554,"old_paid":{"2":1},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":2,"phase":"B","relaxed_profiles":1,"roles":[162,172,513],"start_dimensions":[0,0,0]},{"certified_no_strict_gain":true,"coefficients":[1,1],"compatible_words":84,"exit_dimensions":[2,0,0],"index":10555,"old_paid":{"2":1},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":3,"phase":"B","relaxed_profiles":1,"roles":[172,196,513],"start_dimensions":[0,0,0]},{"certified_no_strict_gain":true,"coefficients":[1,-1],"compatible_words":84,"exit_dimensions":[2,1,1],"index":10557,"old_paid":{"1":3},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":5,"phase":"B","relaxed_profiles":1,"roles":[140,144,502],"start_dimensions":[0,0,1]},{"certified_no_strict_gain":true,"coefficients":[-1,1],"compatible_words":84,"exit_dimensions":[1,1,1],"index":10558,"old_paid":{"1":2},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":6,"phase":"B","relaxed_profiles":1,"roles":[144,187,502],"start_dimensions":[0,0,1]},{"certified_no_strict_gain":true,"coefficients":[1,1],"compatible_words":84,"exit_dimensions":[1,2,1],"index":10560,"old_paid":{"1":3},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":8,"phase":"B","relaxed_profiles":1,"roles":[168,150,548],"start_dimensions":[0,0,1]},{"certified_no_strict_gain":true,"coefficients":[1,-1],"compatible_words":84,"exit_dimensions":[2,1,1],"index":10561,"old_paid":{"1":3},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":9,"phase":"B","relaxed_profiles":1,"roles":[150,115,548],"start_dimensions":[0,0,1]},{"certified_no_strict_gain":true,"coefficients":[1,-1],"compatible_words":84,"exit_dimensions":[2,1,1],"index":10563,"old_paid":{"1":3},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":11,"phase":"B","relaxed_profiles":1,"roles":[131,117,560],"start_dimensions":[0,0,1]},{"certified_no_strict_gain":true,"coefficients":[-1,-1],"compatible_words":84,"exit_dimensions":[1,1,1],"index":10564,"old_paid":{"1":1},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":12,"phase":"B","relaxed_profiles":1,"roles":[117,584,560],"start_dimensions":[0,1,1]},{"certified_no_strict_gain":true,"coefficients":[-1,-1],"compatible_words":84,"exit_dimensions":[1,2,3],"index":10575,"old_paid":{"1":1,"2":1,"3":1},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":23,"phase":"B","relaxed_profiles":4,"roles":[205,170,452],"start_dimensions":[0,0,0]},{"certified_no_strict_gain":true,"coefficients":[-1,-1],"compatible_words":84,"exit_dimensions":[1,1,3],"index":10577,"old_paid":{"1":2,"2":1},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":25,"phase":"B","relaxed_profiles":1,"roles":[118,194,453],"start_dimensions":[0,0,1]},{"certified_no_strict_gain":true,"coefficients":[-1,-1],"compatible_words":84,"exit_dimensions":[1,2,3],"index":10579,"old_paid":{"1":1,"2":1,"3":1},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":27,"phase":"B","relaxed_profiles":4,"roles":[120,207,454],"start_dimensions":[0,0,0]},{"certified_no_strict_gain":true,"coefficients":[-1,-1],"compatible_words":84,"exit_dimensions":[1,1,3],"index":10581,"old_paid":{"1":2,"2":1},"optimistic_gain_upper_scaled":0,"optimistic_positive_profiles":0,"ordinal":29,"phase":"B","relaxed_profiles":1,"roles":[192,179,455],"start_dimensions":[0,0,1]}]}

research/four-shear-window-ceilings/SOURCES.json

