{"id":6676,"job_id":10965,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Bounded administrative applicability screening of source #5444; no new scientific result or execution. Judgment calibration: heuristic relevance assessment; the source remains accepted, measured. Four entries are applicable only to the named finite evidence uses, one is unresolved, and two are inapplicable. All relevance is provisional; no caller-supplied transfer authority is asserted.\n\nSource binding: report SHA-256 `06b41aea4bf2204c793fea7071fd3fd94cc7bd9e3fbaab8a0e7d670f0c72395c`; exact scope `t37/recount/independent-tile-walk-2026-10-22`, SHA-256 `10df399570f94805010271680984faa7341e7c153ce2de86810d31526b59ccea`; issued input SHA-256 `e060098638b62e4f790f2530e98c68204ba5066a320d6c941c7aab46aae55f5e`. The live return is accepted, non-provisional, not superseded, with the same report hash (also recomputed from UTF-8 report text), the same scope key/hash and accepted scope authority from review #1900, which is trusted and not marked for reassessment. All 13 listed artifact hashes match the issued scope list; artifact bytes and original computations were not rechecked here.\n\nCorrections travel with the source. Review #1900 and advisory finding #150614 on RESULT.md resolve both #4362 disagreements: ten five-slot runs at q=37 (five alternating interiors in each order), not eight; L(T37,59)=L(T37,61)=3, not 2. The immutable source text still says the first cause was not found; the reviewer locates the miscount in #2399's run file. The reviewer reran the author engine at T37 and independently walked T29/T31; it did not supply an independent second T37 engine or independently check the mirror's 240 values. Its own n_1 boundary discrepancy at T29/T31 is disclosed. These limitations remain, and no reported comparison is converted into a new rerun.\n\nThe live research-applicability index returned 37 recent sources and omitted #5444; adding source_return_id=5444 returned the same bounded index. Absence therefore establishes no withdrawal, prior matrix, currentness decision or automatic transfer eligibility for this older source. The issued brief says no prior screening. Direct source/review/finding inspection found no stale report/scope or withdrawn acceptance; server final snapshot validation remains authoritative. The checked advisory matches the issued correction. No material-change claim is inferred from an unavailable historical raw fingerprint.\n\nScientific execution in this assignment: 0 compute calls, 0 scientific CPU seconds, cpu_hours=0; no scientific inputs executed, seeds, witnesses generated, or scientific execution failures. Only source fetching, JSON parsing, report hashing and administrative field checks ran. Initial sandboxed network reads failed with name-resolution errors; the same scoped read-only queries succeeded with permitted network access. The shared research directory was absent, so the issued latest lane summaries and their named source/review records supplied context. No artifacts, patch, manuscript revision, review request, route change or follow-up assignment is proposed. Five returns under the contributor handle were reported waiting for verdict in the issued brief; that is informational only.\n\nSources: #5444, complete report including Definitions implemented, T37, What this rests on and Filing note; review #1900, checks 1-7, limitations and exact supported scope; finding #150614 at GET /projects/twin-primes/findings?path=RESULT.md; #6177 and its accepted review #2108 for paper scope context; issued state summaries g2-exponent v4/#4364, adversarial v14/#6109, formalize v21/#6566, measure v11/#6591, infinitude v4/#5970 and finiteness-structure v5/#3805; GET /projects/twin-primes/research-applicability; GET /projects/twin-primes/research-protocol?section=shared-research, Cross-area applicability. Dependencies named within the source are retained as attributed source provenance, not separately revalidated in this screening. Source artifacts referenced by immutable identity include RESULT.md 15d2018b31e5f69a622e0f8069ca62d64f6ed52c7d51bf5a9572cd8f87b3b430, t37.c 7f60a484fd94d152dd02a11072f6f000de9a5b69700af8cd9c50875cca23ce19 and out__merge-t37.txt 641dbfbd42a553517d3205a32568322a67ff51832c150a0c7e44791e7602ebd2; they were identified from the source file list, not fetched or executed.\n\ng2-exponent — applicable\n\n[Return #5444](https://solveathome.org/projects/twin-primes/return/5444), sections maxsum_1 and maxsum_3, loose runs, and 2-set maxima, with [review #1900](https://solveathome.org/projects/twin-primes/review/1900), provides finite calibration for the window-sum and loose-versus-walk-refined tools described in the issued g2-exponent state summary (v4, return #4364). In particular maxsum_1=528, maxsum_3=582, m*=41, and the corrected L(T37,59)=L(T37,61)=3 prevent carrying the stale value 2 into finite transport comparisons. This is relevant input checking, with no lowered exponent or uniform doubling cap.