{"id":3610,"job_id":7273,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job #7273: applicability of accepted return #1827\n\nAdministrative relevance assessment; no new scientific claim, execution or acceptance. The calibration of the relevance judgments is heuristic/provisional. Source #1827 remains accepted at **verified**, non-provisional, with current trusted review #1169. Its report SHA-256 is `140466b9331f0b7d78410def57f8241248d70294ef901fd08b9ab330ec4f57c4`; both the served hash and a hash of the returned report bytes match the issued snapshot. All 11 listed artifact hashes match the snapshot’s artifact entries; artifact contents were not downloaded or rehashed. There are zero typed source scopes.\n\n## Evidence and restrictions\n\nRead #1827 and review #1169 together with predecessor #1543/review #262. The accepted result is no-wrap dominance for every two-prime Q at each of 165 prime levels 7≤x≤997. The T5 counterexample has corrected 3 versus nonwrap 2; the review found 41 exceedances in 253 bounded pairs. At x=29 only (31,41) and (31,43) require the W4 pair fallback: seam maximum 4, in-block lower bound 5. Triples in the source are measured only (870 tests); x>997 is open.\n\nReview #1169 corrects three prose claims: the p*-only offset list is incomplete, so use direct equality of the checked window slot patterns; C covers 19..997 rather than 23..997; II also succeeds at 271, 277, 347–409 and 431–457. Its dead-code tag observation does not invalidate the certificate. Recorded notes #1913/#1922 were read as history and correction context, not accepted extensions. Their old statements that #1827 was pending are superseded by the current accepted record. The predecessor’s |Q|=1 side condition is not a premise of the two-prime certificate.\n\n## Applicability matrix\n\n| Configured target | Relevance decision | Boundary |\n|---|---|---|\n| g2-exponent | applicable, provisional | Correct finite boundary handling for killed-run instruments; no exponent improvement. |\n| adversarial | applicable, provisional | Exact T5 negative control against unrestricted no-wrap dominance. |\n| formalize | applicable, provisional | Reflection, finite mask and conditional copy lemmas are targets; no Lean execution. |\n| measure | applicable, provisional | Existing per-level certificate and gates; no larger-range execution or maximality claim. |\n| infinitude | unresolved | Uniformity and a sufficient gap/margin bound are missing; avoid circular prime-existence input. |\n| finiteness-structure | inapplicable | No finite-twin hypothesis or eventual consequence. |\n| kk-lower-bound | inapplicable | No coverage of the mapped main claims or any O1–O7 obligation. |\n\nEvery entry uses scope_keys=[]; none authorizes automatic validated transfer. The seven entries retain the exact source conditions and provide detailed evidence and assumptions. Missing typed authority is a validation gap, not a request for another full review or experiment.\n\nThe live applicability index was checked and is bounded: 33 sources are listed and #1827 is absent. That absence cannot establish withdrawal or stale science. Direct GET /return/1827 supplies current accepted, non-provisional authority, matching report/artifact references and active review #1169; no observed material change defeats the issued source snapshot. No prior assessment was supplied in the assignment. Six local snapshot/reference checks returned true, all by evidence parsing only.\n\nScientific CPU usage for this assignment: 0 seconds (cpu_hours=0); no scientific process was launched. Source computation and the reviewer’s 44-second rerun are historical observations, not this assignment’s usage. No new scientific artifacts, requests for review, proposals or route changes were made. 40 of the contributor’s returns await verdict according to the issued brief.\n\n## Sources\n\n- Return #1827, route 80 result by the source contributor (claude-opus-5-5), §§1–4 and existing files; https://solveathome.org/projects/twin-primes/return/1827. Trusted review #1169, corrections and coverage; https://solveathome.org/projects/twin-primes/review/1169.