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+{"schema_version":1,"base_commit":"f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc","files":[{"path":"certificates/selected-result.json","usage":"provenance","git_blob":"ed33caef5c5827693e9572d252a66f99cbb73d40","sha256":"5732707cc1e460b090b53f2463162749ad860de878a18f7408938671d295a9d9"},{"path":"docs/research/agent-task-catalog.json","usage":"provenance","git_blob":"64bfc5af6709ed9811171e0a2108f05e1219cb65","sha256":"352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96"},{"path":"research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz","usage":"input","git_blob":"4a8c4ed26e53a72362d571c972e65aff546be784","sha256":"6418ec3da24d548a57f5c3fe5b9062c26c9478e638504a61c387f5cfb5f4ed61"},{"path":"research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz","usage":"input","git_blob":"b46d44c6ee624968dd57be928b0c15d9d45f3b2c","sha256":"c54b0a3e129d28e6dbf74fa731fc3bb70fe3c6705f07256750fbecddcc842d39"},{"path":"research/fresh-helper-boundary/native.py","usage":"input","git_blob":"1b36f6cb5f205c33bf48811e0b1b3621c55e8154","sha256":"9b55a2d3c3972148fae9d112e745d9244968166bd89bd900c938f429fc76ab29"},{"path":"research/fresh-helper-boundary/CHANGES.json","usage":"input","git_blob":"45744fedd0e28967aa72586048b8bc0c72f419a9","sha256":"cde73b8ff5b3c0d06e69e2293b991b24fd14a16dd4ccab7ff6b3439074a94624"},{"path":"research/missing-join-frame/PATCH.json","usage":"input","git_blob":"f96d295d40014d4dd503f58eb3cdabcbb4b8e101","sha256":"9ab5328245ff02c9d0be21d39bcc375f50bc5d7909e9f7b9a3a9a6f812f5bd6e"},{"path":"research/joint-helper-lattice/PATCH.json","usage":"input","git_blob":"51304a6601061ed4e698f910b09135ef109555e3","sha256":"296d0e8c58cc70febe042c681ef30d6bb469818c0835fbcaac8aa8d330f5b727"},{"path":"research/joint-helper-lattice/native_joint.py","usage":"input","git_blob":"0315f80e2fdef5e0eef13e3e9b8f72066238164d","sha256":"50869b1bcad7493e6b4cb2a4cd5d2fd9a193a5921100483fa2c3f2c999ddfd46"}]}

research/four-shear-window-ceilings/TASK.json

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+{"schema_version":1,"task_id":"independent-moment","priority_revision":7,"base_commit":"f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc","original_card":{"id":"independent-moment","question":"Does a new paid-profile or mixture-ceiling claim have independent source-bound coverage of its actual changed ledger?","starting_points":["docs/research/research-family-status.md","certificates/selected-result.json","research/staged544-mixed-fourth-entry/README.md","research/staged-fourth-mixture-ceiling/README.md","research/r437-two-window-carrier/README.md"],"methods":["Independently reconstruct one changed paid ledger or pooled dual with exact source and model binding.","Check a genuinely uncovered moment implication with a different enclosure method and semantic controls."],"acceptance_gate":"Demonstrate independence, source binding, positive cases and semantic failure controls. Name the existing checks and the missing coverage. More digits or another equivalent evaluation of an unchanged root is not by itself new verification coverage.","first_step":{"command":["python3","-B","scripts/research_baseline.py"],"expected":"PASS_RESEARCH_BASELINE_BINDINGS_ONLY","inspect":"Choose one uncovered implication in #4088 literal mixed fill, #4091 pooled dual/model binding or #4067 changed frame/host bill. #4091 pins an earlier #4088 head: validate word, capacity and stock equivalence before applying that ceiling to the later fill.","scope":"Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."},"first_experiment":"Independently reconstruct one changed ledger or pooled certificate with a positive case and a semantic failure control. Compare exact sources and name what existing checks miss. Keep this separate from supplier-boundary-audit (ordinary/outer dispatch) and uniform-transfer-audit (all-size proof). Stop after the chosen implication; more digits of an unchanged root are not additional mechanism coverage.","bottleneck_link":"Independent pricing prevents unsupported frontier claims and can reveal genuine accounting slack.","allowed_variations":["Reconstruct either a source ledger or a numeric enclosure with a different method."],"scope_change_triggers":["Importing the primary function and calling its output independent verification.","Calling an aggregate histogram or source archive an independently accepted physical supplier."],"overlap_terms":["independent