Finite complex construction: four exact U8 B-stage shear rewrites (no new kappa)

research/u8-b-cancellation-seed32/CLAIM.md

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+# Sprint claim — U8 B-gate cancellation audit
+
+- Track / seed: complex supplier (20–39), OS-random assignment seed 32.
+- Base commit: `abdc6a7002abdbcd9e21bfc5e1a795784deacfdf`.
+- Current selected record: PR942 / T37, conditional kappa `1661960547713947/10^18`; no frontier edit is proposed.
+- Three narrow candidates inspected: (1) coalesce fourteen dependency-safe repeated A additions, (2) delete four dependency-safe inverse B-addition pairs, (3) re-lower large cleanup coefficients. Seed 32 selects the B region; candidate (2) has the strongest favorable complete local budget because it removes work rather than changing coefficients.
+- Claimed object: four apparent inverse add pairs in the selected U8 `native/local/CANONICAL-WORD.json.gz`, B indices 176/178, 194/196, 204/206, and 278/280.
+- Method: source-pin the accepted replay archive; independently replay the exact scalar word on arbitrary basis columns before and after deleting each pair; prove a local commutation/cancellation criterion; regenerate the emitted local programs; compare exact semantic, frame, profile, macro, and primitive invoices; include single-deletion and dependency-touch negative controls.
+- Expected deliverable: a scoped finite complex-supplier construction or a precise obstruction if native/frame admission fails. No new kappa without a complete supplier and outer reprice.
+- Expected finish: 2026-10-13 21:00 CEST.
+- Coordination: no pinned sprint coordination issue was found; recent open-PR title/body searches found no U8 B-cancellation claim, so this claim is local.
+
+## Final update
+
+Completed a finite complex-supplier construction. Four three-shear fragments were
+rewritten exactly, saving four B-stage macros and 52 real-component primitives in
+each orientation while preserving the full 728-column B map and local paid profile.
+The standalone verifier and nine controls pass, as do the unchanged emitter/frame
+auditor, optimized and relocated replays, selected-record checker and five selected
+record tests. No global supplier reprice or new kappa is claimed.

research/u8-b-cancellation-seed32/NOTICE.md

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+# Notice and attribution
+
+The frozen selected U8 word and local verifier derive from the PR942/T37 closure and
+its retained complex-supplier lineage: Jonathan Capalbo (#942), Chafik Boukhalfa
+(#890/#741), Jeremy Kothe (#869/#870/#799), Hao Yan (#858), and the earlier work
+credited by `research/complex-sw4-frame8/NOTICE.md` and the selected source manifest.
+
+The four shear rewrites, independent exact checker, proof note and controls were
+prepared for martin Rv with substantial OpenAI assistance in research, mathematics,
+implementation, verification and writing. No independent human review is claimed.
+New material is offered under Apache-2.0. Existing source packages and notices are
+unchanged.
+
+The complete primary verifier and immutable input pins were reconstructed and
+published in response to the maintainer review, with OpenAI Codex assistance.
+Its scalar lowering and binary-Horner invoice follow
+`research/complex-sw4-frame8/local/hpe_emit_local.py`, retaining the attributed
+work of icekylinx and DreamingOfClouds with OpenAI Codex and Anthropic Claude
+assistance, and the source package's full contributor lineage. Additional local
+validation uses the attributed PR514/PR433 independent frame/wrapper auditor.

research/u8-b-cancellation-seed32/PROOF.md

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+# Three-shear rewrite
+
+For distinct registers `x`, `s`, and `y`, let `E(t <- u, q)` denote `t += q u`.
+When no intervening operation writes `x` or `s`, the selected triples have the form
+
+`E(x <- s, a); E(y <- x, q); E(x <- s, -a)`.
+
+Applied to arbitrary incoming values, the outputs are
+
+- `x' = x`,
+- `s' = s`,
+- `y' = y + q(x + a s) = y + q x + q a s`.
+
+Therefore the triple equals
+
+`E(y <- x, q); E(y <- s, q a)`.
+
+All four concrete triples use one common frame, so the replacement introduces no
+frame transition. `verify.py` checks this identity locally and checks the complete
+1,918-event original and 1,914-event candidate B-stage matrices on all 728 arbitrary
+input columns. The unchanged selected local emitter and independent frame/wrapper
+auditor were also run during validation; both orientations retained the exact paid
+profile and 192-bit allowance while saving 52 real-component primitives.
+
+This is a finite local construction. It does not establish that the four rewrites
+can improve the selected exponent without rebuilding global hosting and the outer
+invoice, and it does not discharge inherited all-size/compiler, physical realization,
+precision/tape, exact-recovery or analytic-transfer assumptions.

