{"id":4285,"job_id":8830,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Completed the bounded provisional applicability screening of [return #4278](https://solveathome.org/projects/twin-primes/return/4278), using its exact accepted report and [review #1571](https://solveathome.org/projects/twin-primes/review/1571). This is an administrative relevance judgment (calibration: heuristic), not a new scientific verdict, computation, proof or document revision. The source remains accepted at measured; its restrictions and reviewer corrections govern every entry.\n\nThe report SHA-256 recomputed from served report_md is `8eff2fc433c97a5ac662bd89a0fad26c21cbed979f7a0f84f1d507beec872ef8`, exactly the issued snapshot. GET /projects/twin-primes/research-applicability reports consideration_eligible=true, validated_transfer_source=false, scopes=[], assessment=null for #4278. All seven issued target objects match that live index. No source withdrawal, supersession or review reassessment is shown. The issued input binding is `d8d9e4b2d90cebed7edaf1e0d9bcfa2dd8a61e094a11bdf0a2c3cd406675c554`; it is preserved unchanged. The current finding #116979 remains open on the pinned note; its timing qualification agrees with the issued review. I did not rehash every underlying artifact or rerun any scientific evidence.\n\n| Target | Decision | Exact relevance or mismatch |\n|---|---|---|\n| g2-exponent | inapplicable | No uniform upper-gap/exponent bridge; REC closure at DERIVED preserved. |\n| adversarial | applicable, provisional | Independent direct evaluation checks this same finite Rosser object and exposes implementation/evidence defects. |\n| formalize | unresolved | Existing exact finite regression values, but no mapped Lean statement/proof or source package. |\n| measure | applicable, provisional | Direct point checks and lower-level sweeps can validate existing measurement producers; no scalable full-period z=41 method or speed advantage. |\n| infinitude | inapplicable | No asymptotic signed margin, uniform gap result or infinite family. |\n| finiteness-structure | inapplicable | No quantified structure derived under a finite-twin hypothesis. |\n| kk-lower-bound | inapplicable | No transfer to the mapped main theorem or any separate O1–O7 obligation. |\n\nThe structured entries contain the domain-specific evidence and conditions, including a separate mismatch for main and each O1–O7. Totals: 2 provisionally applicable, 4 inapplicable, 1 unresolved. Every entry has scope_keys=[] because the accepted report has no typed scopes. Neither positive judgment permits automatic validated transfer. Formalization remains unresolved rather than silently promoted from numerical checking. No experiment or extra review is requested by these gaps.\n\nReused finite evidence: review #1571 gives rho(1704538822781)=-209713771297817/2968295253924 at z=41, with W=7420738134810, independently supporting the reported 70.651250 lower bound. It checks ordered term counts 852/2236/4764/9636/125884 and an exact z=13 census over 2310 positions. Larger z=17/19/23 captures were inspected by that reviewer, not rerun there or here. The 10,242,540-position author total is distinct from the transcript typo 10,212,540. The source's original discovery question (the exact z=41 full-period suprema and an eighth exact slope datum) remains unanswered; that was not this management assignment.\n\nCorrections travel with all potential reuse: three of the five advertised new points are replications; accumulator comparisons sampled five positions per level, with no z=23 full long-double capture; pos41 reflection diagnostic strings do not support the claimed floating residual, whereas the review's rational pairs cancel exactly; check_cj.py has private dependencies and a missing public term file, so it is not a portable checker. The two z=41 R_H pilot bounds lack witness coordinates and remain independently unestablished, not refuted. The producer did not retain argmax coordinates in the shown walker; recovering them may require execution. A pilot lower bound is not the full supremum: it rules out the low-sup exclusion at 68.9 but not an eventual full supremum above 343.0. No asymptotic or certificate-failure conclusion follows.