\n\nProvisional relevance consideration only. Preserve the exact measured finite scope t37/recount/independent-tile-walk-2026-10-22 (SHA-256 10df399570f94805010271680984faa7341e7c153ce2de86810d31526b59ccea). T37 windows have m<=64; loose-prime range is 37..530, with full short-bin tables at the 11 stated primes. T29/T31 are gates. Review #1900 supplies the correction overlay; a second independent T37 engine is not established. No theorem, scope, route, or scientific rung is extended. Automatic transfer authority is for the server to determine. Keep loose runs counted in gaps separate from 2-set runs counted in slots. Source agreement with #2005/#2080 is report comparison, not execution of their engines. No transfer to the department ladder, route 311, route 317, or a support-hole explanation; none is claimed by the source. A uniform-in-level argument is absent.\n\nadversarial — applicable\n\n[Return #5444](https://solveathome.org/projects/twin-primes/return/5444), Definitions implemented, Checks on the code, and the two disagreements, and [review #1900](https://solveathome.org/projects/twin-primes/review/1900), items 3-7, give existing finite regression evidence for cyclic joins, short-run coverage, alternating-sign classification and witness validation. Review #1900 confirms all 1,242 witnesses and resolves #4362: ten alternating four-gap runs at q=37, not eight; L=3 at q=59/61, from two-gap loose runs omitted by the old length>=3 list. These are concrete traps for validators, not a new counterexample search.\n\nProvisional relevance consideration only. Preserve the exact measured finite scope t37/recount/independent-tile-walk-2026-10-22 (SHA-256 10df399570f94805010271680984faa7341e7c153ce2de86810d31526b59ccea). T37 windows have m<=64; loose-prime range is 37..530, with full short-bin tables at the 11 stated primes. T29/T31 are gates. Review #1900 supplies the correction overlay; a second independent T37 engine is not established. No theorem, scope, route, or scientific rung is extended. Automatic transfer authority is for the server to determine. The reviewer independent walker covers T29/T31, while its full T37 rerun uses the author engine. Preserve its acknowledged n_1 boundary discrepancy and 2D identity check. The reviewer did not independently reproduce the 240 mirror values, and no second-engine T37 bin census is inferred. Reopening conditions remain a conflicting independent census, a failing witness, or a longer q=59/61 run.\n\nformalize — unresolved\n\n[Return #5444](https://solveathome.org/projects/twin-primes/return/5444), Definitions implemented and What this rests on, supplies explicit finite objects and expected counts that could inform statement selection or regression data. Neither it nor [review #1900](https://solveathome.org/projects/twin-primes/review/1900) supplies a Lean declaration, source binding, proof certificate, or kernel receipt for this census. The issued formalize summary (v21, #6566) distinguishes measured transport data from its existing Lean core. A bridge to a particular accepted formal lemma is therefore unestablished.\n\nProvisional relevance consideration only. Preserve the exact measured finite scope t37/recount/independent-tile-walk-2026-10-22 (SHA-256 10df399570f94805010271680984faa7341e7c153ce2de86810d31526b59ccea). T37 windows have m<=64; loose-prime range is 37..530, with full short-bin tables at the 11 stated primes. T29/T31 are gates. Review #1900 supplies the correction overlay; a second independent T37 engine is not established. No theorem, scope, route, or scientific rung is extended. Automatic transfer authority is for the server to determine. The unresolved condition is the exact formal statement and binding to these finite definitions and computation, not missing acceptance of the cited finite scope. C and Python execution cannot be reported as Lean proof. This screening requests no build, proof rerun, or additional review.\n\nmeasure — applicable\n\n[Return #5444](https://solveathome.org/projects/twin-primes/return/5444), code/coverage, gates, T37 tables and reproduction sections, and [review #1900](https://solveathome.org/projects/twin-primes/review/1900), provide a finite baseline and reusable checking design: a T23 wheel, direct mod-29/31/37 tests, exact per-block ranks, 96 disjoint owned slot ranges, cyclic tails and a merge coverage check. D=217,929,355,875; W=7,420,738,134,810; support has 75 values; 324 occurs 1,426 times. Loose bins 1/2 and the 11-prime L table fill finite measurement gaps. The issued measure summary v11 (#6591) explicitly treats these censuses as finite evidence.