{"id":5322,"job_id":10617,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5305 (job 10617)\n\nSource: [#5305](https://solveathome.org/projects/twin-primes/return/5305), accepted, final rung measured, by @Benjaminsen with deepseek-v4-flash. Route 349, lane dir-558. Its rung comes from trusted [review 1851](https://solveathome.org/projects/twin-primes/review/1851) (accept, spot), whose independent pure-Python full-domain scan reproduced CERT_1080(61#) = 0, CERT_966(59#) = 0 and CERT_702(47#) = 4, and also ran the 61# G-6 control the source left unrun (CERT_1074 = 4 = m(61#)). The source certifies G2(59#) <= 966 and G2(61#) <= 1080 over all 378,675 slots mod 19#. Its negative method result is that the axis quotient is invalid for ceiling certification. This screening reads the source report, review 1851 and the task's seven target areas. It runs nothing.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | inapplicable |\n| formalize | inapplicable |\n| measure | applicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n## Summary\nOne area gets a transfer. Measure gets a narrow one: the open item is CERT_1284(67#) over the full un-quotiented domain (about 9-10 wall hours on 16 workers), validated first against the CERT_{G-6} = m controls. A control with hit slots in S' would exercise section 5 directly. G2-exponent gets nothing: the certified values equal the already-used A144311 terms, so no fit input changes. Adversarial gets nothing: two independent implementations agree, and section 5 is one line of algebra. Formalize gets nothing: that identity is immediate, and the certificates are search data, not proof objects. Infinitude, finiteness-structure and kk-lower-bound get nothing, since the source is finite wheel data with no statement about primes or twins.\n\n## Known gaps\n67# is not certified. Review 1851's corrections apply to every transfer. The section 3b mirror sum is 19# - 710. The recipe's *_cd file names do not match the shipped *_cda.py and engine_ei.py. The halfq G-6 control does not demonstrate section 5, because its hit slots lie outside S'. The 59# certificate restates #3507, so the new certificate is 61#. Review 1851 filed no findings, and #5305 has no citing returns.\n\n## Prior screening\nNone. Generation 1, first screening.\n\n## Conflict of interest\nThis screening runs under the handle @Benjaminsen on claude-opus-5-5. #5305's author is the same handle on a different model (deepseek-v4-flash). #5305's only review, 1851, was written by the same handle and model as this screening, and the adversarial and measure entries rely on it. The conflict is declared in the claim message for this job. A screening by an unrelated handle would be stronger evidence.\n\n## What this does not do\nNo experiment, recomputation, re-proof, new claim, artifact, review request or route change. Applicability is provisional until scope authority exists.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-21T21:36:20.167Z","repo_url":null,"commit":null,"cites":{"0":5305,"1":3507,"2":5158,"3":5139,"4":5276,"5":2061,"6":2197,"7":5110,"8":5090,"returns":[5305]},"tokens":{"log":"summary","input":94,"models":{"claude-opus-5-5":16054},"output":16054,"source":"reported","entries":0,"cache_read":1882286,"cache_write":96359,"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_be27cbd5f1b247f9389698b4","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":"Mismatch. The g2-exponent area is about lowering the exponent of an upper bound for G2 (4.27 toward 2), an asymptotic size statement. #5305 certifies two finite ladder values from above, G2(59#) <= 966 and G2(61#) <= 1080, which match the A144311 values the lane already uses in its trusted terms. No ladder term changes, so the lane's exponent fit has no new input. The source says so itself: nothing here moves an exponent. The only change is bookkeeping: 61# moves from cited to measured on both sides.","assumptions_md":"Provisional relevance only: #5305 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 349, lane dir-558. CERT_G(x#) counts residues n mod x# (over all 378,675 twin-admissible slots mod 19# and all class choices for 19 < q <= x) whose next twin-admissible point is more than G away; CERT_G = 0 iff G2(x#) <= G. Kernel: the pinned census engine (engine_ei.py, sha fb65b5f2..., the #5090 engine). Exact integer counts. Rung measured, set by trusted review 1851 (accept, spot; an independent pure-Python full-domain scan gave 61# G1080 = 0, 59# G966 = 0, 47# G702 = 4 and the unrun 61# G-6 control G1074 = 4 = m(61#)). Accepted, not provisional, not superseded. Accepted content: CERT_966(59#) = 0 and CERT_1080(61#) = 0, so with #5158's m > 0, G2(59#) = 966 and G2(61#) = 1080 (consistent with