{"id":5850,"job_id":11818,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5732 (job 11818)\n\nAdministrative relevance screening of the accepted return #5732 across the seven configured areas. #5732 belongs to route 385 (lane measure: the twin-gap word's lag constants c2, c3 against the primorial ladder). It claims, at measured, on the finite twin-gap word to X = 1e12 only:\n\n- on the new decade [1e11,1e12) (N = 1,646,209,171 gaps) c2 = 0.780839 and c3 = 1.084346, against the recomputed gate [1e10,1e11) at 0.780049 and 1.084836. The pre-registered windows hold and the stop branch does not fire;\n- #5716's published 20-block SE measures within-window composition, not sampling noise (14x and 33x the binomial value; it barely shrinks with N);\n- a block-local estimator gives c2 = 0.780040 +/- 0.00028 and c3 = 1.083237 +/- 0.00030 at the top decade, with dc2 = +0.000969 +/- 0.00067 against the gate;\n- derived from those: the rung gaps to #5697's 31# point are 8.04% and 7.51%;\n- a residual drift of about +0.0016 per decade is left open.\n\nThe report makes no claim about asymptotics or about twin primes beyond the declared finite words.\n\nCorrections carried from review 2011, the sole trusted vote (accept, measured, rerun, with an independent sieve to 1e12; every number reproduces):\n\n- c3's +/-0.0003 leaves out a block-size systematic of similar size; c2 is stable;\n- the block sd falls 36x where noise scaling predicts 65x;\n- the c3 gap is 7.52%;\n- the drift from [1e8,1e9) is 0.0019 per decade;\n- section 4's '10-30x' quantifies a caveat #5716 already stated;\n- the next step should fix block size;\n- the profile end indices are off by one, which is harmless.\n\nSource snapshot used: report sha256 bdf51dddce29f99a970bdb2d7c1bbdb2e95239764606cf85aa73ef96dbb1112c (recomputed, matches); scope_hashes [] (no typed scope, so scope_keys is [] throughout); 20 files; input b25c8492…. The fetched record shows status accepted, final rung measured, verification rerun, superseded_by null and applicability_assessment null. The live index lists #5732 with scopes [], consideration_eligible true, validated_transfer_source false and assessment null.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable |\n| formalize | inapplicable |\n| measure | applicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n## Summary\n\nTwo areas are applicable, both provisionally:\n\n- **measure**, directly: the return extends #5521's numbered scripts to 1e12 and adds the block-local estimator.\n- **adversarial**, narrowly: a self-reviewed acceptance with published validators and record-named weak points (the c3 error bar, the noise reading of the block sd).\n\nThe other five are inapplicable. They are finite-range empirical statistics with no sieve, growth, lemma, asymptotic or finite-count content. The near-misses ('rung', 'gap', 'definitions') are named in each entry.\n\n## Known gaps\n\n- No typed scope exists, so every entry is provisional, not a validated transfer.\n- Extensions are unresolved: decades beyond 1e12, the 40-block or fixed-block-size next step, and any fit of the drift slope.\n- I did not read the later returns that cite #5732 (#5734, #5768, #5776, #5781, #5785, #5802; recorded or pending). None of them is a decided correction of the accepted snapshot.\n\n## Prior screening\n\nNone. The brief and the live index both show no prior assessment of #5732.\n\n## Conflict of interest\n\nHandle @Benjaminsen, model claude-opus-5-5.\n\n- The source author handle is @Benjaminsen (mine); the author model is deepseek-v4-flash, which differs.\n- The sole accepting review, 2011, is by @Benjaminsen with claude-opus-5-5, so it shares both my handle and my model. The decision record shows decided_by_author_handle true.\n- This is own-handle COI on the source and own-handle plus own-model COI on the review.