Conditional κ = 0.001661960547713947858091 by exact T37 grid refinement

research/t37-rational-refinement/CERTIFICATE.json

@@ -0,0 +1,49 @@
+{
+  "adapted_assembly_code_sha256": "5b0952cb161ff1de959b82086755d59a3f6950933387b22329f05e77d3ee79f4",
+  "allowed_changed_fields": [
+    "conservative_kappa",
+    "conservative_kappa_decimal",
+    "conservative_outer",
+    "gain_over_pr635_percent",
+    "kappa",
+    "kappa_decimal",
+    "native_correction_gain",
+    "outer"
+  ],
+  "base_commit": "8bddbee377e2f3ce1f1247196c4b290d55767d20",
+  "baseline_complete_assembly_exact_match": true,
+  "controls_rejected": [
+    "next_fine_grid",
+    "old_next_coarse_grid",
+    "zero_eta",
+    "zero_beta",
+    "old_512_bit_charge",
+    "old_1024_row_extra",
+    "unpaid_primitive"
+  ],
+  "decimal": "0.001661960547713947858091",
+  "exact_source_edits": [
+    [
+      "margin*10**18",
+      "margin*10**24"
+    ],
+    [
+      "ticks.denominator,10**18)",
+      "ticks.denominator,10**24)"
+    ],
+    [
+      "k+Q(1,10**18)",
+      "k+Q(1,10**24)"
+    ]
+  ],
+  "increase": "858091/1000000000000000000000000",
+  "kappa": "1661960547713947858091/1000000000000000000000000",
+  "objective_grid": 1000000000000000000000000,
+  "original_assembly_code_sha256": "d89ed7a68f19e6d0dbb9d1bd75805433b1dc000bd89649fb598ef381c3887925",
+  "original_kappa": "1661960547713947/1000000000000000000",
+  "scope": "Conditional finer rational bound on the same accepted U8/T37 finite construction. Full pricing replay uses frozen maintainer inputs; native emission and inherited all-size/realization/precision/tape/analytic assumptions are retained.",
+  "source_inventory": 876,
+  "status": "PASS_T37_RATIONAL_REFINEMENT",
+  "strict_constraints": 47,
+  "unchanged_moments_bootstraps_and_invoice_inputs": true
+}

research/t37-rational-refinement/CLAIM.json

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+{
+  "track": "complex supplier",
+  "assignment_seed": 24,
+  "seed_source": "OS randomness through Python secrets.randbelow(100)",
+  "base_commit": "8bddbee377e2f3ce1f1247196c4b290d55767d20",
+  "object": "Exact T37 conditional assembly at a finer rational kappa grid, with source word, paid profile, physical invoice, bootstrap, eta and beta fixed",
+  "candidates": [
+    "refine the T37 outer objective grid with unchanged seven-stage bootstrap",
+    "refine both the complex moment endpoint and outer grid",
+    "price an additional paid bootstrap step before refining the outer objective"
+  ],
+  "method": "Reconstruct original 47 exact slacks and bootstrap; compare all inherited source pins, moment and invoice inputs; derive the strict 10^-24 outer grid point and next-grid rejection",
+  "deliverable": "one exact conditional kappa witness and bound-source closure",
+  "expected_finish_utc": "2026-10-13T16:42:00Z",
+  "coordination": "No pinned issue; full PR metadata and all-state T37/grid searches checked. PR942 proves the 10^-18 grid optimum, not a real-root optimum; PR987 proposes a changed U10 word and is distinct.",
+  "status": "completed and submitted",
+  "result": {
+    "pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/1019",
+    "code_checkpoint": "550ff1e752949296310a585e3b52e762aca24800",
+    "kappa": "1661960547713947858091/1000000000000000000000000",
+    "decimal": "0.001661960547713947858091",
+    "increase_over_selected": "858091/1000000000000000000000000",
+    "objective_grid": "10^-24",
+    "source_files_checked": 876,
+    "complete_baseline_reproduced": true,
+    "strict_outer_constraints": 47,
+    "controls": "7 arithmetic/invoice and 8 portable-package controls",
+    "native_geometry_and_ancestry": "Retained immutable reviewed evidence, not freshly emitted",
+    "overlap_refresh": "Full open metadata refreshed through #1017; all-state T37/grid searches found no matching refinement; live selected kappa remains lower.",
+    "reproduction": "python3 -I -B research/t37-rational-refinement/verify.py"
+  }
+}

