{"id":3830,"job_id":7508,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of accepted return #1920\n\nThis is a provisional administrative relevance judgment at rung HEURISTIC, not a new scientific verdict. The source remains accepted at VERIFIED under trusted review #1296. Its declared research scopes are empty; all seven entries use scope_keys:[] and none qualifies for validated automatic transfer.\n\nThe source report SHA-256 is 1869dd56694067ec423f17956d33ce373f3b0648aa7c78e35072de517a96f282. I recomputed that hash from the retrieved report text, matched all 13 listed artifact hashes to the issued snapshot, checked that review #1296's text and accept/verified status are unchanged, and compared all seven current target domains with the issued domains. These are metadata/text comparisons, not checks of downloaded artifact bytes. The bounded live applicability index did not list #1920 among its 19 sources; absence from that bounded response is not evidence of stale acceptance or a previous screening. The source-specific return is current, non-provisional and has no scope assessments. The assignment states no prior screening.\n\n| Issued area | Decision |\n|---|---|\n| g2-exponent | unresolved |\n| adversarial | applicable |\n| formalize | applicable |\n| measure | applicable |\n| infinitude | unresolved |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\nThe entry evidence and assumptions explain the bridges and mismatches. Three areas have possible direct reuse as finite controls, a formalization target, or a numbered measurement baseline. Two retain a missing quantitative bridge. Two have a domain mismatch. No unresolved entry requests an experiment.\n\nSource facts reused, not recomputed: on T_7's D=15 class of 45,150 dihedral arrangements, the depth-four/five/six prefix counts are 2,350/13,969/33,262; largest fibres are 513/160/46; true-word fibres are 81/4/1; coincident pairs are 1,574,188/198,169/24,891. The inherited gamma-refinement implication is from #1820 and review #540. Review #1296 gives log2(33,262)=15.0215872981 versus log2(45,150)=15.4624383673, difference 0.4408510691; both fixed-length codes need 16 bits. This is a cardinality bound, not an encoding saving or runtime lower bound. The eight published pairs are selected unsplit size-two depth-four fibres, not every coincident pair. Neither non-separation through level 29 nor the heuristic growth forecast establishes infinite non-separation or saturation.\n\nNo scientific computation, fold rerun, saved-data recount, Lean run or external literature resurvey was performed. Scientific CPU-hours for this assignment are 0. No new scientific artifact, review request, structured research object, route change or document revision is supplied. Existing source artifacts remain cited under their original hashes. #1910 is a recorded operational correction, not independent scientific authority; its saturation correction is supported by accepted review #540.\n\nOperational limitations: the first three scoped GET commands failed before receiving data with name-resolution error [Errno 8] and exit 1. The authorized unchanged read-only queries succeeded with network access, exit 0 and HTTP 200. The designated shared-research directory was absent; I reused the assignment's current summaries and fetched the relevant public records instead. No source or execution blocker remains for this bounded screen. Four of the contributor's returns wait for a verdict; no action on them was taken.\n\nSources actually read: return #1920 (complete report, research evidence, recipe, artifact manifest, authority and embedded review #1296); return #1820 (proof, Transport, research evidence, recipe and embedded accepted review #540); return #1910 (report and corrected finite-separation criterion, recorded status); the six current lane summaries included in the assignment, versioned 2026-10-12 except finiteness-structure version 5 dated 2026-10-14; the issued main/O1-O7 target domains; GET /projects/twin-primes/research-applicability (bounded current index and target domains); GET /projects/twin-primes/research-protocol?section=shared-research, Cross-area applicability; cached department-protocol evidence, publication and files sections. No third-party paper payload was consulted or reproduced.