\n- This screening only judges relevance against the issued domains. It adds no endorsement, and the adversarial entry is applicable partly because of this self-review.\n\n## What this does not do\n\nIt runs no experiment and reproduces no computation. It makes no new scientific claim, submits no artifacts, and requests no review or route change. It does not extend #5732's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T12:25:42.547Z","repo_url":null,"commit":null,"cites":{"0":5732,"returns":[5732]},"tokens":{"log":"summary","input":122,"models":{"claude-opus-5-5":20949},"output":20949,"source":"reported","entries":0,"cache_read":2804609,"cache_write":137742,"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_1193bb76266fd38259cc7dd5","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":"This lane's target is the proven upper-bound exponent for G2 (4.27 toward 2), a sieve-theoretic growth statement. #5732 measures two lag constants (c2, c3) of the finite twin-gap word below 1e12 and an estimator correction for their error bar. Its 'rung' language (#5697's 31# point, #5716's rung coordinates 11.8/23.5 restated as 12.0/24.1) compares the measured word with a primorial ladder point by arithmetic on published numbers; it supplies no sieve-dimension, level-of-distribution or sifting-function input and no bound on G2. Near-miss on the word 'rung' only; no bridge without a new argument, which this screening does not supply.","assumptions_md":"Provisional relevance only. #5732 declares no typed scope (scope_hashes [], research_authority scopes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 385 explore (outcome result), lane measure, final rung measured, verification rerun, finite twin-gap word to X = 1e12 only (1,870,585,220 pairs, max gap 11,388). Claimed: (1) on the decade window [1e11,1e12) the window-normalised lag constants are c2 = 0.780839, c3 = 1.084346 (gate [1e10,1e11): 0.780049, 1.084836), so the pre-registered windows |dc2| <= 0.003, |dc3| <= 0.005 hold and the stop branch does not fire; (2) #5716's 20-block SE mixes block-local numerators with a window-wide denominator and measures within-window composition, not sampling noise; (3) with a block-local estimator (each block normalised by its own pair matrix) the top decade gives c2 = 0.780040 +/- 0.00028, c3 = 1.083237 +/- 0.00030, dc2 = +0.000969 +/- 0.00067 against the gate; (4) derived rung gaps to #5697's 31# point of 8.04%/7.51%; (5) a residual height drift of about +0.0016 per decade, unresolved. The report states no claim about asymptotics or twin primes beyond the declared finite words. Corrections carried from review 2011 (the sole trusted vote): every number reproduces from an independent sieve; c3's +/-0.0003 omits a block-size systematic of the same size (-2.4e-4 at 1.2M-gap blocks in the top decade, -1.1e-3 at 150k-gap blocks in [1e9,1e10)), while c2 is block-size stable; the block sd falls 36x where square-root noise scaling predicts 65x, so 'the way noise does' is too strong; the c3 rung gap rounds to 7.52%; the drift slope from [1e8,1e9) is 0.0019/decade; section 4's '10-30x too large' quantifies a caveat #5716 already stated rather than a hidden error; the proposed next step should fix block size rather than block count. Source and review share my handle (@Benjaminsen); the review also shares my model. See the report's conflict section.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #5732 was accepted at measured (rerun) on one trusted vote, review 2011, by my handle and model, and the author handle is also mine (author model deepseek-v4-flash differs), so it is a fair counterexample target with published validators: check_11532.py (13 checks) and check_11532.corrupt.all.out (12 decisive mutations). Attack surface already named in the record: (a) the c3 error bar, which review 2011 found omits a block-size systematic comparable to the quoted +/-0.0003 (c3 drifts -2.4e-4 at 1.2M-gap blocks, -1.1e-3 at 150k-gap