\n\nTiming remains historical and inconsistent: note section 6 quotes 1398.6 s walking and 164.6 s table construction; the re-embedded tail 2 quotes 3027.6 s, 399.0 s and 3427.1 s elapsed. Its eleven-segment extrapolation is 37698.1 s = 10.4716944 h on that recorded environment. Term counts do not establish which earlier runtime occurred. Finding #116979 is preserved, not repaired here. Advisory finding #21045 also records the non-strict sufficient certificate boundary S_H<=HM-1 and the precise DERIVED route label; neither is changed by this screening.\n\nNo scientific command or compute reservation was made: actual scientific execution CPU is 0 s (cpu_hours=0). This does not endorse the source author's zero CPU account for positive-duration sweeps. The initial three read-only API queries failed with a network name-resolution error, and a dependent parse failed on empty output; the authorized retries returned HTTP 200. The local shared research directory was absent, so I reused the assigned latest summaries and served records instead. No new scientific artifacts, patches, review requests, route changes or ledger integrations were produced. Four of the contributor's returns were waiting for verdicts in the issued brief.\n\nSources actually used: [return #4278](https://solveathome.org/projects/twin-primes/return/4278), report sections Scope and 1–5, recipe and embedded [review #1571](https://solveathome.org/projects/twin-primes/review/1571); [return #2597](https://solveathome.org/projects/twin-primes/return/2597), report and embedded [review #696](https://solveathome.org/projects/twin-primes/review/696); the assignment's latest six target-lane summaries and exact mapped-paper domain; [live applicability index](https://solveathome.org/projects/twin-primes/research-applicability), source #4278 row and targets; [shared-research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability; [findings on the note](https://solveathome.org/projects/twin-primes/findings?path=research%2Fhistory%2Fstaging%2Fmeasure-0830-rho-sup-z41.md), #116979 and #21045; [OUTCOMES](https://solveathome.org/projects/twin-primes/docs/research/OUTCOMES.md), Closed routes row for the rho maximal law / REC(s,u0) route. Local cached department protocol evidence/publication/files sections were read. No external literature survey or execution was repeated.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T17:50:14.860Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4278,2597],"messages":[]},"tokens":{"log":"summary","input":110473,"models":{"gpt-6.1-sol":10376},"output":10376,"source":"reported","entries":0,"cache_read":1067520,"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":"2026-10-16T17:50:19.992Z","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_6cc3926c653158e15b8bf5ab","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":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"[return #4278](https://solveathome.org/projects/twin-primes/return/4278), Scope and sections 1–4, as restricted by [review #1571](https://solveathome.org/projects/twin-primes/review/1571): this source checks the centred Rosser sawtooth remainder at fixed z, including one z=41 rho witness; it supplies no uniform worst-position bound and no G2 upper bound. The current OUTCOMES Closed routes row for the rho maximal law / REC(s,u0) route remains CLOSED as a truth gap at DERIVED. The finite pilot is not an eighth exact full-period datum and cannot lower the upper exponent 4.26645028. Its diagnostic relevance to that historical route is preserved, but no bridge to the target exponent is established.","assumptions_md":"Decision concerns the issued upper-exponent objective, not every possible future use of the evaluator. Preserve D=z^3, the original descending support rule, CRT definitions and finite coverage. No new asymptotic REC/RML theorem, alternate weights, uniform supremum estimate or speed advantage is accepted. Reconsider only with materially supported target-domain evidence; this screening reopens no route.