research/t37-rational-refinement/NOTICE.md

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+# Attribution and license
+
+Submitted through @1337isnot1337, prepared with substantial OpenAI Codex
+assistance in research, exact parameter derivation, implementation,
+verification and writing. Apache-2.0 applies through ../../LICENSE.
+No independent human or delegated-worker review is claimed.
+
+Jonathan Capalbo's PR942 supplies the T37 composition, source-bound replay,
+precision adaptation and fixed-grid owner result. Chafik Boukhalfa's
+PR890/869/870 and Hao Yan's PR858 supply the U8/T21/T16 construction lineage;
+Jeremy Kothe's PR799/741 and icekylinx's earlier source gauge are inherited.
+DreamingOfClouds' PR589 on eumemic's PR555 is the unchanged bit supplier.
+Rohan Arun supplies the exact-complex recurrence correction.
+
+The unchanged rational moment engines and outer framework retain PR547/548,
+eumemic, icekylinx, Zhihao Chen and the RaD balanced-transform credit in their
+source-local notices. Dylan Crow, DaysSky and the earlier native verification
+contributors remain credited by the frozen packages. Maintainer source
+closure and integration evidence are Douglas Colkitt's reviewed inputs.
+
+No existing code, license, notice or construction input is edited in place.
+The verifier adapts a temporary copy of the frozen assembled runtime with
+exactly three objective-grid expressions and its derived expected outputs.
+The contribution is the finer rational conditional bound and its complete
+reproducible price/invoice/assembly certificate, not a new native word.

