Verified conditional kappa: positive-slack refinement over PR1928 (+2.00336e-10010)

research/fine-prime-slack10030/DEPENDENCY.json

@@ -0,0 +1,8 @@
+{
+  "pr": 1800,
+  "head": "46d865ab92e58098538b8c5348b6a131c99abf45",
+  "repository": "jeremykothe2/integer-mult-bounds",
+  "package": "research/capped-fusion-t74-k554",
+  "manifest_sha256": "b8dba5524f8603e1848c73a8dd675404a0d3d9eed3b0285e9f0cfccde38fd15f",
+  "scope": "Unchanged supplier and analytic construction; refine positive free slack parameters only."
+}

research/fine-prime-slack10030/MANIFEST.json

@@ -0,0 +1,44 @@
+{
+  "CLAIM.json": "f8a49b6a98be4f9f223e409a6d176570650f95339faafa700e7d2cf1a269f667",
+  "DEPENDENCY-MANIFEST.json": "b8dba5524f8603e1848c73a8dd675404a0d3d9eed3b0285e9f0cfccde38fd15f",
+  "DEPENDENCY.json": "57b6fe18ea819cca8860e65b1f9d7de83438dd3f1a309661ea5aad6932ef8213",
+  "NOTICE": "85873634c64b16b1799c78147f91397d73bcccd5788359a21eb1e13a7b5f235c",
+  "PARAMETERS.json": "562c18285feebe4c64ae163d1ab090fef55eb1ae4cb3cb4e2daee023f6fb51a4",
+  "PROOF.md": "49cc2fa36015e7a21d8b2334f7d444e7ae57d54acbaba7f76c10bd1235863b16",
+  "README.md": "e48cf3c96387f50fd43038d830c1e7b969b3c20467c1c721c0034080d458b0ac",
+  "RELEASE-BINDING.json": "9408672b3abc76a95b106ca0298efe8a185da62a36107e9c86e9c303b33f264e",
+  "SOURCE-FETCH.json": "91fd5398dadfab18778516ad53774beef78e31dc9bd9cf0fb044a01118d1b29f",
+  "TASK.md": "0af3d0fd294c06818f2877132764f629dd63d79c4b960b7cfd3964784f9ecdbc",
+  "certify_endpoint.py": "1094730778c8b25256c635b9aabb850d92258550a5a6af263b8115673fba2724",
+  "check_ledger.py": "c081b7df35ce5f8797190adce63e906d7d35b5303c297e3e66a0c82258593906",
+  "evidence/ENDPOINT-REPLAY.json": "8ccd4b4921a726aa45fd39751322a13dceab387c69359d7a8e834386b08ea18f",
+  "evidence/FULL-RESULT.json": "ae76c2129e08f6a389fe5a3f6b856136ae1ecab8566bb3a2742a69dd42f7c7e0",
+  "evidence/FULL-STAGES.json": "5e4b828eeabdbb4777a3564bf0eee35f16fbff853441d4f5e0103692a5e75b33",
+  "evidence/SUPPLIER-RESULT.json": "584591297ec988547b77b4e0cda678f85d55b05b31bb62f356c3d4f586f857ca",
+  "evidence/SUPPLIER-STAGES.json": "e9ca6fdba6f2d4c49a0c60970b96fa5fa77297a11d2eed5f103782df32417a2b",
+  "evidence/VERIFIED-SOURCE-MANIFEST.json": "ef0aa7c086679de44ef1d19d525928a87fc8e984facd9cc7d0ec76791b8c199c",
+  "independent_check.py": "9434771a3f73ebb7a58e7bf162aba2eef05e380ebd6a40a2f67273a32df4c9ee",
+  "inputs/B.json": "3786841ba498af359e3e5920eb2ccdb39a1005021e99f3e29a9ffae66fbbfa6d",
+  "inputs/CLAIM1800.json": "1dd5490597ead36a31634f6008b1cd5ce0b51c4acd48a541b13306212e3f52f1",
+  "inputs/LEADER1839.json": "1cc459f3c79046a2dc025f7e004958d178b886a3b541d64d886e4628f77fc252",
+  "inputs/LEADER1875.json": "c85b80237dfad16c46d590363060341ff358e83de008cd1df44d7198a166e9c0",
+  "inputs/LEADER1928.json": "7ae7276da85eafbeb29591ff8d8196f24f90182867349a045886cf38fd6b703d",
+  "inputs/OUTER-CLAIM1800.json": "c10ff0673ee9152d2efee792fb3532ca25a5edee0bf52c5b700bf86735752779",
+  "inputs/SOURCE-SPEC.json": "41d7bd51c18eb354c6a785780ddefd35b3a8e2513daa2c4f585b236b7173e943",
+  "inputs/SPEC.json": "07b368b62dd9dbac61d9d6a91a682b2710a724c600c20a9d1ad1e9de3cc68103",
+  "moment_interval.py": "a4561baac4a5a2f8066f278b43739b6bc6e1f4c5329fd8ca2b747cdcd9b5e681",
+  "packing-context/RESULT.json": "c2e1cd26b567d21027b4fdce0d90d9573d64c555be9f0992e317aed3c4f4bfcf",
+  "packing-context/SOURCE.json": "f3a748fd2db4d60cd0fd56db9cd7de1955e48079dc3b033aaf5e0518f9acbc6d",
+  "packing-context/ceiling.py": "86a1432870b3b21d8454106ec9162fddc0471472d9214c590a1420f2426cedfc",
+  "packing-context/verify.py": "c467556892990101b613a92e2bde875bc26e1244571a1968ccb9a61666df9968",
+  "reference/check_ledger.py": "58162da8e9e7c02de50a9e63649c05ddc4fc5026b7f9173c9058018d093b9603",
+  "reference/fine_mercator.py": "c0bbb95baff4f301413778c6c595049a0f3fca4ca2cdc86351898137c53e1658",
+  "reference/fine_moment.py": "feaf1d3b6bf0e3b8eaeb22c40bea3a04ca63a98c08534fa5c28ae913c8ed70c2",
+  "reference/independent_check.py": "791c0bd5b1b634e20952914c8946bd8402415f4b1163ed83e94e7881fb657a5e",
+  "reference1982/INPUTS.json": "609c486efb1fe1e03ff2c84ba11085b231b9372e81fb2650bda821ce84e6e1ae",
+  "reference1982/README.md": "d1c74bccb238aaed7b6512a202f18424ed6d8330b11ad23d60a907ed2b2f7d88",
+  "reference1982/SOURCES.json": "9297601e0b659319b43f1bb9cde36e4aa04a545b7257f5f5c08a83e67ec00369",
+  "reference1982/verify.py": "93b65b1ed0aff0f766fa9ae304041e9e79d385b074339289023a11e11cf53098",
+  "replay_outer.py": "f3bef0ca5139984faf357861283f7ed914f236d5a31b9f0dfcf88dcd93183026",
+  "verify.py": "871b39cc0cdf73a9618a7383f18326e347e6fd7b36cbd4b22d714684876df950"
+}