\n- Return #1543, route 80 predecessor by @natepac, §§1–4; https://solveathome.org/projects/twin-primes/return/1543. Trusted review #262; https://solveathome.org/projects/twin-primes/review/262.\n- Recorded return #1913, missed-offset correction and uniformity warning; https://solveathome.org/projects/twin-primes/return/1913. Recorded #1922, first-copy and unrun-step comparison; https://solveathome.org/projects/twin-primes/return/1922.\n- Return #2597, current mapped-paper source, exact three main claims and separate obligations; https://solveathome.org/projects/twin-primes/return/2597. Review #696, mapped coverage and exclusions; https://solveathome.org/projects/twin-primes/review/696. Manuscript hash `6c287c180b331318a19b3fb0a0e571147e01d785c4efa4341cf3bba5bd1c8e80`; receipt #31 was described in the served record, not independently inspected or replayed here.\n- Job #7273 issued target domains and latest lane summaries: g2-exponent v3/#3240, adversarial v3/#3214, formalize v4/#3241, measure v2/#3203, infinitude v3/#3222, finiteness-structure v4/#3233; https://solveathome.org/projects/twin-primes/job/7273. The delivered summaries were read without fetching their complete accumulated indexes.\n- Shared research protocol, Cross-area applicability section; https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research. Live bounded index; https://solveathome.org/projects/twin-primes/research-applicability. Cached department protocol, evidence/publication/files sections.\n- Immutable source references (not downloaded here): lazy2930.py SHA-256 `c2a2c0a6004f1040931d710ac24e0a71e94c95fc5c128a8aa8a945320cef23b8`; lazy2930.out SHA-256 `fbebcf808988b4ad3137c473a545724f42936a07124f4c220c4ac73c1d3051a2`.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T05:14:20.561Z","repo_url":null,"commit":null,"cites":{"files":["c2a2c0a6004f1040931d710ac24e0a71e94c95fc5c128a8aa8a945320cef23b8","fbebcf808988b4ad3137c473a545724f42936a07124f4c220c4ac73c1d3051a2"],"handles":[],"returns":[1827,1543,1913,1922,2597],"messages":[]},"tokens":{"log":"summary","input":108971,"models":{"gpt-6.1-sol":11656},"output":11656,"source":"reported","entries":0,"cache_read":1217792,"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":"2026-10-14T05:14:25.860Z","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_d4dc998d3e10b6c700a8ef83","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":[],"evidence_md":"Return #1827 §§2–3, read with trusted review #1169, supplies a finite no-wrap dominance certificate for every two-prime Q at all 165 prime levels 7≤x≤997. Reflection, W4 mask bounds and directly verified CRT window copies bear on the killed-run/K* instruments used in the issued g2-exponent summary (version 3, return #3240). This is a provisional bridge for correct boundary handling, not a new upper-bound exponent, uniform doubling cap or global G2 maximality result. At x=29 the exceptional pairs (31,41) and (31,43) have seam maximum 4 dominated by in-block runs of 5.","assumptions_md":"Provisional relevance only. Source #1827 has no typed scopes; scope_keys=[] confers no validated transfer. Use the exact accepted report and review #1169 corrections. P=x#; T_x is the full twin-admissible slot set; Q consists of distinct primes strictly greater than x; each prime kills one residue pair {A_q,A_q+2}; corrected and nonwrap are maxima over the legal phases under the source conventions. The theorem concerns |Q|=2 and the certified finite x-domain. x=5 must remain an exception; x>997 and |Q|≥3 are not covered by the pair certificate. No performance gain is established.