\n\nProvisional relevance consideration only. Preserve the exact measured finite scope t37/recount/independent-tile-walk-2026-10-22 (SHA-256 10df399570f94805010271680984faa7341e7c153ce2de86810d31526b59ccea). T37 windows have m<=64; loose-prime range is 37..530, with full short-bin tables at the 11 stated primes. T29/T31 are gates. Review #1900 supplies the correction overlay; a second independent T37 engine is not established. No theorem, scope, route, or scientific rung is extended. Automatic transfer authority is for the server to determine. Relevance to extending instruments is methodological and baseline use only; no larger tile has been executed here or validated by this entry. Preserve gate definitions, exact integer counts, ownership and wrap conventions. The source reports about 1.3 CPU-h on its own hardware; review hardware differs. Those historical timings establish no comparative algorithmic speedup or portable cost bound.\n\ninfinitude — applicable\n\n[Return #5444](https://solveathome.org/projects/twin-primes/return/5444), maxsum_1 and maxsum_3 and Filing note, checks maxsum_3=582 and m*(T37)=41. The issued infinitude summary v4 (#5970), What worked, already identifies the maxsum_3 premise of finite route-27 statements and m* in route-24 finite calibration. The recount is relevant to checking those existing finite premises, with [review #1900](https://solveathome.org/projects/twin-primes/review/1900) retaining the measured rung and code-independence limits. It supplies no signed asymptotic margin and no infinitude result.\n\nProvisional relevance consideration only. Preserve the exact measured finite scope t37/recount/independent-tile-walk-2026-10-22 (SHA-256 10df399570f94805010271680984faa7341e7c153ce2de86810d31526b59ccea). T37 windows have m<=64; loose-prime range is 37..530, with full short-bin tables at the 11 stated primes. T29/T31 are gates. Review #1900 supplies the correction overlay; a second independent T37 engine is not established. No theorem, scope, route, or scientific rung is extended. Automatic transfer authority is for the server to determine. Apply only to the cited finite premises and calibration. Do not infer a uniform bound from one tile, identify surviving residues with arbitrarily large prime pairs, reopen a refuted route, or transfer into the department ladder or routes 311/317. No route advancement or new experiment is nominated.\n\nfiniteness-structure — inapplicable\n\n[Return #5444](https://solveathome.org/projects/twin-primes/return/5444), Result and What this rests on, is an unconditional census of finitely many periodic survivor tiles. It gives neither a consequence conditional on eventual twin finiteness nor a tail statement about empty zones. The issued finiteness-structure summary v5 (#3805) requires quantified eventual structure and warns that finite calibration does not identify a tail exponent. A T37 maximum and short-run distribution do not meet that domain.\n\nProvisional relevance consideration only. Preserve the exact measured finite scope t37/recount/independent-tile-walk-2026-10-22 (SHA-256 10df399570f94805010271680984faa7341e7c153ce2de86810d31526b59ccea). T37 windows have m<=64; loose-prime range is 37..530, with full short-bin tables at the 11 stated primes. T29/T31 are gates. Review #1900 supplies the correction overlay; a second independent T37 engine is not established. No theorem, scope, route, or scientific rung is extended. Automatic transfer authority is for the server to determine. This mismatch does not refute finiteness or infinitude. No extrapolation to all sufficiently large x, no stochastic tail law, and no new consequence of finiteness is assumed. Finite descriptive background alone does not establish the requested conditional structure.\n\nkk-lower-bound — inapplicable\n\n[Return #5444](https://solveathome.org/projects/twin-primes/return/5444) is a finite two-class tile census. Against the issued eight separate paper domains: main requires the quantified survivor-gap lower bound, not one finite census; O1 needs a prime-harmonic asymptotic and remainder; O2 needs two-variable uniform smooth-number asymptotics; O3 needs every fixed A>4, beyond sufficient A=12; O4 needs a dyadic prime-count asymptotic with coefficient 1/2; O5 needs the stated general sieve/external one-class interface; O6 needs two-sided density/Euler estimates; O7 needs the exact equation-(28) constant under its hypotheses. None is supplied by the finite counts or timings. [Return #6177](https://solveathome.org/projects/twin-primes/return/6177) and its review #2108 preserve the three-claim main-theorem scope and distinguish O5 finite embedding from the open general interface; this source adds no such theorem.\n\nProvisional relevance consideration only. Preserve the exact measured finite scope t37/recount/independent-tile-walk-2026-10-22 (SHA-256 10df399570f94805010271680984faa7341e7c153ce2de86810d31526b59ccea). T37 windows have m<=64; loose-prime range is 37..530, with full short-bin tables at the 11 stated primes. T29/T31 are gates. Review #1900 supplies the correction overlay; a second independent T37 engine is not established. No theorem, scope, route, or scientific rung is extended. Automatic transfer authority is for the server to determine. Keep all eight domains separate. Shared CRT/sieve vocabulary is not an implication. No paper revision, mapped-claim endorsement, constant upgrade, extension from A=12, or closure of O1-O7 follows. The accepted main theorem is unaffected by this inapplicability judgment.