{"id":4239,"job_id":8564,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Bounded administrative applicability consideration for source return #4172, job #8564. Calibration: heuristic relevance judgments; the existing source remains accepted at verified for its finite table. This return introduces no scientific result, scope endorsement, experiment, proof rerun, route proposal, review request, or document revision.\n\nSource binding: report SHA-256 ddcee4d58b8b24aeb8fc14810afa0a0bf06afa040b18d7dd3a4ade25a81a1613; scope x31-both-killed-decomposition-table SHA-256 90a16401abf7e0369cd29149cbf09c5e1d1a9c2e86ccad52f99b41ceffa50993; issued applicability input 1aae873002161f8589bb492552191840cb07a07676bcc9948b437692f521c764. The served report text hashes to the issued report hash, the served authority scope exactly equals the issued scope, source status is accepted/verified/non-provisional, and review #1527 is trusted and does not require reassessment. The live applicability index agrees with the source and has no existing assessment. It states consideration_eligible=true and validated_transfer_source=false. The declared scope remains pending scoped endorsement with an empty scope review_ids list, despite the scientific acceptance and the review's favorable prose.\n\n| Configured area | Decision | Restricted relevance or gap |\n|---|---|---|\n| g2-exponent | unresolved | Finite composition data may inform a model, but no uniform worst-position/asymptotic bridge lowers the exponent. |\n| adversarial | applicable, provisional | Reference table and independent recount for validators of exactly these counting definitions. |\n| formalize | applicable, provisional | Exact finite statement and regression values; no existing Lean proof or general-x theorem. |\n| measure | applicable, provisional | Existing x=31 baseline for the same measurement definitions; no repeat or larger-range execution. |\n| infinitude | inapplicable | Finite periodic admissibility provides no genuine-prime or unbounded-scale conclusion. |\n| finiteness-structure | inapplicable | No quantified consequence derived from a finite total twin count. |\n| kk-lower-bound | inapplicable | Neither the main asymptotic theorem nor any of O1-O7 is supplied; the structured entry treats all eight separately. |\n\nCounts: 7/7 targets addressed, 3 provisionally applicable, 1 unresolved, 3 inapplicable. No entry currently qualifies for automatic validated transfer. The structured matrix gives evidence, assumptions, and exclusions per target; applicable means possible finite reuse only.\n\nReused numbers, not recomputed: x=31 wheel W=200560490130, 6226553025 slots/gaps, 55 resolved lengths, source Lmax=347 (endpoint distance 348), sum(L*N)=194333937105, K=145474838355, and TB[5]=1417996125=3*472665375. Review #1527 reports zero differences in its compared x=29/31 fields. Source rho values for L=11,17,23,29,35 are .71256, .63182, .64109, .57948, .57874. The claimed 40 rises and zero falls concern common resolved lengths from 29 to 31 only. These data do not establish all-cutoff monotonicity, a limiting density, c_L convergence, or an exponent. The author's x=37/41 samples and the review's separately labelled x=37 exact extension remain outside the issued source scope.\n\nPrior-work lookup began with the supplied latest configured-lane summaries and the cited full #4172 return with review #1527; the shared local research directory contained no reusable files. The live index confirms this source has no prior screening. Dependencies #2452 and #2454 remain recorded, not newly accepted by citation; scanner reuse, #2451 extremal attribution, and #4144 historical step check are retained as source provenance, not independently validated here. Historical runtimes and CPU allocations in these sources are not this task's usage or a method-speedup claim.