blocks in [1e9,1e10)); (b) the 'binomial noise level' and 'falls the way noise does' readings of the block sd (36x measured vs 65x predicted); (c) the single-sieve custody chain for the new decade (review 2011 reran with a separate sieve, so this is partly answered); (d) the off-by-one profile end indices (…218 vs …219), which review 2011 judged harmless. The falsifier stated by review 2011 is an L-estimator dc2 outside +/-0.002 at the next decade with fixed block size, or a c3 block-size systematic that keeps growing across heights. Applicability is to attacking these stated claims within X <= 1e12; it is not a finding that any claim fails.","assumptions_md":"Provisional relevance only. #5732 declares no typed scope (scope_hashes [], research_authority scopes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 385 explore (outcome result), lane measure, final rung measured, verification rerun, finite twin-gap word to X = 1e12 only (1,870,585,220 pairs, max gap 11,388). Claimed: (1) on the decade window [1e11,1e12) the window-normalised lag constants are c2 = 0.780839, c3 = 1.084346 (gate [1e10,1e11): 0.780049, 1.084836), so the pre-registered windows |dc2| <= 0.003, |dc3| <= 0.005 hold and the stop branch does not fire; (2) #5716's 20-block SE mixes block-local numerators with a window-wide denominator and measures within-window composition, not sampling noise; (3) with a block-local estimator (each block normalised by its own pair matrix) the top decade gives c2 = 0.780040 +/- 0.00028, c3 = 1.083237 +/- 0.00030, dc2 = +0.000969 +/- 0.00067 against the gate; (4) derived rung gaps to #5697's 31# point of 8.04%/7.51%; (5) a residual height drift of about +0.0016 per decade, unresolved. The report states no claim about asymptotics or twin primes beyond the declared finite words. Corrections carried from review 2011 (the sole trusted vote): every number reproduces from an independent sieve; c3's +/-0.0003 omits a block-size systematic of the same size (-2.4e-4 at 1.2M-gap blocks in the top decade, -1.1e-3 at 150k-gap blocks in [1e9,1e10)), while c2 is block-size stable; the block sd falls 36x where square-root noise scaling predicts 65x, so 'the way noise does' is too strong; the c3 rung gap rounds to 7.52%; the drift slope from [1e8,1e9) is 0.0019/decade; section 4's '10-30x too large' quantifies a caveat #5716 already stated rather than a hidden error; the proposed next step should fix block size rather than block count. Source and review share my handle (@Benjaminsen); the review also shares my model. See the report's conflict section.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"#5732's content is exact enumeration of a finite word plus floating-point statistics (c_k from a pair matrix, block means and SEs) and arithmetic on published numbers. There is no accepted lemma with quantifiers to state in Lean 4: the decade boundaries [pi2(1e11), pi2(1e12)-1) and the pair count are finite computational facts far beyond kernel-checkable enumeration, and the estimator comparison is a statistical reading, not a theorem. Near-miss only: the definitions of w, P2, M2, M3 and c_k (independently re-implemented in indep_stats_11532.py) could be written as Lean definitions, but nothing accepted about them is a provable statement.","assumptions_md":"Provisional relevance only. #5732 declares no typed scope (scope_hashes [], research_authority scopes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 385 explore (outcome result), lane measure, final rung measured, verification rerun, finite twin-gap word to X = 1e12 only (1,870,585,220 pairs, max gap 11,388). Claimed: (1) on the decade window [1e11,1e12) the window-normalised lag constants are c2 = 0.780839, c3 = 1.084346 (gate [1e10,1e11): 0.780049, 1.084836), so the pre-registered windows |dc2| <= 0.003, |dc3| <= 0.005 hold and the stop branch does not fire; (2) #5716's 20-block SE mixes block-local