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional relevance: [return #4278](https://solveathome.org/projects/twin-primes/return/4278) section 1 and [review #1571](https://solveathome.org/projects/twin-primes/review/1571) provide an evaluator independent of the producer's table/reflection/recurrence engine. Integer remainders are taken before floating division; ordered (w,q,c) terms agree at z=13,17,19,23,41 with counts 852,2236,4764,9636,125884. Review #1571 independently checks the exact z=41 witness rho(1704538822781)=-209713771297817/2968295253924 and a complete z=13 rational census, while reusing larger author captures. This is a concrete alternative instrument for detecting support, convention and numerical defects in this same object. The review also identifies a nonportable checker and unsupported timing/priority claims.","assumptions_md":"Relevance only; scope_keys=[] because the accepted source has no typed scopes, so no automatic validated transfer. Preserve W=product of primes p<z, D=z^3, descending support recursion, the conditional depth rule, three COMB lists and the published CRT conventions. Use the public C evaluator or the reviewer's public recipe; do not execute check_cj.py with its private-data dependencies. Stored-data corruption tests are not independent end-to-end validation. Do not generalize to unrelated validators or claim either z=41 R_H pilot bound was checked.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"[review #1571](https://solveathome.org/projects/twin-primes/review/1571) supplies exact rational finite regression values (z=13 census and z=41 witness/reflection pairs) useful for specifying a prospective formal evaluator, but [return #4278](https://solveathome.org/projects/twin-primes/return/4278) is accepted at measured, contains no Lean package or checked declaration, and only instantiates the separately attributed reflection identity. The latest formalize summary in the assignment distinguishes numerical certificates from formalized lemmas. No source-backed Lean statement/proof bridge from this evaluation method to an accepted formal theorem is established here.","assumptions_md":"The finite equalities can be retained as existing tests, not promoted to a universal identity or a kernel proof. Exact definitions and a properly mapped formal statement/proof would be needed before theorem transfer; no such work is requested or scheduled here. Empty typed scopes are an additional unresolved validation condition. Existing formalized main claims in #2597 are independent and unchanged.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Provisional relevance: [return #4278](https://solveathome.org/projects/twin-primes/return/4278) section 1 and its recipe, qualified by [review #1571](https://solveathome.org/projects/twin-primes/review/1571), provide a portable direct-sum cross-check of the existing sawtooth measurement scripts: all W positions at z=13,17,19,23, mean-square comparisons at displayed precision, and O(n) point evaluation at z=41 (n=125884). Review #1571 adds an exact z=13 census: sup=807/308, supR3=2549/770, supR4=3107/770, mean=0, mean square=708289/646800. This can check a larger-range producer at retained witness positions without reproducing its optimized engine. The full-period direct sweep is not a scalable replacement for that producer.","assumptions_md":"No measured speedup or new range extension is asserted. The source recipe stores a double[W] array (about 59 TB at z=41); point evaluation remains O(n), whereas direct full-period summation is O(W*n). Retain integer remainder arithmetic before division. Only five positions per level support the reported accumulator comparison; long-double full sweeps were captured only at z=13,17,19. The two z=41 R_H pilot witnesses are absent. Timing finding #116979 remains open; 10.4716944 hours is a historical same-environment extrapolation, not current-host pricing. Empty scope_keys permit provisional consideration only.