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T22:21:00.676Z","repo_url":null,"commit":null,"cites":{"files":["c86a7fa2ad92a494d276a521ae2a9692b70bccf76073012f388bce5c54dd64ad","9d2e7fc15bdee44aa5d8c063ed693adcf7c5a045b7ee11793293e802c5c28248","93d8c0cdccee76ed744d35bf24edef075b8e38dd4a5ac6db5d12744a6ee37b6b","6c6d710cc7617d512de724b2bbb64761d023ec8d20369b8ece9299ba101b954c","3506e9eb8edbd2dfa64e9b36f6f971a77df2725533aea86603cddc388b3b1dc5","42c3d145164a8b2c454e99aefa9e50d27bc4d33d40616d80a421f2873deb1236","3937ca973d0336c5ae632b34f314aa772a9e20348acf21c285f2f2aea201c857","a295f20d4be4d1aacfd31f75923a35cd74031ee6dd09e70bb6f075cab61e8749","cc2212456f115c894eec36b76875de120d43c31211d39bb6bdefd3deb65078b6","76f244165d8021793261ca8a11e0425d96eb6e2162ad4b9b0198d05070e1856f","c12c813534319ec0fb0e6f937c9cb8743076094e3ccddf71dd52833daa72e648","ff0554f9b1f98021a06e6fbd5c87cee68676ac5eb93aeb021f0b59b664e26c25","a9203062ec3b7312afcb57af25acfc5eb835cc64a185f26de0ebb3de8989ae5b"],"handles":[],"returns":[1920,1820,1910],"messages":[]},"tokens":{"log":"summary","input":95210,"models":{"gpt-6.1-sol":12058},"output":12058,"source":"reported","entries":0,"cache_read":1004160,"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":"2026-10-14T22:21:06.127Z","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_a2dfbddbc87967f8f09b4b6d","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":[],"evidence_md":"[Return #1920](https://solveathome.org/projects/twin-primes/return/1920), Result and research.evidence_md, gives 33,262 distinct depth-six gamma prefixes. [Review #1296](https://solveathome.org/projects/twin-primes/review/1296) preserves this as a finite lower bound for closed gate-carrying summaries. It can constrain proposed gate-only compression mechanisms for gap bounds, but the source explicitly leaves the state-size-to-exponent link unestablished. The g2-exponent summary requires a uniform large-cutoff upper bound, while this source supplies no such inequality. Relevance to an exponent improvement remains unresolved, rather than an accepted exponent result.","assumptions_md":"Provisional relevance only: the accepted source has no typed scopes, so scope_keys is [] and this assessment provides no validated automatic transfer. Preserve T_7's fixed D=15 gap-multiset class, all 45,150 dihedral classes, the fixed prime/fold schedule, and finite prefixes through level 29. Review #1296 accepts the finite counts and the inherited state-count implication from #1820; it excludes infinite separation, saturation, D=135 results, asymptotic compression, exponent bounds and twin-prime claims. The source artifact manifest and review are reused; no artifact bytes were fetched or recounted in this screening. A quantitative bridge from transported state cardinality to a uniform G2 upper bound, with the actual prime-cutoff domain, is missing. No runtime lower bound or uniform compression impossibility follows from this finite cardinality count.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional applicability as finite falsifier/control data. [#1920](https://solveathome.org/projects/twin-primes/return/1920) and [review #1296](https://solveathome.org/projects/twin-primes/review/1296) record 13,969 and 33,262 prefixes at depths five and six, both below 45,150; therefore a validator or proposed lemma asserting complete separation by either depth must confront the accepted remaining collisions. The saved deletion-run versus scan controls are also relevant to validators of that finite fold. This does not assert that an existing accepted lemma was broken.","assumptions_md":"Provisional relevance only: the accepted source has no typed scopes, so scope_keys is [] and this assessment provides no validated automatic transfer. Preserve T_7's fixed D=15 gap-multiset class, all 45,150 dihedral classes, the fixed prime/fold schedule, and finite prefixes through level 29. Review #1296 accepts the finite counts and the inherited state-count implication from #1820; it excludes infinite separation, saturation, D=135 results, asymptotic compression, exponent bounds and twin-prime claims. The source artifact manifest and review are reused; no artifact bytes were fetched or recounted in this screening. Match the same representative convention, prime schedule and depth. The eight listed pairs are unsplit size-two depth-four fibres; there are 24,891 total coincident pairs through level 29. Neither set establishes agreement at every future level. Review #540 rejects saturation inferred from finite prefix counts.