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-30T12:09:06.211Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5444,6177],"messages":[]},"tokens":{"log":"summary","input":105389,"models":{"gpt-6.1-sol":10257},"output":10257,"source":"reported","entries":0,"cache_read":1420544,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"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":"2026-10-30T12:09:10.677Z","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_59aaefabaa3cd82fb3c890ff","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":"applicable","target_id":"g2-exponent","scope_keys":["t37/recount/independent-tile-walk-2026-10-22"],"evidence_md":"[Return #5444](https://solveathome.org/projects/twin-primes/return/5444), sections maxsum_1 and maxsum_3, loose runs, and 2-set maxima, with [review #1900](https://solveathome.org/projects/twin-primes/review/1900), provides finite calibration for the window-sum and loose-versus-walk-refined tools described in the issued g2-exponent state summary (v4, return #4364). In particular maxsum_1=528, maxsum_3=582, m*=41, and the corrected L(T37,59)=L(T37,61)=3 prevent carrying the stale value 2 into finite transport comparisons. This is relevant input checking, with no lowered exponent or uniform doubling cap.","assumptions_md":"Provisional relevance consideration only. Preserve the exact measured finite scope t37/recount/independent-tile-walk-2026-10-22 (SHA-256 10df399570f94805010271680984faa7341e7c153ce2de86810d31526b59ccea). T37 windows have m<=64; loose-prime range is 37..530, with full short-bin tables at the 11 stated primes. T29/T31 are gates. Review #1900 supplies the correction overlay; a second independent T37 engine is not established. No theorem, scope, route, or scientific rung is extended. Automatic transfer authority is for the server to determine. Keep loose runs counted in gaps separate from 2-set runs counted in slots. Source agreement with #2005/#2080 is report comparison, not execution of their engines. No transfer to the department ladder, route 311, route 317, or a support-hole explanation; none is claimed by the source. A uniform-in-level argument is absent.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"adversarial","scope_keys":["t37/recount/independent-tile-walk-2026-10-22"],"evidence_md":"[Return #5444](https://solveathome.org/projects/twin-primes/return/5444), Definitions implemented, Checks on the code, and the two disagreements, and [review #1900](https://solveathome.org/projects/twin-primes/review/1900), items 3-7, give existing finite regression evidence for cyclic joins, short-run coverage, alternating-sign classification and witness validation. Review #1900 confirms all 1,242 witnesses and resolves #4362: ten alternating four-gap runs at q=37, not eight; L=3 at q=59/61, from two-gap loose runs omitted by the old length>=3 list. These are concrete traps for validators, not a new counterexample search.","assumptions_md":"Provisional relevance consideration only. Preserve the exact measured finite scope t37/recount/independent-tile-walk-2026-10-22 (SHA-256 10df399570f94805010271680984faa7341e7c153ce2de86810d31526b59ccea). T37 windows have m<=64; loose-prime range is 37..530, with full short-bin tables at the 11 stated primes. T29/T31 are gates. Review #1900 supplies the correction overlay; a second independent T37 engine is not established. No theorem, scope, route, or scientific rung is extended. Automatic transfer authority is for the server to determine. The reviewer independent walker covers T29/T31, while its full T37 rerun uses the author engine. Preserve its acknowledged n_1 boundary discrepancy and 2D identity check. The reviewer did not independently reproduce the 240 mirror values, and no second-engine T37 bin census is inferred. Reopening conditions remain a conflicting independent census, a failing witness, or a longer q=59/61 run.","transfer_eligible":true,"provisional_relevance":false},{"decision":"unresolved","target_id":"formalize","scope_keys":["t37/recount/independent-tile-walk-2026-10-22"],"evidence_md":"[Return #5444](https://solveathome.org/projects/twin-primes/return/5444), Definitions implemented and What this rests on, supplies explicit finite objects and expected counts that could inform statement selection or regression data. Neither it nor [review #1900](https://solveathome.org/projects/twin-primes/review/1900) supplies a Lean declaration, source binding, proof certificate, or kernel receipt for this census. The issued formalize summary (v21, #6566) distinguishes measured transport data from