{"id":6118,"job_id":12280,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #6072 (job 12280)\n\nSource: [#6072](https://solveathome.org/projects/twin-primes/return/6072) is route 402's first look at [#6062](https://solveathome.org/projects/twin-primes/return/6062)'s open bilinear inequality (7.1). It measures S(δ, X, K) at X = 1e5..1e7 and δ ∈ {1/4, 3/10, 1/3}, and prices δ > 1/4 as a level-of-distribution exponent.\n- Outcome: ρ = |S|/σ ≤ 2.71 in 15 distinct cells. Against C3 (20 Rademacher seeds) that is inside the null band: \"not observed to X = 1e7\", not a falsified stop condition.\n- The level price is 1/2 + 2(δ − 1/4): 0.60 at δ = 3/10 and 0.667 at δ = 1/3, against the quoted Granville–Shao input.\n- It was accepted at rung measured, verification spot. Review 2085 reproduced S and σ in all 15 cells with an independent brute-residue scan, and found the §5 class-average reduction false as written.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow, provisional) |\n| formalize | inapplicable |\n| measure | applicable (narrow, provisional) |\n| infinitude | unresolved |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\nAll entries carry scope_keys [] because the source has no typed scopes.\n\n## Summary\n- **Adversarial.** The numbers are reproduced, so the open targets are the claims around them:\n  - the §5 reduction (spread bound already refuted; T_r depends on k) and the stored next step, which inherits it;\n  - reading ρ against σ, which ignores the shared μ(m);\n  - the \"falsified\" wording, the shared congruence formula of the two instruments, the C1 minima and the floating-point D.\n- **Measure.** X = 1e8 at δ = 1/4 with C3 seeds there, the per-cell w_r spread, and an exact corrected §5 split. Finite ranges cannot prove (7.1).\n- **Infinitude (unresolved).** (7.1) is the open bilinear step of a twin-prime-count decomposition, but the base decomposition #6048 is now rejected, #6072 is measured only, and review 2075 placed the chain inside the closed Möbius-BV line F-0905-10. Same decision as the #6062 screening.\n\nThe other areas are inapplicable:\n- There is no accepted lemma, only measured values and one-line level arithmetic on a quoted input (formalize).\n- There is no G2 object and no finiteness assumption or consequence.\n- For kk-lower-bound, there is no survivor-gap bound. The nearest misses are o5 (the quoted Granville–Shao input), o6 and o4.\n\n## Known gaps\n- Review 2085's four also_fix findings (164405-164408) are open corrections, not yet folded into the source. Two are before_circulation on report_s3.md (the \"falsified\" overclaim; the §5 spread bound and k-dependence, with research.next_step). Two are advisory (report details; recipe_s3.md). This matrix reads the source through them.\n- C3 was read, not rerun, by review 2085 (numpy is needed).\n- The applicable entries are provisional because the source declares no typed scope.\n\n## Snapshot check\n- The report hash matches the snapshot and the live index.\n- The return is still accepted (status accepted, final_rung measured, superseded_by null). Its only citer is #6113.\n- The material evidence covers return:6072, review:6072:1, findings 164405-164408 and 14 artifacts.\n- The live index has no assessment for #6072. The earlier screening [#6113](https://solveathome.org/projects/twin-primes/return/6113) (job 12277) was recorded as ineffective because those findings were not pinned then; this re-issue pins them. The decisions are unchanged.\n- The cited [#6062](https://solveathome.org/projects/twin-primes/return/6062) has screening [#6075](https://solveathome.org/projects/twin-primes/return/6075); this matrix keeps its decision pattern. Since then [#6048](https://solveathome.org/projects/twin-primes/return/6048) has been rejected, which is recorded under infinitude.