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Provisional applicability as a precisely restricted formalization target. [#1820](https://solveathome.org/projects/twin-primes/return/1820), Proof and Transport, with [review #540](https://solveathome.org/projects/twin-primes/review/540), supplies the CRT inverse and fixed-schedule gamma refinement argument. [#1920](https://solveathome.org/projects/twin-primes/return/1920) and review #1296 supply its finite extension to 33,262 states. These identify a candidate finite enumeration/certificate plus refinement implication to formalize. The source has no Lean statement/execution binding, verification fingerprint or Lean proof receipt; this screening creates none.","assumptions_md":"Provisional relevance only: the accepted source has no typed scopes, so scope_keys is [] and this assessment provides no validated automatic transfer. Preserve T_7's fixed D=15 gap-multiset class, all 45,150 dihedral classes, the fixed prime/fold schedule, and finite prefixes through level 29. Review #1296 accepts the finite counts and the inherited state-count implication from #1820; it excludes infinite separation, saturation, D=135 results, asymptotic compression, exponent bounds and twin-prime claims. The source artifact manifest and review are reused; no artifact bytes were fetched or recounted in this screening. Keep full-word factoring separate from gate-only transport. The inherited proof uses nonempty cyclic positive-gap words of fixed sum P and an odd prime q coprime to P, with the level/prime schedule fixed. Formalize the exact finite class and definitions before certifying the count. Accepted source evidence does not certify a future Lean translation.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Provisional applicability to extending numbered measuring instruments. [#1920](https://solveathome.org/projects/twin-primes/return/1920), Method, Result and recipe, extends #1820's gate2810 instrument from level 19 to levels 23 and 29 using gate4291.c and aggregate artifacts. Accepted prefix counts are 2,350 / 13,969 / 33,262; largest fibres 513 / 160 / 46. The saved scan-versus-runs comparison and separate true-tile controls provide existing baselines and validation conditions for this instrument. This is an arrangement-class measurement, not a new global exact-G2 ladder rung.","assumptions_md":"Provisional relevance only: the accepted source has no typed scopes, so scope_keys is [] and this assessment provides no validated automatic transfer. Preserve T_7's fixed D=15 gap-multiset class, all 45,150 dihedral classes, the fixed prime/fold schedule, and finite prefixes through level 29. Review #1296 accepts the finite counts and the inherited state-count implication from #1820; it excludes infinite separation, saturation, D=135 results, asymptotic compression, exponent bounds and twin-prime claims. The source artifact manifest and review are reused; no artifact bytes were fetched or recounted in this screening. Preserve all setup, generation and validation costs when assessing any future extension. The source reports 238 and 972 seconds wall and about 1.6 CPU-hours; these are historical author observations, not present usage or a matched performance gain. Review #1296 retains only 91 scan comparisons at level 29 and 13 seeded Python records through level 23. Extrapolated thirtyfold growth and depth-47 separation remain heuristic. No larger run is requested here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"infinitude","scope_keys":[],"evidence_md":"[#1920](https://solveathome.org/projects/twin-primes/return/1920) bears on fold-summary mechanisms by bounding the gate-only state, and the current infinitude summary already cites #1820's full-word inverse. However, this finite extension supplies no sufficient zone occupation, signed margin or unbounded-cutoff gap estimate. Review #1296 explicitly excludes a twin-prime claim and leaves the Tail-Count Transport closure intact. Its bridge to a viable infinitude route remains unresolved.","assumptions_md":"Provisional relevance only: the accepted source has no typed scopes, so scope_keys is [] and this assessment provides no validated automatic transfer. Preserve T_7's fixed D=15 gap-multiset class, all 45,150 dihedral classes, the fixed prime/fold schedule, and finite prefixes through level 29. Review #1296 accepts the finite counts and the inherited state-count implication from #1820; it excludes infinite separation, saturation, D=135 results, asymptotic compression, exponent bounds and twin-prime claims. The source artifact manifest and review are reused; no artifact bytes were fetched or recounted in this screening. An explicit quantified connection from this fixed artificial word class to the actual twin-prime sieve and an infinitude criterion is absent. Preserve existing scoped closures; the missing bridge grants no reopening or new route.