research/fine-prime-slack10030/NOTICE

@@ -0,0 +1,14 @@
+New research prepared by Rohan Arun with substantial OpenAI Codex assistance. Apache-2.0. Parent words and build recipe method derive from Jeremy Kothe PR1274 and Rohan Arun PR1218, with lineage credited in README.md. All inherited mathematical qualifications are retained.
+Additional pivot555 and567 composition by Rohan Arun with substantial OpenAI Codex assistance.
+
+T74 exact-fill owner construction by Rohan Arun with substantial OpenAI Codex assistance.
+
+PR1377 grid refinement credited to Jeremy Kothe. Outer witness refinement by Rohan Arun with OpenAI Codex assistance; construction unchanged.
+
+Pivot-566 kernel, words, edits, rebuild.py and rebind.py: PR1625 (mdumitrean). Endpoint/outer-witness stacking, fine_cache.py and oracle stage by jeremykothe2 with oh-my-pi assistance.
+
+This refinement also credits Jeremy Kothe and PR1839 contributors for the finer endpoint recertification, and Rohan Arun PR1828 for parameterized positive-slack replay. Original retained enclosure engines and predecessor files are unchanged in reference/. New endpoint, parameters, binding checker and documentation prepared by Rohan Arun with substantial OpenAI Codex assistance. No independent human review is claimed.
+
+400-digit extension credits the concurrent PR1875 comparison by Rohan Arun with Anthropic Claude assistance. Exact conditional arithmetic extension and verification package prepared with OpenAI Codex assistance.
+
+PR1982 independent moment checker: Aaron Wang with opencode assistance, Apache-2.0; retained unchanged. PR1928 endpoint and ledger: Jeremy Kothe and contributors. Slack10030 arithmetic adaptation: Rohan Arun with substantial OpenAI Codex assistance.