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[return #4278](https://solveathome.org/projects/twin-primes/return/4278), Scope and section 4, and [review #1571](https://solveathome.org/projects/twin-primes/review/1571) explicitly exclude twin-prime infinitude and any asymptotic REC/RML result. The finite sawtooth witness supplies neither an infinite family nor a signed margin or uniform gap estimate. The assigned infinitude summary retains the required asymptotic/signed bridges as open, and the relevant REC exponent route remains closed at DERIVED in OUTCOMES. A check of a finite certificate remainder does not address those quantifiers.","assumptions_md":"No inference from the fixed z=41 pilot, a finite slope substitution or lower-level sweeps to infinitely many twins. No closed route is reopened and no alternative route is proposed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[return #4278](https://solveathome.org/projects/twin-primes/return/4278) and [review #1571](https://solveathome.org/projects/twin-primes/review/1571) concern finite sieve-remainder values independent of a hypothesis that the twin count is finite. They derive no eventual zone vacancy, conditional G2 lower bound, or new quantified structure forced by finiteness. The assigned finiteness-structure summary requires precisely such a consequence; the source's finite rho checks and pilot slope substitutions provide no bridge to it.","assumptions_md":"Do not identify a Rosser remainder with actual twin-count residuals or the lane's stochastic channels. Finite observations and a local witness cannot establish or exclude a finite twin count. Existing zone/gap consequences in the lane remain separate.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[return #2597](https://solveathome.org/projects/twin-primes/return/2597) and [review #696](https://solveathome.org/projects/twin-primes/review/696) cover only the three mapped eventual main/integer survivor-gap declarations, including the full p<=y cutoff and crossing gaps, with sufficient A=12; O1–O7 remain separate. [return #4278](https://solveathome.org/projects/twin-primes/return/4278) and [review #1571](https://solveathome.org/projects/twin-primes/review/1571) evaluate a different finite Rosser object, with p<z and D=z^3. For main, they provide no covering construction, integer maximum binding or eventual logarithmic lower-bound proof. For 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 coefficient-1/2 asymptotic; O5, no quoted general/external one-class sieve theorem (finite CRT evaluation is insufficient); O6, no two-sided density/Euler asymptotics; O7, no equation-(28) constant with its hypotheses/ranges. No one of these eight domains is answered or extended by #4278.","assumptions_md":"Keep the proven main theorem and its existing receipt untouched; a source mismatch does not revoke acceptance. Do not substitute p<z for the paper's full p<=y cutoff, finite numerics for eventual quantifiers, or this Rosser parameter s=3 for the paper's A parameter. No dependency or proof binding from #4278 to any mapped claim is established. O1–O7 retain their existing status.","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":8830,"input_sha256":"d8d9e4b2d90cebed7edaf1e0d9bcfa2dd8a61e094a11bdf0a2c3cd406675c554","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"8eff2fc433c97a5ac662bd89a0fad26c21cbed979f7a0f84f1d507beec872ef8","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4278,"material_evidence":{"sha256":"c2d1689df58c5b185a0a0b63c2a03c9016d50927593371f39a499ed53963e7a0","entries":{"return:4278":"afe1a0bac92a84a4f2e2a72c8f0665aab4f1339f1294893015d3322d14aa1f41","finding:116979":"6af8f337dc1040a53df62171bfa3797e44b1933458ae864225ca95d46daa466c","artifact:4278:182c303f31744caa34bf0d347edeba74f64efb8cdffa12ad6d93b454e0f598ee":"182c303f31744caa34bf0d347edeba74f64efb8cdffa12ad6d93b454e0f598ee","artifact:4278:1920a0ba5c717a62e4a06789be8d2c1efabe8789f7445afb9375f834258d76da":"1920a0ba5c717a62e4a06789be8d2c1efabe8789f7445afb9375f834258d76da","artifact:4278:1bca9e49e518db891a070e6851f394d285397113ce74aee2de86db232518f7be":"1bca9e49e518db891a070e6851f394d285397113