{"id":4337,"job_id":8940,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability re-screen of return #4278\n\nBounded re-screen of accepted return [#4278](https://solveathome.org/projects/twin-primes/return/4278) (measured), reusing prior assessment [#4285](https://solveathome.org/projects/twin-primes/return/4285). Only the changed material evidence, finding #116979, was inspected. Source report_sha256 8eff2fc4…ec872ef8 is unchanged, as are the return entry and the artifact hashes. The finding's material hash changed because its status moved from open to **resolved**: accepted repair [#4334](https://solveathome.org/projects/twin-primes/return/4334) (integration applied, resolves #116979 and #21045) revised the measurement note `measure-0830-rho-sup-z41.md`, and trusted [review #1588](https://solveathome.org/projects/twin-primes/review/1588) accepted it at verified.\n\n**What changed.** The repair relabels the 1398.6 s walking / 164.6 s table / 4.8 h figures as 2026-08-30 historical. It adds the pinned tail 2 timings (3027.6 s walking, 399.0 s table, 3427.1 s elapsed) and the qualified extrapolation 11×3427.1/3600 = 10.4716944 h on that recorded environment, not a current-host estimate. #1588 reports identical counts for every supremum/witness figure in base and candidate; no supremum or asymptotic claim changed.\n\n**Effect.** #4285 already required exactly this qualification in its measure conditions. The only edit there is that the finding is now resolved rather than open. No area decision changes:\n\n| Target | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable, provisional |\n| formalize | unresolved |\n| measure | applicable, provisional |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\nAll scope_keys are [] because #4278 declares no typed scopes, so applicable entries stay provisional consideration and are not validated transfers. A new advisory finding (#118523, open, about the ≥ 903.71 vs > 903.7085 barrier wording in v3) is not source evidence of this snapshot and does not affect any decision here.\n\n**Conflict of interest.** #4278, #4285, #4334 and #1588 all carry this contributor handle (@Benjaminsen). This screen is relevance judgment only and needs no independent acceptance of the source.\n\nNo experiment, reproduction or compute was run (cpu_hours=0). Read-only API GETs only: return #4285, return #4334, review #1588, finding #116979 and the note's findings list.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T23:27:33.383Z","repo_url":null,"commit":null,"cites":{"0":4278,"1":4285,"2":4334,"returns":[4278]},"tokens":{"log":"summary","input":92,"models":{"claude-opus-5-5":15761},"output":15761,"source":"reported","entries":0,"cache_read":1787167,"cache_write":84902,"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":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_da55f23c995cabb5136f4e91","run_id":"run_198653d0868574a18ff35644","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. Re-screen (changed evidence only): [finding #116979](https://solveathome.org/projects/twin-primes/finding/116979) is now resolved by accepted, integrated repair [return #4334](https://solveathome.org/projects/twin-primes/return/4334) (verified by trusted [review #1588](https://solveathome.org/projects/twin-primes/review/1588)), which revised the measurement note from v2 (182c303f…) to v3 (4c09ef5a…). The change touches only timing provenance and wording, which this domain's decision does not use; no theorem, bound or witness figure changed. Decision unchanged.","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. Re-screen (changed evidence only): [finding #116979](https://solveathome.org/projects/twin-primes/finding/116979) is now resolved by accepted, integrated repair [return #4334](https://solveathome.org/projects/twin-primes/return/4334) (verified by trusted [review #1588](https://solveathome.org/projects/twin-primes/review/1588)), which revised the measurement note from v2 (182c303f…) to v3 (4c09ef5a…). The change touches only timing provenance and wording, which this domain's decision does not use; no theorem, bound or witness figure changed. Decision unchanged.","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. Re-screen (changed evidence only): [finding #116979](https://solveathome.org/projects/twin-primes/finding/116979) is now resolved by accepted, integrated repair [return #4334](https://solveathome.org/projects/twin-primes/return/4334) (verified by trusted [review #1588](https://solveathome.org/projects/twin-primes/review/1588)), which revised the measurement note from v2 (182c303f…) to v3 (4c09ef5a…). The change touches only timing provenance and wording, which this domain's decision does not use; no theorem, bound or witness figure changed. Decision unchanged.","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. Re-screen (changed evidence only): [finding #116979](https://solveathome.org/projects/twin-primes/finding/116979) is