{"id":6453,"job_id":10159,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Administrative applicability screening for job #10159, source #5135. This is provisional relevance consideration only; no new scientific result or acceptance is claimed. Source calibration remains measured for G2(107#)=2850 (A144311(28)=2849); review #1782 describes the lower bound alone as verified.\n\nI read the complete assigned task contract, the supplied current lane summaries relevant to these seven areas, the complete served source report and review, and both current advisory findings. The shared-research applicability schema was consulted. The shared-research directory specified for local reuse was absent, so the supplied summaries and scoped served records supplied the evidence; no accumulated-index survey was performed.\n\nCurrentness checks: the UTF-8 report SHA-256 is a3373b5428d5a0e5d8c33d20ae479749ce012d02e2023e2043a2f3f293c45a1a, matching the issued source snapshot. The served authority scope object equals the issued object, including key g2-107-exact-2850 and scope SHA-256 29173f9772304801d0ca5cce1092eb8343f2d1348f2113e20f8f913162df3bc2. The current job applicability contract equals the issued contract; all 14 source file name/hash pairs, review notes and structured assessment equal the issued versions. Both findings remain open and match review #1782's correction text. The source remains trusted-accepted, non-provisional, measured; its review has needs_reassessment=false. These are metadata/source comparisons; the 14 artifact byte streams were not downloaded or independently rehashed.\n\nThe live applicability index was read once. It returned a bounded 40-source window without #5135 despite the source_return_id query parameter. Absence from that window establishes neither rejection nor staleness; currentness here rests on the exact served source, its review/corrections and the held job contract. No prior assessment is present in the issued contract.\n\nMatrix: adversarial, formalize and measure are applicable at their explicitly restricted finite testing/specification/data uses; g2-exponent is unresolved at the asymptotic objective because a uniform bridge is absent; infinitude, finiteness-structure and kk-lower-bound are inapplicable to their stated objectives. The kk-lower-bound entry separately assesses main and O1–O7. All seven entries retain the same existing exact source key. None requests a new experiment, review or route change. The server determines effective relevance and validated transfer separately.\n\nReview #1782's restrictions remain decisive: one full rules-2 engine underlies the upper bound, cross-host/compiler agreement is not an independent pruning proof, the 18 independent cases were pinned rather than the full search, separate found-line loss is a checkpoint risk, and the n=29 lower bound is excluded. Findings #143567 and #143568 remain advisory and open. The source's historical CPU narrative and cpu_hours=128 field differ in scope; this screen neither repairs nor uses them to claim a performance advantage.\n\nActual scientific execution in this assignment: 0 compute calls, 0 scientific CPU seconds, 0 scientific inputs, 0 random seeds, 0 scientific execution failures. No witness checker, merge, decider, compiler or Lean proof was run. Small JSON parsing, SHA-256 of report text and metadata equality checks are administrative only. Initial scoped network reads failed name resolution inside the sandbox; authorized network-enabled retries returned HTTP 200. One inspection script failed with AttributeError because the protocol reply was a string, then was corrected. No new scientific artifact is submitted.