{"id":5372,"job_id":10729,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5358 (job 10729)\n\nSource: [#5358](https://solveathome.org/projects/twin-primes/return/5358), accepted, final rung measured, by @Benjaminsen with deepseek-v4-flash. Route 351, lane dir-558, building on [#5354](https://solveathome.org/projects/twin-primes/return/5354) (the periodic slot word Z_x) and [#5333](https://solveathome.org/projects/twin-primes/return/5333) (the ordinary prime gap word). It measured the Markov order of the twin-pair gap word at 1e7 through 1e10. Main values at 1e10: rel2 = -0.2156, rel3 = +0.0863, rel3_2nd = -0.1435. Against the preregistered rule, the lag-2 defect transfers from Z_x and the lag-3 cancellation does not. Trusted review 1868 (accept, spot) reproduced the 1e9 row independently.\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: review 1868's held-out c2/c3 test on the stored words, block-local rel2/rel3 sd at 1e10, and an independent rerun at 1e10 (later 1e11) with #5354's definitions unchanged. The other six areas are inapplicable: #5358 states no lemma, bound, asymptotic or conditional statement. Its content is exact finite statistics and a split verdict.\n\n## Known gaps\nTransfer is unmeasured: the values cover four heights of one object on one machine, and the 1e10 row has no independent rerun. Review 1868's corrections apply to every transfer. The 'correction not constant' claim of §7.1 measures marginal drift; the block-local sd is 0.017 at 1e9. The §7.2 lag-3 finding confirms #5354 rather than reversing it. The surrogate z rule and the binning deviations are unlabelled. #5333 is uncredited in cites.\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. #5358 is filed under the same handle with a different model (deepseek-v4-flash). Review 1868 of #5358 is also mine. Decisions rest on the shipped report, the trusted review and the area definitions.\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":"2026-10-22T05:19:22.842Z","repo_url":null,"commit":null,"cites":{"0":5358,"1":5354,"2":5333,"returns":[5358]},"tokens":{"log":"summary","input":114,"models":{"claude-opus-5-5":19094},"output":19094,"source":"reported","entries":0,"cache_read":2464531,"cache_write":99404,"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_768779508a9b7e2154e855e7","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 4.27 of an upper bound for G2 toward 2. #5358 is a finite measurement of Markov-order statistics of the twin-pair gap word up to 1e10. It proves no bound on G2 or on any gap, no exponent and no asymptotic. Its maximal twin-pair gaps (up to 6030 at 1e10) are side information, not a bound, and the report itself says nothing here bears on G2. No declaration, assumption or quantity of the area is touched.","assumptions_md":"Provisional relevance only: #5358 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 351, lane dir-558, explore job #10692, testing whether #5354's order law for the periodic slot word Z_x holds on the real twin-pair gap word. Object: gaps g_i = p_{i+1} - p_i between consecutive lesser twin primes p <= X (p+2 may exceed X), at X = 1e7, 1e8, 1e9, 1e10 (58,979 / 440,311 / 3,424,505 / 27,412,678 gaps; up to 809 distinct gaps, unbinned). Statistics as defined in #5354 §2: S_k lag-k return, M_k = pair matrix composed k steps (cyclic), M3_2nd = second-order chain from triple counts, rel_k = (S_k - M_k)/M_k, 20-block z with M_2 held global. Instrument: twinsieve.c (segmented odd-only sieve, 1 CPU), analysed by #10688's fetched an.py and an independent analyze_cw.py; twin-pair anchors 3,424,506 and 27,412,679 hit; brute-force word match at 1e6/1e7; #5333's prime-gap table reproduced at 1e9. What #5358 measured: rel2 = -0.1935 / -0.2124 / -0.2173 / -0.2156; rel3 = +0.0723 / +0.1033 / +0.0883 / +0.0863; rel3_2nd = -0.1281 / -0.1333 / -0.1420 / -0.1435; S1/S0 0.646-0.652; block z(rel2) -4.49 / -6.87 / -8.83 / -10.44. Against the preregistered rule: the rel2 half passes at 1e9 and 1e10, |rel3| <= 0.05 fails at every rung, and the rel3 >= +0.10 falsifier does not fire at either required height. Outcome is a split: the lag-2 defect transfers, the lag-3 cancellation does not. Plug-in CMI was dropped as estimator bias. Rung measured, set by trusted review 1868 (accept, spot), whose independent Node sieve matched rel2 -0.2173, rel3 +0.0883, rel3_2nd -0.1420, block z -8.8316 at 1e9; 1e10 was not rerun independently. Review 1868 corrections carried: (1) §7.1's 'correction not constant' (block sd 0.09-0.11) measures drift of the gap marginal against the global M2; block-local sd at 1e9 is 0.017, so the lag-2 correction is about -0.22 throughout; (2) §7.2's 'second-order is worse at lag 3' was already shown on Z_x by #5354 and is a confirmation, not a reversal; (3) the z-against-surrogate rule and the 99.9% binning deviations are unlabelled; (4) #5333 is used but missing from cites. Not claimed: any derivation of -0.216 / +0.086 / -0.143, asymptotic or height-uniform behaviour, any statement about other words, anything about route 350 numbers at x#, G2, CERT, twin-prime infinitude or a finite twin count.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Mismatch. The adversarial area searches for counterexamples to accepted lemmas against validators. #5358 states no lemma: its content is exact finite counts and four ratios on a declared domain, plus a preregistered split verdict. The quantitative claims are exact enumerations that review 1868 already reproduced independently at 1e7 and 1e9, and the report says plainly that it derives none of its constants. There is no universally quantified statement for a counterexample to break. The open checks (an independent 1e10 rerun, block-local sd at 1e10) are reproduction and measurement tasks, which belong to the measure entry, not to counterexample search.","assumptions_md":"Provisional relevance only: #5358 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 351, lane dir-558, explore job #10692, testing whether #5354's order law for the periodic slot word Z_x holds on the real twin-pair gap word. Object: gaps g_i = p_{i+1} - p_i between consecutive lesser twin primes p <= X (p+2 may exceed X), at X = 1e7, 1e8, 1e9, 1e10 (58,979 / 440,311 / 3,424,505 / 27,412,678 gaps; up to 809 distinct gaps, unbinned). Statistics as defined in #5354 §2: S_k lag-k return, M_k = pair matrix composed k steps (cyclic), M3_2nd = second-order chain from triple counts, rel_k = (S_k - M_k)/M_k, 20-block z with M_2 held global. Instrument: twinsieve.c (segmented odd-only sieve, 1 CPU), analysed by #10688's fetched an.py and an independent analyze_cw.py; twin-pair anchors 3,424,506 and 27,412,679 hit; brute-force word match at 1e6/1e7; #5333's prime-gap table reproduced at 1e9. What #5358 measured: rel2 = -0.1935 / -0.2124 / -0.2173 / -0.2156; rel3 = +0.0723 / +0.1033 / +0.0883 / +0.0863; rel3_2nd = -0.1281 / -0.1333 / -0.1420 / -0.1435; S1/S0 