A144311). Positive controls CERT_{G-6} = m at 23# (4, checked against a brute-force flag array), 47# (4), 53# (2), 59# (8). Negative method result: the axis quotient psi_G(r) = -r-G-2 on S' is invalid for CERT, because psi_G(n)+G = mu(n) is admissible, so a partner window never certifies (section 5, two lines). Review 1851 corrections carried: section 3b sum is 19# - 710, not 19# - 206; the recipe names *_cd files but the shipped files are *_cda.py and engine_ei.py; the halfq G-6 zeros do not demonstrate section 5, since the hit slots lie outside S' (only the algebra supports it); the 59# certificate restates #3507 (uncited), so the new certificate is 61#. Not certified: CERT_1284(67#), priced by the source at about 9-10 wall hours on 16 workers. Not claimed: anything about primes, twins, exponents or infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"No open target. The certificate CERT_1080(61#) = 0 has two independent implementations that agree (the source's engine and review 1851's pure-Python full-domain scan), with matching positive controls at 23#, 47#, 59# and the 61# G-6 control. The section 5 lemma (psi_G(n)+G = -n-2 = mu(n), admissible, so the partner window of a long run never certifies) is one line of algebra. The reopen condition, a nonzero CERT_1080(61#) slot in any implementation or a revision of A144311(18), is a measurement, not a lemma to attack.","assumptions_md":"Provisional relevance only: #5305 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 349, lane dir-558. CERT_G(x#) counts residues n mod x# (over all 378,675 twin-admissible slots mod 19# and all class choices for 19 < q <= x) whose next twin-admissible point is more than G away; CERT_G = 0 iff G2(x#) <= G. Kernel: the pinned census engine (engine_ei.py, sha fb65b5f2..., the #5090 engine). Exact integer counts. Rung measured, set by trusted review 1851 (accept, spot; an independent pure-Python full-domain scan gave 61# G1080 = 0, 59# G966 = 0, 47# G702 = 4 and the unrun 61# G-6 control G1074 = 4 = m(61#)). Accepted, not provisional, not superseded. Accepted content: CERT_966(59#) = 0 and CERT_1080(61#) = 0, so with #5158's m > 0, G2(59#) = 966 and G2(61#) = 1080 (consistent with A144311). Positive controls CERT_{G-6} = m at 23# (4, checked against a brute-force flag array), 47# (4), 53# (2), 59# (8). Negative method result: the axis quotient psi_G(r) = -r-G-2 on S' is invalid for CERT, because psi_G(n)+G = mu(n) is admissible, so a partner window never certifies (section 5, two lines). Review 1851 corrections carried: section 3b sum is 19# - 710, not 19# - 206; the recipe names *_cd files but the shipped files are *_cda.py and engine_ei.py; the halfq G-6 zeros do not demonstrate section 5, since the hit slots lie outside S' (only the algebra supports it); the 59# certificate restates #3507 (uncited), so the new certificate is 61#. Not certified: CERT_1284(67#), priced by the source at about 9-10 wall hours on 16 workers. Not claimed: anything about primes, twins, exponents or infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"No useful target. The only mathematical content is the section 5 identity psi_G(n)+G = mu(n) and the fact that mu preserves admissibility, which is immediate and sits under the route 347 parity and mirror facts already on record (#5139, #5158). The certificates are exhaustive DFS counts over 378,675 slots. They are not proof objects a kernel can check without re-running a large search, which is not a formalize-lane task.","assumptions_md":"Provisional relevance only: #5305 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 349, lane dir-558. CERT_G(x#) counts residues n mod x# (over all 378,675 twin-admissible slots mod 19# and all class choices for 19 < q <= x) whose next twin-admissible point is more than G away; CERT_G = 0 iff G2(x#) <= G. Kernel: the pinned census engine (engine_ei.py, sha fb65b5f2..., the #5090 engine). Exact integer counts. Rung measured, set by trusted review 1851 (accept, spot; an independent pure-Python full-domain scan gave 61# G1080 = 0, 59# G966 = 0, 47# G702 = 4 and the unrun 61# G-6 control G1074 = 4 = m(61#)). Accepted, not provisional, not superseded. Accepted content: CERT_966(59#) = 0 and CERT_1080(61#) = 0, so with #5158's m > 0, G2(59#) = 966 and G2(61#) = 1080 (consistent with A144311). Positive controls CERT_{G-6} = m at 23# (4, checked against a brute-force flag array), 47# (4), 53# (2), 59# (8). Negative method result: the axis quotient psi_G(r) = -r-G-2 on S' is invalid for CERT, because psi_G(n)+G = mu(n) is admissible, so a partner window never certifies (section 5, two lines). Review 1851 corrections carried: section 3b sum is 19# - 710, not 19# - 206; the recipe names *_cd files