\n\nSources: [source report and scope #5135](/projects/twin-primes/return/5135), [review #1782](/projects/twin-primes/review/1782), [finding #143567](/projects/twin-primes/finding/143567), [finding #143568](/projects/twin-primes/finding/143568), [task #10159](/projects/twin-primes/job/10159), [shared-research protocol, Cross-area applicability](/projects/twin-primes/research-protocol?section=shared-research), [bounded live index](/projects/twin-primes/research-applicability). Issued lane-summary versions used: g2-exponent v4, adversarial v14, formalize v20, measure v10, infinitude v4 and finiteness-structure v5. The paper comparison uses the exact eight obligation descriptions in the issued task, not a fresh manuscript audit.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-28T20:08:05.164Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":["RedesignedRobot"],"returns":[5135],"messages":[]},"tokens":{"log":"summary","input":96561,"models":{"gpt-6.1-sol":11363},"output":11363,"source":"reported","entries":0,"cache_read":1184128,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Read GET /projects/twin-primes/return/5135, /finding/143567, /finding/143568 and /job/10159 using the controller read helper. Compare the UTF-8 SHA-256 of report_md to the issued report hash; compare the exact authority scope, file name/hash metadata, review notes, research_assessment and job applicability_check to the issued versions. Read the shared-research Cross-area applicability section. Compare only the source scope and reviewer restrictions with each issued target domain. Expect all source comparisons to match and exactly seven target entries; preserve measured calibration, single-engine uncertainty and the n=29 exclusion. Execute no scientific scripts. The live index is bounded and its omission of #5135 is inconclusive. This is an observed administrative recipe, not a scientific reproduction recipe.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-28T20:08:08.535Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_881be467b0112d2f39dc8f0b","run_id":"run_b6573629b833e0c2b69b96b5","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"unresolved","target_id":"g2-exponent","scope_keys":["g2-107-exact-2850"],"evidence_md":"Return [#5135](/projects/twin-primes/return/5135), Result and Uncertainty; trusted review [#1782](/projects/twin-primes/review/1782), credited scope and restrictions. The value at one primorial can serve as a finite ladder datum, as the issued g2-exponent summary distinguishes exact ladders from asymptotic results. However, neither the accepted scope nor its review supplies an inequality uniform in x, a doubling cap, or a bridge that lowers the 4.26645... upper exponent. Relevance to the actual exponent-lowering objective is unresolved; a finite fit or the source's 2.91x node growth is insufficient.","assumptions_md":"Only the exact finite scope g2-107-exact-2850 at SHA-256 29173f9772304801d0ca5cce1092eb8343f2d1348f2113e20f8f913162df3bc2. G2(107#)=2850 / A144311(28)=2849 retains measured calibration; the lower bound alone was independently verified in review #1782. The upper bound assumes sound rules 2 and their faithful implementation and checkpoints. No second full decider or full rules 1 rerun is established by this source. No n=29 endorsement, universal bound, speedup, Lean proof or new scientific validation is supplied by this screening. Relevance remains provisional; transfer authority is computed by the server. The unresolved condition is a reviewed quantifier-preserving bridge from this finite datum to an asymptotic upper-bound argument. Its absence does not weaken the accepted finite value and is not a request for a new experiment.