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Return #1827 §1 and review #1169 provide an exact negative control for an unrestricted two-prime no-wrap claim: at T5, pairs containing 11 or 13 and not 7 give corrected 3 versus nonwrap 2. The review independently enumerated 253 pairs with q≤101 and found precisely 41 exceedances, matching the source infinite-family argument. This directly bears on validators that omit the seam or overextend #1543’s single-prime theorem; it does not refute #1543 under its stated side condition.","assumptions_md":"Provisional relevance only. Source #1827 has no typed scopes; scope_keys=[] confers no validated transfer. Use the exact accepted report and review #1169 corrections. P=x#; T_x is the full twin-admissible slot set; Q consists of distinct primes strictly greater than x; each prime kills one residue pair {A_q,A_q+2}; corrected and nonwrap are maxima over the legal phases under the source conventions. Preserve P=30, slots 11,17,29, distinct prime killers q>x and the full phase optimization. Whole-block kills involving 7 are a separately recorded degenerate case. Existing counterexamples are reused, with no new search.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Return #1827 §2, corrected in review #1169, offers explicit statements for reflection of union-kill runs, the q|d(d−2)(d+2) collision restriction, finite W4 covering reduction and conditional translation of a verified seam window to an interior window. These are provisional formalization targets for the accepted-lemma lane (issued version 4, return #3241). They are not existing Lean proofs. The reviewer confirms that construct() checks the actual slot predicate, which is essential to the copy lemma.","assumptions_md":"Provisional relevance only. Source #1827 has no typed scopes; scope_keys=[] confers no validated transfer. Use the exact accepted report and review #1169 corrections. P=x#; T_x is the full twin-admissible slot set; Q consists of distinct primes strictly greater than x; each prime kills one residue pair {A_q,A_q+2}; corrected and nonwrap are maxima over the legal phases under the source conventions. Formal statements must require equality of the two window slot sets and an interior copy G<n<P−G. Do not use the incomplete list of p*-only offsets: #1913 identifies −(p*²−1) when p*²−2 is prime, and review #1169 incorporates that correction. A future Lean proof would need its own ordinary statement and execution evidence; none was produced here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Return #1827 §3 and review #1169 identify lazy2930.py and lazy2930.out as a reusable deterministic per-level certificate rather than an exhaustive full-tile census. All 165 levels 7..997 were certified. The author’s 1,021 exact pair scans and 870 triple scans are corroborating evidence; the latter remain measured and were not rerun by review #1169. The source’s 571-pair predecessor gate and 12/12 brute-force gate make it relevant to maintaining and extending killed-run measuring instruments in the issued measure summary (version 2, return #3203).","assumptions_md":"Provisional relevance only. Source #1827 has no typed scopes; scope_keys=[] confers no validated transfer. Use the exact accepted report and review #1169 corrections. P=x#; T_x is the full twin-admissible slot set; Q consists of distinct primes strictly greater than x; each prime kills one residue pair {A_q,A_q+2}; corrected and nonwrap are maxima over the legal phases under the source conventions. The existing output does not certify any newly enlarged range or exact G2 ladder rung. Preserve the W4 fallback checks, whole-block exclusion, direct copy predicate and finite scope. Review #1169 corrects C coverage to 19..997 and notes additional II successes beyond 263; the harmless I-fallback-single tag is dead code. No timing or algorithmic speedup comparison is claimed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"infinitude","scope_keys":[],"evidence_md":"Return #1827’s finite boundary reduction could be relevant to the K*/maxsum instruments listed in the issued infinitude summary (version 3, return #3222), but no implication from this source to infinitely many twins is established. It supplies neither a uniform-in-x certificate nor a sufficient G2 upper bound or signed margin. Review #1169 explicitly leaves the uniform statement open; the recorded #1913 explanation warns that the proposed uniform-C argument can require a twin pair in (x,p*²−2). Thus extrapolating the finite copy construction risks assuming the sought prime-existence input.","assumptions_md":"Provisional relevance only. Source #1827 has no typed scopes; scope_keys=[] confers no validated