research/u8-b-cancellation-seed32/README.md

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+# Four exact U8 B-stage shear rewrites
+
+**Finite complex-supplier construction; no new kappa.** Four three-add fragments in
+the selected PR942 U8 local word admit the exact rewrite
+
+`x += a*s; y += q*x; x -= a*s` -> `y += q*x; y += (q*a)*s`.
+
+The B stage drops from 1,918 to 1,914 scalar operations. Under the unchanged selected
+binary-Horner invoice, each orientation saves 52 real-component primitives:
+193,306 -> 193,254 forward and 193,354 -> 193,302 backward. All 728 arbitrary
+columns and the paid rank profile are unchanged.
+
+## Reproduce
+
+From repository root, using Python 3.10+ and the standard library:
+
+```sh
+python3 -I -B research/u8-b-cancellation-seed32/verify.py
+python3 -I -B research/u8-b-cancellation-seed32/test_package.py
+```
+
+Expected:
+
+```text
+PASS_U8_B_SHEAR_REWRITE_SEED32 rewrites=4 B=1918->1914 primitives=193306->193254/193354->193302 columns=728 controls=9 no_new_kappa
+PASS_U8_B_SHEAR_PACKAGE deterministic_result=1
+PASS_U8_B_SHEAR_PACKAGE_CLOSURE normal_and_optimized=PASS relocated=PASS controls=4
+```
+
+## Evidence and scope
+
+`verify.py` pins the accepted `t37-replay.tar.gz` and canonical-word payload, applies
+the four literal rewrites, compares complete exact sparse-rational B-stage matrices,
+checks each symbolic three-register identity separately, reproduces baseline receipts,
+and rejects nine controls: four single deletions, four wrong cross terms and one
+intervening dependency touch.
+
+`SOURCES.json` declares the complete immutable input closure: the already committed
+`research/community-frontier942-audit/t37-replay.tar.gz` and the hashes of its
+canonical word, baseline emitted programs, and baseline local receipts. The checker
+reads only these pinned regular members, never extracts the archive, imports no
+construction code, and needs no network access. It regenerates both complete baseline
+programs, checks them against the archived programs and receipts, and replays the
+candidate in both orientations using exact rational arithmetic. The generated result
+must match the original committed `RESULT.json` byte for byte.
+
+The package test runs normal and optimized isolated Python processes, then repeats
+them in a relocated fixture containing only this package and its declared archive.
+It also requires rejection of missing source pins, changed archive bytes, a wrong
+canonical-word member pin, and changed result bytes. All checks use explicit failures
+and remain active with `-O`.
+
+The unchanged `hpe_emit_local.py` and `hpe_audit_local.py` additionally passed on the
+candidate during validation: 728 columns in each orientation, unchanged paid profile,
+25 inherited frame/wrapper controls rejected, and prefix bounds of 55/72 bits under
+the retained 192-bit allowance. These validation commands are source-bound to the
+original base and recorded with exact source digests in `VALIDATION.json`; they are
+not needed by the one-command independent replay. To reproduce this additional
+validation, create an empty directory and run (POSIX shell example):
+
+```sh
+replay=$(mktemp -d)
+python3 -I -B research/u8-b-cancellation-seed32/verify.py --write-candidate "$replay/CANONICAL-WORD.json.gz"
+python3 -I -B research/complex-sw4-frame8/local/hpe_emit_local.py "$replay"
+python3 -I -B research/complex-sw4-frame8/local/hpe_audit_local.py "$replay"
+```
+
+The restored verifier and committed source pins address the maintainer's review of
+the incomplete submitted head `c9d2523a3d30b8f6b16cf038bf723a191342ff20`.
+
+No global owner map, complete complex-supplier invoice or outer 47-inequality assembly
+was rebuilt, so no kappa change is claimed. All-size/compiler, common-label and
+mutable-source realization, whole-call hosting, physical routing, precision/tape,
+exact recovery and analytic transfer remain inherited. Finite replay is not a formal
+proof of the multiplication theorem.
+
+Base commit: `abdc6a7002abdbcd9e21bfc5e1a795784deacfdf`. OS-random assignment seed:
+32 (complex-supplier track). The selected PR942 certificate remains unchanged.