research/fine-prime-slack10030/PARAMETERS.json

@@ -0,0 +1,8 @@
+{
+  "root_digits": 10000,
+  "slack_digits": 10030,
+  "zeta_digits": 10032,
+  "stop_digits": 10036,
+  "backoff_digits": 10042,
+  "kappa_grid_digits": 10070
+}

research/fine-prime-slack10030/PROOF.md

@@ -0,0 +1,11 @@
+# Finer endpoint with fixed positive slacks
+
+The physical supplier and paid rank profile are unchanged from PR1800 at its pinned head. This package re-certifies that profile's moment root on the same 10^-10000 rational grid certified in PR1928. The input source specification is preserved byte for byte as inputs/SOURCE-SPEC.json. The derived SPEC differs only in expected.complex_lower. The unchanged independent PR1982 checker proves M(B)<1<M(B+10^-10000), using outward integer rounding and explicit series tails. The new ledger directly encloses its own interior b and rejects B+10^-10000 using that same checked interval kernel; these two calls are not claimed as independent algorithms. M is strictly increasing because every child rank lies strictly between zero and the parent dimension. No floating-point root finder is used by verification.
+
+Write h=10^-10030, b=B-h, q=B-2h, a=B-3h/2, delta=2h, epsilon=1-delta, beta=1-3delta, r0=slack=h, stop=10^-10036 and zeta=10^-10032. As in PR1800 and PR1828, c=3/32 and xi=epsilon*(1+q)-c+slack. The source-axis absorption gap is delta-r0=h>0; the membership gap is delta>0; the Gaussian gap is delta*(1-2q)>0; the effective-router gap is h/2>0. The stopping condition stop*b<h/2 is checked exactly. The remaining inherited inequalities and nine cost powers are regenerated as exact rationals with 17 rejecting controls.
+
+K=floor(epsilon*q*10^10070)/10^10070-10^-10042. Both independently implemented balance calculations must agree on this exact rational. K must strictly exceed the exact PR1928 rational pinned in inputs/LEADER1928.json (and the earlier PR1839/1875 comparison points). Decimal displays play no role in comparison.
+
+The full replay checks the immutable PR1800 dependency, all inherited outer replays and complete supplier admission. The actual assembly must match the preserved original specification and exactly the re-certified profile, dimension, live count and bit endpoint. The endpoint certificate binds that same profile to the new derived specification; it does not rely on changing an old receipt's number. The original native admission's lower endpoint is a weaker valid endpoint, not an upper ceiling.
+
+All slacks are fixed positive constants. The predecessor's eventual polynomial and polylogarithmic absorption arguments therefore transfer with a potentially larger unspecified cutoff if those written arguments are valid. No limit point epsilon=1, uniform cutoff as h tends to zero, new physical supplier, or practical speedup is claimed. All inherited compiler, hosting, online precision, fixed-tape, source-prime, locality, recovery, interchange and analytic hypotheses remain. Finite replay does not prove those all-size hypotheses.