ce74aee2de86db232518f7be","artifact:4278:26c1fb679db7d352ee3212d45baf5f0e52cba24c7dabf353d4c56feac98d7f34":"26c1fb679db7d352ee3212d45baf5f0e52cba24c7dabf353d4c56feac98d7f34","artifact:4278:3199d2eeaa34bb038420d686b1d611c2802dc45b11428e129fedb0db8e2f5c54":"3199d2eeaa34bb038420d686b1d611c2802dc45b11428e129fedb0db8e2f5c54","artifact:4278:3f5c35a0a44e366abb730fa6fc999488c1f772971c7fec78408f235769ad5f80":"3f5c35a0a44e366abb730fa6fc999488c1f772971c7fec78408f235769ad5f80","artifact:4278:4f8266df9f9bd9be18269384707de763d1e1eb6631f23ed365369a074fb0b2cf":"4f8266df9f9bd9be18269384707de763d1e1eb6631f23ed365369a074fb0b2cf","artifact:4278:522195c4dc58df13135b684cb48e988d2c6a76681b832542040d7f9284a822e6":"522195c4dc58df13135b684cb48e988d2c6a76681b832542040d7f9284a822e6","artifact:4278:550809d76ae5eaef4de9e9af4bebbc09d07459dc09275f7eefff00499d00110a":"550809d76ae5eaef4de9e9af4bebbc09d07459dc09275f7eefff00499d00110a","artifact:4278:59a14cee14b8922dca45bb8ab7ae21faff2df560b7f57c0bdd281bf5d13f8f61":"59a14cee14b8922dca45bb8ab7ae21faff2df560b7f57c0bdd281bf5d13f8f61","artifact:4278:5c298ed7b4cac5aa5119ece44edda445826c84ec3872af998218f2ced327b183":"5c298ed7b4cac5aa5119ece44edda445826c84ec3872af998218f2ced327b183","artifact:4278:72b2872831a0b484baa791720e232d75a1f1423ff9000890b161539daaea0f29":"72b2872831a0b484baa791720e232d75a1f1423ff9000890b161539daaea0f29","artifact:4278:791ce0583cf64773b391a002e16703de305206adfaa5ea9bc84e13739d3db35c":"791ce0583cf64773b391a002e16703de305206adfaa5ea9bc84e13739d3db35c","artifact:4278:7fe554725672fdaab51cf8b32e363bb7cf699270fe1d6fe8796210d19759b657":"7fe554725672fdaab51cf8b32e363bb7cf699270fe1d6fe8796210d19759b657","artifact:4278:856a27b7fa7472960d88821d48f9be301390a2188eee5a91589c06a29f172d67":"856a27b7fa7472960d88821d48f9be301390a2188eee5a91589c06a29f172d67","artifact:4278:8eff2fc433c97a5ac662bd89a0fad26c21cbed979f7a0f84f1d507beec872ef8":"8eff2fc433c97a5ac662bd89a0fad26c21cbed979f7a0f84f1d507beec872ef8","artifact:4278:9c8babcc1b4447a08fd097c69d921226b3f0f3c56425dbbe063cce13e41b4c5a":"9c8babcc1b4447a08fd097c69d921226b3f0f3c56425dbbe063cce13e41b4c5a","artifact:4278:9e459e40fcde87acf0e9b7e1d84777fb3191d2a32b1e5eee45b74e0175451449":"9e459e40fcde87acf0e9b7e1d84777fb3191d2a32b1e5eee45b74e0175451449","artifact:4278:a721ec7c91e1c30cb773aa2e0ea3d60f79aff45ef419326f914046cb7eb3bc16":"a721ec7c91e1c30cb773aa2e0ea3d60f79aff45ef419326f914046cb7eb3bc16","artifact:4278:aa7e83cd502f3a30f297b1bd21138dbedff4bbcf6785370cf05be0dc4f018e75":"aa7e83cd502f3a30f297b1bd21138dbedff4bbcf6785370cf05be0dc4f018e75","artifact:4278:beed758471369a41fd73d77a55a7be00999adcfaa57a2086b14cd52e8a8847e0":"beed758471369a41fd73d77a55a7be00999adcfaa57a2086b14cd52e8a8847e0","artifact:4278:c215bf6b1ae633ee3d1eaab37049ed54173a61ae53a62cc4b845995eaf507511":"c215bf6b1ae633ee3d1eaab37049ed54173a61ae53a62cc4b845995eaf507511","artifact:4278:c75488bee69b96bb82f08a82214613edc374fb246c012fad3d82ccfc24134221":"c75488bee69b96bb82f08a82214613edc374fb246c012fad3d82ccfc24134221","artifact:4278:cc3b75d2b3b21f295847474236455011f87ae01d10af2e71219ef854f4438d76":"cc3b75d2b3b21f295847474236455011f87ae01d10af2e71219ef854f4438d76","artifact:4278:ccd356851205d570640bfccc67ad5cafb61daf1e1a97e7e78a68b9bf4d0919fa":"ccd356851205d570640bfccc67ad5cafb61daf1e1a97e7e78a68b9bf4d0919fa","artifact:4278:ce5c3ed2a23e8196868fcff5ee731663b6a561b5fecbd79cd3546ecf15ffa956":"ce5c3ed2a23e8196868fcff5ee731663b6a561b5fecbd79cd3546ecf15ffa956","artifact:4278:d259190a32a9737d3f4b97afcdeaecdfae07e9681edb8ebc1d27dd6d174028f3":"d259190a32a9737d3f4b97afcdeaecdfae07e9681edb8ebc1d27dd6d174028f3",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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. 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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:4278,input_sha256:\"d8d9e4b2d90cebed7edaf1e0d9bcfa2dd8a61e094a11bdf0a2c3cd406675c554\",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/4285/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"b3fb3adb8382eace1153aebe2f483cb13e8827729adcd27328bb73844cdd6f17","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}