Conditional κ ≈ 0.001720398337: two-sided helper extraction and charged T74 packing

research/two-sided-helper-extraction/.gitattributes

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+vendor/** -text
+data/** -text
+evidence/** -text
+allocation/** -text

research/two-sided-helper-extraction/ALLOCATION-PINS.json

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+{
+  "allocation/DISPATCH.json": "65e435bd68e97243c003677271b88485a29d4d0fae2dff1354100404a145e74c",
+  "allocation/FILL.json.gz": "d6585a3b05fb86efd08b1925c5ae0a03265c30f895f5e2c4e1cdfe91978cd3ef",
+  "allocation/ORDER.json": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+  "allocation/PROFILE.json": "ab0840eda08fa501d444be22c7298bf38b70061b91964ad1b9dd9db388720199",
+  "allocation/PROVIDERS.json": "91a212677bc21d45990ad811dba16a6ce2f89fc43b61e67f75a09c35c6eace3b",
+  "allocation/RESULT.json": "5ba974e706ff58a523097693bfdc0e00935ddf4ad5d5ea467c38dc8a4fad4210",
+  "allocation/baseline/CLAIM.json": "29cd4aa92059a561437d7670b574c51ae4e1cfeaaf6feb6cc318d915869e6d30",
+  "allocation/baseline/ORDER.json": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+  "allocation/baseline/PROFILE.json": "528400282a268b6e5983a5251af6040450fa0e7d9ddf7d65e4a0aa6a0b9096a6",
+  "allocation/vendor/PLAN.json.gz": "d566cfb87b71639d4138e1f89b543e2dd6a7772070226a2a14c799a6835bf21e",
+  "allocation/vendor/TEMPLATE.json.gz": "21297b20f1f2dc76eb9dd8124416068c3cb096bab9df17fa4da19bc68dfe082e",
+  "allocation/vendor/independent_owners.py": "77a848729159e271ba64f403dfd59dddb13044b17b2950fa56700f442e2fe461"
+}

research/two-sided-helper-extraction/CLAIM.json

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+{
+  "baseline_head": "18d03c447886895ef9abf888398178e0428533ca",
+  "baseline_kappa": "17201845283774695330739999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "baseline_pr": 2894,
+  "calls": 666,
+  "complete_package_manifest_sha256": "a6d0e45723ea87f43ed8026758306adbf44b5cfc8473464c77acb57f32530783",
+  "complex_lower": "1720398337354237885931/1000000000000000000000000",
+  "gain": "213808976768352857/1000000000000000000000000",
+  "helpers": 408,
+  "independent_inputs": 632,
+  "kappa": "17203983373542378859309999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "kappa_decimal": "0.0017203983373542378859309999999999999999999998999999999999999999999999",
+  "live_families": 66304,
+  "native_receipt_sha256": "3280682ab975f412ab25e8ec433b2e52d8d3b6226db712ccabbbd2babcc2b84d",
+  "physical_families": 66795,
+  "profile": {
+    "1": 1620344,
+    "2": 426241,
+    "23": 1,
+    "3": 180732,
+    "32": 14,
+    "4": 85248,
+    "48": 26837,
+    "5": 25700,
+    "6": 120,
+    "7": 1,
+    "8": 5328
+  },
+  "release_receipt_sha256": "c3fd39e0645b10681a26b74afd08b429e04a139222e156f533654486c4f70214",
+  "replicas": 74,
+  "scope": "Conditional finite supplier/outer certificate. Inherited all-size/compiler/theorem hypotheses remain; no selected frontier change, no optimality or independent-human-review claim. Both changed native chains are fresh; retained parent/native evidence explicitly reused by complete receipts.",
+  "source_manifest_sha256": "56cf455752722051d598a7da1e5ee700637fbaef09189f534413dbe6e0525a83",
+  "status": "CONDITIONAL_CANDIDATE_COMPLETE_FINITE_RELEASE",
+  "zero_buffers": 73
+}