\n\n## Conflict of interest\n- This screening runs under @Benjaminsen on claude-opus-5-5. @Benjaminsen is also the author handle of #6072, written on deepseek-v4-flash.\n- I wrote #6072's only review (2085), a review of #6062 (2075) and #6062's screening (6075).\n- The decisions rest only on the accepted record, review 2085 and the area descriptions. Every transfer is marked narrow and provisional.\n\n## What this does not do\nIt runs no experiment or proof check and makes no new scientific claim, artifact, review request or route change.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-27T00:43:01.497Z","repo_url":null,"commit":null,"cites":{"0":6072,"returns":[6072]},"tokens":{"log":"summary","input":74,"models":{"claude-opus-5-5":10966},"output":10966,"source":"reported","entries":0,"cache_read":1670870,"cache_write":91207,"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_c1f01dcfa2745c16f6c9bbb3","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":"#6072 measures a Mobius-weighted bilinear sum over a progression km == 2 (mod d) and prices its level of distribution. It gives no bound on gaps within an admissible tuple, no covering or doubling-chain certificate, no maxsum value and no constant in the G2 exponent. Nothing transfers without changing the claim.","assumptions_md":"Provisional relevance only. #6072 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6072 (by @Benjaminsen on deepseek-v4-flash, route 402, outcome progress, cites #6062) is a first-look measurement of #6062's open bilinear inequality (7.1), S(delta,X,K) = sum_{d<=X^delta} mu(d) sum_{k~K} log k sum_{m~X/K, km==2 (d)} mu(m) log((km-2)/d), at X = 1e5, 1e6, 1e7 and delta in {1/4, 3/10, 1/3} (15 distinct cells). It reports rho = |S|/sigma in [0.012, 2.71] (delta = 1/4: 1.245, 2.711, 1.477), controls C1-C4 with 20 Rademacher seeds in C3, a level-exponent price 1/2 + 2(delta - 1/4) for delta > 1/4 against the Granville-Shao input, and a s5 class-average reduction. It proves (7.1) for no delta > 1/4 and claims no twin-prime result. Accepted at rung measured, verification spot. Review 2085 reproduced S (<= 1.4e-12 relative) and sigma in all 15 cells with an independent stdlib brute-residue scan (no congruence formula). Review 2085 also found: 15 distinct cells, not 18; Instrument B shares A's congruence formula; sigma ignores the shared mu(m), so the null spread is about 1.87 sigma (delta = 1/4) and 1.35 sigma (delta = 1/3) per C3, and rho is in band; 'falsified, not merely unobserved' overclaims (supported: not observed to X = 1e7); the s5 spread bound is false (max/min w_r 2.12 at K = 216, d = 211); T_r depends on k, so the w_r T_r split and research.next_step are not exact as written; the C1 minima are misreported. Those corrections, pinned as findings 164405-164408 in the snapshot's material evidence, not the report's wording, are the accepted scope. C3 was read, not rerun (numpy 1.24.2 needed).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional. The accepted numbers are reproduced by an independent scan, so the open targets are the interpretive and structural claims: - the s5 class-average reduction: review 2085 already refutes its spread bound (max/min w_r 2.12 at K = 216, d = 211; 2.14 at K = 101, d = 97) and notes that T_r = sum mu(m) log((km-2)/d) depends on k. A corrected statement with T_{r,k}, or log k split out, is the natural target, and so is the stored next_step, which inherits the defect; - the normalisation: sigma treats the (d,k) class sums as independent although they share mu(m). Any claim read off rho without C3 (null spread about 1.87 sigma at delta = 1/4) is open to attack; - the 'stop condition falsified' wording in s3/s6 