research/u8-b-cancellation-seed32/RESULT.json

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+{
+  "all_exact_columns": 728,
+  "archive_sha256": "48285025105210b56a32d3d4d57a21b7591760acc709d38073e4dca339eb06fe",
+  "assignment_seed": 32,
+  "b_events": [
+    1918,
+    1914
+  ],
+  "backward_real_component_primitives": [
+    193354,
+    193302
+  ],
+  "base_commit": "abdc6a7002abdbcd9e21bfc5e1a795784deacfdf",
+  "canonical_word_sha256": "387a2266ffe006d20042221d967f67a4b18d9bb8de1cd1e01d4031b539fa74a5",
+  "controls_rejected": [
+    "drop_first_0",
+    "drop_first_1",
+    "drop_first_2",
+    "drop_first_3",
+    "wrong_cross_term_0",
+    "wrong_cross_term_1",
+    "wrong_cross_term_2",
+    "wrong_cross_term_3",
+    "intervening_target_write"
+  ],
+  "forward_real_component_primitives": [
+    193306,
+    193254
+  ],
+  "new_kappa": false,
+  "paid_profile_unchanged": {
+    "1": 2548,
+    "2": 338,
+    "3": 446,
+    "4": 162,
+    "5": 72,
+    "8": 8
+  },
+  "real_component_primitives_saved_each_orientation": 52,
+  "rewrite_count": 4,
+  "scalar_macros_saved_each_orientation": 4,
+  "scope": "Exact finite B-stage identity and unchanged-emitter local admission; global hosting, outer pricing, all-size/compiler, precision/tape and analytic transfer are not rebuilt.",
+  "status": "PASS_U8_B_SHEAR_REWRITE_SEED32",
+  "track": "complex supplier"
+}

research/u8-b-cancellation-seed32/SOURCES.json

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+{
+  "schema": "u8-b-shear-immutable-inputs-v1",
+  "base_commit": "abdc6a7002abdbcd9e21bfc5e1a795784deacfdf",
+  "archive": {
+    "path": "research/community-frontier942-audit/t37-replay.tar.gz",
+    "sha256": "48285025105210b56a32d3d4d57a21b7591760acc709d38073e4dca339eb06fe"
+  },
+  "members": {
+    "native/local/CANONICAL-WORD.json.gz": "387a2266ffe006d20042221d967f67a4b18d9bb8de1cd1e01d4031b539fa74a5",
+    "native/local/LOCAL-CHECKS.json": "a99aef882cd6f7631127fd8a116ad4bbaed60e3822455d4f846ae0f45b5af575",
+    "native/local/LOCAL-PROGRAMS.json.gz": "8b6a9e3a2411a04e5ca79ba6cd1dd449b21c95f65ca127475167d9b97c80a1ce"
+  }
+}