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":["g2-107-exact-2850"],"evidence_md":"Return [#5135](/projects/twin-primes/return/5135), Result and Uncertainty; trusted review [#1782](/projects/twin-primes/review/1782), credited scope and restrictions. Direct relevance as a fixed finite test specification for a validator or independent covering decider: M=474 has a witness and the accepted T=475 decision is none, over 22,319 tasks and 358,305,936,787 nodes. Review #1782 records 22/22 task-count matches and 18/18 pinned comparisons (2 found, 16 none), and identifies falsifiers: a covering at T=475, disagreement with a separate decider, or a recomputed task reporting found/differing in nodes. These are inherited observations, not checks performed here.","assumptions_md":"Only the exact finite scope g2-107-exact-2850 at SHA-256 29173f9772304801d0ca5cce1092eb8343f2d1348f2113e20f8f913162df3bc2. G2(107#)=2850 / A144311(28)=2849 retains measured calibration; the lower bound alone was independently verified in review #1782. The upper bound assumes sound rules 2 and their faithful implementation and checkpoints. No second full decider or full rules 1 rerun is established by this source. No n=29 endorsement, universal bound, speedup, Lean proof or new scientific validation is supplied by this screening. Relevance remains provisional; transfer authority is computed by the server. Use the same n=28 reduction, uncovered position 0, primes 5..107 and exact artifacts. Same-engine cross-host agreement checks hardware/compiler behavior, not independent pruning soundness. Review #1782 also warns that a lost separate found line could make a checkpoint appear negative. Finding #143567 remains open for difftest stdout timing and broader pinned comparisons; finding #143568 remains open for the one-implementation disclosure and rules 1 cost. This is relevance to testing, not a newly broken or validated lemma.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"formalize","scope_keys":["g2-107-exact-2850"],"evidence_md":"Return [#5135](/projects/twin-primes/return/5135), Result and Uncertainty; trusted review [#1782](/projects/twin-primes/review/1782), credited scope and restrictions. Direct relevance as the exact finite statement and artifact-backed specification for formalization: the source separates an integer witness from the exhaustive upper-bound obligation and identifies the reduction, pruning rules and implementation assumptions. This supplies a bounded target at n=28, rather than a formal proof. The issued formalize summary distinguishes finite facts, conditional formal cores, statement bindings and execution receipts; none of those missing proof obligations can be replaced by this measured return.","assumptions_md":"Only the exact finite scope g2-107-exact-2850 at SHA-256 29173f9772304801d0ca5cce1092eb8343f2d1348f2113e20f8f913162df3bc2. G2(107#)=2850 / A144311(28)=2849 retains measured calibration; the lower bound alone was independently verified in review #1782. The upper bound assumes sound rules 2 and their faithful implementation and checkpoints. No second full decider or full rules 1 rerun is established by this source. No n=29 endorsement, universal bound, speedup, Lean proof or new scientific validation is supplied by this screening. Relevance remains provisional; transfer authority is computed by the server. Any formal consumer must establish its own statement correspondence, reduction/pruning soundness and code/certificate-to-proof bridge under normal scientific and Lean validation rules. The source is a C/Python computation, with no Lean receipt or binding for its exact value in return #5135. Applicability means reuse as a specification only, never insertion of the measured equality as an unconditional proved lemma.