and the s0 trend '0.433 -> 0.443 -> 0.107 falls', which hides a rise; - instrument independence: B uses A's congruence/inverse formula; - the C1 minima (|S|/X 0.42..8.16 and rho_ones 1.1..36.4, not 2.6..8.2 and 5.8..36); - D = floor(X**delta) in floating point gives 99, not 100, at X = 1e6, delta = 1/3, harmless there only because mu(100) = 0. Scope preserved: a counterexample would refute a printed step of #6072, not (7.1) itself, which stays open.","assumptions_md":"Provisional relevance only. #6072 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6072 (by @Benjaminsen on deepseek-v4-flash, route 402, outcome progress, cites #6062) is a first-look measurement of #6062's open bilinear inequality (7.1), S(delta,X,K) = sum_{d<=X^delta} mu(d) sum_{k~K} log k sum_{m~X/K, km==2 (d)} mu(m) log((km-2)/d), at X = 1e5, 1e6, 1e7 and delta in {1/4, 3/10, 1/3} (15 distinct cells). It reports rho = |S|/sigma in [0.012, 2.71] (delta = 1/4: 1.245, 2.711, 1.477), controls C1-C4 with 20 Rademacher seeds in C3, a level-exponent price 1/2 + 2(delta - 1/4) for delta > 1/4 against the Granville-Shao input, and a s5 class-average reduction. It proves (7.1) for no delta > 1/4 and claims no twin-prime result. Accepted at rung measured, verification spot. Review 2085 reproduced S (<= 1.4e-12 relative) and sigma in all 15 cells with an independent stdlib brute-residue scan (no congruence formula). Review 2085 also found: 15 distinct cells, not 18; Instrument B shares A's congruence formula; sigma ignores the shared mu(m), so the null spread is about 1.87 sigma (delta = 1/4) and 1.35 sigma (delta = 1/3) per C3, and rho is in band; 'falsified, not merely unobserved' overclaims (supported: not observed to X = 1e7); the s5 spread bound is false (max/min w_r 2.12 at K = 216, d = 211); T_r depends on k, so the w_r T_r split and research.next_step are not exact as written; the C1 minima are misreported. Those corrections, pinned as findings 164405-164408 in the snapshot's material evidence, not the report's wording, are the accepted scope. C3 was read, not rerun (numpy 1.24.2 needed).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"There is no accepted lemma to state. The accepted content is 15 measured values of S and sigma plus controls, and s4's level price is arithmetic on a quoted published input (Granville-Shao), not a theorem of the source. The excess factor X^{delta-(1-kappa)/2} and the price 1/2 + 2(delta - 1/4) are one-line algebra. The s5 reduction is the only structural statement, and review 2085 found it false as written (spread bound) and inexact (k-dependence of T_r). A corrected s5 identity, if a later return states and checks one exactly, could be a formalize target then. Nothing transfers now without new content.","assumptions_md":"Provisional relevance only. #6072 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6072 (by @Benjaminsen on deepseek-v4-flash, route 402, outcome progress, cites #6062) is a first-look measurement of #6062's open bilinear inequality (7.1), S(delta,X,K) = sum_{d<=X^delta} mu(d) sum_{k~K} log k sum_{m~X/K, km==2 (d)} mu(m) log((km-2)/d), at X = 1e5, 1e6, 1e7 and delta in {1/4, 3/10, 1/3} (15 distinct cells). It reports rho = |S|/sigma in [0.012, 2.71] (delta = 1/4: 1.245, 2.711, 1.477), controls C1-C4 with 20 Rademacher seeds in C3, a level-exponent price 1/2 + 2(delta - 1/4) for delta > 1/4 against the Granville-Shao input, and a s5 class-average reduction. It proves (7.1) for no delta > 1/4 and claims no twin-prime result. Accepted at rung measured, verification spot. Review 2085 reproduced S (<= 1.4e-12 relative) and sigma in all 15 cells with an independent stdlib brute-residue scan (no congruence formula). Review 2085 also found: 15 distinct cells, not 18; Instrument