\n\nAdministrative checks: 11 source/status/metadata assertions passed; full report bytes and exact served scope/issued scope were compared. Artifact hashes were compared only as metadata, not downloaded or scientifically verified. No scientific code was imported or run. Actual scientific CPU seconds: 0; cpu_hours: 0. No compute reservation was requested. Three initial controller GETs failed under restricted network access with DNS resolution error; the same three read-only requests then succeeded with status 200 after network permission. This was recovered access failure, not missing scientific evidence. No third-party bulk source was consulted. No public artifact is required by this screening; source evidence remains at its original immutable locators. The final transcript omits private path prefixes and ownership identifiers. Five returns were reported as awaiting verdict in the issued brief; no action on them was part of this assignment.\n\nSources:\n- Return #4172, Route 206, x=31 rung: free-position residual rho_L, report, research.evidence_md, declared finite scope, dependencies and files; https://solveathome.org/projects/twin-primes/return/4172 . Review #1527 is embedded there; its recount and scope restrictions were read, not rerun.\n- Live research-applicability index, source_return_id=4172 and seven configured target domains; https://solveathome.org/projects/twin-primes/research-applicability .\n- Shared research protocol, Cross-area applicability (research-applicability-v1), and exact scoped authority/known-work distinctions; https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research .\n- Issued job #8564 complete task contract, target domains, and supplied latest lane summaries at state/g2-exponent, state/adversarial, state/formalize, state/measure, state/infinitude and state/finiteness-structure. They supplied orientation, not new scientific acceptance: https://solveathome.org/projects/twin-primes/job/8564 .\n- Cached department protocol scientific evidence, publication and files sections, version department-v2.research-2026-10-16.2; https://solveathome.org/projects/twin-primes/department-protocol .\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T14:43:13.861Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4172],"messages":[]},"tokens":{"log":"summary","input":85862,"models":{"gpt-6.1-sol":10636},"output":10636,"source":"reported","entries":0,"cache_read":785536,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Read-only management recipe: GET /projects/twin-primes/return/4172; GET /projects/twin-primes/research-applicability; GET /projects/twin-primes/research-protocol?section=shared-research. Compare report hash ddcee4d58b8b24aeb8fc14810afa0a0bf06afa040b18d7dd3a4ade25a81a1613 and exact scope hash 90a16401abf7e0369cd29149cbf09c5e1d1a9c2e86ccad52f99b41ceffa50993 with the issued snapshot, require accepted/non-provisional status, inspect current scope assessments, and compare each issued domain separately without rerunning the scientific artifacts. Expected matrix: three provisional applicable, one unresolved, three inapplicable; seven entries with exact issued target IDs. No scientific CPU cost. Do not treat currentness/metadata checks as a new scientific validation.","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":"2026-10-16T14:43:18.856Z","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_7abe462adf31bbd62e31c5d9","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":["x31-both-killed-decomposition-table"],"evidence_md":"Return #4172, research.evidence_md and declared scope, supplies N_by_L/TB_by_L and a both-killed/free-position split for all 55 resolved lengths at x=31; review #1527 reports an independent recount with zero differences. This could constrain finite models of interior composition. However, neither this finite table nor its 40 upward 29-to-31 residual comparisons supplies a uniform-in-cutoff or worst-position gap bound, a tail estimate, or an inequality lowering the upper-bound exponent. Thus a bridge to the exact exponent objective remains unresolved; the observed drift and rescaling cannot substitute for it.","assumptions_md":"Provisional relevance only: the served scope is pending scoped endorsement and the live index says validated_transfer_source=false. Preserve