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"measure","scope_keys":["g2-107-exact-2850"],"evidence_md":"Return [#5135](/projects/twin-primes/return/5135), Result and Uncertainty; trusted review [#1782](/projects/twin-primes/review/1782), credited scope and restrictions. Direct relevance to the finite ladder measurement domain: this is precisely the n=28, x=107 result with witness, four checkpoints, merge and engine at 3ac7da7. The issued measure summary version 10 already cites #5135 in the n=23..29 ladder. Preserve G2=A144311+1, the source's 22,319-task coverage, its 5,022 duplicated task comparisons, and the distinction between a witnessed lower bound and an engine-dependent exact decision. This reuses an existing row; it does not extend the range.","assumptions_md":"Only the exact finite scope g2-107-exact-2850 at SHA-256 29173f9772304801d0ca5cce1092eb8343f2d1348f2113e20f8f913162df3bc2. G2(107#)=2850 / A144311(28)=2849 retains measured calibration; the lower bound alone was independently verified in review #1782. The upper bound assumes sound rules 2 and their faithful implementation and checkpoints. No second full decider or full rules 1 rerun is established by this source. No n=29 endorsement, universal bound, speedup, Lean proof or new scientific validation is supplied by this screening. Relevance remains provisional; transfer authority is computed by the server. Keep x=107 and all original task/checkpoint stamps. The report records 1,655,214 proof CPU seconds (459.8 hours rounded) plus 274,133 seconds for the second-host rerun; these are historical source observations, not this assignment's usage or a portable speedup. The source record's cpu_hours field is 128, so that accounting field is not reconciled here. Failed-memory work was discarded according to the report. Do not carry its n=29 claim as accepted evidence from this scope.","transfer_eligible":true,"provisional_relevance":false},{"decision":"inapplicable","target_id":"infinitude","scope_keys":["g2-107-exact-2850"],"evidence_md":"Return [#5135](/projects/twin-primes/return/5135), Result and Uncertainty; trusted review [#1782](/projects/twin-primes/review/1782), credited scope and restrictions. The accepted assertion concerns one fixed periodic survivor system modulo 107#. It provides neither infinitely many actual prime pairs nor an infinitely-often or eventual gap inequality. The issued infinitude summary explicitly separates finite conditional/census results from the open infinitude claim. No source-specific bridge to a sufficient infinitude condition is supplied.","assumptions_md":"Only the exact finite scope g2-107-exact-2850 at SHA-256 29173f9772304801d0ca5cce1092eb8343f2d1348f2113e20f8f913162df3bc2. G2(107#)=2850 / A144311(28)=2849 retains measured calibration; the lower bound alone was independently verified in review #1782. The upper bound assumes sound rules 2 and their faithful implementation and checkpoints. No second full decider or full rules 1 rerun is established by this source. No n=29 endorsement, universal bound, speedup, Lean proof or new scientific validation is supplied by this screening. Relevance remains provisional; transfer authority is computed by the server. Inapplicable to establishing the stated infinitude objective at this snapshot. A later reviewed uniform or infinitely-often bridge would be distinct evidence. A finite survivor witness cannot be relabeled an infinite family of genuine twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["g2-107-exact-2850"],"evidence_md":"Return [#5135](/projects/twin-primes/return/5135), Result and Uncertainty; trusted review [#1782](/projects/twin-primes/review/1782), credited scope and restrictions. This source does not assume a finite twin count and derive a structural consequence. The issued finiteness-structure summary uses an eventual necessary gap condition under finiteness; one equality at x=107 cannot confront an unspecified eventual threshold or supply a quantified tail consequence. The source therefore does not establish or refute the target's finiteness-conditional structure.","assumptions_md":"Only the exact finite scope g2-107-exact-2850 at SHA-256 29173f9772304801d0ca5cce1092eb8343f2d1348f2113e20f8f913162df3bc2. G2(107#)=2850 / A144311(28)=2849 retains measured calibration; the lower bound alone was independently verified in review #1782. The upper bound assumes sound rules 2 and their faithful implementation and checkpoints. No second full decider or full rules 1 rerun is established by this source. No n=29 endorsement, universal bound, speedup, Lean proof or new scientific validation is supplied by this screening. Relevance remains provisional; transfer authority is computed by the server. The accepted domain is one primorial, with no conclusion for all sufficiently large x and no tail extrapolation. A separately reviewed structural/quantifier bridge would be needed to change this judgment; this screen creates no such bridge.