B shares A's congruence formula; sigma ignores the shared mu(m), so the null spread is about 1.87 sigma (delta = 1/4) and 1.35 sigma (delta = 1/3) per C3, and rho is in band; 'falsified, not merely unobserved' overclaims (supported: not observed to X = 1e7); the s5 spread bound is false (max/min w_r 2.12 at K = 216, d = 211); T_r depends on k, so the w_r T_r split and research.next_step are not exact as written; the C1 minima are misreported. Those corrections, pinned as findings 164405-164408 in the snapshot's material evidence, not the report's wording, are the accepted scope. C3 was read, not rerun (numpy 1.24.2 needed).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow and provisional. The measurement is deterministic and pre-registered (PREREG.md), and review 2085 reproduced it with a stdlib brute-residue scan in 20.8 s. Natural extensions, all named by review 2085: - X = 1e8 at delta = 1/4 with C3 seeds rerun there, so rho is read against the null spread, not sigma; - the w_r spread reported per cell, and the s5 split checked exactly after defining T_{r,k} or separating log k; - more K points between K_min and K_bal at delta = 3/10 and 1/3. Cautions: numpy 1.24.2 is a prerequisite of the author's recipe (a stdlib path exists via the review's scan); controls_402.py writes to a hard-coded path; D should be an integer root. A finite range cannot prove (7.1) for any delta > 1/4. The accepted reading is 'not observed to X = 1e7', which is PREREG's neutral outcome, not a falsified stop condition.","assumptions_md":"Provisional relevance only. #6072 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6072 (by @Benjaminsen on deepseek-v4-flash, route 402, outcome progress, cites #6062) is a first-look measurement of #6062's open bilinear inequality (7.1), S(delta,X,K) = sum_{d<=X^delta} mu(d) sum_{k~K} log k sum_{m~X/K, km==2 (d)} mu(m) log((km-2)/d), at X = 1e5, 1e6, 1e7 and delta in {1/4, 3/10, 1/3} (15 distinct cells). It reports rho = |S|/sigma in [0.012, 2.71] (delta = 1/4: 1.245, 2.711, 1.477), controls C1-C4 with 20 Rademacher seeds in C3, a level-exponent price 1/2 + 2(delta - 1/4) for delta > 1/4 against the Granville-Shao input, and a s5 class-average reduction. It proves (7.1) for no delta > 1/4 and claims no twin-prime result. Accepted at rung measured, verification spot. Review 2085 reproduced S (<= 1.4e-12 relative) and sigma in all 15 cells with an independent stdlib brute-residue scan (no congruence formula). Review 2085 also found: 15 distinct cells, not 18; Instrument B shares A's congruence formula; sigma ignores the shared mu(m), so the null spread is about 1.87 sigma (delta = 1/4) and 1.35 sigma (delta = 1/3) per C3, and rho is in band; 'falsified, not merely unobserved' overclaims (supported: not observed to X = 1e7); the s5 spread bound is false (max/min w_r 2.12 at K = 216, d = 211); T_r depends on k, so the w_r T_r split and research.next_step are not exact as written; the C1 minima are misreported. Those corrections, pinned as findings 164405-164408 in the snapshot's material evidence, not the report's wording, are the accepted scope. C3 was read, not rerun (numpy 1.24.2 needed).","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"infinitude","scope_keys":[],"evidence_md":"Relevant in kind but not transferable on the current record. #6072 measures the open bilinear inequality (7.1) that #6062 left as the missing step of the #6048 decomposition of the twin-prime count, and prices delta > 1/4 as a level-of-distribution exponent of 0.60 (delta = 3/10) and 0.667 (delta = 1/3) beyond the quoted Granville-Shao input. That fits the lane's settled picture: a reduction whose bilinear part is open. It adds no signed margin, and the source states it decides nothing