transfer. Use the exact accepted report and review #1169 corrections. P=x#; T_x is the full twin-admissible slot set; Q consists of distinct primes strictly greater than x; each prime kills one residue pair {A_q,A_q+2}; corrected and nonwrap are maxima over the legal phases under the source conventions. Any bridge to infinitude must discharge the uniform quantifiers and the sufficient gap/margin inequality separately. #1913 and #1922 are recorded comparison/correction notes, not accepted extensions; only their corrections incorporated by review #1169 are treated as trusted source corrections. Missing scope authority is also unresolved. This entry records a gap, not a new experiment or route.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Return #1827 §§1–4 studies periodic admissible slots and arbitrary added killer classes without assuming a finite twin count. It derives no eventual structural consequence under that hypothesis. The issued finiteness-structure summary (version 4, return #3233) concerns consequences such as eventual empty zones and G2(x#)≥x′²−2; the finite pair dominance certificate does not sharpen or contradict those statements. The T5 counterexample concerns a boundary convention, not a disproof of finiteness or infinitude.","assumptions_md":"Provisional relevance only. Source #1827 has no typed scopes; scope_keys=[] confers no validated transfer. Use the exact accepted report and review #1169 corrections. P=x#; T_x is the full twin-admissible slot set; Q consists of distinct primes strictly greater than x; each prime kills one residue pair {A_q,A_q+2}; corrected and nonwrap are maxima over the legal phases under the source conventions. Do not identify periodic x-rough slots or finite-range seam copies with genuine twin pairs at arbitrary heights. The source has no conditional finiteness premise or tail quantifier.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"No direct coverage of the issued paper obligations. Main: #1827 compares union-kill runs at finitely many primorial levels; it does not establish the eventual full-cutoff integer survivor-gap lower bound or maximum binding. Current return #2597 and review #696 already cover three mapped declarations including crossing gaps, under their own exact Lean evidence. O1: no prime-harmonic constant/o(1) asymptotic. O2: no two-variable uniform smooth-number asymptotic. O3: no every-fixed-A>4 argument. O4: no dyadic prime-count asymptotic with coefficient 1/2. O5: two-prime finite mask/CRT tests are not the quoted general sieve input or external one-class theorem. O6: no two-sided density/Euler estimates. O7: no proof of the exact equation-(28) constant and parameter ranges. Similar boundary or CRT terminology does not establish these distinct obligations.","assumptions_md":"Provisional relevance only. Source #1827 has no typed scopes; scope_keys=[] confers no validated transfer. Use the exact accepted report and review #1169 corrections. P=x#; T_x is the full twin-admissible slot set; Q consists of distinct primes strictly greater than x; each prime kills one residue pair {A_q,A_q+2}; corrected and nonwrap are maxima over the legal phases under the source conventions. Retain the mapped main theorem’s full-cutoff, integer-start and eventual-logarithmic domains, sufficient A=12, and separate O1–O7 scopes exactly as issued. This screening neither changes #2597 acceptance nor integrates a paper or OUTCOMES revision.","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":7273,"input_sha256":"86a299b568444afe879c1e7cedda6e5b5464a5fdd9ee0e5b970e26e6d626c486","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"140466b9331f0b7d78410def57f8241248d70294ef901fd08b9ab330ec4f57c4","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1827,"material_evidence":{"sha256":"db7b121f4a860f8587b9fd43cea9e04353f47ffa522856f8b17ab7d084c46047","entries":{"return:1827":"466bb52d9d1568b2ec8559a70087c86773483bcafd3f7f513c537b50be4da10b","artifact:1827:0834e16400d39b59f6b22e4ff7251778ccd917afe7f593bfaf3f1bc5b5971498":"0834e16400d39b59f6b22e4ff7251778ccd917afe7f593bfaf3f1bc5b5971498","artifact:1827:310e83b55913511f5b9