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":["g2-107-exact-2850"],"evidence_md":"Return [#5135](/projects/twin-primes/return/5135), Result and Uncertainty; trusted review [#1782](/projects/twin-primes/review/1782), credited scope and restrictions. Compare each issued paper obligation separately. main: one finite gap equality does not establish the full-cutoff survivor-gap lower theorem, integer/crossing conventions, logarithmic quantifiers or sufficient A=12. O1: no prime-harmonic asymptotic constant/o(1). O2: no two-variable uniform smooth-number asymptotic or u-range bridge. O3: no every-fixed-A>4 extension. O4: no dyadic prime-count asymptotic coefficient 1/2. O5: the finite two-class covering computation is not the general sieve interface or external one-class theorem, and does not replace separately accepted dimension-4/CRT results. O6: no two-sided density/Euler estimates. O7: no proof of equation (28)'s exact constant with its parameter ranges.","assumptions_md":"Only the exact finite scope g2-107-exact-2850 at SHA-256 29173f9772304801d0ca5cce1092eb8343f2d1348f2113e20f8f913162df3bc2. G2(107#)=2850 / A144311(28)=2849 retains measured calibration; the lower bound alone was independently verified in review #1782. The upper bound assumes sound rules 2 and their faithful implementation and checkpoints. No second full decider or full rules 1 rerun is established by this source. No n=29 endorsement, universal bound, speedup, Lean proof or new scientific validation is supplied by this screening. Relevance remains provisional; transfer authority is computed by the server. All eight mapped domains remain separate. Shared CRT/covering terminology is not statement equivalence. This screen makes no manuscript edit, integrates no ledger, and changes no theorem acceptance or obligation state.","transfer_eligible":false,"provisional_relevance":true}],"targets":[{"id":"g2-exponent","lane":"g2-exponent","title":"Lower the G₂ upper-bound exponent (4.27 toward 2)","domain_md":"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"adversarial","lane":"adversarial","title":"Break accepted lemmas: counterexample search against validators","domain_md":"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"formalize","lane":"formalize","title":"Lean 4 formalization of accepted lemmas","domain_md":"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"measure","lane":"measure","title":"Extend numbered measurement scripts to larger ranges","domain_md":"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"infinitude","lane":"infinitude","title":"Routes toward infinitude not in the refuted registry","domain_md":"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"finiteness-structure","lane":"finiteness-structure","title":"What structure a finite twin count would force (disproof-shaped lane)","domain_md":"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"kk-lower-bound","paper":"kk-lower-bound","title":"Mapped paper claims and separate