research/two-sided-helper-extraction/CONSTRUCTION.md

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+# Paired input/output extraction
+
+Let M denote the complete non-target forward operator of the pinned PR2894
+word: the A gates after the entry prelude, the B gates and formal invertible
+warps, and the restore gates. Target writes are omitted in this definition;
+they are checked separately by the full independent word auditor. Operators
+are noncommuting formal symbols, so the argument uses no numerical sampling.
+
+Let H contain zero-entry helper registers which are neither existing restored
+helpers nor sources of the initial operator corrections. For a terminal
+hyperplane E, let R consist of registers whose current terminal frames lie in
+E. Seek a column y and a row alpha, supported on R, such that
+
+- v = M^-1 y is scalar and supported on H;
+- u = alpha M is scalar and supported on H;
+- alpha y = u v = 1.
+
+These are two exact nullspace conditions with a nonzero pairing. Finite-field
+linear algebra can nominate candidates, but every published identity here is
+replayed over rational coefficients in the free operator algebra.
+
+Choose an invertible dyadic input change S and output change T with
+`S e_h = v`, `u S = e_h^T`, `T y = e_h`, and `e_h^T T = alpha`.
+Then the h column and h row of `T M S` are both the corresponding identity
+column and row. Register h is restored exactly for every arbitrary dirty
+helper input and is not read by other output registers. This supplies the
+cold endpoint needed by the inverse-reverse cleanup contract.
+
+For h=408, E is the binary hyperplane perpendicular to 52, with canonical
+basis `(256,128,64,36,20,8,2,1)`. The output certificate is especially small:
+
+```
+alpha = e_408^T + (1/2)e_42^T + e_105^T
+y = 2 e_42
+
+408 += (1/2) * 42
+408 += 105
+42  -= 2 * 408
+```
+
+All three terminal additions use frame E. The 24 input gates in
+`data/TRANSFORM.json` act at frame zero. They include one scaling by 2 and
+otherwise dyadic additions. `structure.py` derives S, T, M, u, v, alpha and y
+from the literal gates and checks all seven identities, independently of the
+word producer. `verify.py` also checks both full target maps and the dual
+orientation with the inherited exact auditor.
+
+The target correction becomes `C S`. The initial operator corrections retain
+their inputs because S acts only outside their source set. Warps, the cut,
+ports, target levels, removed helpers and the entry prelude are unchanged.
+The changed sections are exactly A, restore, helper_final, compensation,
+report and cleanup. Inverse-reverse cleanup is regenerated and checked from
+the full new word; its new private buffer is allocated, cleared and charged.
+
+The complete per-call profile changes from
+`{1:2404,2:642,3:262,4:128,5:26,8:8}` to
+`{1:2407,2:640,3:262,4:128,5:26,8:8}`. Helper408 changes width 9 to 8;
+there remain 408 live helpers and 632 independent inputs, with **73** private
+zero buffers instead of 72.
+
+# Owner allocation and cost
+
+Keeping PR2894's fill is worse despite the local improvement. The shipped fill
+starts from that literal T74 allocation, makes 545 same-call width exchanges,
+then 222 whole-role relocations. The exchanges preserve the set of physical
+owner families at each call. Every relocation explicitly checks the owner
+window and rejects a family already used in the call; the final independent
+auditor rechecks all 271,728 roles, compact offsets, capacity, chronology and
+family distinctness. These are discovery heuristics, with no optimality claim.
+
+The actual paid profile is
+`{1:1620344,2:426241,3:180732,4:85248,5:25700,6:120,7:1,8:5328,23:1,32:14,48:26837}`.
+Its rank mass is exactly `65088*74`. It includes every unused owner remainder.
+The complete physical stock is `66304 + 408 + 8 + 73 + 2 = 66795`.
+The inherited owner-only checker has a historical 72-buffer display field;
+our wrapper explicitly replaces that field and labels its provenance. The
+complete rebind, block-norm certificate and outer invoice independently check
+the actual 73-buffer namespace, endpoints, stock and prefix reserve.
+
+The admission adapter preserves all inherited tests, with the new source pin
+and buffer constants bound explicitly. In particular, the dimension-72
+symplectic-group stock factor is unchanged: it is not a private-buffer count.
+The old source/parent artifacts are read-only. Both new providers run the full
+five native stages; retained providers and the 16-stage retained parent may be
+reused only through exact complete-cache/source/claim receipts, and the replay
+records this distinction.

research/two-sided-helper-extraction/CREDITS.md

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+# Credit and scope
+
+Jeremy Diviney, with substantial OpenAI Codex assistance, contributed the
+paired input/output subspace search, the explicit helper408 extraction, the
+exact structural certificate, the owner-width exchange/relocation repair,
+and the source-bound 73-buffer integration. No independent human review is
+claimed. This is a new application of ordinary exact linear algebra to these
+literal words, not a claim to have invented nullspace or basis-change methods.
+
+The immediate parent is Jeremy Kothe / `jeremykothe2`, PR2894 at
+`18d03c447886895ef9abf888398178e0428533ca`. Its two preload-resynthesized quartets,
+T74 owner order and fill, reconstruction, and complete admission remain
+credited. `vendor/preload_move.py` is unchanged from that package.
+
+The construction inherits Yiyang Lu / `Lyy-iiis`'s PR2857 staged shared kernels
+and source-bound overlay/native/release tooling; Dugongue's PR2863 packing;
+Marius-Paul Dumitrean's PR2843/PR2802 pattern-flow and retired-helper lineage;
+Jeremy Kothe's PR2833 dirt-entry supplier; and Philippe Van Velzen's PR2853
+cost and block-energy lineage. Tekalign's PR2751/PR2839 owner audit and
+admission lineage is retained in the corresponding code headers. The exact
+moment auditor is PR2894's `tools/audit_moment2857.py`, changing only the
+comparison pin and label to PR2894.
+
+The independently written exact scalar/frame auditor retains its original
+icekylinx attribution. The fast native package is copied byte-for-byte from
+PR2833's `new/fastnative`; it retains the PR2768 sparse engine and all nested
+PR2226 Clifford/operator notices. The copied material, including its original
+line endings, is pinned in `PINS.json`.
+
+The new terminal recovery changes literal gates and adds a cold endpoint.
+PR2904's fixed-gate dirty-entry/refit negative census does not cover this
+operation. The initial compensation-kernel search failed before this pivot;
+it is not presented as a new universal obstruction. Advisory overlap was
+checked against open PRs and Discussion bodies before discovery and again
+before submission. That coverage is not a novelty guarantee.
+
+The selected repository result is not changed. A passing finite release uses
+the inherited all-size/compiler/outer hypotheses and does not establish an
+unconditional integer-multiplication theorem.