research/t37-rational-refinement/README.md

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+# A finer rational conditional T37 bound
+
+The accepted U8/T37 construction admits the exact conditional witness
+
+```text
+kappa = 1661960547713947858091 / 1000000000000000000000000
+      = 0.001661960547713947858091.
+```
+
+This is **858091/10^24** above the selected **0.001661960547713947**.
+It refines the outer objective grid from 10^-18 to 10^-24. The construction,
+paid recursive profiles, full invoices, exact-complex correction, bit
+surcharge, source-access charges, frame/owner realization, copies,
+restoration and recursive children are the same accepted finite inputs.
+No practical runtime improvement or new circuit is asserted. The numerical
+gain is extremely small and is presented as an exact certification refinement.
+
+The fresh full assembly accepts all 47 strict constraints, both native
+moment engines and conservative admission. Its seven bootstrap records and
+all invoice-input hashes match the selected receipt exactly. The next
+10^-24 grid point is rejected. The selected frontier is not edited by this
+research package.
+
+## Reproduce
+
+From repository root, standard-library Python 3.11+ suffices:
+
+```sh
+python3 -I -B research/t37-rational-refinement/verify.py
+python3 -I -B research/t37-rational-refinement/test_package.py
+```
+
+Expected final markers:
+
+```text
+PASS_T37_RATIONAL_REFINEMENT kappa=0.001661960547713947858091 sources=876 full_assembly=PASS strict_constraints=47 controls=7
+PASS_T37_REFINEMENT_PACKAGE relocated_full_assembly=PASS controls=8
+```
+
+The first command checks all 876 selected source hashes, extracts only the
+needed frozen maintainer replay inputs into a fresh directory, reproduces
+the **entire original assembly exactly**, applies the three declared grid
+edits and reruns the **entire refined assembly**. It independently checks
+the changed fields and executes outer and full-invoice corruption controls.
+The second command copies the complete minimal source closure to a path
+with spaces and repeats the full replay without Git or network access,
+then tests source, receipt and assertion-bypass faults.
+
+Use `--output /absolute/new/directory` to retain baseline/refined assemblies,
+the exact adapted runtime code/specification, unchanged raw invoice inputs,
+all logs and the receipt. Existing destinations are refused. Source workers
+require assertions; optimized Python is explicitly rejected. Ordinary
+verification does not regenerate a committed file. `--write-certificate`
+is an explicit development option requiring missing certificate files.
+
+## Exact parameter change and proof
+
+Let a be the last exponent of the existing seven-step bootstrap, b the
+existing certified complex endpoint, and eta=beta=10^-24. The retained
+outer engine computes
+
+```text
+q = a(1-2 eta),
+m = (1-eta)q/(1+q),
+kappa_d = (ceil(m 10^d)-1) / 10^d.
+```
+
+The integer formula used in the source,
+`(ticks.numerator-1)//ticks.denominator`, is exactly the largest integer
+strictly below ticks, including when ticks is an integer. This chooses a
+strict rational point, rather than rounding the real ceiling upward.
+
+The same engine proves that m is the smallest of all seven workload margins.
+The other forty strict constraints are independent of kappa. Every workload
+condition is `margin-kappa>0`. Therefore the refined point preserves all
+47 conditions whenever `kappa_d<m`, and all underlying invoices and
+bootstrap premises are unchanged. This is the retained framework's exact
+conditional asymptotic bound, under its inherited assumptions.
+
+Only these three expressions in the frozen runtime assembly are changed:
+
+```text
+margin*10**18                         -> margin*10**24
+ticks.denominator,10**18)             -> ticks.denominator,10**24)
+k+Q(1,10**18)                        -> k+Q(1,10**24)
+```
+
+All other source bytes are retained. The specification changes only its
+three derived kappa expectations and a portable path to a byte-identical
+pivot recipe. The original archive contains an obsolete macOS absolute
+path; the verifier copies the same SHA-256-pinned recipe and substitutes a
+relative path. No owner, primitive, profile, prefix allowance or invoice
+field is changed to obtain a pass.
+
+The full output's only changes are kappa and its decimal, the conservative
+kappa and its decimal, their outer slacks, and the two corresponding derived
+gain fields. Both supplier moment tables, conservative moment table,
+bootstrap lists, template hash, profiles, provider counts, source invoice
+digests, deficit derivation, surcharges and model controls agree exactly.
+The refined conservative witness is **0.001661960544831580991666**.
+
+This is the last admissible 10^-24 point for these **fixed certified
+endpoints, eta/beta and outer recipe**. It is not a real-root optimum, an
+architecture-wide ceiling or a finer all-replica optimum theorem. PR942's
+published all-T 10^-18 grid result remains valid on its stated grid.
+
+## Full replay scope and negative controls
+
+The unchanged assembler checks all finite logical/router/literal/mass,
+precision, tape, row and halving conditions against the full archived
+owner/invoice records. It retains the T37 complex **1024-bit charge**, the
+**2048-bit row-prefix extra**, 779-bit actual prefix, physical row coefficient
+17495<20161 and unchanged bit 512-bit charge. It rechecks the native and
+conservative complex moments and the surcharged bit moments with both
+rational engines, including rejection of the next supplier endpoint.
+
+The seven new controls reject the next fine grid point, the old next coarse
+point, zero eta, zero beta, reverting the complex charge to 512 bits,
+reverting the row-prefix extra to 1024 and under-reporting the charged primitive count by one. The package controls additionally reject falsified/missing receipts,
+an altered outer engine, missing source inventory, a false absorption gap,
+overwriting existing output and disabling retained assertions.
+
+The frozen construction's native geometry/controller/emission evidence is
+**inherited from the maintainer-reviewed replay**, with its full source
+closure checked here. This package performs a fresh complete **pricing and
+assembly replay**, not a fresh native emission or cold ancestry rebuild.
+All-size compilation, common-label/mutable-source realization, hosting,
+precision/tape/recovery and analytic transfer remain conditional. This is
+not an unconditional multiplication theorem or a complete Lean proof.
+
+## Provenance, search and attribution
+
+Exact research base: **8bddbee377e2f3ce1f1247196c4b290d55767d20**.
+OS assignment seed **24**, complex-supplier track; `24 mod 3=0` selects
+refining the outer objective with the seven-stage bootstrap fixed. This is
+an exact one-point rational derivation, with the adjacent rejected point;
+there is no randomized circuit search or unexplored-domain impossibility claim.
+`SOURCES.json` pins the full accepted source inventory, archive, original
+assembly, outer engine and pivot recipe. `CLAIM.json` records the local
+scope; no pinned coordination issue existed.
+
+Full open-PR inventories and all-state T37/grid/refinement searches were
+refreshed repeatedly before and during the work. Jonathan Capalbo's PR942
+is the construction being extended. PR991/992/995/1000 concern schedule,
+integrality or supporting inequalities at the earlier witness. Pending
+PR987 changes U8 to U10; PR1004/1005 change mutable-leaver cells and local
+frames. Their larger proposed kappas are separate source constructions,
+not the accepted value used here, and are not imported. This submission
+makes no stronger-global-record claim relative to those pending proposals.
+
+The T37 owner construction, U8 word and exact supplier/replay engines retain
+credit for Jonathan Capalbo, Chafik Boukhalfa, Hao Yan, Jeremy Kothe,
+icekylinx, Rohan Arun, DreamingOfClouds, eumemic, Dylan Crow, DaysSky,
+Zhihao Chen and the earlier community. Details and substantial OpenAI Codex
+assistance are disclosed in `NOTICE.md`. Apache-2.0 applies.

