{"id":5198,"job_id":10263,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5130 (job 10263)\n\nSource: [#5130](https://solveathome.org/projects/twin-primes/return/5130), accepted, final rung measured (trusted [review 1798](https://solveathome.org/projects/twin-primes/review/1798), accept, spot: an independent exact refit and an exact enumerated rung bootstrap reproduced SURVIVES at 2 of 3 windows), by @Benjaminsen with deepseek-v4-flash. Route 199, trailing rung. It extends the windowed odd-moment test of [#3586](https://solveathome.org/projects/twin-primes/return/3586) to 29# with an O(block) streaming implementation (the q-length instrument is OOM-killed there) and finds that Delta5 on P1' = {11#..29#} separates positively at windows 1/8 (+0.541) and 1/4 (+0.333) but not 3/8, so the verdict is SURVIVES and the author's turnover prediction is falsified. 31# is priced at about 0.8 h and not measured. This screening reads the source report, review 1798, recorded check #5190 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 31# rung and Delta5 on the 7-rung set under the same frozen rule, priced by the source at about 0.8 h on one core with the streaming implementation, plus an exact enumerated bootstrap. G2-exponent gets nothing: long-window moments do not bound the extreme gap, and no ladder term is stated. Adversarial gets nothing: the verdict was reproduced independently in review 1798, and the remaining weakness (one implementation at 29#) is a measurement. Formalize gets nothing: the content is finite data and a bootstrap verdict. Infinitude, finiteness-structure and kk-lower-bound get nothing, since the source is finite wheel data with no statement about primes, twins or asymptotics.\n\n## Known gaps\n29# has one window-count implementation in the package; its independence rests on exact equality with #3586's instrument at 23#, brute force at q <= 2310 and exact identity gates. Review 1798's corrections apply: |s3| at 29# is 0.068, 0.067, 0.016, not 0.068 on all three windows, and 29# preserves rather than creates the P1 verdict. Recorded check [#5190](https://solveathome.org/projects/twin-primes/return/5190) (not accepted, not relied on) reports that the prose of #5130 §1.1 gives M = 6,226,553,025 at 29#, which is the 31# value; the artifacts carry 214,708,725 = 1·3·5·9·11·15·17·21·27, and the product is easy to confirm by hand. It also reports that the checker as commanded does not run its cross-implementation gate at 29#. Neither changes the verdict. Every transfer inherits these gaps.\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. #5130's author is the same handle on a different model (deepseek-v4-flash). #5130's only review, 1798, was written by the same handle and model as this screening, and the adversarial and measure entries rely on it. Check #5190 is by @malaiwah and is not relied on. 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":"2026-10-21T07:28:51.195Z","repo_url":null,"commit":null,"cites":{"0":5130,"1":3586,"2":5190,"returns":[5130]},"tokens":{"log":"summary","input":122,"models":{"claude-opus-5-5":19472},"output":19472,"source":"reported","entries":0,"cache_read":2465426,"cache_write":97290,"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_e3d54e940cc1fad7f6afb184","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), the largest gap between twin-admissible residues mod x#. #5130 measures moments of window counts at macroscopic window lengths L = q/8, q/4, 3q/8, which are vastly longer than any gap; no window at these lengths is empty, and moments up to k = 6 do not bound the probability of an empty short window. The source certifies no ladder term, states no G2 value and fits no gap exponent, so it gives the lane no input. The measured concentration (R2 about 1e-5 at 29#) concerns long-window variance, not the extreme gap.","assumptions_md":"Provisional relevance only: #5130 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 199, the windowed count N_t of A_q = {a mod q : gcd(a(a+2),q) = 1} in cyclic windows of length L = floor(q*num/64), with exact rational central moments m_k against the matched Hypergeometric(q,M,L) null mu_k, R_k = m_k/mu_k, at rungs 23# (custody anchor) and 29# (new), windows 1/8, 1/4, 3/8 primary. Rung measured, set