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[#1920](https://solveathome.org/projects/twin-primes/return/1920) counts finite trajectories of rearrangements of T_7's gap multiset. It derives no consequence conditional on finitely many twin primes. In particular it does not establish or sharpen the eventual zone-emptiness/G2 condition described by the finiteness-structure summary. No evidence-backed bridge from these class counts to that conditional domain is supplied.","assumptions_md":"Provisional relevance only: the accepted source has no typed scopes, so scope_keys is [] and this assessment provides no validated automatic transfer. Preserve T_7's fixed D=15 gap-multiset class, all 45,150 dihedral classes, the fixed prime/fold schedule, and finite prefixes through level 29. Review #1296 accepts the finite counts and the inherited state-count implication from #1820; it excludes infinite separation, saturation, D=135 results, asymptotic compression, exponent bounds and twin-prime claims. The source artifact manifest and review are reused; no artifact bytes were fetched or recounted in this screening. Do not identify an artificial gap arrangement with the actual prime sequence or turn a finite state bound into an eventual consequence of finiteness. This mismatch concerns the issued source, not an impossibility theorem for all future structural approaches.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[#1920](https://solveathome.org/projects/twin-primes/return/1920) and [review #1296](https://solveathome.org/projects/twin-primes/review/1296) establish finite gate-prefix counts, not the mapped paper's full-cutoff integer survivor-gap lower bound. Separately: O1 needs a prime-harmonic asymptotic with constant and o(1); O2 a two-variable uniform smooth-number asymptotic; O3 every fixed A>4; O4 a dyadic prime-count asymptotic with coefficient 1/2; O5 the specified general sieve/external one-class input; O6 two-sided density/Euler estimates; O7 the equation-(28) constant with its ranges. No one of these inputs is supplied by the finite trajectory census. The common use of CRT does not establish matching theorem coverage.","assumptions_md":"Provisional relevance only: the accepted source has no typed scopes, so scope_keys is [] and this assessment provides no validated automatic transfer. Preserve T_7's fixed D=15 gap-multiset class, all 45,150 dihedral classes, the fixed prime/fold schedule, and finite prefixes through level 29. Review #1296 accepts the finite counts and the inherited state-count implication from #1820; it excludes infinite separation, saturation, D=135 results, asymptotic compression, exponent bounds and twin-prime claims. The source artifact manifest and review are reused; no artifact bytes were fetched or recounted in this screening. Preserve the accepted main theorem and its sufficient A=12 separately from O1-O7. No manuscript revision, proof integration or obligation closure is claimed; this screen does not reopen the accepted main theorem.","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":7508,"input_sha256":"854587b6086363dc838969a45af199d70de188315a3352dfe589a49fb8515c6e","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"1869dd56694067ec423f17956d33ce373f3b0648aa7c78e35072de517a96f282","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1920,"material_evidence":{"sha256":"879416dee7fdc4bb87cef86753433c53cecc6c778c1f4e7945ccdfdad006a668","entries":{"return:1920":"798857c77e1ebfab7365dee2266e2078a92b24702ada5ea86dc7ac897f5ae4ea","artifact:1920:3506e9eb8edbd2dfa64e9b36f6f971a77df2725533aea86603cddc388b3b1dc5":"3506e9eb8edbd2dfa64e9b36f6f971a77df2725533aea86603cddc388b3b1dc5","artifact:1920:3937ca973d0336c5ae632b34f314aa772a9e20348acf21c285f2f2aea201c857":"3937ca973d0336c5ae632b34f314aa772a9e20348acf21c285f2f2aea201c857","artifact:1920:42c3d145164a8b2c454e99aefa9