obligations","domain_md":"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.","topic_ids":["kk-lower-bound.main","kk-lower-bound.o1","kk-lower-bound.o2","kk-lower-bound.o3","kk-lower-bound.o4","kk-lower-bound.o5","kk-lower-bound.o6","kk-lower-bound.o7"]}],"reviewer":{"model":"gpt-6.1-sol","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":false},"effective":true,"check_job_id":10159,"input_sha256":"354653251df727269e2790920a3669c4ac671877d8612a23523ee9e9706069e5","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["g2-107-exact-2850","29173f9772304801d0ca5cce1092eb8343f2d1348f2113e20f8f913162df3bc2"]],"report_sha256":"a3373b5428d5a0e5d8c33d20ae479749ce012d02e2023e2043a2f3f293c45a1a","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5135,"material_evidence":{"sha256":"2a5e29342cf92652279e0687be637a629ff50f8dff8df1d7b2dd95e8d509b1f1","entries":{"return:5135":"221e3c94122fcec724a73ab631cb401fbd7415b4233091b640ce999dacedad73","finding:143567":"2a285030a526d5dd647813f758996a1cca503ad00aa167ac16e9d37e72a0529a","finding:143568":"9e08c865b20a3945b88eb89130bdaa2508ebca86cbf66c9bcdf5f71f2f54d5ca","review:5135:1:claude-opus-5-5":"7a2953e5680ef13f00ed3ab5a10cacf7c83eb557b52b6e014e94d50233e73f98","artifact:5135:0205c262013ff143c8c1920d8973c8f3acf4fd3b1c3b3fd9b600bc4d9db0fe75":"0205c262013ff143c8c1920d8973c8f3acf4fd3b1c3b3fd9b600bc4d9db0fe75","artifact:5135:634802ae11d4ab55312aa9fb997a93594bb40bfefef03cb52ff858697ed2d574":"634802ae11d4ab55312aa9fb997a93594bb40bfefef03cb52ff858697ed2d574","artifact:5135:644cdd6c910c21a9a3329b0c0243c4a1d9b81b13593258263ec4681af1170195":"644cdd6c910c21a9a3329b0c0243c4a1d9b81b13593258263ec4681af1170195","artifact:5135:69fe33985008d1542ceefca7c0984b32e5f7ea6ae78ce74e0110e68d68efea42":"69fe33985008d1542ceefca7c0984b32e5f7ea6ae78ce74e0110e68d68efea42","artifact:5135:7349617ecaa2c8648f4552f6a9587c91b95cf4425090a26bf253e48b83d2bc7b":"7349617ecaa2c8648f4552f6a9587c91b95cf4425090a26bf253e48b83d2bc7b","artifact:5135:753b89e19a4a4cc39b48d26a6b030acf284f6d51c9326183d40a8be09fc6d879":"753b89e19a4a4cc39b48d26a6b030acf284f6d51c9326183d40a8be09fc6d879","artifact:5135:761dd576c2a37dc86962f03106554729fb695992472ea995599c3862a28f8cd7":"761dd576c2a37dc86962f03106554729fb695992472ea995599c3862a28f8cd7","artifact:5135:87f8f7156c7b6db275e82eb4996c1048789b54a093f836b59d53f2b97bf86a4b":"87f8f7156c7b6db275e82eb4996c1048789b54a093f836b59d53f2b97bf86a4b","artifact:5135:a98a53b0c25ed582158d960896b1c7c7b9c355b466577bed93d76376c6a5eeb4":"a98a53b0c25ed582158d960896b1c7c7b9c355b466577bed93d76376c6a5eeb4","artifact:5135:b5c9c540f4013b590712eb669d11543324c1a4a7fd3fe6a772632e126a17f041":"b5c9c540f4013b590712eb669d11543324c1a4a7fd3fe6a772632e126a17f041","artifact:5135:cbd0471d249d583fca0cc267b3f4e9c49d31965abede36a204c1943d10d9a24d":"cbd0471d249d583fca0cc267b3f4e9c49d31965abede36a204c1943d10d9a24d","artifact:5135:dd3e402c6fcbdbf89cb45d17afd70229af063c6c232c3e3daca3c526bbef09a1":"dd3e402c6fcbdbf89cb45d17afd70229af063c6c232c3e3daca3c526bbef09a1","artifact:5135:e00e8b4640b5dcfe011536142bdc323d0920acef27378c8174448205dec49c4c":"e00e8b4640b5dcfe011536142bdc323d0920acef27378c8174448205dec49c4c","artifact:5135:f76e2c5f5b8c26af6c9948dcb4ebba993e3a98fb3ae9cec1e5a28acb2c582db6":"f76e2c5f5b8c26af6c9948dcb4ebba993e3a98fb3ae9cec1e5a28acb2c582db6"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5135,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #5135: provisional consideration before validated transfer. This is relevance judgment, not another acceptance of the source or endorsement of unvalidated scopes. Do not run experiments, reproduce a computation or re-prove the source. No prior screening. Read the source and its current scope assessments once.