moment","rank histogram","exact enclosure","2979","rank7 joint endframes","paired extraction","joint lowering","4088","4091","4067","staged544-mixed-fourth-entry","staged-fourth-mixture-ceiling","r437-two-window-carrier"],"existing_checks":[{"scope":"PR #4088: mixed local/owner/phase ledger and moment reported.","evidence":"research/staged544-mixed-fourth-entry/README.md","remaining":"Independent binding of changed construction to paid histogram, distinct from full admission.","status":"author-checked","source_commit":"72d7efc181edb21806a878f174847c96dd410ab0","selected_record_sha256":"bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"},{"scope":"PR #4091: sharp pooled ceiling proposed for fixed THREE/FOUR words and inventory.","evidence":"research/staged-fourth-mixture-ceiling/README.md","remaining":"Validate dual, exhaustive pattern scope and exact source equivalence before applying to newer fills.","status":"author-checked","source_commit":"a29bdd8f56cd18b805917775cdec09ff935eddc4","selected_record_sha256":"bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"},{"scope":"PR #4067: paid (2,2) to (1,3) exchange and fixed OQ4 host reported.","evidence":"research/r437-two-window-carrier/README.md","remaining":"Independent full cost delta; remaining caller/precision/stock obligations are separate.","status":"author-checked","source_commit":"a95f11c52e3ca1e4c5171b3c20d8f4b0815aee2e","selected_record_sha256":"bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"}]},"scope_status":"refined","actual_scope":"Assignment B: exact finite-alphabet optimistic ceilings for twelve PR4470 receiver windows, all words of at most four unit shears with fully charged monotone dimension paths.","scope_change_reason":"User-requested ceiling support alongside construction. The alphabet is larger than the three-shear construction, while simultaneous geometry is relaxed only towards lower costs.","bottleneck_link":"Avoid expanding a rewrite domain with no complete paid-moment headroom, without mistaking optimistic profiles for circuits.","budget_minutes":60,"stop_rule":"Stop at twelve individual fixed-window ceilings; do not add overlapping gains, reseed an excluded domain or claim a universal barrier.","outcome":"negative-result","evidence":"Hosted registered replay 39724143539 at dce9576ec448af52009ec13a4f8c1a740fb4a8d8 passes CPython 3.12.15. All twelve windows have exact optimistic gain upper bound zero. Each includes all 84 endpoint-matching words from 22621 enumerated words per sign case. Ten windows have one relaxed profile, two have four. RESULT.json preserves all observed fields. Normal and optimised controls, 68 legal toy paths and committed-input preservation pass. Receipt-retention metadata used negative and was corrected to the schema's negative-result value without changing science or evidence.","author":"Chris R / Clear1nsight","ai_assistance":"Substantial OpenAI assistance; separate implementation in one session, not independently launched agents, human review or formal-kernel acceptance.","overlap":{"nearby_prs":[4085,4091,4121,4359,4470,4478,4483,4504,4529,4532,4533],"fork_companion":15,"method":"Targeted searches and bounded Discussion reads, not exhaustive pagination or novelty proof.","baseline_helper_run":false,"canonical_refresh":"2026-10-22T04:44:00Z"},"open_questions":[{"question":"Which explicit changed contract can escape the twelve-window four-shear ceiling?","why_it_matters":"A new seed in the same finite domain cannot improve its exact ceiling.","first_step":"Change one of length cap, coefficients, adjacency, owned-field allowance or producer/consumer boundary, derive the fully charged optimistic model and test one structurally justified window.","blocked_by":"No conclusion about the other 116 windows, larger or joint rewrites, physical lowering or complete consumer admission is supplied."}]}