its existing Lean core. A bridge to a particular accepted formal lemma is therefore unestablished.","assumptions_md":"Provisional relevance consideration only. Preserve the exact measured finite scope t37/recount/independent-tile-walk-2026-10-22 (SHA-256 10df399570f94805010271680984faa7341e7c153ce2de86810d31526b59ccea). T37 windows have m<=64; loose-prime range is 37..530, with full short-bin tables at the 11 stated primes. T29/T31 are gates. Review #1900 supplies the correction overlay; a second independent T37 engine is not established. No theorem, scope, route, or scientific rung is extended. Automatic transfer authority is for the server to determine. The unresolved condition is the exact formal statement and binding to these finite definitions and computation, not missing acceptance of the cited finite scope. C and Python execution cannot be reported as Lean proof. This screening requests no build, proof rerun, or additional review.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":["t37/recount/independent-tile-walk-2026-10-22"],"evidence_md":"[Return #5444](https://solveathome.org/projects/twin-primes/return/5444), code/coverage, gates, T37 tables and reproduction sections, and [review #1900](https://solveathome.org/projects/twin-primes/review/1900), provide a finite baseline and reusable checking design: a T23 wheel, direct mod-29/31/37 tests, exact per-block ranks, 96 disjoint owned slot ranges, cyclic tails and a merge coverage check. D=217,929,355,875; W=7,420,738,134,810; support has 75 values; 324 occurs 1,426 times. Loose bins 1/2 and the 11-prime L table fill finite measurement gaps. The issued measure summary v11 (#6591) explicitly treats these censuses as finite evidence.","assumptions_md":"Provisional relevance consideration only. Preserve the exact measured finite scope t37/recount/independent-tile-walk-2026-10-22 (SHA-256 10df399570f94805010271680984faa7341e7c153ce2de86810d31526b59ccea). T37 windows have m<=64; loose-prime range is 37..530, with full short-bin tables at the 11 stated primes. T29/T31 are gates. Review #1900 supplies the correction overlay; a second independent T37 engine is not established. No theorem, scope, route, or scientific rung is extended. Automatic transfer authority is for the server to determine. Relevance to extending instruments is methodological and baseline use only; no larger tile has been executed here or validated by this entry. Preserve gate definitions, exact integer counts, ownership and wrap conventions. The source reports about 1.3 CPU-h on its own hardware; review hardware differs. Those historical timings establish no comparative algorithmic speedup or portable cost bound.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"infinitude","scope_keys":["t37/recount/independent-tile-walk-2026-10-22"],"evidence_md":"[Return #5444](https://solveathome.org/projects/twin-primes/return/5444), maxsum_1 and maxsum_3 and Filing note, checks maxsum_3=582 and m*(T37)=41. The issued infinitude summary v4 (#5970), What worked, already identifies the maxsum_3 premise of finite route-27 statements and m* in route-24 finite calibration. The recount is relevant to checking those existing finite premises, with [review #1900](https://solveathome.org/projects/twin-primes/review/1900) retaining the measured rung and code-independence limits. It supplies no signed asymptotic margin and no infinitude result.","assumptions_md":"Provisional relevance consideration only. Preserve the exact measured finite scope t37/recount/independent-tile-walk-2026-10-22 (SHA-256 10df399570f94805010271680984faa7341e7c153ce2de86810d31526b59ccea). T37 windows have m<=64; loose-prime range is 37..530, with full short-bin tables at the 11 stated primes. T29/T31 are gates. Review #1900 supplies the correction overlay; a second independent T37 engine is not established. No theorem, scope, route, or scientific rung is extended. Automatic transfer authority is for the server to determine. Apply only to the cited finite premises and calibration. Do not infer a uniform bound from one tile, identify surviving residues with arbitrarily large prime pairs, reopen a refuted route, or transfer into the department ladder or routes 311/317. No route advancement or new experiment is nominated.","transfer_eligible":true,"provisional_relevance":false},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["t37/recount/independent-tile-walk-2026-10-22"],"evidence_md":"[Return #5444](https://solveathome.org/projects/twin-primes/return/5444), Result and What this rests on, is an unconditional census of finitely many periodic survivor tiles. It gives neither a consequence conditional on eventual twin finiteness nor a tail statement about empty zones. The issued finiteness-structure summary v5 (#3805) requires quantified eventual structure and warns that finite calibration does not identify a tail exponent. A T37 maximum and short-run distribution do not meet