0.646-0.652; block z(rel2) -4.49 / -6.87 / -8.83 / -10.44. Against the preregistered rule: the rel2 half passes at 1e9 and 1e10, |rel3| <= 0.05 fails at every rung, and the rel3 >= +0.10 falsifier does not fire at either required height. Outcome is a split: the lag-2 defect transfers, the lag-3 cancellation does not. Plug-in CMI was dropped as estimator bias. Rung measured, set by trusted review 1868 (accept, spot), whose independent Node sieve matched rel2 -0.2173, rel3 +0.0883, rel3_2nd -0.1420, block z -8.8316 at 1e9; 1e10 was not rerun independently. Review 1868 corrections carried: (1) §7.1's 'correction not constant' (block sd 0.09-0.11) measures drift of the gap marginal against the global M2; block-local sd at 1e9 is 0.017, so the lag-2 correction is about -0.22 throughout; (2) §7.2's 'second-order is worse at lag 3' was already shown on Z_x by #5354 and is a confirmation, not a reversal; (3) the z-against-surrogate rule and the 99.9% binning deviations are unlabelled; (4) #5333 is used but missing from cites. Not claimed: any derivation of -0.216 / +0.086 / -0.143, asymptotic or height-uniform behaviour, any statement about other words, anything about route 350 numbers at x#, G2, CERT, twin-prime infinitude or a finite twin count.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"Mismatch. The formalize area covers Lean 4 formalization of accepted lemmas. #5358 contains no lemma or proof. Its results are numerical statistics over 2.7e7 gaps from a C sieve and Python analysis, accepted at rung measured, not proven. The only exact anchors (twin-pair counts 3,424,506 and 27,412,679 below 1e9 and 1e10) are known values, not new statements. Formalizing finite enumerations of this size is not what the area asks for, and no definition, assumption or quantifier of a Lean target is supplied or changed.","assumptions_md":"Provisional relevance only: #5358 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 351, lane dir-558, explore job #10692, testing whether #5354's order law for the periodic slot word Z_x holds on the real twin-pair gap word. Object: gaps g_i = p_{i+1} - p_i between consecutive lesser twin primes p <= X (p+2 may exceed X), at X = 1e7, 1e8, 1e9, 1e10 (58,979 / 440,311 / 3,424,505 / 27,412,678 gaps; up to 809 distinct gaps, unbinned). Statistics as defined in #5354 §2: S_k lag-k return, M_k = pair matrix composed k steps (cyclic), M3_2nd = second-order chain from triple counts, rel_k = (S_k - M_k)/M_k, 20-block z with M_2 held global. Instrument: twinsieve.c (segmented odd-only sieve, 1 CPU), analysed by #10688's fetched an.py and an independent analyze_cw.py; twin-pair anchors 3,424,506 and 27,412,679 hit; brute-force word match at 1e6/1e7; #5333's prime-gap table reproduced at 1e9. What #5358 measured: rel2 = -0.1935 / -0.2124 / -0.2173 / -0.2156; rel3 = +0.0723 / +0.1033 / +0.0883 / +0.0863; rel3_2nd = -0.1281 / -0.1333 / -0.1420 / -0.1435; S1/S0 0.646-0.652; block z(rel2) -4.49 / -6.87 / -8.83 / -10.44. Against the preregistered rule: the rel2 half passes at 1e9 and 1e10, |rel3| <= 0.05 fails at every rung, and the rel3 >= +0.10 falsifier does not fire at either required height. Outcome is a split: the lag-2 defect transfers, the lag-3 cancellation does not. Plug-in CMI was dropped as estimator bias. Rung measured, set by trusted review 1868 (accept, spot), whose independent Node sieve matched rel2 -0.2173, rel3 +0.0883, rel3_2nd -0.1420, block z -8.8316 at 1e9; 1e10 was not