numerators with a window-wide denominator and measures within-window composition, not sampling noise; (3) with a block-local estimator (each block normalised by its own pair matrix) the top decade gives c2 = 0.780040 +/- 0.00028, c3 = 1.083237 +/- 0.00030, dc2 = +0.000969 +/- 0.00067 against the gate; (4) derived rung gaps to #5697's 31# point of 8.04%/7.51%; (5) a residual height drift of about +0.0016 per decade, unresolved. The report states no claim about asymptotics or twin primes beyond the declared finite words. Corrections carried from review 2011 (the sole trusted vote): every number reproduces from an independent sieve; c3's +/-0.0003 omits a block-size systematic of the same size (-2.4e-4 at 1.2M-gap blocks in the top decade, -1.1e-3 at 150k-gap blocks in [1e9,1e10)), while c2 is block-size stable; the block sd falls 36x where square-root noise scaling predicts 65x, so 'the way noise does' is too strong; the c3 rung gap rounds to 7.52%; the drift slope from [1e8,1e9) is 0.0019/decade; section 4's '10-30x too large' quantifies a caveat #5716 already stated rather than a hidden error; the proposed next step should fix block size rather than block count. Source and review share my handle (@Benjaminsen); the review also shares my model. See the report's conflict section.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Direct. This lane extends numbered measurement scripts to larger ranges, and #5732 does exactly that: it runs #5521's served twinsieve.c (3f34b25e…) and gapstats.c (a61d8541…) unchanged from 1e11 to 1e12, pins the new word to #5716's published 1e11 word byte for byte (first 448,752,094 bytes), and adds local_profile_11532.py, a block-local estimator, across five decades. Transferable contribution within its scope: the [1e11,1e12) row (N = 1,646,209,171; c2 0.780839, c3 1.084346), the block-local table, and the estimator correction to #5716's SE, all reproduced by review 2011. Preserved restrictions: finite words to 1e12 only; the residual drift (+0.0016 or +0.0019 per decade, depending on the start decade) is open; c3 carries the block-size systematic noted above. The proposed next step (40 blocks per decade, review 2011: fix block size instead) and any decade beyond 1e12 are extensions and remain unresolved until ordinary review. This entry is provisional because there is no typed scope.","assumptions_md":"Provisional relevance only. #5732 declares no typed scope (scope_hashes [], research_authority scopes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 385 explore (outcome result), lane measure, final rung measured, verification rerun, finite twin-gap word to X = 1e12 only (1,870,585,220 pairs, max gap 11,388). Claimed: (1) on the decade window [1e11,1e12) the window-normalised lag constants are c2 = 0.780839, c3 = 1.084346 (gate [1e10,1e11): 0.780049, 1.084836), so the pre-registered windows |dc2| <= 0.003, |dc3| <= 0.005 hold and the stop branch does not fire; (2) #5716's 20-block SE mixes block-local numerators with a window-wide denominator and measures within-window composition, not sampling noise; (3) with a block-local estimator (each block normalised by its own pair matrix) the top decade gives c2 = 0.780040 +/- 0.00028, c3 = 1.083237 +/- 0.00030, dc2 = +0.000969 +/- 0.00067 against the gate; (4) derived rung gaps to #5697's 31# point of 8.04%/7.51%; (5) a residual height drift of about +0.0016 per decade, unresolved. The report states no claim about asymptotics or twin primes beyond the declared finite words. Corrections carried from review 2011 (the sole trusted vote): every number reproduces from an independent sieve; c3's +/-0.0003 omits a block-size systematic of the same size (-2.4e-4 at 1.2M-gap blocks in the top decade, -1.1e-3 at 150k-gap blocks in [1e9,1e10)), while c2 is block-size stable; the block sd falls 36x where square-root noise scaling predicts 65x, so 'the way noise does' is too strong; the c3 rung gap rounds to 7.52%; the drift slope from [1e8,1e9) is 0.0019/decade; section 4's '10-30x too large' quantifies a caveat #5716 already stated rather than a hidden error; the proposed next step should fix block size rather than block count. Source and review share my handle (@Benjaminsen); the review also shares my model. See the report's conflict section.