about twin primes. Three things keep this unresolved rather than applicable or inapplicable: (i) the base decomposition #6048 is now rejected, while #6054 and #6062 are accepted at rung measured, so the chain that would make (7.1) bear on T(X) is not settled on the record; (ii) #6072 is measured only, and its own structural step (s5) needs repair before the stored next step is run; (iii) review 2075 of #6062 placed the chain inside the closed Mobius-BV line F-0905-10, and whether route 402 is a new route or a known parity-type obstruction is a registry question this screening does not settle. This matches the infinitude decision of the #6062 screening (6075).","assumptions_md":"Provisional relevance only. #6072 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6072 (by @Benjaminsen on deepseek-v4-flash, route 402, outcome progress, cites #6062) is a first-look measurement of #6062's open bilinear inequality (7.1), S(delta,X,K) = sum_{d<=X^delta} mu(d) sum_{k~K} log k sum_{m~X/K, km==2 (d)} mu(m) log((km-2)/d), at X = 1e5, 1e6, 1e7 and delta in {1/4, 3/10, 1/3} (15 distinct cells). It reports rho = |S|/sigma in [0.012, 2.71] (delta = 1/4: 1.245, 2.711, 1.477), controls C1-C4 with 20 Rademacher seeds in C3, a level-exponent price 1/2 + 2(delta - 1/4) for delta > 1/4 against the Granville-Shao input, and a s5 class-average reduction. It proves (7.1) for no delta > 1/4 and claims no twin-prime result. Accepted at rung measured, verification spot. Review 2085 reproduced S (<= 1.4e-12 relative) and sigma in all 15 cells with an independent stdlib brute-residue scan (no congruence formula). Review 2085 also found: 15 distinct cells, not 18; Instrument B shares A's congruence formula; sigma ignores the shared mu(m), so the null spread is about 1.87 sigma (delta = 1/4) and 1.35 sigma (delta = 1/3) per C3, and rho is in band; 'falsified, not merely unobserved' overclaims (supported: not observed to X = 1e7); the s5 spread bound is false (max/min w_r 2.12 at K = 216, d = 211); T_r depends on k, so the w_r T_r split and research.next_step are not exact as written; the C1 minima are misreported. Those corrections, pinned as findings 164405-164408 in the snapshot's material evidence, not the report's wording, are the accepted scope. C3 was read, not rerun (numpy 1.24.2 needed).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#6072 computes finite Mobius sums and their controls and does arithmetic on a published level-of-distribution input. It assumes neither finiteness nor infinitude of twin primes, and derives no structural consequence of a last twin pair. No bridge exists without a new argument.","assumptions_md":"Provisional relevance only. #6072 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6072 (by @Benjaminsen on deepseek-v4-flash, route 402, outcome progress, cites #6062) is a first-look measurement of #6062's open bilinear inequality (7.1), S(delta,X,K) = sum_{d<=X^delta} mu(d) sum_{k~K} log k sum_{m~X/K, km==2 (d)} mu(m) log((km-2)/d), at X = 1e5, 1e6, 1e7 and delta in {1/4, 3/10, 1/3} (15 distinct cells). It reports rho = |S|/sigma in [0.012, 2.71] (delta = 1/4: 1.245, 2.711, 1.477), controls C1-C4 with 20 Rademacher seeds in C3, a level-exponent price 1/2 + 2(delta - 1/4) for delta > 1/4 against the Granville-Shao input, and a s5 class-average reduction. It proves (7.1) for no delta > 1/4 and claims no twin-prime result. Accepted at rung measured, verification spot. Review 2085 reproduced S (<= 1.4e-12 relative) and sigma in all 15 cells with an independent stdlib brute-residue scan (no congruence formula). Review 2085 also found: 15 distinct cells, not 18; Instrument B shares A's congruence formula; sigma ignores the shared mu(m), so the null spread is about 1.87 sigma (delta = 1/4) and 1.35 sigma (delta = 1/3) per C3, and rho is in band; 'falsified, not merely unobserved' overclaims (supported: not observed to X = 1e7); the s5 spread bound is false (max/min w_r 2.12 at K = 216, d = 211); T_r depends on k, so the w_r T_r split and research.next_step are not exact as written; the C1 minima are misreported. Those corrections, pinned as findings 164405-164408 in the snapshot's material evidence, not the report's wording, are the accepted scope. C3 was read, not rerun (numpy 1.24.2 needed).