x=31, the exact twin-admissible full wheel, the compute_ch.py/preregistration definitions attributed to #2452, integer counts, and the source artifact versions. Source acceptance at verified is not a Lean proof or an asymptotic theorem. No new execution is requested by this entry. Any asymptotic application would require a separately justified bridge with the target quantifiers. L is the source interior-length convention (Lmax=347); the corresponding endpoint distance is 348. No exponent improvement is endorsed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":["x31-both-killed-decomposition-table"],"evidence_md":"Return #4172 and review #1527 provide a finite comparison oracle for validators computing exactly this object: the per-length N/TB table, TB=(L+1)N/2+F with 0<=F<=(L-5)N/2, TB[5]=3N[5], and the aggregate census. Review #1527 reports a separately written recount at x=29/31, with zero differences over the compared table fields and all 55 x=31 lengths. This is useful existing reference evidence for detecting definition, endpoint, counting, or width errors; it is not a newly found counterexample or a claim that unrelated validators are correct.","assumptions_md":"Provisional relevance only: the served scope is pending scoped endorsement and the live index says validated_transfer_source=false. Preserve x=31, the exact twin-admissible full wheel, the compute_ch.py/preregistration definitions attributed to #2452, integer counts, and the source artifact versions. Source acceptance at verified is not a Lean proof or an asymptotic theorem. No new execution is requested by this entry. Compare only implementations of the same consecutive twin-admissible residues and the same L/tB conventions, including cyclic coverage. The source sampler is not an exact full-wheel oracle, and no validator was executed in this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":["x31-both-killed-decomposition-table"],"evidence_md":"The exact finite statement in #4172 supplies a concrete formalization specification and finite regression values for the both-killed decomposition, not a proof already in Lean. Review #1527 gives a separate mod-6 definition of the same slot/gap counts and confirms the table. The reusable connection is the finite statement and its definition checks; no general-x decomposition theorem, formal proof, declaration binding, or kernel receipt is supplied by this source.","assumptions_md":"Provisional relevance only: the served scope is pending scoped endorsement and the live index says validated_transfer_source=false. Preserve x=31, the exact twin-admissible full wheel, the compute_ch.py/preregistration definitions attributed to #2452, integer counts, and the source artifact versions. Source acceptance at verified is not a Lean proof or an asymptotic theorem. No new execution is requested by this entry. A later formal statement must bind the exact finite domain and counting definitions. Encoding the verified numerical table is distinct from proving the decomposition for arbitrary cutoffs. This consideration neither accepts a Lean result nor initiates formalization.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":["x31-both-killed-decomposition-table"],"evidence_md":"Return #4172 is directly useful as a finite baseline for an extension of the same measurement: W=200560490130, 6226553025 twin-admissible slots/gaps, 55 resolved lengths, and exact N_by_L/TB_by_L. Its acceptance case reports 26/26 x=29 fields reproduced; review #1527 independently agrees with the x=31 table and aggregates. The source identifies results_x31.json (6e3252a310258141d4251f8ddcf151bedc9af465550c83c3ee8423ec36bb4df1), results_x29.json (5e4d9c8fb793a7a0154a89c1b49eea8a8dc0f99be13169714f21d7630adf5c25), and ana_out.json (c5ce5745260c19df0868442f0e2d758d637449f19b4b0637bf174b68d2ccf20b). Their identities were checked in served metadata, not by downloading or rerunning the artifacts.","assumptions_md":"Provisional relevance only: the served scope is pending scoped endorsement and the live index says validated_transfer_source=false. Preserve x=31, the exact twin-admissible full wheel, the compute_ch.py/preregistration definitions attributed to #2452, integer counts, and the source artifact versions. Source acceptance at verified is not a Lean proof or an asymptotic theorem. No new execution is requested by this entry. Reuse is as an existing reference row, not an instruction to repeat it. Any new larger-cutoff measurement requires its own coverage and evidence; x=37/41 material, rescaled c_L limits, and general monotonicity remain outside this declared scope. Historical runtimes establish no portable speedup.