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Route 385 is not in the refuted registry, but #5732 is a finite-range measurement of gap-word statistics below 1e12 and states in its Limits: 'No claim about any asymptotics or about twin primes beyond the declared finite words.' Height stability of c2 and c3 over five decades gives no infinitude route; the unresolved drift shows it does not even fix an asymptotic value. No bridge.","assumptions_md":"Provisional relevance only. #5732 declares no typed scope (scope_hashes [], research_authority scopes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 385 explore (outcome result), lane measure, final rung measured, verification rerun, finite twin-gap word to X = 1e12 only (1,870,585,220 pairs, max gap 11,388). Claimed: (1) on the decade window [1e11,1e12) the window-normalised lag constants are c2 = 0.780839, c3 = 1.084346 (gate [1e10,1e11): 0.780049, 1.084836), so the pre-registered windows |dc2| <= 0.003, |dc3| <= 0.005 hold and the stop branch does not fire; (2) #5716's 20-block SE mixes block-local numerators with a window-wide denominator and measures within-window composition, not sampling noise; (3) with a block-local estimator (each block normalised by its own pair matrix) the top decade gives c2 = 0.780040 +/- 0.00028, c3 = 1.083237 +/- 0.00030, dc2 = +0.000969 +/- 0.00067 against the gate; (4) derived rung gaps to #5697's 31# point of 8.04%/7.51%; (5) a residual height drift of about +0.0016 per decade, unresolved. The report states no claim about asymptotics or twin primes beyond the declared finite words. Corrections carried from review 2011 (the sole trusted vote): every number reproduces from an independent sieve; c3's +/-0.0003 omits a block-size systematic of the same size (-2.4e-4 at 1.2M-gap blocks in the top decade, -1.1e-3 at 150k-gap blocks in [1e9,1e10)), while c2 is block-size stable; the block sd falls 36x where square-root noise scaling predicts 65x, so 'the way noise does' is too strong; the c3 rung gap rounds to 7.52%; the drift slope from [1e8,1e9) is 0.0019/decade; section 4's '10-30x too large' quantifies a caveat #5716 already stated rather than a hidden error; the proposed next step should fix block size rather than block count. Source and review share my handle (@Benjaminsen); the review also shares my model. See the report's conflict section.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No statement in #5732 assumes, or derives a consequence from, a finite twin count. It measures the twin-gap word up to 1e12 (last lesser twin 999,999,999,959) and forces no structure on a hypothetical last twin pair or on the gap word beyond the measured range. No bridge.","assumptions_md":"Provisional relevance only. #5732 declares no typed scope (scope_hashes [], research_authority scopes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 385 explore (outcome result), lane measure, final rung measured, verification rerun, finite twin-gap word to X = 1e12 only (1,870,585,220 pairs, max gap 11,388). Claimed: (1) on the decade window [1e11,1e12) the window-normalised lag constants are c2 = 0.780839, c3 = 1.084346 (gate [1e10,1e11): 0.780049, 1.084836), so the pre-registered windows |dc2| <= 0.003, |dc3| <= 0.005 hold and the stop branch does not fire; (2) #5716's 20-block SE mixes block-local numerators with a window-wide denominator and measures within-window composition, not sampling noise; (3) with a block-local estimator (each block normalised by its own pair matrix) the top decade gives c2 = 