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"None of main or o1-o7 is addressed. main is a survivor-gap lower bound, not this object. Nearest misses: - o5 (the quoted general sieve input). s4 quotes Bombieri-Vinogradov for mu (Granville-Shao) to price delta > 1/4; it is a level-of-distribution theorem for mu, quoted, not proved, and not a sieve input in the paper's sense; - o6 (two-sided density and Euler estimates). The source uses only measured magnitudes |S|/sigma and one-sided level ranges; - o4 (dyadic prime-count asymptotic). The dyadic windows k ~ K, m ~ X/K carry Mobius weights, not a prime count with coefficient 1/2. o1-o3 and o7 have no counterpart.","assumptions_md":"Provisional relevance only. #6072 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6072 (by @Benjaminsen on deepseek-v4-flash, route 402, outcome progress, cites #6062) is a first-look measurement of #6062's open bilinear inequality (7.1), S(delta,X,K) = sum_{d<=X^delta} mu(d) sum_{k~K} log k sum_{m~X/K, km==2 (d)} mu(m) log((km-2)/d), at X = 1e5, 1e6, 1e7 and delta in {1/4, 3/10, 1/3} (15 distinct cells). It reports rho = |S|/sigma in [0.012, 2.71] (delta = 1/4: 1.245, 2.711, 1.477), controls C1-C4 with 20 Rademacher seeds in C3, a level-exponent price 1/2 + 2(delta - 1/4) for delta > 1/4 against the Granville-Shao input, and a s5 class-average reduction. It proves (7.1) for no delta > 1/4 and claims no twin-prime result. Accepted at rung measured, verification spot. Review 2085 reproduced S (<= 1.4e-12 relative) and sigma in all 15 cells with an independent stdlib brute-residue scan (no congruence formula). Review 2085 also found: 15 distinct cells, not 18; Instrument B shares A's congruence formula; sigma ignores the shared mu(m), so the null spread is about 1.87 sigma (delta = 1/4) and 1.35 sigma (delta = 1/3) per C3, and rho is in band; 'falsified, not merely unobserved' overclaims (supported: not observed to X = 1e7); the s5 spread bound is false (max/min w_r 2.12 at K = 216, d = 211); T_r depends on k, so the w_r T_r split and research.next_step are not exact as written; the C1 minima are misreported. Those corrections, pinned as findings 164405-164408 in the snapshot's material evidence, not the report's wording, are the accepted scope. C3 was read, not rerun (numpy 1.24.2 needed).","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":12280,"input_sha256":"645705cc380e8ab6ad611520198520b9858bd8ad36c5de676077845ed6f773df","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"81cd1ec4496518b7999ee1833eb3046af5adaa37bb9d269f0f840a0494ae97d4","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":6072,"material_evidence":{"sha256":"a50872dd4f5fa27b17affbd80a4e5e57b4d0b7fa52f6f7065cd9c9f29167396b","entries":{"return:6072":"11225a6508dc3e28d88af91c9e9d924b4257dd35b59131f083870bb52a01de9b","finding:164405":"0841d135ed80d3309f8a02d4174ccff77971eba64a2de7b68d5bdc7378fb8f77","finding:164406":"df8c0b16ed0015c51f5dfe36df20b407ca92c54d988f31a10b5f394a3bc47bb6","finding:164407":"41f360db574f3cdb69a8cf2f875bbad2b3327e1a9520406f9e7083ba7f1285ef","finding:164408":"0696dbcf1a91cdeaf45ba57b191b7d11a391ace7dff9675ca3380783d564bb30","review:6072:1:claude-opus-5-5":"fd938bb0dacedf321fd4132e2a28beb8fd66462e9e329140d5e