research/fine-prime-slack10030/README.md

@@ -0,0 +1,21 @@
+Locally verified conditional refinement of PR #1928 at head `07e4e4231459e36b1055396306dcbd950248df62`.
+
+The exact candidate exceeds that ledger by approximately **2.0033595099133e-10010**. Its decimal prefix remains `0.0016797549561255445213356709939207025769983114385025802954603275201628645482603256388263056561328`. Exact rationals and the full decimal are in CLAIM.json; the comparison uses rational arithmetic, not rounded displays.
+
+This is an extremely small positive-slack improvement of the same supplier, not a structural construction or practical speedup. It retains the PR1928 10,000-digit native endpoint B and uses h=10^-10030, b=B-h, q=B-2h, epsilon=1-2h, beta=1-6h. The kappa is floor(epsilon*q*10^10070)/10^10070 - 10^-10042.
+
+Local checks completed: the unchanged independent PR1982 endpoint checker, including its four brackets, nesting checks and ten rejecting controls; 57 strict rational outer inequalities; 17 rejecting controls; and a separate nine-cost balance derivation agreeing exactly. Fresh complete supplier replay PASSED locally, including inherited outer replay, both native supplier variants, parent and strict T74 admission, and final assembly-to-endpoint-to-ledger bindings. No hosted CI pass or independent human review is claimed.
+
+Reproduce arithmetic with Python 3.11+: `PYTHONINTMAXSTRDIGITS=0 python3 -B research/fine-prime-slack10030/verify.py --work /absolute/new/work --arithmetic-only`. For complete replay omit `--arithmetic-only`; optionally pass `--dependency /path/to/immutable/PR1800/package`. Outputs and fetched dependency files stay under the fresh work directory. Full replay binds the unchanged PR1800 native assembly to the new separately enclosed endpoint and ledger.
+
+This leaves the unchanged native moment ceiling untouched and moves only closer to its endpoint. The physical supplier, paid profile, packing cap and structural headroom are unchanged. It does not improve the packing cap or address the P104 construction obligations.
+
+Conditional on all inherited PR1800/1786/1758/1673 compiler, common-label/mutable-source, hosting, semantic online precision C1=1, fixed-tape/prime-packing, interchange, recovery and analytic assumptions, plus the cited Trudgian prime theorem. Finite arithmetic does not establish the written all-size prime/precision/locality or accretive-circuit arguments. No unconditional theorem, practical cutoff or maintainer acceptance is claimed.
+
+Open next questions: Can a complete P104 low-rank channel and compatible side correction reduce the actual paid moment? This matters for a material gain; first price and replay one complete frame-compatible local word. The unresolved side correction, native compilation and chronological hosting are blockers for that separate structural route. Further precision-only changes have negligible practical significance.
+
+Credits: Jeremy Kothe and PR1928/1800 contributors; Aaron Wang with opencode assistance for the independently derived PR1982 moment checker (retained unchanged at b10c1a196cf5fbbdedc43c9fd26ff2e834849600); Chafik Boukhalfa / PR1786, Tim Trudgian, Vlado Vojdanovski / PR1673, PR1758 contributors, LeverRank, mdumitrean, midhatn and all inherited supplier authors. Retained original sources and notices accompany the derived checkers. Prepared by Rohan Arun with substantial OpenAI Codex assistance. Apache-2.0.
+
+Fixed-mixture packing context: native saving ceiling bracket ['843830269237/500000000000000', '67506421539/40000000000000']. This candidate realizes approximately 99.53156560995382% of that native upper ceiling. This uses the exact 249-A/417-B average profile, rank cap51 and retained coverage identity; it is not a universal bound or the older balanced a/(1+a) transfer. Reproduce the supplement with `PYTHONINTMAXSTRDIGITS=0 python3 -B research/fine-prime-slack10030/packing-context/verify.py research/fine-prime-slack10030`. Credit Douglas Colkitt with Claude assistance for the retained ceiling engine.
+
+Full verification: PASS_CONDITIONAL_SLACK_REFINEMENT_FINITE_ADMISSION. Evidence includes the exact replayed source manifest and stage/log hashes. Only status prose and claim metadata change after replay; mathematical inputs, parameters, verifier code and the exact candidate rational are unchanged. This is local AI-assisted finite verification, not a full unconditional proof or hosted CI acceptance.

research/fine-prime-slack10030/RELEASE-BINDING.json

@@ -0,0 +1,10 @@
+{
+  "replayed_head": "4f0093ad905e3229472a44177f910064fda86c01",
+  "replayed_manifest": "ef0aa7c086679de44ef1d19d525928a87fc8e984facd9cc7d0ec76791b8c199c",
+  "changed_existing_files": [
+    "CLAIM.json",
+    "README.md"
+  ],
+  "unchanged_code_parameters_inputs": true,
+  "full_receipt_sha256": "ae76c2129e08f6a389fe5a3f6b856136ae1ecab8566bb3a2742a69dd42f7c7e0"
+}