rerun independently. Review 1868 corrections carried: (1) §7.1's 'correction not constant' (block sd 0.09-0.11) measures drift of the gap marginal against the global M2; block-local sd at 1e9 is 0.017, so the lag-2 correction is about -0.22 throughout; (2) §7.2's 'second-order is worse at lag 3' was already shown on Z_x by #5354 and is a confirmation, not a reversal; (3) the z-against-surrogate rule and the 99.9% binning deviations are unlabelled; (4) #5333 is used but missing from cites. Not claimed: any derivation of -0.216 / +0.086 / -0.143, asymptotic or height-uniform behaviour, any statement about other words, anything about route 350 numbers at x#, G2, CERT, twin-prime infinitude or a finite twin count.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow transfer. The measure area extends numbered measurement scripts to larger ranges, and #5358 is a measurement ladder (1e7-1e10) with shipped instruments: twinsieve.c, analyze_cw.py, binned_cw.py and #10688's an.py. Relevant next measurements, in the source's own terms: (a) review 1868's held-out test, fitting c2 = S2/M2 and c3 = S3/M3 at one height and predicting S2/S3 at the others within +-2%, which is the source's next_step on the stored 1e10 word (~0.1 CPU-h); (b) block-local rel2/rel3 sd at 1e10, since the reported 0.09-0.11 measures marginal drift; (c) an independent 1e10 rerun, then possibly 1e11, of rel2, rel3 and rel3_2nd. Conditions for any extension: keep the object (consecutive lesser twin primes, p <= X, unbinned) and #5354's definitions; report block-local and global-M2 block statistics separately; keep CMI out unless a matched first-order surrogate is shown; preregister rungs before running. This transfers only the method and the open checks. It does not extend the accepted values beyond 1e10, does not make the split verdict height-uniform, and does not carry any route-350 number to twin primes.","assumptions_md":"Provisional relevance only: #5358 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 351, lane dir-558, explore job #10692, testing whether #5354's order law for the periodic slot word Z_x holds on the real twin-pair gap word. Object: gaps g_i = p_{i+1} - p_i between consecutive lesser twin primes p <= X (p+2 may exceed X), at X = 1e7, 1e8, 1e9, 1e10 (58,979 / 440,311 / 3,424,505 / 27,412,678 gaps; up to 809 distinct gaps, unbinned). Statistics as defined in #5354 §2: S_k lag-k return, M_k = pair matrix composed k steps (cyclic), M3_2nd = second-order chain from triple counts, rel_k = (S_k - M_k)/M_k, 20-block z with M_2 held global. Instrument: twinsieve.c (segmented odd-only sieve, 1 CPU), analysed by #10688's fetched an.py and an independent analyze_cw.py; twin-pair anchors 3,424,506 and 27,412,679 hit; brute-force word match at 1e6/1e7; #5333's prime-gap table reproduced at 1e9. What #5358 measured: rel2 = -0.1935 / -0.2124 / -0.2173 / -0.2156; rel3 = +0.0723 / +0.1033 / +0.0883 / +0.0863; rel3_2nd = -0.1281 / -0.1333 / -0.1420 / -0.1435; S1/S0 0.646-0.652; block z(rel2) -4.49 / -6.87 / -8.83 / -10.44. Against the preregistered rule: the rel2 half passes at 1e9 and 1e10, |rel3| <= 0.05 fails at every rung, and the rel3 >= +0.10 falsifier does not fire at either required height. Outcome is a split: the lag-2 defect transfers, the lag-3 cancellation does not. Plug-in CMI was dropped as estimator bias. Rung measured, set by trusted review 1868 (accept, spot), whose independent Node sieve matched rel2 -0.2173, rel3 +0.0883, rel3_2nd -0.1420, block z -8.8316 at 1e9; 1e10 was not rerun independently. Review 1868 corrections carried: (1) §7.1's 'correction not constant' (block sd 0.09-0.11) measures drift of the gap marginal against the global M2; block-local sd at 1e9 is 0.017, so the lag-2 correction is about -0.22 throughout; (2) §7.2's 'second-order is worse at lag 3' was already shown on Z_x by #5354 and is a confirmation, not a reversal; (3) the z-against-surrogate rule and the 99.9% binning deviations are unlabelled; (4) #5333 is used but missing from cites. Not claimed: any derivation of -0.216 / +0.086 / -0.143, asymptotic or height-uniform behaviour, any statement about other words, anything about route 350 numbers at x#, G2, CERT, twin-prime infinitude or a finite twin count.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Mismatch. The infinitude area seeks routes toward infinitely many twin primes outside the refuted registry. #5358 measures correlations between consecutive twin-pair gaps below 1e10. Gap-word memory (a lag-2 defect relative to the composed pair matrix) is a statistic of a finite sequence that presupposes the twins exist. It gives no lower bound on twin counts, no sieve input and no mechanism that persists as X grows. The 'continuum indexed by sieving' reading in §6 is interpretation, and the report explicitly does not derive it. No route, premise or obligation of the area is supplied.","assumptions_md":"Provisional relevance only: #5358 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 351, lane dir-558, explore job #10692, testing whether #5354's order law for the periodic slot word Z_x holds on the real twin-pair gap word. Object: gaps g_i = p_{i+1} - p_i between consecutive lesser twin primes p <= X (p+2 may exceed X), at X = 1e7, 1e8, 1e9, 1e10 (58,979 / 440,311 / 3,424,505 / 27,412,678 gaps; up to 809 distinct gaps, unbinned). Statistics as defined in #5354 §2: S_k lag-k return, M_k = pair matrix composed k steps (cyclic), M3_2nd = second-order chain from triple counts, rel_k = (S_k - M_k)/M_k, 20-block z with M_2 held global. Instrument: twinsieve.c (segmented odd-only sieve, 1 CPU), analysed by #10688's fetched an.py and an independent analyze_cw.py; twin-pair anchors 3,424,506 and 27,412,679 hit; brute-force word match at 1e6/1e7; #5333's prime-gap table reproduced at 1e9. What #5358 measured: rel2 = -0.1935 / -0.2124 / -0.2173 / -0.2156; rel3 = +0.0723 / +0.1033 / +0.0883 / +0.0863; rel3_2nd = -0.1281 / -0.1333 / -0.1420 / -0.1435; S1/S0 0.646-0.652; block z(rel2) -4.49 / -6.87 / -8.83 / -10.44. Against the preregistered rule: the rel2 half passes at 1e9 and 1e10, |rel3| <= 0.05 fails at every rung, and the rel3 >= +0.10 falsifier does not fire at either required height. Outcome is a split: the lag-2 defect transfers, the lag-3 cancellation does not. Plug-in CMI was dropped as estimator bias. Rung measured, set by trusted review 1868 (accept, spot), whose independent Node sieve matched rel2 -0.2173, rel3 +0.0883, rel3_2nd -0.1420, block z -8.8316 at 1e9; 1e10 was not rerun independently. Review 1868 corrections carried: (1) §7.1's 'correction not constant' (block sd 0.09-0.11) measures drift of the gap marginal against the global M2; block-local sd at 1e9 is 0.017, so the lag-2 correction is about -0.22 throughout; (2) §7.2's 'second-order is worse at lag 3' was already shown on Z_x by #5354 and is a confirmation, not a reversal; (3) the z-against-surrogate rule and the 99.9% binning deviations are unlabelled; (4) #5333 is used but missing from cites. Not claimed: any derivation of -0.216 / +0.086 / -0.143, asymptotic or height-uniform behaviour, any statement about other words, anything about route 350 numbers at x#, G2, CERT, twin-prime infinitude or a finite twin count.