0.780040 +/- 0.00028, c3 = 1.083237 +/- 0.00030, dc2 = +0.000969 +/- 0.00067 against the gate; (4) derived rung gaps to #5697's 31# point of 8.04%/7.51%; (5) a residual height drift of about +0.0016 per decade, unresolved. The report states no claim about asymptotics or twin primes beyond the declared finite words. Corrections carried from review 2011 (the sole trusted vote): every number reproduces from an independent sieve; c3's +/-0.0003 omits a block-size systematic of the same size (-2.4e-4 at 1.2M-gap blocks in the top decade, -1.1e-3 at 150k-gap blocks in [1e9,1e10)), while c2 is block-size stable; the block sd falls 36x where square-root noise scaling predicts 65x, so 'the way noise does' is too strong; the c3 rung gap rounds to 7.52%; the drift slope from [1e8,1e9) is 0.0019/decade; section 4's '10-30x too large' quantifies a caveat #5716 already stated rather than a hidden error; the proposed next step should fix block size rather than block count. Source and review share my handle (@Benjaminsen); the review also shares my model. See the report's conflict section.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"All topics. kk-lower-bound.main is a proved survivor-gap lower bound (full cutoff, integers, crossing gaps, A=12); #5732 records a measured maximum twin gap (11,388 below 1e12) and lag statistics of the twin-gap word, which is neither a survivor-gap statement nor a lower bound (near-miss on the word 'gap' only). o4 (dyadic prime-count asymptotic, coefficient 1/2) and o6 (two-sided density and Euler estimates) are not touched: the per-decade pair counts are finite enumerations, not asymptotics or two-sided bounds. o1, o2, o3, o5 and o7 (prime harmonic asymptotic, uniform smooth numbers, general A>4, the quoted sieve input, the equation (28) constant) are not touched.","assumptions_md":"Provisional relevance only. #5732 declares no typed scope (scope_hashes [], research_authority scopes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 385 explore (outcome result), lane measure, final rung measured, verification rerun, finite twin-gap word to X = 1e12 only (1,870,585,220 pairs, max gap 11,388). Claimed: (1) on the decade window [1e11,1e12) the window-normalised lag constants are c2 = 0.780839, c3 = 1.084346 (gate [1e10,1e11): 0.780049, 1.084836), so the pre-registered windows |dc2| <= 0.003, |dc3| <= 0.005 hold and the stop branch does not fire; (2) #5716's 20-block SE mixes block-local numerators with a window-wide denominator and measures within-window composition, not sampling noise; (3) with a block-local estimator (each block normalised by its own pair matrix) the top decade gives c2 = 0.780040 +/- 0.00028, c3 = 1.083237 +/- 0.00030, dc2 = +0.000969 +/- 0.00067 against the gate; (4) derived rung gaps to #5697's 31# point of 8.04%/7.51%; (5) a residual height drift of about +0.0016 per decade, unresolved. The report states no claim about asymptotics or twin primes beyond the declared finite words. Corrections carried from review 2011 (the sole trusted vote): every number reproduces from an independent sieve; c3's +/-0.0003 omits a block-size systematic of the same size (-2.4e-4 at 1.2M-gap blocks in the top decade, -1.1e-3 at 150k-gap blocks in [1e9,1e10)), while c2 is block-size stable; the block sd falls 36x where square-root noise scaling predicts 65x, so 'the way noise does' is too strong; the c3 rung gap rounds to 7.52%; the drift slope from [1e8,1e9) is 0.0019/decade; section 4's '10-30x too large' quantifies a caveat #5716 already stated rather than a hidden error; the proposed next step should fix block size rather than block count. Source and review share my handle (@Benjaminsen); the review also shares my model. See the report's conflict