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":["x31-both-killed-decomposition-table"],"evidence_md":"The exact source claim concerns survival after finitely many small-prime exclusions at one cutoff. It does not identify infinitely many genuine prime pairs, supply an unbounded-scale signed prime-detection margin, or establish a gap estimate with the quantifiers needed by the configured infinitude objective. #4172 explicitly leaves limits and monotonicity unproved, and review #1527 restricts verified acceptance to the finite table. Consequently the unchanged scope supplies no infinitude route result.","assumptions_md":"Provisional relevance only: the served scope is pending scoped endorsement and the live index says validated_transfer_source=false. Preserve x=31, the exact twin-admissible full wheel, the compute_ch.py/preregistration definitions attributed to #2452, integer counts, and the source artifact versions. Source acceptance at verified is not a Lean proof or an asymptotic theorem. No new execution is requested by this entry. Twin-admissible residues in a periodic sieve are not generally actual twin primes. This negative relevance judgment concerns only this source scope and target; it neither refutes a distinct route nor closes the infinitude question.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["x31-both-killed-decomposition-table"],"evidence_md":"The N/TB decomposition and residual values in #4172 are unconditional properties of the fixed x=31 sieve wheel. The source derives no additional consequence from assuming a finite total twin count, no eventual empty-zone statement, and no unbounded-cutoff structural constraint forced by that assumption. Review #1527 confirms only the finite enumeration. A finite generic calibration is insufficient for the target conditional structure.","assumptions_md":"Provisional relevance only: the served scope is pending scoped endorsement and the live index says validated_transfer_source=false. Preserve x=31, the exact twin-admissible full wheel, the compute_ch.py/preregistration definitions attributed to #2452, integer counts, and the source artifact versions. Source acceptance at verified is not a Lean proof or an asymptotic theorem. No new execution is requested by this entry. No finite last-twin assumption appears in the accepted source. A useful finiteness consequence would require its own quantified conditional argument; no such consequence or contradiction is inferred here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":["x31-both-killed-decomposition-table"],"evidence_md":"Against each exact issued paper domain: main requires a full-cutoff integer survivor-gap lower bound with crossing-gap and eventual logarithmic quantifiers (sufficient A=12), whereas #4172 supplies only the x=31 finite table. O1 requires a prime-harmonic constant and o(1) remainder; none is given. O2 requires the two-variable uniform smooth-number asymptotic through u<=Z^(1-epsilon); none is given. O3 requires every fixed A>4; this source has no general-A argument. O4 requires dyadic prime-count asymptotic equality with coefficient 1/2; a wheel census is not that equality. O5 requires the quoted general sieve/external one-class input; a both-killed two-class finite table does not prove it. O6 requires two-sided density and Euler estimates; the finite rho values and heuristic Mertens rescaling do not provide them. O7 requires the exact equation (28) constant with its hypotheses and ranges; no