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch. The finiteness-structure area asks what structure a finite twin count would force. #5358 studies the internal order statistics of the twin-gap sequence up to 1e10, where 27.4 million pairs exist. It makes no conditional statement 'if twins are finite, then ...' and no claim about behaviour beyond the measured heights, which is where a finite count would act. The measured rel_k are consistent with both outcomes of the twin prime question, so they constrain neither. Nothing in the area's disproof-shaped program is supplied.","assumptions_md":"Provisional relevance only: #5358 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 351, lane dir-558, explore job #10692, testing whether #5354's order law for the periodic slot word Z_x holds on the real twin-pair gap word. Object: gaps g_i = p_{i+1} - p_i between consecutive lesser twin primes p <= X (p+2 may exceed X), at X = 1e7, 1e8, 1e9, 1e10 (58,979 / 440,311 / 3,424,505 / 27,412,678 gaps; up to 809 distinct gaps, unbinned). Statistics as defined in #5354 §2: S_k lag-k return, M_k = pair matrix composed k steps (cyclic), M3_2nd = second-order chain from triple counts, rel_k = (S_k - M_k)/M_k, 20-block z with M_2 held global. Instrument: twinsieve.c (segmented odd-only sieve, 1 CPU), analysed by #10688's fetched an.py and an independent analyze_cw.py; twin-pair anchors 3,424,506 and 27,412,679 hit; brute-force word match at 1e6/1e7; #5333's prime-gap table reproduced at 1e9. What #5358 measured: rel2 = -0.1935 / -0.2124 / -0.2173 / -0.2156; rel3 = +0.0723 / +0.1033 / +0.0883 / +0.0863; rel3_2nd = -0.1281 / -0.1333 / -0.1420 / -0.1435; S1/S0 0.646-0.652; block z(rel2) -4.49 / -6.87 / -8.83 / -10.44. Against the preregistered rule: the rel2 half passes at 1e9 and 1e10, |rel3| <= 0.05 fails at every rung, and the rel3 >= +0.10 falsifier does not fire at either required height. Outcome is a split: the lag-2 defect transfers, the lag-3 cancellation does not. Plug-in CMI was dropped as estimator bias. Rung measured, set by trusted review 1868 (accept, spot), whose independent Node sieve matched rel2 -0.2173, rel3 +0.0883, rel3_2nd -0.1420, block z -8.8316 at 1e9; 1e10 was not rerun independently. Review 1868 corrections carried: (1) §7.1's 'correction not constant' (block sd 0.09-0.11) measures drift of the gap marginal against the global M2; block-local sd at 1e9 is 0.017, so the lag-2 correction is about -0.22 throughout; (2) §7.2's 'second-order is worse at lag 3' was already shown on Z_x by #5354 and is a confirmation, not a reversal; (3) the z-against-surrogate rule and the 99.9% binning deviations are unlabelled; (4) #5333 is used but missing from cites. Not claimed: any derivation of -0.216 / +0.086 / -0.143, asymptotic or height-uniform behaviour, any statement about other words, anything about route 350 numbers at x#, G2, CERT, twin-prime infinitude or a finite twin count.","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 asymptotic with coefficient 1/2; O5 the quoted sieve input and one-class statement; O6 two-sided density and Euler estimates; O7 the exact constant of equation (28). #5358 proves no asymptotic, density estimate, sieve bound or constant. Its twin-pair and prime-gap counts below 1e9/1e10 are known finite anchors, and its rel_k values are finite empirical ratios. O4 and O6 say explicitly that finite one-sided data do not close them. No declaration or assumption of main or O1-O7 is touched.","assumptions_md":"Provisional relevance only: #5358 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 351, lane dir-558, explore job #10692, testing whether #5354's order law for the periodic slot word Z_x holds on the real twin-pair gap word. Object: gaps g_i = p_{i+1} - p_i between consecutive lesser twin primes p <= X (p+2 may exceed X), at X = 1e7, 1e8, 1e9, 1e10 (58,979 / 440,311 / 3,424,505 / 27,412,678 gaps; up to 809 distinct gaps, unbinned). Statistics as defined in #5354 §2: S_k lag-k return, M_k = pair matrix composed k steps (cyclic), M3_2nd = second-order chain from triple counts, rel_k = (S_k - M_k)/M_k, 20-block z with M_2 held global. Instrument: twinsieve.c (segmented odd-only sieve, 1 CPU), analysed by #10688's fetched an.py and an independent analyze_cw.py; twin-pair anchors 3,424,506 and 27,412,679 hit; brute-force word match at 1e6/1e7; #5333's prime-gap table reproduced at 1e9. What #5358 measured: rel2 = -0.1935 / -0.2124 / -0.2173 / -0.2156; rel3 = +0.0723 / +0.1033 / +0.0883 / +0.0863; rel3_2nd = -0.1281 / -0.1333 / -0.1420 / -0.1435; S1/S0 0.646-0.652; block z(rel2) -4.49 / -6.87 / -8.83 / -10.44. Against the preregistered rule: the rel2 half passes at 1e9 and 1e10, |rel3| <= 0.05 fails at every rung, and the rel3 >= +0.10 falsifier does not fire at either required height. Outcome is a split: the lag-2 defect transfers, the lag-3 cancellation does not. Plug-in CMI was dropped as estimator bias. Rung measured, set by trusted review 1868 (accept, spot), whose independent Node sieve matched rel2 -0.2173, rel3 +0.0883, rel3_2nd -0.1420, block z -8.8316 at 1e9; 1e10 was not rerun independently. Review 1868 corrections carried: (1) §7.1's 'correction not constant' (block sd 0.09-0.11) measures drift of the gap marginal against the global M2; block-local sd at 1e9 is 0.017, so the lag-2 correction is about -0.22 throughout; (2) §7.2's 'second-order is worse at lag 3' was already shown on Z_x by #5354 and is a confirmation, not a reversal; (3) the z-against-surrogate rule and the 99.9% binning deviations are unlabelled; (4) #5333 is used but missing from cites. Not claimed: any derivation of -0.216 / +0.086 / -0.143, asymptotic or height-uniform behaviour, any statement about other words, anything about route 350 numbers at x#, G2, CERT, twin-prime infinitude or a finite twin count.","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":false,"check_job_id":10729,"input_sha256":"a893ab6c93d4200aa0383236e0b8a73756441743441aae3710b678e6a5e15809","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"cdf7b757f894c4c6012e3b640c6557799d80b277d3ed17e64f3b8505ed95bac9","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5358,"material_evidence":{"sha256":"b34159b95e5bb1a236baee13361ac579c0b675b7995e09977487c2d6bb5af479","entries":{"return:5358":"8b9a4e3bd8ddab50c7dea0963acf63b77a5ee427b547b25d1fca2e9729b29188","review:5358:1:claude-opus-5-5":"a32afd98ad100f0cdd32abff5336951a7a04a53b9b49d9fd0c96c7e34d4f548f","artifact:5358:09e95f0f47b70bf85607b0f89decbf763e6bc0aeea85c07f77c93dcbed5e008e":"09e95f0f47b70bf85607b0f89decbf763e6bc0aeea85c07f77c93dcbed5e008e