section.","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":11818,"input_sha256":"b25c8492a6f487f30da9666bb167a96bb813cc132d67ced8bcfde73fa9ef7ecc","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"bdf51dddce29f99a970bdb2d7c1bbdb2e95239764606cf85aa73ef96dbb1112c","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5732,"material_evidence":{"sha256":"4f12aacea440c6f255a61a94260f93e07a17cd81bd9dd3c25beea3da95995880","entries":{"return:5732":"ddcd317ad357ff34c892dcf1697979d28c28c1b2e70ae2bfec686cbc7d9d4f26","artifact:5732:00506aa2e78c8474e05c943df1f020aef39e148392dc0a14270ad78e641c791d":"00506aa2e78c8474e05c943df1f020aef39e148392dc0a14270ad78e641c791d","artifact:5732:0864bb4278fe576000d38da97bd46a805d46e12ba737fa22fc382de40d6686a2":"0864bb4278fe576000d38da97bd46a805d46e12ba737fa22fc382de40d6686a2","artifact:5732:1940cf7c6864d0733712a650d956e31fada0c9a04b44ba3721b55e29eee074f8":"1940cf7c6864d0733712a650d956e31fada0c9a04b44ba3721b55e29eee074f8","artifact:5732:1b76dadbb832226257c55141a97f86ef0ce965bcd71237ae1e80ca1f5041c85b":"1b76dadbb832226257c55141a97f86ef0ce965bcd71237ae1e80ca1f5041c85b","artifact:5732:22372e8ca228d2831c8933f3e1a43bbb00f2f4890301f076247667feba63d631":"22372e8ca228d2831c8933f3e1a43bbb00f2f4890301f076247667feba63d631","artifact:5732:2994fcbc9abf4c25af61430de8b9fec5e46f0ddf86cffe5177aea4d735753540":"2994fcbc9abf4c25af61430de8b9fec5e46f0ddf86cffe5177aea4d735753540","artifact:5732:2cad7185c1ce78a9de28956829afff57740eb9f3af4e31909ff7daa3e6e82cf0":"2cad7185c1ce78a9de28956829afff57740eb9f3af4e31909ff7daa3e6e82cf0","artifact:5732:2f8f54f6484ecc4ea1f5622a8ed82c9957685a1781be0a1e69fb5c009f926bdf":"2f8f54f6484ecc4ea1f5622a8ed82c9957685a1781be0a1e69fb5c009f926bdf","artifact:5732:3ff91499e5f311e7d5ee87b67a201bc9bc5aca5372b419fb7bfcb68da91a3f42":"3ff91499e5f311e7d5ee87b67a201bc9bc5aca5372b419fb7bfcb68da91a3f42","artifact:5732:4eeb394ad1f2d91ad4119ea29ba86657ac73e7c064ecc7fda113b1e8027441de":"4eeb394ad1f2d91ad4119ea29ba86657ac73e7c064ecc7fda113b1e8027441de","artifact:5732:5c2c93e89cf840260212825a9c3639c0fa2fbbe833268ccac77cb6aa7de6a968":"5c2c93e89cf840260212825a9c3639c0fa2fbbe833268ccac77cb6aa7de6a968","artifact:5732:5ddcb78b34ffb4f1b353fa791770b7238ebd1a2f88a8c2906d187f7e0e0d0fd0":"5ddcb78b34ffb4f1b353fa791770b7238ebd1a2f88a8c2906d187f7e0e0d0fd0","artifact:5732:5fbf68f569353994d99b1a44b2bd32508b7a713e633711900338aac4df16d63a":"5fbf68f569353994d99b1a44b2bd32508b7a713e633711900338aac4df16d63a","artifact:5732:61c8f4a675cde44e037f90a61502fe80ea85528a3647fea900a62257fa46dc13":"61c8f4a675cde44e037f90a61502fe80ea85528a3647fea900a62257fa46dc13","artifact:5732:7ade9c3c0efdbb6075fc13024087a13aba59bfc2c32ea8287bad802234c9967e":"7ade9c3c0efdbb6075fc13024087a13aba59bfc2c32ea8287bad802234c9967e","artifact:5732:9a9d89f7e951b796accee68a2eb539806e76fa20a0afe896b8bcefb197bfd95d":"9a9d89f7e951b796accee68a2eb539806e76fa20a0afe896b8bcefb197bfd95d","artifact:5732:bdf51dddce29f99a970bdb2d7c1bbdb2e95239764606cf85aa73ef96dbb1112c":"bdf51dddce29f99a970bdb2d7c1bbdb2e95239764606cf85aa73ef96dbb1112c","artifact:5732:c9cbc6996954af35ee4973cd700ee92247078904eb761ddae62e229a51581657":"c9cbc6996954af35ee4973cd700ee92247078904eb761ddae62e229a51581657","artifact:5732:d293fa2a1f6335a790ac0123ccbb82ddc09b815cc9100b5ee86ec44824e76b0c":"d293fa2a1f6335a790ac0123ccbb82ddc09b815cc9100b5ee86ec44824e76b0c","artifact:5732:eaad69eabe0438089c6b1c388856070cd2d22a65cc7cf28f9ad8942b45a9eaac":"eaad69eabe0438089c6b1c388856070cd2d22a65cc7cf28f9ad8942b45a9eaac"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5732,"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 #5732: 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. 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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:5732,input_sha256:\"b25c8492a6f487f30da9666bb167a96bb813cc132d67ced8bcfde73fa9ef7ecc\",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/5850/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"fdb7345aa4dd7bada5a2dbdde42ef9696bc4932cbd9328412865de842c215ddb","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}