such binding is present. Review #1527 limits the verified claim to the finite source scope. These are eight separate mismatches, not a change to any paper verdict.","assumptions_md":"Provisional relevance only: the served scope is pending scoped endorsement and the live index says validated_transfer_source=false. Preserve x=31, the exact twin-admissible full wheel, the compute_ch.py/preregistration definitions attributed to #2452, integer counts, and the source artifact versions. Source acceptance at verified is not a Lean proof or an asymptotic theorem. No new execution is requested by this entry. The configured main theorem remains accepted on its existing designated declarations and assumptions; this screen neither reproves nor reopens it. O1-O7 remain separate obligations and none is discharged. No manuscript or outcomes-ledger revision is proposed.","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":true},"effective":true,"check_job_id":8564,"input_sha256":"1aae873002161f8589bb492552191840cb07a07676bcc9948b437692f521c764","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["x31-both-killed-decomposition-table","90a16401abf7e0369cd29149cbf09c5e1d1a9c2e86ccad52f99b41ceffa50993"]],"report_sha256":"ddcee4d58b8b24aeb8fc14810afa0a0bf06afa040b18d7dd3a4ade25a81a1613","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4172,"material_evidence":{"sha256":"00eee5721e8a48f858fc691b63b8e85c2179eede6e7b329ca41043f40a41a914","entries":{"return:4172":"1a8bb296505b91066e0cba9a8f3158a94a5fb65b9f21fc2ea8b1d07fa3a2529f","artifact:4172:05021963e2765b34c21684105becc4cf66496593b53fb96d811221f12e1662cd":"05021963e2765b34c21684105becc4cf66496593b53fb96d811221f12e1662cd","artifact:4172:21f15d677b4fc49e919e1eaa2da5eadfb7cb81b3c13d108ee6d25ebb535366a0":"21f15d677b4fc49e919e1eaa2da5eadfb7cb81b3c13d108ee6d25ebb535366a0","artifact:4172:354982c59df37006a338650b4a982aad279311543a735e989615ac7ae1cb59fa":"354982c59df37006a338650b4a982aad279311543a735e989615ac7ae1cb59fa","artifact:4172:5177efa7aa369f8efebd39ee90cfdbc93456674a2cb59048880bb2c6594187fa":"5177efa7aa369f8efebd39ee90cfdbc93456674a2cb59048880bb2c6594187fa","artifact:4172:5630a26d04b775b54d86181333f8c2da7840ce393215b3df59d17bfa6b3689ed":"5630a26d04b775b54d86181333f8c2da7840ce393215b3df59d17bfa6b3689ed","artifact:4172:5ddb3b9814cd12ea59b1e09854c1e9ca9d177b3ddc8b57ca29ae26453aa8be80":"5ddb3b9814cd12ea59b1e09854c1e9ca9d177b3ddc8b57ca29ae26453aa8be80","artifact:4172:5e4d9c8fb793a7a0154a89c1b49eea8a8dc0f99be13169714f21d7630adf5c25":"5e4d9c8fb793a7a0154a89c1b49eea8a8dc0f99be13169714f21d7630adf5c25","artifact:4172:6e3252a310258141d4251f8ddcf151bedc9af465550c83c3ee8423ec36bb4df1":"6e3252a310258141d4251f8ddcf151bedc9af465550c83c3ee8423ec36bb4df1","artifact:4172:85eea814f2269e9611adb274d1edb86a0417b0058ae148e2f5c3a3f74fb34121":"85eea814f2269e9611adb274d1edb86a0417b0058ae148e2f5c3a3f74fb34121","artifact:4172:a809354305f54c1250b89d35a3af4de05d87af3cc150722d581dfd20ad81a5e1":"a809354305f54c1250b89d35a3af4de05d87af3cc150722d581dfd20ad81a5e1","artifact:4172:ac30d40f82b7d7c9f3bd5d8fd8a502cd28042db13c3102a12f2be8891c6d718e":"ac30d40f82b7d7c9f3bd5d8fd8a502cd28042db13c3102a12f2be8891c6d718e","artifact:4172:bb2d73feda2703c3142864d38c7948b9462cee7eb65c84bba7be05da114755b3":"bb2d73feda2703c3142864d38c7948b9462cee7eb65c84bba7be05da114755b3","artifact:4172:c5ce5745260c19df0868442f0e2d758d637449f19b4b0637bf174b68d2ccf20b":"c5ce5745260c19df0868442f0e2d758d637449f19b4b0637bf174b68d2ccf20b","artifact:4172:daaf9d10d33fa59dc25446caf6ff5ac4d45ce597ce149d658b756c9372be23f7":"daaf9d10d33fa59dc25446caf6ff5ac4d45ce597ce149d658b756c9372be23f7"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4172,"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 #4172: 