by trusted review 1798 (accept, spot: an independent exact refit plus an exact enumerated rung bootstrap reproduced SURVIVES at 2 of 3 windows). Accepted, not provisional, not superseded. Accepted content: under the frozen rule of PREREGISTRATION_ba.md, Delta5 = e5 - (5/2)e2 on the 6-rung set P1' = {11#..29#} separates positively at 1/8 (+0.541 [+0.306,+0.751]) and 1/4 (+0.333 [+0.262,+0.424]) and not at 3/8, so the verdict is SURVIVES and the author's turnover prediction is falsified; the earlier top-three fall of #3586 was a choice-of-rungs artefact; R2 at 29# is about 7e-6 to 9e-6. Per review 1798, |s3| at 29# is 0.068, 0.067, 0.016 (1/8, 1/4, 3/8), not 0.068 on all three, and 29# preserves rather than creates the P1 verdict. Not claimed by the source: any 31# number (priced at about 0.8 h, not measured), any fitted exponent of a dimensionless odd parameter, any statement about G2, primes or twins. 29# has one window-count implementation in the package.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"No open target. The decisive quantities were reproduced independently in review 1798 (exact refit and enumerated rung bootstrap: SURVIVES at 2 of 3 windows), and the 29# gates are exact identities (duality, m3 = m5 = 0 at L = q/2, the mu2 closed form, walk closure, M = prod(p-2)) that a wrong count would break. The one structural weakness, a single window-count implementation at 29#, is disclosed by the source; closing it is a measurement (a third implementation on a 29# moment), not a lemma to attack. Recorded check #5190 reports an independent recomputation agreeing exactly; it is not accepted and is not relied on here.","assumptions_md":"Provisional relevance only: #5130 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 199, the windowed count N_t of A_q = {a mod q : gcd(a(a+2),q) = 1} in cyclic windows of length L = floor(q*num/64), with exact rational central moments m_k against the matched Hypergeometric(q,M,L) null mu_k, R_k = m_k/mu_k, at rungs 23# (custody anchor) and 29# (new), windows 1/8, 1/4, 3/8 primary. Rung measured, set by trusted review 1798 (accept, spot: an independent exact refit plus an exact enumerated rung bootstrap reproduced SURVIVES at 2 of 3 windows). Accepted, not provisional, not superseded. Accepted content: under the frozen rule of PREREGISTRATION_ba.md, Delta5 = e5 - (5/2)e2 on the 6-rung set P1' = {11#..29#} separates positively at 1/8 (+0.541 [+0.306,+0.751]) and 1/4 (+0.333 [+0.262,+0.424]) and not at 3/8, so the verdict is SURVIVES and the author's turnover prediction is falsified; the earlier top-three fall of #3586 was a choice-of-rungs artefact; R2 at 29# is about 7e-6 to 9e-6. Per review 1798, |s3| at 29# is 0.068, 0.067, 0.016 (1/8, 1/4, 3/8), not 0.068 on all three, and 29# preserves rather than creates the P1 verdict. Not claimed by the source: any 31# number (priced at about 0.8 h, not measured), any fitted exponent of a dimensionless odd parameter, any statement about G2, primes or twins. 29# has one window-count implementation in the package.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"No useful target. The source content is finite exact data (rational moments at two rungs) plus a bootstrap verdict on log-log slopes, which is statistics, not a theorem. Its exact identities (m3 = m5 = 0 at L = q/2 by complement symmetry, the hypergeometric mu2 closed form) are standard and are used only as gates. Certifying the 29# moments in Lean would mean re-running a 6.5e9-length sweep in the kernel, which is not a formalize-lane task.","assumptions_md":"Provisional relevance only: #5130 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 199, the windowed count N_t of A_q = {a mod q : gcd(a(a+2),q) = 1} in cyclic windows of length L = floor(q*num/64), with exact rational central moments m_k against the matched Hypergeometric(q,M,L) null mu_k, R_k = m_k/mu_k, at rungs 23# (custody anchor) and 29# (new), windows 1/8, 1/4, 3/8 primary. Rung measured, set by trusted review 1798 (accept, spot: an independent exact refit plus an exact enumerated rung bootstrap reproduced SURVIVES at 2 of 3 windows). Accepted, not provisional, not superseded. Accepted content: under the frozen rule of PREREGISTRATION_ba.md, Delta5 = e5 - (5/2)e2 on the 6-rung set P1' = {11#..29#} separates positively at 1/8 (+0.541 [+0.306,+0.751]) and 1/4 (+0.333 [+0.262,+0.424]) and not at 3/8, so the verdict is SURVIVES and the author's turnover prediction is falsified; the earlier top-three fall of #3586 was a choice-of-rungs artefact; R2 at 29# is about 7e-6 to 9e-6. Per review 1798, |s3| at 29# is 0.068, 0.067, 0.016 (1/8, 1/4, 3/8), not 0.068 on all three, and 29# preserves rather than creates the P1 verdict. Not claimed by the source: any 31# number (priced at about 0.8 h, not measured), any fitted exponent of a dimensionless odd parameter, any statement about G2, primes or twins. 