research/u8-b-cancellation-seed32/VALIDATION.json

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+{
+  "base_commit": "abdc6a7002abdbcd9e21bfc5e1a795784deacfdf",
+  "environment": {
+    "platform": "Windows",
+    "python": "3.12.14"
+  },
+  "independent_frame_wrapper_audit": {
+    "local": {
+      "backward": {
+        "all_exact_columns": 728,
+        "charged_payload_bits": 192,
+        "prefix_bits_upper": 72,
+        "prefix_l1_upper": "48299247708513087628079/16",
+        "private_work_erased": true
+      },
+      "forward": {
+        "all_exact_columns": 728,
+        "charged_payload_bits": 192,
+        "prefix_bits_upper": 55,
+        "prefix_l1_upper": "6812058044968180837/256",
+        "private_work_erased": true
+      }
+    },
+    "negative_controls_rejected": [
+      "wrong_scale",
+      "missing_center",
+      "wrong_common_frame",
+      "wrong_child_rank",
+      "missing_pre_wrapper",
+      "missing_post_wrapper",
+      "wrapper_with_wrong_frame",
+      "wrapper_in_wrong_phase",
+      "wrapper_on_a_data_register",
+      "wrapper_on_a_target_register",
+      "wrapper_on_a_centre_register",
+      "hpe_pre_wrapper_resolved_to_full_recipe",
+      "hpe_post_wrapper_without_terminal_frame",
+      "hpe_post_wrapper_wrong_terminal_frame",
+      "hpe_tail_gate_at_full_frame",
+      "hpe_tail_climb_dropped",
+      "hpe_helper_exit_adapter_to_full",
+      "hpe_tail_gate_moved_into_full_cleanup",
+      "cold_hpe_pre_wrapper_replaced_by_identity_entry_adapter",
+      "cold_hpe_pre_wrapper_dropped",
+      "cold_hpe_post_wrapper_replaced_by_exit_adapter",
+      "cold_hpe_pre_wrapper_resolved_to_cold_full_convention",
+      "cold_hpe_wrapper_with_nonzero_entrance",
+      "cold_hpe_post_wrapper_wrong_terminal_frame",
+      "cold_hpe_premix_gate_before_pre_wrapper"
+    ],
+    "paid_profiles": {
+      "backward": {
+        "1": 2548,
+        "2": 338,
+        "3": 446,
+        "4": 162,
+        "5": 72,
+        "8": 8
+      },
+      "forward": {
+        "1": 2548,
+        "2": 338,
+        "3": 446,
+        "4": 162,
+        "5": 72,
+        "8": 8
+      }
+    },
+    "status": "PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY"
+  },
+  "primary_and_package_replay": {
+    "normal_isolated": "PASS",
+    "optimized_isolated": "PASS",
+    "original_result_byte_equality": true,
+    "package_controls_rejected": [
+      "missing_source_pins",
+      "archive_byte_mutation",
+      "canonical_member_pin_mutation",
+      "result_byte_mutation"
+    ],
+    "relocated_normal_isolated": "PASS",
+    "relocated_optimized_isolated": "PASS",
+    "rewrite_controls_rejected": 9
+  },
+  "prior_submitted_head": "c9d2523a3d30b8f6b16cf038bf723a191342ff20",
+  "retained_emitter_checks": {
+    "backward": {
+      "all_columns": 728,
+      "events": 24411,
+      "paid_profile": {
+        "1": 2548,
+        "2": 338,
+        "3": 446,
+        "4": 162,
+        "5": 72,
+        "8": 8
+      },
+      "private_centers_cleared": true,
+      "private_coefficient_stream_cleared_after_each_macro": true,
+      "real_component_primitive_bound": 193302,
+      "scalar_macros": 19209,
+      "sha256": "71afac81d844bd4a23fecfc138e1654dcbb34c17f8605fb45920db1727d48cfe"
+    },
+    "forward": {
+      "all_columns": 728,
+      "events": 24411,
+      "paid_profile": {
+        "1": 2548,
+        "2": 338,
+        "3": 446,
+        "4": 162,
+        "5": 72,
+        "8": 8
+      },
+      "private_centers_cleared": true,
+      "private_coefficient_stream_cleared_after_each_macro": true,
+      "real_component_primitive_bound": 193254,
+      "scalar_macros": 19209,
+      "sha256": "bd6271c5b3a8563757d61d5f0353b136916b31f433c29da0bc39a65caecce1df"
+    }
+  },
+  "scope": "Finite B-stage identity and local admission only; no global supplier reprice or new kappa.",
+  "trial_main": {
+    "base_head": "ae95f60feec79897b153dba6459bb3f9fd4d7b8e",
+    "patch_applies_cleanly": true,
+    "optimized_package_replay": "PASS"
+  },
+  "validation_sources_at_original_base": {
+    "research/complex-sw4-frame8/local/hpe_audit_local.py": "6bd9a1e279c9c9e4f3767d9f82e537b559292906feb2ddab02f380fb6523a810",
+    "research/complex-sw4-frame8/local/hpe_emit_local.py": "7e4a6fbc38c8228157b6311457d1496bf460291393043932d2c365f004f77805"
+  }
+}