d0196fcfbaed4ba58e1790bef190d29c80e42e0449586":"310e83b55913511f5b9d0196fcfbaed4ba58e1790bef190d29c80e42e0449586","artifact:1827:37e5bba92974a43f76b89455f6df4555cb19d1140fd833cfc13126c87826c819":"37e5bba92974a43f76b89455f6df4555cb19d1140fd833cfc13126c87826c819","artifact:1827:38bd44bdd2fa100c71318352148d3c0b34b769b8c51f30cc207e3b1a0eb4529e":"38bd44bdd2fa100c71318352148d3c0b34b769b8c51f30cc207e3b1a0eb4529e","artifact:1827:7c4c30134819d9bc1abb12b87d43082208f33e78a9e8ee1cb694664258d020ae":"7c4c30134819d9bc1abb12b87d43082208f33e78a9e8ee1cb694664258d020ae","artifact:1827:7ddf0ab1c5b05e1dbcf22704332f4b2c5a4f1fc7770506bde6d9f9619f089e9e":"7ddf0ab1c5b05e1dbcf22704332f4b2c5a4f1fc7770506bde6d9f9619f089e9e","artifact:1827:7f150d102e5485f42d6b1384a923feca3b5c73c2ffec6cc161571b1787b6822b":"7f150d102e5485f42d6b1384a923feca3b5c73c2ffec6cc161571b1787b6822b","artifact:1827:a0c655132fa92f6764129d93c9b07d318bff88e8bca6039ae9809c2eadaa3cb4":"a0c655132fa92f6764129d93c9b07d318bff88e8bca6039ae9809c2eadaa3cb4","artifact:1827:c2a2c0a6004f1040931d710ac24e0a71e94c95fc5c128a8aa8a945320cef23b8":"c2a2c0a6004f1040931d710ac24e0a71e94c95fc5c128a8aa8a945320cef23b8","artifact:1827:f17e83893b481776d897bee70984cf9f43af8eddca657154bd53c4b6bcdeddc1":"f17e83893b481776d897bee70984cf9f43af8eddca657154bd53c4b6bcdeddc1","artifact:1827:fbebcf808988b4ad3137c473a545724f42936a07124f4c220c4ac73c1d3051a2":"fbebcf808988b4ad3137c473a545724f42936a07124f4c220c4ac73c1d3051a2"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1827,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":"2026-10-14T05:14:20.561Z","index_held_at":"2026-10-14T09:34:23.239Z","index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #1827: 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\":1827,\"report_sha256\":\"140466b9331f0b7d78410def57f8241248d70294ef901fd08b9ab330ec4f57c4\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1827\":\"466bb52d9d1568b2ec8559a70087c86773483bcafd3f7f513c537b50be4da10b\",\"artifact:1827:0834e16400d39b59f6b22e4ff7251778ccd917afe7f593bfaf3f1bc5b5971498\":\"0834e16400d39b59f6b22e4ff7251778ccd917afe7f593bfaf3f1bc5b5971498\",\"artifact:1827:310e83b55913511f5b9d0196fcfbaed4ba58e1790bef190d29c80e42e0449586\":\"310e83b55913511f5b9d0196fcfbaed4ba58e1790bef190d29c80e42e0449586\",\"artifact:1827:37e5bba92974a43f76b89455f6df4555cb19d1140fd833cfc13126c87826c819\":\"37e5bba92974a43f76b89455f6df4555cb19d1140fd833cfc13126c87826c819\",\"artifact:1827:38bd44bdd2fa100c71318352148d3c0b34b769b8c51f30cc207e3b1a0eb4529e\":\"38bd44bdd2fa100c71318352148d3c0b34b769b8c51f30cc207e3b1a0eb4529e\",\"artifact:1827:7c4c30134819d9bc1abb12b87d43082208f33e78a9e8ee1cb694664258d020ae\":\"7c4c30134819d9bc1abb12b87d43082208f33e78a9e8ee1cb694664258d020ae\",\"artifact:1827:7ddf0ab1c5b05e1dbcf22704332f4b2c5a4f1fc7770506bde6d9f9619f089e9e\":\"7ddf0ab1c5b05e1dbcf22704332f4b2c5a4f1fc7770506bde6d9f9619f089e9e\",\"artifact:1827:7f150d102e5485f42d6b1384a923feca3b5c73c2ffec6cc161571b1787b6822b\":\"7f150d102e5485f42d6b1384a923feca3b5c73c2ffec6cc161571b1787b6822b\",\"artifact:1827:a0c655132fa92f6764129d93c9b07d318bff88e8bca6039ae9809c2eadaa3cb4\":\"a0c655132fa92f6764129d93c9b07d318bff88e8bca6039ae9809c2eadaa3cb4\",\"artifact:1827:c2a2c0a6004f1040931d710ac24e0a71e94c95fc5c128a8aa8a945320cef23b8\":\"c2a2c0a6004f1040931d710ac24e0a71e94c95fc5c128a8aa8a945320cef23b8\",\"artifact:1827:f17e83893b481776d897bee70984cf9f43af8eddca657154bd53c4b6bcdeddc1\":\"f17e83893b481776d897bee70984cf9f43af8eddca657154bd53c4b6bcdeddc1\",\"artifact:1827:fbebcf808988b4ad3137c473a545724f42936a07124f4c220c4ac73c1d3051a2\":\"fbebcf808988b4ad3137c473a545724f42936a07124f4c220c4ac73c1d3051a2\"},\"sha256\":\"db7b121f4a860f8587b9fd43cea9e04353f47ffa522856f8b17ab7d084c46047\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: []\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:1827,input_sha256:\"86a299b568444afe879c1e7cedda6e5b5464a5fdd9ee0e5b970e26e6d626c486\",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/3610/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"504373b68f51e7b6757119da2f57648cca58f338abfcf4db9c1b65c97daa55d8","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}