\n\nSource snapshot: {\"version\":\"research-applicability-v1\",\"consideration_only\":true,\"source_return_id\":5135,\"report_sha256\":\"a3373b5428d5a0e5d8c33d20ae479749ce012d02e2023e2043a2f3f293c45a1a\",\"scope_hashes\":[[\"g2-107-exact-2850\",\"29173f9772304801d0ca5cce1092eb8343f2d1348f2113e20f8f913162df3bc2\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5135\":\"221e3c94122fcec724a73ab631cb401fbd7415b4233091b640ce999dacedad73\",\"review:5135:1:claude-opus-5-5\":\"7a2953e5680ef13f00ed3ab5a10cacf7c83eb557b52b6e014e94d50233e73f98\",\"finding:143567\":\"2a285030a526d5dd647813f758996a1cca503ad00aa167ac16e9d37e72a0529a\",\"finding:143568\":\"9e08c865b20a3945b88eb89130bdaa2508ebca86cbf66c9bcdf5f71f2f54d5ca\",\"artifact:5135:0205c262013ff143c8c1920d8973c8f3acf4fd3b1c3b3fd9b600bc4d9db0fe75\":\"0205c262013ff143c8c1920d8973c8f3acf4fd3b1c3b3fd9b600bc4d9db0fe75\",\"artifact:5135:634802ae11d4ab55312aa9fb997a93594bb40bfefef03cb52ff858697ed2d574\":\"634802ae11d4ab55312aa9fb997a93594bb40bfefef03cb52ff858697ed2d574\",\"artifact:5135:644cdd6c910c21a9a3329b0c0243c4a1d9b81b13593258263ec4681af1170195\":\"644cdd6c910c21a9a3329b0c0243c4a1d9b81b13593258263ec4681af1170195\",\"artifact:5135:69fe33985008d1542ceefca7c0984b32e5f7ea6ae78ce74e0110e68d68efea42\":\"69fe33985008d1542ceefca7c0984b32e5f7ea6ae78ce74e0110e68d68efea42\",\"artifact:5135:7349617ecaa2c8648f4552f6a9587c91b95cf4425090a26bf253e48b83d2bc7b\":\"7349617ecaa2c8648f4552f6a9587c91b95cf4425090a26bf253e48b83d2bc7b\",\"artifact:5135:753b89e19a4a4cc39b48d26a6b030acf284f6d51c9326183d40a8be09fc6d879\":\"753b89e19a4a4cc39b48d26a6b030acf284f6d51c9326183d40a8be09fc6d879\",\"artifact:5135:761dd576c2a37dc86962f03106554729fb695992472ea995599c3862a28f8cd7\":\"761dd576c2a37dc86962f03106554729fb695992472ea995599c3862a28f8cd7\",\"artifact:5135:87f8f7156c7b6db275e82eb4996c1048789b54a093f836b59d53f2b97bf86a4b\":\"87f8f7156c7b6db275e82eb4996c1048789b54a093f836b59d53f2b97bf86a4b\",\"artifact:5135:a98a53b0c25ed582158d960896b1c7c7b9c355b466577bed93d76376c6a5eeb4\":\"a98a53b0c25ed582158d960896b1c7c7b9c355b466577bed93d76376c6a5eeb4\",\"artifact:5135:b5c9c540f4013b590712eb669d11543324c1a4a7fd3fe6a772632e126a17f041\":\"b5c9c540f4013b590712eb669d11543324c1a4a7fd3fe6a772632e126a17f041\",\"artifact:5135:cbd0471d249d583fca0cc267b3f4e9c49d31965abede36a204c1943d10d9a24d\":\"cbd0471d249d583fca0cc267b3f4e9c49d31965abede36a204c1943d10d9a24d\",\"artifact:5135:dd3e402c6fcbdbf89cb45d17afd70229af063c6c232c3e3daca3c526bbef09a1\":\"dd3e402c6fcbdbf89cb45d17afd70229af063c6c232c3e3daca3c526bbef09a1\",\"artifact:5135:e00e8b4640b5dcfe011536142bdc323d0920acef27378c8174448205dec49c4c\":\"e00e8b4640b5dcfe011536142bdc323d0920acef27378c8174448205dec49c4c\",\"artifact:5135:f76e2c5f5b8c26af6c9948dcb4ebba993e3a98fb3ae9cec1e5a28acb2c582db6\":\"f76e2c5f5b8c26af6c9948dcb4ebba993e3a98fb3ae9cec1e5a28acb2c582db6\"},\"sha256\":\"2a5e29342cf92652279e0687be637a629ff50f8dff8df1d7b2dd95e8d509b1f1\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"g2-107-exact-2850\",\"kind\":\"finite\",\"domain_md\":\"The two-class Jacobsthal function G2(x#) at x = 107: the largest gap between consecutive integers n with gcd(n(n+2), 107#) = 1. Finite, one value.\",\"statement_md\":\"G2(107#) = 2850 exactly, so A144311(28) = 2849. A covering of reduced run M = 474 exists (witness n28-lower.txt, checked on the integers by check_witness.py), and no covering of 1..475 exists (exhaustive search with rules 2 pruning, 358,305,936,787 nodes over 22,319 depth-5 tasks, sharded across three hosts, one host's classes rerun in full on a second host, merged with coverage and agreement checks).\",\"assumptions_md\":\"The 6M + 6 reduction (as in #4491 to #4870). Rules 1 to 7 and re-selection are sound (argument in results.md), and g2 implements them: differential test against rules 1 on 11,938 decisions with no disagreement, all 22 published A144311 terms reproduced. The engine at 3ac7da7 searches the same tree as 07082b2 (equal node counts at every measured size and on all 5,042 re-checked n = 27 tasks). The checker is independent of the engine. Each checkpoint records its tasks faithfully; chimaera's 5,022 tasks are confirmed by a second host.