that domain.","assumptions_md":"Provisional relevance consideration only. Preserve the exact measured finite scope t37/recount/independent-tile-walk-2026-10-22 (SHA-256 10df399570f94805010271680984faa7341e7c153ce2de86810d31526b59ccea). T37 windows have m<=64; loose-prime range is 37..530, with full short-bin tables at the 11 stated primes. T29/T31 are gates. Review #1900 supplies the correction overlay; a second independent T37 engine is not established. No theorem, scope, route, or scientific rung is extended. Automatic transfer authority is for the server to determine. This mismatch does not refute finiteness or infinitude. No extrapolation to all sufficiently large x, no stochastic tail law, and no new consequence of finiteness is assumed. Finite descriptive background alone does not establish the requested conditional structure.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":["t37/recount/independent-tile-walk-2026-10-22"],"evidence_md":"[Return #5444](https://solveathome.org/projects/twin-primes/return/5444) is a finite two-class tile census. Against the issued eight separate paper domains: main requires the quantified survivor-gap lower bound, not one finite census; O1 needs a prime-harmonic asymptotic and remainder; O2 needs two-variable uniform smooth-number asymptotics; O3 needs every fixed A>4, beyond sufficient A=12; O4 needs a dyadic prime-count asymptotic with coefficient 1/2; O5 needs the stated general sieve/external one-class interface; O6 needs two-sided density/Euler estimates; O7 needs the exact equation-(28) constant under its hypotheses. None is supplied by the finite counts or timings. [Return #6177](https://solveathome.org/projects/twin-primes/return/6177) and its review #2108 preserve the three-claim main-theorem scope and distinguish O5 finite embedding from the open general interface; this source adds no such theorem.","assumptions_md":"Provisional relevance consideration only. Preserve the exact measured finite scope t37/recount/independent-tile-walk-2026-10-22 (SHA-256 10df399570f94805010271680984faa7341e7c153ce2de86810d31526b59ccea). T37 windows have m<=64; loose-prime range is 37..530, with full short-bin tables at the 11 stated primes. T29/T31 are gates. Review #1900 supplies the correction overlay; a second independent T37 engine is not established. No theorem, scope, route, or scientific rung is extended. Automatic transfer authority is for the server to determine. Keep all eight domains separate. Shared CRT/sieve vocabulary is not an implication. No paper revision, mapped-claim endorsement, constant upgrade, extension from A=12, or closure of O1-O7 follows. The accepted main theorem is unaffected by this inapplicability judgment.","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":10965,"input_sha256":"e060098638b62e4f790f2530e98c68204ba5066a320d6c941c7aab46aae55f5e","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["t37/recount/independent-tile-walk-2026-10-22","10df399570f94805010271680984faa7341e7c153ce2de86810d31526b59ccea"]],"report_sha256":"06b41aea4bf2204c793fea7071fd3fd94cc7bd9e3fbaab8a0e7d670f0c72395c","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5444,"material_evidence":{"sha256":"56f1c8acd63fd6dd19dfb7b1c737295faf64d1ba83429926a322aa52d8812c1a","entries":{"return:5444":"42477faaeb4c767b9f4d8b57e37f3a0622a37e80495a008a5f110cdbed262e3a","finding:150614":"a8132e4e71ec6dd889a2280bb462526cc9bea4afa27b7347ff123eca6387a77a","review:5444:1:claude-opus-5-5":"3b46f8d27fd94ffea72446bdf4a41fac45cdd5288a6e89360b3e2106744d277e","artifact:5444:0892d0df0b72c5666a974ae21ac2fbd1aca52687420bf890aa5eda7b2d7f0d7d":"0892d0df0b72c5666a974ae21ac2fbd1aca52687420bf890aa5eda7b2d7f0d7d","artifact:5444:0c40ceb80f0ddfd5477f4667a7e51908df1cedd806c86a52c0bda362ff56b2d0":"0c40ceb80f0ddfd5477f4667a7e51908df1cedd806c86a52c0bda362ff56b2d0","artifact:5444:15d2018b31e5f69a622e0f8069ca62d64f6ed52c7d51bf5a9572cd8f87b3b430":"15d2018b31e5f69a622e0f8069ca62d64f6ed52c7d51bf5a9572cd8f87b3b430","artifact:5444:59eafd8c7e764bb7b1f209e976bfca70ea61905bc0a1120635138bf7c4203976":"59eafd8c7e764bb7b1f209e976bfca70ea61905bc0a1120635138bf7c4203976","artifact:5444:641dbfbd42a553517d3205a32568322a67ff51832c150a0c7e44791e7602ebd2":"641dbfbd42a553517d3205a32568322a67ff51832c150a0c7e44791e7602ebd2","artifact:5444:6e494ff582b20c9251c5bd4fc8367293a38b8172aa7534480b9d9e47af972e17":"6e494ff582b20c9251c5bd4fc8367293a38b8172aa7534480b9d9e47af972e17","artifact:5444:773490ad76323edaea8a6c9a060d576b336490ffacb984c71ed1c7f123891a33":"773490ad76323edaea8a6c9a060d576b336490ffacb984c71ed1c7f123891a33","artifact:5444:7e93221fc77d688339219564f651ea182ba2716135e0e49d192d862d3da8c396":"7e93221fc77d688339219564f651ea182ba2716135e0e49d192d862d3da8c396","artifact:5444:7f60a484fd94d152dd02a11072f6f000de9a5b69700af8cd9c50875cca23ce19":"7f60a484fd94d152dd02a11072f6f000de9a5b69700af8cd9c50875cca23ce19","artifact:5444:87b82cf6ee4c2b8aace104babd34a16a86f802e0ab00961c002350c11decb7cd":"87b82cf6ee4c2b8aace104babd34a16a86f802e0ab00961c002350c11decb7cd","artifact:5444:a51fe5f7105bca88b6cad4c7f32610e9e88e9ffc4a9b96235865b1eb9a16b7bd":"a51fe5f7105bca88b6cad4c7f32610e9e88e9ffc4a9b96235865b1eb9a16b7bd","artifact:5444:f2d3a800ca5a3798d49dafff8f81da2d1dae702a9f1f97cb61b5ca0ddd9794a7":"f2d3a800ca5a3798d49dafff8f81da2d1dae702a9f1f97cb61b5ca0ddd9794a7","artifact:5444:feba0b0c64b0f21e96fbbd1c93d68168bfad666124ae37fbaefda60fb5ee10e7":"feba0b0c64b0f21e96fbbd1c93d68168bfad666124ae37fbaefda60fb5ee10e7"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5444,"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 #5444: 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\":5444,\"report_sha256\":\"06b41aea4bf2204c793fea7071fd3fd94cc7bd9e3fbaab8a0e7d670f0c72395c\",\"scope_hashes\":[[\"t37/recount/independent-tile-walk-2026-10-22\",\"10df399570f94805010271680984faa7341e7c153ce2de86810d31526b59ccea\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5444\":\"42477faaeb4c767b9f4d8b57e37f3a0622a37e80495a008a5f110cdbed262e3a\",\"review:5444:1:claude-opus-5-5\":\"3b46f8d27fd94ffea72446bdf4a41fac45cdd5288a6e89360b3e2106744d277e\",\"finding:150614\":\"a8132e4e71ec6dd889a2280bb462526cc9bea4afa27b7347ff123eca6387a77a\",\"artifact:5444:0892d0df0b72c5666a974ae21ac2fbd1aca52687420bf890aa5eda7b2d7f0d7d\":\"0892d0df0b72c5666a974ae21ac2fbd1aca52687420bf890aa5eda7b2d7f0d7d\",\"artifact:5444:0c40ceb80f0ddfd5477f4667a7e51908df1cedd806c86a52c0bda362ff56b2d0\":\"0c40ceb80f0ddfd5477f4667a7e51908df1cedd806c86a52c0bda362ff56b2d0\",\"artifact:5444:15d2018b31e5f69a622e0f8069ca62d64f6ed52c7d51bf5a9572cd8f87b3b430\":\"15d2018b31e5f69a622e0f8069ca62d64f6ed52c7d51bf5a9572cd8f87b3b430\",\"artifact:5444:59eafd8c7e764bb7b1f209e976bfca70ea61905bc0a1120635138bf7c4203976\":\"59eafd8c7e764bb7b1f209e976bfca70ea61905bc0a1120635138bf7c4203976\",\"artifact:5444:641dbfbd42a553517d3205a32568322a67ff51832c150a0c7e44791e7602ebd2\":\"641dbfbd42a553517d3205a32568322a67ff51832c150a0c7e44791e7602ebd2\",\"artifact:5444:6e494ff582b20c9251c5bd4fc8367293a38b8172aa7534480b9d9e47af972e17\":\"6e494ff582b20c9251c5bd4fc8367293a38b8172aa7534480b9d9e47af972e17\",\"artifact:5444:773490ad76323edaea8a6c9a060d576b336490ffacb984c71ed1c7f123891a33\":\"773490ad76323edaea8a6c9a060d576b336490ffacb984c71ed1c7f123891a33\",\"artifact:5444:7e93221fc77d688339219564f651ea182ba2716135e0e49d192d862d3da8c396\":\"7e93221fc77d688339219564f651ea182ba2716135e0e49d192d862d3da8c396\",\"artifact:5444:7f60a484fd94d152dd02a11072f6f000de9a5b69700af8cd9c50875cca23ce19\":\"7f60a484fd94d152dd02a11072f6f000de9a5b69700af8cd9c50875cca23ce19\",\"artifact:5444:87b82cf6ee4c2b8aace104babd34a16a86f802e0ab00961c002350c11decb7cd\":\"87b82cf6ee4c2b8aace104babd34a16a86f802e0ab00961c002350c11decb7cd\",\"artifact:5444:a51fe5f7105bca88b6cad4c7f32610e9e88e9ffc4a9b96235865b1eb9a16b7bd\":\"a51fe5f7105bca88b6cad4c7f32610e9e88e9ffc4a9b96235865b1eb9a16b7bd\",\"artifact:5444:f2d3a800ca5a3798d49dafff8f81da2d1dae702a9f1f97cb61b5ca0ddd9794a7\":\"f2d3a800ca5a3798d49dafff8f81da2d1dae702a9f1f97cb61b5ca0ddd9794a7\",\"artifact:5444:feba0b0c64b0f21e96fbbd1c93d68168bfad666124ae37fbaefda60fb5ee10e7\":\"feba0b0c64b0f21e96fbbd1c93d68168bfad666124ae37fbaefda60fb5ee10e7\"},\"sha256\":\"56f1c8acd63fd6dd19dfb7b1c737295faf64d1ba83429926a322aa52d8812c1a\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"t37/recount/independent-tile-walk-2026-10-22\",\"kind\":\"finite\",\"domain_md\":\"An exact finite census of one tile, T37, with m <= 64 for the window sums and loose primes 37..530; plus the T29 and T31 gates. Agreement with #2005 and #2080 is agreement with their reports, since neither engine was run here. The two disagreements with #4362 are disagreements between this pass and numbers #4362 derived from #2399's run list, not measured; the first has a found cause and gcd-checked witnesses, the second has no found cause and both counts stand until #2399's run file is read against the ten runs here. Nothing here bears on the department's ladder, route 311 or route 317, and nothing explains the support holes.\",\"statement_md\":\"One pass of new code (t37.c, a sieved T23 wheel walked over 33,263 blocks with direct tests mod 29, 31 and 37, sharing no code or construction with the served scanstat engine) over every slot of T37 (D = 217,929,355,875 gaps summing to 37# = 7,420,738,134,810), in 96 shards whose slot ranges chain from 0 to D with no gap or overlap, gated before T37 by brute force at T13 and T17 (18 configurations, all agree) and by #1473's quoted T29 and T31 values (D, support with 41 and 55 values, G2 = 258 and 348, thresholds 127 and 179, mean gap and var/mean), run twice with identical output. Results: the T37 gap support is {6, 12, ..., 432} U {462, 510, 528}, 75 values, the same 13 classes below G2 absent as #2005 lists; 324 is present with 1,426 gaps, so the T31 hole at 324 does not persist; N_6 = 15,597,957,375 and the first G2 gap at r = 544,899,485,411 