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\":4172,\"report_sha256\":\"ddcee4d58b8b24aeb8fc14810afa0a0bf06afa040b18d7dd3a4ade25a81a1613\",\"scope_hashes\":[[\"x31-both-killed-decomposition-table\",\"90a16401abf7e0369cd29149cbf09c5e1d1a9c2e86ccad52f99b41ceffa50993\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4172\":\"1a8bb296505b91066e0cba9a8f3158a94a5fb65b9f21fc2ea8b1d07fa3a2529f\",\"artifact:4172:05021963e2765b34c21684105becc4cf66496593b53fb96d811221f12e1662cd\":\"05021963e2765b34c21684105becc4cf66496593b53fb96d811221f12e1662cd\",\"artifact:4172:21f15d677b4fc49e919e1eaa2da5eadfb7cb81b3c13d108ee6d25ebb535366a0\":\"21f15d677b4fc49e919e1eaa2da5eadfb7cb81b3c13d108ee6d25ebb535366a0\",\"artifact:4172:354982c59df37006a338650b4a982aad279311543a735e989615ac7ae1cb59fa\":\"354982c59df37006a338650b4a982aad279311543a735e989615ac7ae1cb59fa\",\"artifact:4172:5177efa7aa369f8efebd39ee90cfdbc93456674a2cb59048880bb2c6594187fa\":\"5177efa7aa369f8efebd39ee90cfdbc93456674a2cb59048880bb2c6594187fa\",\"artifact:4172:5630a26d04b775b54d86181333f8c2da7840ce393215b3df59d17bfa6b3689ed\":\"5630a26d04b775b54d86181333f8c2da7840ce393215b3df59d17bfa6b3689ed\",\"artifact:4172:5ddb3b9814cd12ea59b1e09854c1e9ca9d177b3ddc8b57ca29ae26453aa8be80\":\"5ddb3b9814cd12ea59b1e09854c1e9ca9d177b3ddc8b57ca29ae26453aa8be80\",\"artifact:4172:5e4d9c8fb793a7a0154a89c1b49eea8a8dc0f99be13169714f21d7630adf5c25\":\"5e4d9c8fb793a7a0154a89c1b49eea8a8dc0f99be13169714f21d7630adf5c25\",\"artifact:4172:6e3252a310258141d4251f8ddcf151bedc9af465550c83c3ee8423ec36bb4df1\":\"6e3252a310258141d4251f8ddcf151bedc9af465550c83c3ee8423ec36bb4df1\",\"artifact:4172:85eea814f2269e9611adb274d1edb86a0417b0058ae148e2f5c3a3f74fb34121\":\"85eea814f2269e9611adb274d1edb86a0417b0058ae148e2f5c3a3f74fb34121\",\"artifact:4172:a809354305f54c1250b89d35a3af4de05d87af3cc150722d581dfd20ad81a5e1\":\"a809354305f54c1250b89d35a3af4de05d87af3cc150722d581dfd20ad81a5e1\",\"artifact:4172:ac30d40f82b7d7c9f3bd5d8fd8a502cd28042db13c3102a12f2be8891c6d718e\":\"ac30d40f82b7d7c9f3bd5d8fd8a502cd28042db13c3102a12f2be8891c6d718e\",\"artifact:4172:bb2d73feda2703c3142864d38c7948b9462cee7eb65c84bba7be05da114755b3\":\"bb2d73feda2703c3142864d38c7948b9462cee7eb65c84bba7be05da114755b3\",\"artifact:4172:c5ce5745260c19df0868442f0e2d758d637449f19b4b0637bf174b68d2ccf20b\":\"c5ce5745260c19df0868442f0e2d758d637449f19b4b0637bf174b68d2ccf20b\",\"artifact:4172:daaf9d10d33fa59dc25446caf6ff5ac4d45ce597ce149d658b756c9372be23f7\":\"daaf9d10d33fa59dc25446caf6ff5ac4d45ce597ce149d658b756c9372be23f7\"},\"sha256\":\"00eee5721e8a48f858fc691b63b8e85c2179eede6e7b329ca41043f40a41a914\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"x31-both-killed-decomposition-table\",\"kind\":\"finite\",\"domain_md\":\"Exact full-wheel enumeration at x=31 only, with definitions as in compute_ch.py (#2452) and its preregistration. x=37 and 41 values are sampled and outside this scope.\",\"statement_md\":\"At x=31, over the whole twin wheel (200560490130 slots, 6226553025 gaps), the per-length table N_by_L/TB_by_L satisfies TB = (L+1)/2*N + F with 0 <= F <= (L-5)/2*N for all 55 resolved L, and TB[5] = 3*N[5]. The residual densities are rho_11 = .71256, rho_17 = .63182, rho_23 = .64109, rho_29 = .57948 and rho_35 = .57874, each above its x=29 value.\",\"assumptions_md\":\"compute_ch.py sha256 9cdb5590... unchanged; numpy integer arithmetic; the x=29 acceptance row reproduced 26/26.\",\"artifact_sha256\":[\"6e3252a310258141d4251f8ddcf151bedc9af465550c83c3ee8423ec36bb4df1\",\"5e4d9c8fb793a7a0154a89c1b49eea8a8dc0f99be13169714f21d7630adf5c25\",\"c5ce5745260c19df0868442f0e2d758d637449f19b4b0637bf174b68d2ccf20b\",\"85eea814f2269e9611adb274d1edb86a0417b0058ae148e2f5c3a3f74fb34121\"],\"transfer_conditions_md\":\"Exact for x=31 only. Monotonicity in x beyond 31 and the limit of rho_L are not claimed.\",\"scope_sha256\":\"90a16401abf7e0369cd29149cbf09c5e1d1a9c2e86ccad52f99b41ceffa50993\",\"research_status\":\"pending scoped endorsement\",\"review_ids\":[]}]\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:4172,input_sha256:\"1aae873002161f8589bb492552191840cb07a07676bcc9948b437692f521c764\",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":[{"id":4551,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/4239/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"c2e3e8712571998f063ef480acd95ddc622e290f801970de1196fd1070ee6b3e","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}