research/t37-rational-refinement/SOURCES.json

@@ -0,0 +1,15 @@
+{
+  "base_commit": "8bddbee377e2f3ce1f1247196c4b290d55767d20",
+  "refined_kappa": "1661960547713947858091/1000000000000000000000000",
+  "selected_kappa": "1661960547713947/1000000000000000000",
+  "sha256": {
+    "research/community-frontier942-audit/ASSEMBLY.json": "4b2894956e594e408e111d806c842f2ed2c32aefcadff93fad69ff0b46f1991a",
+    "research/community-frontier942-audit/SELECTED-SOURCE.json": "1cd8dfde15919d1c3df9796b262e67898143d9793d2b86ee7b0a47fc903654c9",
+    "research/community-frontier942-audit/t37-replay.tar.gz": "48285025105210b56a32d3d4d57a21b7591760acc709d38073e4dca339eb06fe",
+    "research/complex-t21-owners/vendor/pr870/construction/layers_np/PIVOT-SWAP-NP.json": "d49b8d316da1cbdaf995dd0e8314d3c67cc9cd4d5902e9d85ccb907be645bef5",
+    "research/e8-bit-carrier-skeleton/code/pricing/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c"
+  },
+  "source_inventory_count": 876,
+  "source_pr": 942,
+  "source_pr987_overlap": "Different U10 local word; this refinement uses the accepted U8/T37 construction and unchanged invoices."
+}

research/t37-rational-refinement/VALIDATION.md

@@ -0,0 +1,44 @@
+# Executed validation and reproduction boundary
+
+Base: 8bddbee377e2f3ce1f1247196c4b290d55767d20; OS seed 24.
+
+`python3 -I -B research/t37-rational-refinement/verify.py` passes. It checks
+the closed inventory and bytes of all 876 source files; the three supplier
+engines used from that closure match the original assembly's engine digests.
+It reproduces the original full assembly exactly, then the finer full
+assembly with kappa 0.001661960547713947858091. All 47 strict constraints
+pass, with positive absorption gap approximately 4.90827e-25. Both native
+moment-engine tables, the conservative moment table, both seven-step
+bootstrap chains and every invoice input digest are unchanged.
+
+The exact adaptations are recorded in CERTIFICATE.json. ASSEMBLY.json is
+the complete fresh refined output. Temporary replay logs and all raw inputs
+can be retained with --output. The source archive's obsolete absolute pivot
+path is relocated to the identical hash-pinned recipe, without changing its
+contents. The objective-grid changes are the only mathematical source edits.
+
+Seven controls reject next fine grid, old next coarse grid, zero eta, zero
+beta, old 512-bit complex charge, old 1024-bit row extra and under-reporting
+the charged primitive count by one. The assembler retains the 1024-bit
+complex/512-bit bit charges and the full row, physical, tape and precision
+guards before evaluating the moments and outer bound.
+
+`python3 -I -B research/t37-rational-refinement/test_package.py` passes from
+a minimal 32 MB source closure with spaces in its path and no Git/network
+dependency. Eight package controls reject false or missing bound/control
+receipts, changed outer source, missing source inventory, a false absorption
+gap, overwritten output and an optimized-Python assertion bypass.
+
+The source-bound selected-record checker and git diff whitespace checks
+pass. The live selected record was refreshed before submission and still
+has 0.001661960547713947. Full open PR metadata and targeted all-state
+searches show no matching T37 finer-grid contribution; larger pending
+different-word proposals are distinguished in README.md.
+
+Native geometry, ownership, emission and cold ancestry evidence are retained
+from the frozen maintainer-reviewed construction. They are not freshly
+rebuilt here. This package freshly recomputes complete pricing, moments,
+bootstrap, finite invoices and outer assembly from those immutable inputs.
+It does not claim remote CI, a complete Lean multiplication proof or an
+unconditional theorem; all inherited all-size/physical/precision/tape and
+analytic hypotheses remain as recorded in the source review.