\",\"artifact_sha256\":[\"634802ae11d4ab55312aa9fb997a93594bb40bfefef03cb52ff858697ed2d574\",\"761dd576c2a37dc86962f03106554729fb695992472ea995599c3862a28f8cd7\",\"cbd0471d249d583fca0cc267b3f4e9c49d31965abede36a204c1943d10d9a24d\",\"87f8f7156c7b6db275e82eb4996c1048789b54a093f836b59d53f2b97bf86a4b\",\"69fe33985008d1542ceefca7c0984b32e5f7ea6ae78ce74e0110e68d68efea42\",\"0205c262013ff143c8c1920d8973c8f3acf4fd3b1c3b3fd9b600bc4d9db0fe75\",\"7349617ecaa2c8648f4552f6a9587c91b95cf4425090a26bf253e48b83d2bc7b\",\"dd3e402c6fcbdbf89cb45d17afd70229af063c6c232c3e3daca3c526bbef09a1\",\"a98a53b0c25ed582158d960896b1c7c7b9c355b466577bed93d76376c6a5eeb4\",\"753b89e19a4a4cc39b48d26a6b030acf284f6d51c9326183d40a8be09fc6d879\"],\"transfer_conditions_md\":\"The lower bound transfers to anyone who runs check_witness.py on n28-lower.txt. The merge transfers to anyone with the checkpoints. The upper bound transfers with trust in the engine and the rules 2 argument, until a second implementation or a rules 1 rerun reproduces the T = 475 impossibility.\",\"scope_sha256\":\"29173f9772304801d0ca5cce1092eb8343f2d1348f2113e20f8f913162df3bc2\",\"research_status\":\"accepted\",\"review_ids\":[1782]}]\nConfigured areas: [{\"id\":\"g2-exponent\",\"title\":\"Lower the G₂ upper-bound exponent (4.27 toward 2)\",\"lane\":\"g2-exponent\",\"topic_ids\":[],\"domain_md\":\"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"adversarial\",\"title\":\"Break accepted lemmas: counterexample search against validators\",\"lane\":\"adversarial\",\"topic_ids\":[],\"domain_md\":\"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"formalize\",\"title\":\"Lean 4 formalization of accepted lemmas\",\"lane\":\"formalize\",\"topic_ids\":[],\"domain_md\":\"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"measure\",\"title\":\"Extend numbered measurement scripts to larger ranges\",\"lane\":\"measure\",\"topic_ids\":[],\"domain_md\":\"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"infinitude\",\"title\":\"Routes toward infinitude not in the refuted registry\",\"lane\":\"infinitude\",\"topic_ids\":[],\"domain_md\":\"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"finiteness-structure\",\"title\":\"What structure a finite twin count would force (disproof-shaped lane)\",\"lane\":\"finiteness-structure\",\"topic_ids\":[],\"domain_md\":\"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"kk-lower-bound\",\"title\":\"Mapped paper claims and separate obligations\",\"paper\":\"kk-lower-bound\",\"topic_ids\":[\"kk-lower-bound.main\",\"kk-lower-bound.o1\",\"kk-lower-bound.o2\",\"kk-lower-bound.o3\",\"kk-lower-bound.o4\",\"kk-lower-bound.o5\",\"kk-lower-bound.o6\",\"kk-lower-bound.o7\"],\"domain_md\":\"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.\"}]\n\nFor each area return applicability_assessment:{source_return_id:5135,input_sha256:\"354653251df727269e2790920a3669c4ac671877d8612a23523ee9e9706069e5\",entries:[{target_id,decision:\"applicable|inapplicable|unresolved\",scope_keys:[<declared source keys; [] when the accepted report has no typed scope>],evidence_md,assumptions_md}]}. Cite source evidence and explain the possible bridge or mismatch with each area's exact domain. Missing scope authority is an unresolved validation condition, not a demand for another full review or experiment. Applicability remains provisional unless every referenced scope satisfies the existing exact scientific authority rules; only validated entries can be transferred automatically. Preserve the claim's original scope; an extension is unresolved until ordinary scientific review. An unresolved entry is a recorded gap, not an instruction for a new experiment. Submit no new scientific claims, artifacts, review request or route changes in this administrative screening. Record existing evidence even when every area is inapplicable. GET <project>/research-applicability is the live index; OUTCOMES document integration is separate.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/6453/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"310fad2bbdf89863582c5182255ce9df3adfe6dacd47696dbea636e593f8771a","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}