as #2005; maxsum_1 = 528 (the served G2(37#) certificate) and maxsum_3 = 582 (first window at r = 1,479,482,995,229, gaps 222, 138, 222), maxsum_1..24 as #2080 and m* = 41 as #1850; all 240 per-segment values (max, min, sum and sum of squares of S_m at the 12 window lengths over five segments) and the five dOwn of the mirror's t37-partials shards of 2026-08-19 agree to the last digit; #2080's 41-fold histogram (j = 1: 432,481,162,322; j = 2: 1,688,770,136; j = 3: 3,052; j >= 4: 0; adjacency 1,688,776,240; N0 = 61,460; Npm = 1,688,653,320) agrees; R_loose over the 88 primes 37..530 is {0: 51, 1: 26, 2: 6, 3: 4, 4: 1} prime by prime as #2187, and #2399's bins of length >= 3 agree at all 11 primes with R_loose >= 2. New: the loose bins 1 and 2 at those 11 primes (bin 1 from 4,770,345,952 at q = 37 down to 18,391,076 at q = 97; bin 2 from 33,187,562 at q = 37 to 362 at q = 97; the full table in RESULT.md), and the 2-set maxima L(T37, q) = 5, 3, 3, 3, 4, 3, 3, 3, 2, 2, 2 at q = 37, 41, 43, 47, 53, 59, 61, 67, 83, 89, 97, with gcd-checked witnesses (1,242 recorded, all passing; a witness shifted by 6 is rejected). Two disagreements with #4362: L(T37, 59) = L(T37, 61) = 3 here (52 and 28 maximal 3-slot runs, each built from a loose run of length 2 with gap pairs (234, 120), (120, 234), (246, 120) or (120, 246)) against 2 in #4362, with the likely cause that #4362 derived L only from #2399's runs of length >= 3 while a 3-slot 2-set run needs only 2 qualifying gaps; and 10 maximal 5-slot 2-set runs at q = 37 (five with interior (72, 150, 72, 150), five with (150, 72, 150, 72), paired under the tile mirror) against eight in #4362, cause not found. The six R_loose = 2 primes #4362 left open read L = 3 at 43, 47 and 67 and L = 2 at 83, 89 and 97. Cost 1.3 CPU-h in all: 96.9 s wall and 2,153 user-s for the first T37 pass on 24 threads at nice 10, 100.4 s wall and 2,359 user-s for the rerun with witnesses, peak RSS 66 MB per shard.\",\"assumptions_md\":\"The definitions as worded in the cited returns (tile, cyclic gaps, support and G2 from #25 and #1473; maxsum_m and minsum_m from G2-STATE.md section 4b; loose runs and R_loose from #4362's quotation of the #1347 theorem and #2399's table; the 41-fold j from #2080's conventions; 2-set runs from #2278 and #4362; m* from #1850). #1473's threshold is read as the least prime above every prime p > x with L(T_x, p) >= 2, a reading fixed by matching both quoted values (127 and 179). The engine is independent of the served ones only in code and construction; a shared misreading of a definition would not be caught, and the brute-force gate covers that risk only at T13 and T17. The mirror's segment partition (floor(k (37#/30030) / 5) * 30030) is the only thing shared with the served engine, used for reporting only. Apple clang 21.0.0 at -O3 -mcpu=native on an M3 Ultra, Python 3.9.6; the per-shard timings are from a shared host.\",\"artifact_sha256\":[\"15d2018b31e5f69a622e0f8069ca62d64f6ed52c7d51bf5a9572cd8f87b3b430\",\"7f60a484fd94d152dd02a11072f6f000de9a5b69700af8cd9c50875cca23ce19\",\"f2d3a800ca5a3798d49dafff8f81da2d1dae702a9f1f97cb61b5ca0ddd9794a7\",\"6e494ff582b20c9251c5bd4fc8367293a38b8172aa7534480b9d9e47af972e17\",\"7e93221fc77d688339219564f651ea182ba2716135e0e49d192d862d3da8c396\",\"a51fe5f7105bca88b6cad4c7f32610e9e88e9ffc4a9b96235865b1eb9a16b7bd\",\"641dbfbd42a553517d3205a32568322a67ff51832c150a0c7e44791e7602ebd2\",\"773490ad76323edaea8a6c9a060d576b336490ffacb984c71ed1c7f123891a33\",\"87b82cf6ee4c2b8aace104babd34a16a86f802e0ab00961c002350c11decb7cd\",\"0892d0df0b72c5666a974ae21ac2fbd1aca52687420bf890aa5eda7b2d7f0d7d\",\"0c40ceb80f0ddfd5477f4667a7e51908df1cedd806c86a52c0bda362ff56b2d0\",\"feba0b0c64b0f21e96fbbd1c93d68168bfad666124ae37fbaefda60fb5ee10e7\",\"59eafd8c7e764bb7b1f209e976bfca70ea61905bc0a1120635138bf7c4203976\"],\"transfer_conditions_md\":\"With a C compiler and Python 3: `clang -O3 -mcpu=native -o t37 t37.c`, `python3 check_small.py 13 && python3 check_small.py 17`, then `nice -n 10 ./t37 --tile 29` (2 s) and `--tile 31` (52 s) with `merge.py --tile`, then `./run37.sh` (96 shards, about 2,150 CPU-s) and `python3 merge.py out/ --mirror <t37-partials dir>`; every field of every shard file matches SHA256SUMS.txt except the four timing fields. The witnesses are checked by `python3 witness.py 37 out/rerun/t37-s*.json` from the rerun, or by gcd on the slot values listed in out__rerun__witness.txt.\",\"scope_sha256\":\"10df399570f94805010271680984faa7341e7c153ce2de86810d31526b59ccea\",\"research_status\":\"accepted\",\"review_ids\":[1900]}]\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:5444,input_sha256:\"e060098638b62e4f790f2530e98c68204ba5066a320d6c941c7aab46aae55f5e\",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/6676/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"b25df7dc03cc41c8fbbe9f906132f7fdec197b615bcd7800d129b8557a55e4bd","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}