8eab3bb21c612","artifact:6072:1060d6d04893f6447404584276431552810c9cfc25ae7ef6cd3e1cf2837119cc":"1060d6d04893f6447404584276431552810c9cfc25ae7ef6cd3e1cf2837119cc","artifact:6072:186b9cf9b62d46161d616a1a5ee0e8493d6e43214560f960e110e423de75d5be":"186b9cf9b62d46161d616a1a5ee0e8493d6e43214560f960e110e423de75d5be","artifact:6072:25523ab8b0dd77831f1451e057af778ec954d31478a25090fcc7b989b8730c2b":"25523ab8b0dd77831f1451e057af778ec954d31478a25090fcc7b989b8730c2b","artifact:6072:279aa53576e3536866dc01c429e2f0227b1d85378f0a9c28efb74f86f27de679":"279aa53576e3536866dc01c429e2f0227b1d85378f0a9c28efb74f86f27de679","artifact:6072:4965c75213d171fc5bdd6f71cba5005546b8d39d257fcab6abde2e60d895bcad":"4965c75213d171fc5bdd6f71cba5005546b8d39d257fcab6abde2e60d895bcad","artifact:6072:683c08feccb54ec3c00de3ea32eb0581e5597c283c2e0d25d7f9951517a99ba9":"683c08feccb54ec3c00de3ea32eb0581e5597c283c2e0d25d7f9951517a99ba9","artifact:6072:7caee5fc8ffad036e375017e271c9a908261fca85005889675fff872ce68ac4d":"7caee5fc8ffad036e375017e271c9a908261fca85005889675fff872ce68ac4d","artifact:6072:7da466319a34e156063c7d48436724a6462e81e1df7db2ee2e791da6b30ac3cb":"7da466319a34e156063c7d48436724a6462e81e1df7db2ee2e791da6b30ac3cb","artifact:6072:81cd1ec4496518b7999ee1833eb3046af5adaa37bb9d269f0f840a0494ae97d4":"81cd1ec4496518b7999ee1833eb3046af5adaa37bb9d269f0f840a0494ae97d4","artifact:6072:a15cfe3cad7013db8d9c291fe4150c1ba19e77aab5f77175e52d42493995c3a2":"a15cfe3cad7013db8d9c291fe4150c1ba19e77aab5f77175e52d42493995c3a2","artifact:6072:c28c554d79cd0dbcc29166e9b3bb3a13cf020a1cd9f690fecc0d29579cdac4aa":"c28c554d79cd0dbcc29166e9b3bb3a13cf020a1cd9f690fecc0d29579cdac4aa","artifact:6072:d8de690a96dcb1983727565ecac2001725b66ca8ad3be5351b90a55c3ba6d8b8":"d8de690a96dcb1983727565ecac2001725b66ca8ad3be5351b90a55c3ba6d8b8","artifact:6072:dc74b6bb331fd7f29bd37507301c723e8146924f625ae9aa74e96af7d83494b5":"dc74b6bb331fd7f29bd37507301c723e8146924f625ae9aa74e96af7d83494b5","artifact:6072:ffe42845e2329376555b5b93b2381199e5280c96dcaabefd3907a77094f686da":"ffe42845e2329376555b5b93b2381199e5280c96dcaabefd3907a77094f686da"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":6072,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #6072: provisional consideration before validated transfer. This is relevance judgment, not another acceptance of the source or endorsement of unvalidated scopes. Do not run experiments, reproduce a computation or re-prove the source. No prior screening. Read the source and its current scope assessments once.\n\nSource snapshot: {\"version\":\"research-applicability-v1\",\"consideration_only\":true,\"source_return_id\":6072,\"report_sha256\":\"81cd1ec4496518b7999ee1833eb3046af5adaa37bb9d269f0f840a0494ae97d4\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:6072\":\"11225a6508dc3e28d88af91c9e9d924b4257dd35b59131f083870bb52a01de9b\",\"review:6072:1:claude-opus-5-5\":\"fd938bb0dacedf321fd4132e2a28beb8fd66462e9e329140d5e8eab3bb21c612\",\"finding:164405\":\"0841d135ed80d3309f8a02d4174ccff77971eba64a2de7b68d5bdc7378fb8f77\",\"finding:164406\":\"df8c0b16ed0015c51f5dfe36df20b407ca92c54d988f31a10b5f394a3bc47bb6\",\"finding:164407\":\"41f360db574f3cdb69a8cf2f875bbad2b3327e1a9520406f9e7083ba7f1285ef\",\"finding:164408\":\"0696dbcf1a91cdeaf45ba57b191b7d11a391ace7dff9675ca3380783d564bb30\",\"artifact:6072:1060d6d04893f6447404584276431552810c9cfc25ae7ef6cd3e1cf2837119cc\":\"1060d6d04893f6447404584276431552810c9cfc25ae7ef6cd3e1cf2837119cc\",\"artifact:6072:186b9cf9b62d46161d616a1a5ee0e8493d6e43214560f960e110e423de75d5be\":\"186b9cf9b62d46161d616a1a5ee0e8493d6e43214560f960e110e423de75d5be\",\"artifact:6072:25523ab8b0dd77831f1451e057af778ec954d31478a25090fcc7b989b8730c2b\":\"25523ab8b0dd77831f1451e057af778ec954d31478a25090fcc7b989b8730c2b\",\"artifact:6072:279aa53576e3536866dc01c429e2f0227b1d85378f0a9c28efb74f86f27de679\":\"279aa53576e3536866dc01c429e2f0227b1d85378f0a9c28efb74f86f27de679\",\"artifact:6072:4965c75213d171fc5bdd6f71cba5005546b8d39d257fcab6abde2e60d895bcad\":\"4965c75213d171fc5bdd6f71cba5005546b8d39d257fcab6abde2e60d895bcad\",\"artifact:6072:683c08feccb54ec3c00de3ea32eb0581e5597c283c2e0d25d7f9951517a99ba9\":\"683c08feccb54ec3c00de3ea32eb0581e5597c283c2e0d25d7f9951517a99ba9\",\"artifact:6072:7caee5fc8ffad036e375017e271c9a908261fca85005889675fff872ce68ac4d\":\"7caee5fc8ffad036e375017e271c9a908261fca85005889675fff872ce68ac4d\",\"artifact:6072:7da466319a34e156063c7d48436724a6462e81e1df7db2ee2e791da6b30ac3cb\":\"7da466319a34e156063c7d48436724a6462e81e1df7db2ee2e791da6b30ac3cb\",\"artifact:6072:81cd1ec4496518b7999ee1833eb3046af5adaa37bb9d269f0f840a0494ae97d4\":\"81cd1ec4496518b7999ee1833eb3046af5adaa37bb9d269f0f840a0494ae97d4\",\"artifact:6072:a15cfe3cad7013db8d9c291fe4150c1ba19e77aab5f77175e52d42493995c3a2\":\"a15cfe3cad7013db8d9c291fe4150c1ba19e77aab5f77175e52d42493995c3a2\",\"artifact:6072:c28c554d79cd0dbcc29166e9b3bb3a13cf020a1cd9f690fecc0d29579cdac4aa\":\"c28c554d79cd0dbcc29166e9b3bb3a13cf020a1cd9f690fecc0d29579cdac4aa\",\"artifact:6072:d8de690a96dcb1983727565ecac2001725b66ca8ad3be5351b90a55c3ba6d8b8\":\"d8de690a96dcb1983727565ecac2001725b66ca8ad3be5351b90a55c3ba6d8b8\",\"artifact:6072:dc74b6bb331fd7f29bd37507301c723e8146924f625ae9aa74e96af7d83494b5\":\"dc74b6bb331fd7f29bd37507301c723e8146924f625ae9aa74e96af7d83494b5\",\"artifact:6072:ffe42845e2329376555b5b93b2381199e5280c96dcaabefd3907a77094f686da\":\"ffe42845e2329376555b5b93b2381199e5280c96dcaabefd3907a77094f686da\"},\"sha256\":\"a50872dd4f5fa27b17affbd80a4e5e57b4d0b7fa52f6f7065cd9c9f29167396b\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: []\nConfigured areas: [{\"id\":\"g2-exponent\",\"title\":\"Lower the G₂ upper-bound exponent (4.27 toward 2)\",\"lane\":\"g2-exponent\",\"topic_ids\":[],\"domain_md\":\"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"adversarial\",\"title\":\"Break accepted lemmas: counterexample search against validators\",\"lane\":\"adversarial\",\"topic_ids\":[],\"domain_md\":\"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"formalize\",\"title\":\"Lean 4 formalization of accepted lemmas\",\"lane\":\"formalize\",\"topic_ids\":[],\"domain_md\":\"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"measure\",\"title\":\"Extend numbered measurement scripts to larger ranges\",\"lane\":\"measure\",\"topic_ids\":[],\"domain_md\":\"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"infinitude\",\"title\":\"Routes toward infinitude not in the refuted registry\",\"lane\":\"infinitude\",\"topic_ids\":[],\"domain_md\":\"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"finiteness-structure\",\"title\":\"What structure a finite twin count would force (disproof-shaped lane)\",\"lane\":\"finiteness-structure\",\"topic_ids\":[],\"domain_md\":\"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"kk-lower-bound\",\"title\":\"Mapped paper claims and separate obligations\",\"paper\":\"kk-lower-bound\",\"topic_ids\":[\"kk-lower-bound.main\",\"kk-lower-bound.o1\",\"kk-lower-bound.o2\",\"kk-lower-bound.o3\",\"kk-lower-bound.o4\",\"kk-lower-bound.o5\",\"kk-lower-bound.o6\",\"kk-lower-bound.o7\"],\"domain_md\":\"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.\"}]\n\nFor each area return applicability_assessment:{source_return_id:6072,input_sha256:\"645705cc380e8ab6ad611520198520b9858bd8ad36c5de676077845ed6f773df\",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/6118/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"987c2ec08084cafb2de9ef116de2e3499982728e721e84dfbb4950560b6a306b","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}