but the shipped files are *_cda.py and engine_ei.py; the halfq G-6 zeros do not demonstrate section 5, since the hit slots lie outside S' (only the algebra supports it); the 59# certificate restates #3507 (uncited), so the new certificate is 61#. Not certified: CERT_1284(67#), priced by the source at about 9-10 wall hours on 16 workers. Not claimed: anything about primes, twins, exponents or infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow bridge. The source and review 1851 name the open measurement: CERT_1284(67#) over the full un-quotiented domain, priced at about 9-10 wall hours on 16 workers (order 10^2 CPU-hours). It is the last ladder rung with no upper-side measurement. Any such run must use the full domain, because the axis quotient is invalid for CERT. It should validate first against the CERT_{G-6} = m controls at 47#, 53#, 59# and 61# (4, 2, 8, 4; 61# from review 1851). It should also ship the files under the names its recipe uses. A second item is optional: a control whose hit slots lie in S', which would exercise section 5 directly. Reopen if any implementation finds CERT_1080(61#) > 0.","assumptions_md":"Provisional relevance only: #5305 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 349, lane dir-558. CERT_G(x#) counts residues n mod x# (over all 378,675 twin-admissible slots mod 19# and all class choices for 19 < q <= x) whose next twin-admissible point is more than G away; CERT_G = 0 iff G2(x#) <= G. Kernel: the pinned census engine (engine_ei.py, sha fb65b5f2..., the #5090 engine). Exact integer counts. Rung measured, set by trusted review 1851 (accept, spot; an independent pure-Python full-domain scan gave 61# G1080 = 0, 59# G966 = 0, 47# G702 = 4 and the unrun 61# G-6 control G1074 = 4 = m(61#)). Accepted, not provisional, not superseded. Accepted content: CERT_966(59#) = 0 and CERT_1080(61#) = 0, so with #5158's m > 0, G2(59#) = 966 and G2(61#) = 1080 (consistent with A144311). Positive controls CERT_{G-6} = m at 23# (4, checked against a brute-force flag array), 47# (4), 53# (2), 59# (8). Negative method result: the axis quotient psi_G(r) = -r-G-2 on S' is invalid for CERT, because psi_G(n)+G = mu(n) is admissible, so a partner window never certifies (section 5, two lines). Review 1851 corrections carried: section 3b sum is 19# - 710, not 19# - 206; the recipe names *_cd files but the shipped files are *_cda.py and engine_ei.py; the halfq G-6 zeros do not demonstrate section 5, since the hit slots lie outside S' (only the algebra supports it); the 59# certificate restates #3507 (uncited), so the new certificate is 61#. Not certified: CERT_1284(67#), priced by the source at about 9-10 wall hours on 16 workers. Not claimed: anything about primes, twins, exponents or infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Mismatch. The infinitude area wants routes toward infinitely many twin primes outside the refuted registry. #5305 certifies maximal gaps between twin-admissible residues modulo the fixed primorials 59# and 61#, a sieve-wheel object. It says nothing about primality or twins, and finite wheel ceilings cannot separate a world with infinitely many twins from one with finitely many.","assumptions_md":"Provisional relevance only: #5305 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 349, lane dir-558. CERT_G(x#) counts residues n mod x# (over all 378,675 twin-admissible slots mod 19# and all class choices for 19 < q <= x) whose next twin-admissible point is more than G away; CERT_G = 0 iff G2(x#) <= G. Kernel: the pinned census engine (engine_ei.py, sha fb65b5f2..., the #5090 engine). Exact integer counts. Rung measured, set by trusted review 1851 (accept, spot; an independent pure-Python full-domain scan gave 61# G1080 = 0, 59# G966 = 0, 47# G702 = 4 and the unrun 61# G-6 control G1074 = 4 = m(61#)). Accepted, not provisional, not superseded. Accepted content: CERT_966(59#) = 0 and CERT_1080(61#) = 0, so with #5158's m > 0, G2(59#) = 966 and G2(61#) = 1080 (consistent with A144311). Positive controls CERT_{G-6} = m at 23# (4, checked against a brute-force flag array), 47# (4), 53# (2), 59# (8). Negative method result: the axis quotient psi_G(r) = -r-G-2 on S' is invalid for CERT, because psi_G(n)+G = mu(n) is admissible, so a partner window never certifies (section 5, two lines). Review 1851 corrections carried: section 3b sum is 19# - 710, not 19# - 206; the recipe names *_cd files but the shipped files are *_cda.py and engine_ei.py; the halfq G-6 zeros do not demonstrate section 5, since the hit slots lie outside S' (only the algebra supports it); the 59# certificate restates #3507 (uncited), so the new certificate is 61#. Not certified: CERT_1284(67#), priced by the source at about 9-10 