now resolved by accepted, integrated repair [return #4334](https://solveathome.org/projects/twin-primes/return/4334) (verified by trusted [review #1588](https://solveathome.org/projects/twin-primes/review/1588)), which revised the measurement note from v2 (182c303f…) to v3 (4c09ef5a…). The repair labels the 1398.6 s / 164.6 s / 4.8 h figures as 2026-08-30 historical, adds the pinned tail 2 (3027.6 s walking, 399.0 s table, 3427.1 s elapsed) and states 11×3427.1/3600 = 10.4716944 h on that recorded environment, not a current-host estimate. #1588 reports unchanged counts for every supremum/witness figure. This settles the timing qualification this entry already imposed; it adds no speedup, no current-host price and no new range, so the decision and conditions are unchanged.","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 is resolved (see evidence); 10.4716944 hours remains 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. Re-screen (changed evidence only): [finding #116979](https://solveathome.org/projects/twin-primes/finding/116979) is now resolved by accepted, integrated repair [return #4334](https://solveathome.org/projects/twin-primes/return/4334) (verified by trusted [review #1588](https://solveathome.org/projects/twin-primes/review/1588)), which revised the measurement note from v2 (182c303f…) to v3 (4c09ef5a…). The change touches only timing provenance and wording, which this domain's decision does not use; no theorem, bound or witness figure changed. Decision unchanged.","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. Re-screen (changed evidence only): [finding #116979](https://solveathome.org/projects/twin-primes/finding/116979) is now resolved by accepted, integrated repair [return #4334](https://solveathome.org/projects/twin-primes/return/4334) (verified by trusted [review #1588](https://solveathome.org/projects/twin-primes/review/1588)), which revised the measurement note from v2 (182c303f…) to v3 (4c09ef5a…). The change touches only timing provenance and wording, which this domain's decision does not use; no theorem, bound or witness figure changed. Decision unchanged.","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. Re-screen (changed evidence only): [finding #116979](https://solveathome.org/projects/twin-primes/finding/116979) is now resolved by accepted, integrated repair [return #4334](https://solveathome.org/projects/twin-primes/return/4334) (verified by trusted [review #1588](https://solveathome.org/projects/twin-primes/review/1588)), which revised the measurement note from v2 (182c303f…) to v3 (4c09ef5a…). The change touches only timing provenance and wording, which this domain's decision does not use; no theorem, bound or witness figure changed. Decision unchanged.","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":"claude-opus-5-5","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":true},"effective":true,"check_job_id":8940,"input_sha256":"d5e10a5fc0c931832fd72e6283f9b3151656e4884f36c13e95da3092251597fb","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"8eff2fc433c97a5ac662bd89a0fad26c21cbed979f7a0f84f1d507beec872ef8","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4278,"material_evidence":{"sha256":"6e7f6fee50697df9e7663a9a1ab3b5af6721791b0a22a5340242a4c0bdb763d7","entries":{"return:4278":"afe1a0bac92a84a4f2e2a72c8f0665aab4f1339f1294893015d3322d14aa1f41","finding:116979":"c9fb97dbec9999b1f99df28499f11bddec95c206a864e2b91de14308b0d02658","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":"d259190a32a9737d3f4b97afcdeaecdfae07e9681edb8ebc1d27dd6d174028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applicability screening of accepted scientific return #4278: 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. Prior assessment return #4285: [{\"target_id\":\"g2-exponent\",\"decision\":\"inapplicable\",\"scope_keys\":[]},{\"target_id\":\"adversarial\",\"decision\":\"applicable\",\"scope_keys\":[]},{\"target_id\":\"formalize\",\"decision\":\"unresolved\",\"scope_keys\":[]},{\"target_id\":\"measure\",\"decision\":\"applicable\",\"scope_keys\":[]},{\"target_id\":\"infinitude\",\"decision\":\"inapplicable\",\"scope_keys\":[]},{\"target_id\":\"finiteness-structure\",\"decision\":\"inapplicable\",\"scope_keys\":[]},{\"target_id\":\"kk-lower-bound\",\"decision\":\"inapplicable\",\"scope_keys\":[]}]. Read its full conditions at GET <project>/return/4285. Reuse unchanged entries; inspect only changed source evidence: finding:116979.\n\nSource snapshot: 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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:\"d5e10a5fc0c931832fd72e6283f9b3151656e4884f36c13e95da3092251597fb\",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/4337/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"32aa1bbb41e64cfae0f110a8f85cd804851dcdf8f84e24a51deb7a09fbf848c5","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}