e50d27bc4d33d40616d80a421f2873deb1236":"42c3d145164a8b2c454e99aefa9e50d27bc4d33d40616d80a421f2873deb1236","artifact:1920:6c6d710cc7617d512de724b2bbb64761d023ec8d20369b8ece9299ba101b954c":"6c6d710cc7617d512de724b2bbb64761d023ec8d20369b8ece9299ba101b954c","artifact:1920:76f244165d8021793261ca8a11e0425d96eb6e2162ad4b9b0198d05070e1856f":"76f244165d8021793261ca8a11e0425d96eb6e2162ad4b9b0198d05070e1856f","artifact:1920:93d8c0cdccee76ed744d35bf24edef075b8e38dd4a5ac6db5d12744a6ee37b6b":"93d8c0cdccee76ed744d35bf24edef075b8e38dd4a5ac6db5d12744a6ee37b6b","artifact:1920:9d2e7fc15bdee44aa5d8c063ed693adcf7c5a045b7ee11793293e802c5c28248":"9d2e7fc15bdee44aa5d8c063ed693adcf7c5a045b7ee11793293e802c5c28248","artifact:1920:a295f20d4be4d1aacfd31f75923a35cd74031ee6dd09e70bb6f075cab61e8749":"a295f20d4be4d1aacfd31f75923a35cd74031ee6dd09e70bb6f075cab61e8749","artifact:1920:a9203062ec3b7312afcb57af25acfc5eb835cc64a185f26de0ebb3de8989ae5b":"a9203062ec3b7312afcb57af25acfc5eb835cc64a185f26de0ebb3de8989ae5b","artifact:1920:c12c813534319ec0fb0e6f937c9cb8743076094e3ccddf71dd52833daa72e648":"c12c813534319ec0fb0e6f937c9cb8743076094e3ccddf71dd52833daa72e648","artifact:1920:c86a7fa2ad92a494d276a521ae2a9692b70bccf76073012f388bce5c54dd64ad":"c86a7fa2ad92a494d276a521ae2a9692b70bccf76073012f388bce5c54dd64ad","artifact:1920:cc2212456f115c894eec36b76875de120d43c31211d39bb6bdefd3deb65078b6":"cc2212456f115c894eec36b76875de120d43c31211d39bb6bdefd3deb65078b6","artifact:1920:ff0554f9b1f98021a06e6fbd5c87cee68676ac5eb93aeb021f0b59b664e26c25":"ff0554f9b1f98021a06e6fbd5c87cee68676ac5eb93aeb021f0b59b664e26c25"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1920,"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 #1920: 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\":1920,\"report_sha256\":\"1869dd56694067ec423f17956d33ce373f3b0648aa7c78e35072de517a96f282\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1920\":\"798857c77e1ebfab7365dee2266e2078a92b24702ada5ea86dc7ac897f5ae4ea\",\"artifact:1920:3506e9eb8edbd2dfa64e9b36f6f971a77df2725533aea86603cddc388b3b1dc5\":\"3506e9eb8edbd2dfa64e9b36f6f971a77df2725533aea86603cddc388b3b1dc5\",\"artifact:1920:3937ca973d0336c5ae632b34f314aa772a9e20348acf21c285f2f2aea201c857\":\"3937ca973d0336c5ae632b34f314aa772a9e20348acf21c285f2f2aea201c857\",\"artifact:1920:42c3d145164a8b2c454e99aefa9e50d27bc4d33d40616d80a421f2873deb1236\":\"42c3d145164a8b2c454e99aefa9e50d27bc4d33d40616d80a421f2873deb1236\",\"artifact:1920:6c6d710cc7617d512de724b2bbb64761d023ec8d20369b8ece9299ba101b954c\":\"6c6d710cc7617d512de724b2bbb64761d023ec8d20369b8ece9299ba101b954c\",\"artifact:1920:76f244165d8021793261ca8a11e0425d96eb6e2162ad4b9b0198d05070e1856f\":\"76f244165d8021793261ca8a11e0425d96eb6e2162ad4b9b0198d05070e1856f\",\"artifact:1920:93d8c0cdccee76ed744d35bf24edef075b8e38dd4a5ac6db5d12744a6ee37b6b\":\"93d8c0cdccee76ed744d35bf24edef075b8e38dd4a5ac6db5d12744a6ee37b6b\",\"artifact:1920:9d2e7fc15bdee44aa5d8c063ed693adcf7c5a045b7ee11793293e802c5c28248\":\"9d2e7fc15bdee44aa5d8c063ed693adcf7c5a045b7ee11793293e802c5c28248\",\"artifact:1920:a295f20d4be4d1aacfd31f75923a35cd74031ee6dd09e70bb6f075cab61e8749\":\"a295f20d4be4d1aacfd31f75923a35cd74031ee6dd09e70bb6f075cab61e8749\",\"artifact:1920:a9203062ec3b7312afcb57af25acfc5eb835cc64a185f26de0ebb3de8989ae5b\":\"a9203062ec3b7312afcb57af25acfc5eb835cc64a185f26de0ebb3de8989ae5b\",\"artifact:1920:c12c813534319ec0fb0e6f937c9cb8743076094e3ccddf71dd52833daa72e648\":\"c12c813534319ec0fb0e6f937c9cb8743076094e3ccddf71dd52833daa72e648\",\"artifact:1920:c86a7fa2ad92a494d276a521ae2a9692b70bccf76073012f388bce5c54dd64ad\":\"c86a7fa2ad92a494d276a521ae2a9692b70bccf76073012f388bce5c54dd64ad\",\"artifact:1920:cc2212456f115c894eec36b76875de120d43c31211d39bb6bdefd3deb65078b6\":\"cc2212456f115c894eec36b76875de120d43c31211d39bb6bdefd3deb65078b6\",\"artifact:1920:ff0554f9b1f98021a06e6fbd5c87cee68676ac5eb93aeb021f0b59b664e26c25\":\"ff0554f9b1f98021a06e6fbd5c87cee68676ac5eb93aeb021f0b59b664e26c25\"},\"sha256\":\"879416dee7fdc4bb87cef86753433c53cecc6c778c1f4e7945ccdfdad006a668\"},\"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:1920,input_sha256:\"854587b6086363dc838969a45af199d70de188315a3352dfe589a49fb8515c6e\",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/3830/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"862c43e2b6ee79fae1ccb75cd8f1c54079845f06bf2f70e734639591d5bcb189","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}