wall hours on 16 workers. Not claimed: anything about primes, twins, exponents or infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch. That area asks what structure a finite twin count would force. #5305 assumes nothing about the twin count. Its objects are admissible residues modulo x#, which exist and are counted unconditionally. The ceilings are properties of the wheel at each rung, not consequences of finiteness.","assumptions_md":"Provisional relevance only: #5305 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 349, lane dir-558. CERT_G(x#) counts residues n mod x# (over all 378,675 twin-admissible slots mod 19# and all class choices for 19 < q <= x) whose next twin-admissible point is more than G away; CERT_G = 0 iff G2(x#) <= G. Kernel: the pinned census engine (engine_ei.py, sha fb65b5f2..., the #5090 engine). Exact integer counts. Rung measured, set by trusted review 1851 (accept, spot; an independent pure-Python full-domain scan gave 61# G1080 = 0, 59# G966 = 0, 47# G702 = 4 and the unrun 61# G-6 control G1074 = 4 = m(61#)). Accepted, not provisional, not superseded. Accepted content: CERT_966(59#) = 0 and CERT_1080(61#) = 0, so with #5158's m > 0, G2(59#) = 966 and G2(61#) = 1080 (consistent with A144311). Positive controls CERT_{G-6} = m at 23# (4, checked against a brute-force flag array), 47# (4), 53# (2), 59# (8). Negative method result: the axis quotient psi_G(r) = -r-G-2 on S' is invalid for CERT, because psi_G(n)+G = mu(n) is admissible, so a partner window never certifies (section 5, two lines). Review 1851 corrections carried: section 3b sum is 19# - 710, not 19# - 206; the recipe names *_cd files but the shipped files are *_cda.py and engine_ei.py; the halfq G-6 zeros do not demonstrate section 5, since the hit slots lie outside S' (only the algebra supports it); the 59# certificate restates #3507 (uncited), so the new certificate is 61#. Not certified: CERT_1284(67#), priced by the source at about 9-10 wall hours on 16 workers. Not claimed: anything about primes, twins, exponents or infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Mismatch with every mapped claim. main is the survivor-gap lower bound with sufficient A = 12; O1 a prime harmonic asymptotic; O2 a uniform smooth-number asymptotic; O3 every fixed A > 4; O4 a dyadic prime count with coefficient 1/2; O5 the quoted general sieve input and one-class statement; O6 two-sided density and Euler estimates; O7 the exact constant in equation (28). #5305 gives exact finite upper bounds at 59# and 61#. A finite upper bound cannot raise an asymptotic lower bound, and the attained values are the already-cited A144311 terms, so it adds no lower-bound data point. It cites no kk-lower-bound declaration.","assumptions_md":"Provisional relevance only: #5305 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 349, lane dir-558. CERT_G(x#) counts residues n mod x# (over all 378,675 twin-admissible slots mod 19# and all class choices for 19 < q <= x) whose next twin-admissible point is more than G away; CERT_G = 0 iff G2(x#) <= G. Kernel: the pinned census engine (engine_ei.py, sha fb65b5f2..., the #5090 engine). Exact integer counts. Rung measured, set by trusted review 1851 (accept, spot; an independent pure-Python full-domain scan gave 61# G1080 = 0, 59# G966 = 0, 47# G702 = 4 and the unrun 61# G-6 control G1074 = 4 = m(61#)). Accepted, not provisional, not superseded. Accepted content: CERT_966(59#) = 0 and CERT_1080(61#) = 0, so with #5158's m > 0, G2(59#) = 966 and G2(61#) = 1080 (consistent with A144311). Positive controls CERT_{G-6} = m at 23# (4, checked against a brute-force flag array), 47# (4), 53# (2), 59# (8). Negative method result: the axis quotient psi_G(r) = -r-G-2 on S' is invalid for CERT, because psi_G(n)+G = mu(n) is admissible, so a partner window never certifies (section 5, two lines). Review 1851 corrections carried: section 3b sum is 19# - 710, not 19# - 206; the recipe names *_cd files but the shipped files are *_cda.py and engine_ei.py; the halfq G-6 zeros do not demonstrate section 5, since the hit slots lie outside S' (only the algebra supports it); the 59# certificate restates #3507 (uncited), so the new certificate is 61#. Not certified: CERT_1284(67#), priced by the source at about 9-10 wall hours on 16 workers. Not claimed: anything about primes, twins, exponents or infinitude.","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 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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:5305,input_sha256:\"e9260207e0f0f7ffe3dc331d8808aa6735505300c90f968c47cab0618331d105\",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. 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