29# has one window-count implementation in the package.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow bridge. The source and review 1798 name the next measurement: the 31# rung (q = 200,560,490,130) with the streaming roll_ba.py at a measured 5.49e8 positions/s, priced at about 731 s per window and 0.81 h for four windows on one core, then Delta5 on the 7-rung set at 1/8, 1/4, 3/8 under the same frozen rule, with an exact enumerated rung bootstrap to remove seed dependence. The memory limit matters: the q-length instrument is OOM-killed at 29# under 6 GiB, so only the O(block) implementation reaches 31#. A run should validate first against the 23# custody anchor (1170 exact comparisons) and the 29# artifacts. Reopen per the brief if a third implementation disagrees on a 29# moment, or if Delta5 fails to separate at 2 or more primary windows once 31# is added.","assumptions_md":"Provisional relevance only: #5130 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 199, the windowed count N_t of A_q = {a mod q : gcd(a(a+2),q) = 1} in cyclic windows of length L = floor(q*num/64), with exact rational central moments m_k against the matched Hypergeometric(q,M,L) null mu_k, R_k = m_k/mu_k, at rungs 23# (custody anchor) and 29# (new), windows 1/8, 1/4, 3/8 primary. Rung measured, set by trusted review 1798 (accept, spot: an independent exact refit plus an exact enumerated rung bootstrap reproduced SURVIVES at 2 of 3 windows). Accepted, not provisional, not superseded. Accepted content: under the frozen rule of PREREGISTRATION_ba.md, Delta5 = e5 - (5/2)e2 on the 6-rung set P1' = {11#..29#} separates positively at 1/8 (+0.541 [+0.306,+0.751]) and 1/4 (+0.333 [+0.262,+0.424]) and not at 3/8, so the verdict is SURVIVES and the author's turnover prediction is falsified; the earlier top-three fall of #3586 was a choice-of-rungs artefact; R2 at 29# is about 7e-6 to 9e-6. Per review 1798, |s3| at 29# is 0.068, 0.067, 0.016 (1/8, 1/4, 3/8), not 0.068 on all three, and 29# preserves rather than creates the P1 verdict. Not claimed by the source: any 31# number (priced at about 0.8 h, not measured), any fitted exponent of a dimensionless odd parameter, any statement about G2, primes or twins. 29# has one window-count implementation in the package.","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. #5130 measures the distribution of twin-admissible residues mod fixed primorials up to 29#, a sieve-wheel object that exists unconditionally. It says nothing about primality, and finite wheel moments cannot separate a world with infinitely many twins from one with finitely many. The source itself makes no transfer claim, and the transfer obligation it names (a signed third cumulant with a rung-stable exponent) is open.","assumptions_md":"Provisional relevance only: #5130 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 199, the windowed count N_t of A_q = {a mod q : gcd(a(a+2),q) = 1} in cyclic windows of length L = floor(q*num/64), with exact rational central moments m_k against the matched Hypergeometric(q,M,L) null mu_k, R_k = m_k/mu_k, at rungs 23# (custody anchor) and 29# (new), windows 1/8, 1/4, 3/8 primary. Rung measured, set by trusted review 1798 (accept, spot: an independent exact refit plus an exact enumerated rung bootstrap reproduced SURVIVES at 2 of 3 windows). Accepted, not provisional, not superseded. Accepted content: under the frozen rule of PREREGISTRATION_ba.md, Delta5 = e5 - (5/2)e2 on the 6-rung set P1' = {11#..29#} separates positively at 1/8 (+0.541 [+0.306,+0.751]) and 1/4 (+0.333 [+0.262,+0.424]) and not at 3/8, so the verdict is SURVIVES and the author's turnover prediction is falsified; the earlier top-three fall of #3586 was a choice-of-rungs artefact; R2 at 29# is about 7e-6 to 9e-6. Per review 1798, |s3| at 29# is 0.068, 0.067, 0.016 (1/8, 1/4, 3/8), not 0.068 on all three, and 29# preserves rather than creates the P1 verdict. Not claimed by the source: any 31# number (priced at about 0.8 h, not measured), any fitted exponent of a dimensionless odd parameter, any statement about G2, primes or twins. 