research/fine-prime-slack10030/SOURCE-FETCH.json

@@ -0,0 +1,26 @@
+{
+  "reference1982/verify.py": {
+    "url": "https://raw.githubusercontent.com/navinor/integer-mult-bounds/b10c1a196cf5fbbdedc43c9fd26ff2e834849600/research/t74-k554-root-enclosure/verify.py",
+    "sha256": "93b65b1ed0aff0f766fa9ae304041e9e79d385b074339289023a11e11cf53098"
+  },
+  "reference1982/INPUTS.json": {
+    "url": "https://raw.githubusercontent.com/navinor/integer-mult-bounds/b10c1a196cf5fbbdedc43c9fd26ff2e834849600/research/t74-k554-root-enclosure/INPUTS.json",
+    "sha256": "609c486efb1fe1e03ff2c84ba11085b231b9372e81fb2650bda821ce84e6e1ae"
+  },
+  "reference1982/README.md": {
+    "url": "https://raw.githubusercontent.com/navinor/integer-mult-bounds/b10c1a196cf5fbbdedc43c9fd26ff2e834849600/research/t74-k554-root-enclosure/README.md",
+    "sha256": "d1c74bccb238aaed7b6512a202f18424ed6d8330b11ad23d60a907ed2b2f7d88"
+  },
+  "reference1982/SOURCES.json": {
+    "url": "https://raw.githubusercontent.com/navinor/integer-mult-bounds/b10c1a196cf5fbbdedc43c9fd26ff2e834849600/research/t74-k554-root-enclosure/SOURCES.json",
+    "sha256": "9297601e0b659319b43f1bb9cde36e4aa04a545b7257f5f5c08a83e67ec00369"
+  },
+  "SPEC1928.json": {
+    "url": "https://raw.githubusercontent.com/jeremykothe2/integer-mult-bounds/07e4e4231459e36b1055396306dcbd950248df62/research/capped-fusion-t74-k554/new/SPEC.json",
+    "sha256": "75510fe5113baa42468c5835ebc9728bdc204acd6e07b898b3bc300e453d3443"
+  },
+  "LEDGER1928.json": {
+    "url": "https://raw.githubusercontent.com/jeremykothe2/integer-mult-bounds/07e4e4231459e36b1055396306dcbd950248df62/research/capped-fusion-t74-k554/outer/LEDGER.json",
+    "sha256": "2bbf7a8e1e0bb5cc8a086bd0eb3f23cc140d38ff71a0490712ef6713c14181a8"
+  }
+}

research/fine-prime-slack10030/TASK.md

@@ -0,0 +1 @@
+Explicit user assignment: beat the highest comparable conditional kappa, publishing a draft before full verification. Scope: exact positive-slack refinement at the unchanged PR1928 endpoint. Acceptance: strict exact gain over pinned PR1928, independently certified native endpoint, 57 inequalities and 17 controls, distinct balance derivation, full native supplier and outer replay bindings. No structural gain claimed. Nearest overlap: PR1928 endpoint/slack package and PR1982 independent certificate. This adds a strictly interior parameter point at smaller positive slacks.

research/fine-prime-slack10030/certify_endpoint.py

@@ -0,0 +1,19 @@
+"""Bind the independent endpoint certificate to the unchanged native supplier."""
+import json,sys,hashlib
+from pathlib import Path
+from fractions import Fraction as Q
+from moment_interval import v,src,moment,BITS
+P=Path(__file__).resolve().parent
+source=json.loads((P/'inputs/SOURCE-SPEC.json').read_text())
+spec=json.loads((P/'inputs/SPEC.json').read_text())
+assert {k:x for k,x in source.items() if k!='expected'}=={k:x for k,x in spec.items() if k!='expected'}
+assert {k:x for k,x in source['expected'].items() if k!='complex_lower'}=={k:x for k,x in spec['expected'].items() if k!='complex_lower'}
+assert Q(spec['expected']['complex_lower'])==Q(src['complex_lower'])
+assert source['expected']['global_profile']==src['global_profile']
+assert source['expected']['live']==int(src['live'])
+result=v.run()
+assert result['status']=='PASS_T74_K554_ROOT_ENCLOSURE_INDEPENDENT'
+result['status']='PASS_INDEPENDENT_ENDPOINT_BRACKET_AND_BINDING'
+result['source_spec_sha256']=hashlib.sha256((P/'inputs/SOURCE-SPEC.json').read_bytes()).hexdigest()
+Path(sys.argv[1]).write_text(json.dumps(result,indent=2)+'\n')
+print(result['status'])