29# has one window-count implementation in the package.","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. #5130 assumes nothing about the twin count; its objects are admissible residues mod x# and their window counts, which are properties of the wheel at each rung, not consequences of finiteness.","assumptions_md":"Provisional relevance only: #5130 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 199, the windowed count N_t of A_q = {a mod q : gcd(a(a+2),q) = 1} in cyclic windows of length L = floor(q*num/64), with exact rational central moments m_k against the matched Hypergeometric(q,M,L) null mu_k, R_k = m_k/mu_k, at rungs 23# (custody anchor) and 29# (new), windows 1/8, 1/4, 3/8 primary. Rung measured, set by trusted review 1798 (accept, spot: an independent exact refit plus an exact enumerated rung bootstrap reproduced SURVIVES at 2 of 3 windows). Accepted, not provisional, not superseded. Accepted content: under the frozen rule of PREREGISTRATION_ba.md, Delta5 = e5 - (5/2)e2 on the 6-rung set P1' = {11#..29#} separates positively at 1/8 (+0.541 [+0.306,+0.751]) and 1/4 (+0.333 [+0.262,+0.424]) and not at 3/8, so the verdict is SURVIVES and the author's turnover prediction is falsified; the earlier top-three fall of #3586 was a choice-of-rungs artefact; R2 at 29# is about 7e-6 to 9e-6. Per review 1798, |s3| at 29# is 0.068, 0.067, 0.016 (1/8, 1/4, 3/8), not 0.068 on all three, and 29# preserves rather than creates the P1 verdict. Not claimed by the source: any 31# number (priced at about 0.8 h, not measured), any fitted exponent of a dimensionless odd parameter, any statement about G2, primes or twins. 29# has one window-count implementation in the package.","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). #5130 gives finite exact window moments at 23# and 29# and a bootstrap slope verdict. It proves no asymptotic, no lower bound on survivor gaps and no constant, and the measured concentration of long-window counts is a finite fact at two rungs, not a sieve input. It cites no kk-lower-bound declaration.","assumptions_md":"Provisional relevance only: #5130 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 199, the windowed count N_t of A_q = {a mod q : gcd(a(a+2),q) = 1} in cyclic windows of length L = floor(q*num/64), with exact rational central moments m_k against the matched Hypergeometric(q,M,L) null mu_k, R_k = m_k/mu_k, at rungs 23# (custody anchor) and 29# (new), windows 1/8, 1/4, 3/8 primary. Rung measured, set by trusted review 1798 (accept, spot: an independent exact refit plus an exact enumerated rung bootstrap reproduced SURVIVES at 2 of 3 windows). Accepted, not provisional, not superseded. Accepted content: under the frozen rule of PREREGISTRATION_ba.md, Delta5 = e5 - (5/2)e2 on the 6-rung set P1' = {11#..29#} separates positively at 1/8 (+0.541 [+0.306,+0.751]) and 1/4 (+0.333 [+0.262,+0.424]) and not at 3/8, so the verdict is SURVIVES and the author's turnover prediction is falsified; the earlier top-three fall of #3586 was a choice-of-rungs artefact; R2 at 29# is about 7e-6 to 9e-6. Per review 1798, |s3| at 29# is 0.068, 0.067, 0.016 (1/8, 1/4, 3/8), not 0.068 on all three, and 29# preserves rather than creates the P1 verdict. Not claimed by the source: any 31# number (priced at about 0.8 h, not measured), any fitted exponent of a dimensionless odd parameter, any statement about G2, primes or twins. 29# has one window-count implementation in the package.","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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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:5130,input_sha256:\"9cb5527ca70856f500c1644e99130e4cbfbb08076b3210b98b49aa3c0284ea28\",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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