","artifact:5358:2599b53a5caa74344586fa99983659dd6049c70b61599d15f9190a6c899a2f02":"2599b53a5caa74344586fa99983659dd6049c70b61599d15f9190a6c899a2f02","artifact:5358:2eb282739e5fd0f50d0fdcc11ecefa149ef1a431bb15292933fc7450b5cfb71e":"2eb282739e5fd0f50d0fdcc11ecefa149ef1a431bb15292933fc7450b5cfb71e","artifact:5358:44ce5905693dc272a36232e00fbaf9960bcae83d37edce1f34bf747168fdbb10":"44ce5905693dc272a36232e00fbaf9960bcae83d37edce1f34bf747168fdbb10","artifact:5358:4d442e602049444ff7fc952b314965c4a89b929cbf7799d080ffdaeeaa42063d":"4d442e602049444ff7fc952b314965c4a89b929cbf7799d080ffdaeeaa42063d","artifact:5358:4d7dd563456f05aab431ca743feeb961cee4d9150999bd83c59813b39c600656":"4d7dd563456f05aab431ca743feeb961cee4d9150999bd83c59813b39c600656","artifact:5358:622f65a5739a58d9eefb4d4e8ca005a7b8b60818a3b13d85147cf2e126ec99e7":"622f65a5739a58d9eefb4d4e8ca005a7b8b60818a3b13d85147cf2e126ec99e7","artifact:5358:65aff82fd5949a86ba34e7b82a7c4dc8d3a63d314ea7424a2718adba7a442243":"65aff82fd5949a86ba34e7b82a7c4dc8d3a63d314ea7424a2718adba7a442243","artifact:5358:7adaed5cd3b79e3691ad7885573f1d4f2d154ad238bd1e3cc24a9c6f1785611d":"7adaed5cd3b79e3691ad7885573f1d4f2d154ad238bd1e3cc24a9c6f1785611d","artifact:5358:af8e6df0462187aa8f783a9845ab8ef44ccd58712439cfa9b32bcb5523460a14":"af8e6df0462187aa8f783a9845ab8ef44ccd58712439cfa9b32bcb5523460a14","artifact:5358:bf3ceebb53850b3ab34940089020ddeeb35c197357a0767f86875ffb82ded788":"bf3ceebb53850b3ab34940089020ddeeb35c197357a0767f86875ffb82ded788","artifact:5358:c109f40b58108664ea0eca8aaa2e48a09a13bba62d8946c30e37322c0d47aa25":"c109f40b58108664ea0eca8aaa2e48a09a13bba62d8946c30e37322c0d47aa25","artifact:5358:cdf7b757f894c4c6012e3b640c6557799d80b277d3ed17e64f3b8505ed95bac9":"cdf7b757f894c4c6012e3b640c6557799d80b277d3ed17e64f3b8505ed95bac9","artifact:5358:d2e5c48a1020ef85aa0442137ea4e6402a151f8c4955bbc678f182d1781a6a51":"d2e5c48a1020ef85aa0442137ea4e6402a151f8c4955bbc678f182d1781a6a51","artifact:5358:d88926e06a6090b8676810d565236447d3da639adbeb233f06c7b06fd0dcd1a4":"d88926e06a6090b8676810d565236447d3da639adbeb233f06c7b06fd0dcd1a4","artifact:5358:db1aaaf698047919b6e027843363dc71c7f10bc2307f842444cd06a884a304b8":"db1aaaf698047919b6e027843363dc71c7f10bc2307f842444cd06a884a304b8","artifact:5358:dff50e0b08fe9687d7444f6d98325ac56ff10f135b034d51a1a5e5ac9a95d595":"dff50e0b08fe9687d7444f6d98325ac56ff10f135b034d51a1a5e5ac9a95d595","artifact:5358:ef0a11eb584ac9cc5705a60bbe90366134eb0a19e6b07a2987ce59beab83464d":"ef0a11eb584ac9cc5705a60bbe90366134eb0a19e6b07a2987ce59beab83464d","artifact:5358:f57c374f8ad028610c3a8e2ab1e8e565af098d4a501ea5df4b7e418228eaf2c1":"f57c374f8ad028610c3a8e2ab1e8e565af098d4a501ea5df4b7e418228eaf2c1"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5358,"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 #5358: 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\":5358,\"report_sha256\":\"cdf7b757f894c4c6012e3b640c6557799d80b277d3ed17e64f3b8505ed95bac9\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5358\":\"8b9a4e3bd8ddab50c7dea0963acf63b77a5ee427b547b25d1fca2e9729b29188\",\"review:5358:1:claude-opus-5-5\":\"a32afd98ad100f0cdd32abff5336951a7a04a53b9b49d9fd0c96c7e34d4f548f\",\"artifact:5358:09e95f0f47b70bf85607b0f89decbf763e6bc0aeea85c07f77c93dcbed5e008e\":\"09e95f0f47b70bf85607b0f89decbf763e6bc0aeea85c07f77c93dcbed5e008e\",\"artifact:5358:2599b53a5caa74344586fa99983659dd6049c70b61599d15f9190a6c899a2f02\":\"2599b53a5caa74344586fa99983659dd6049c70b61599d15f9190a6c899a2f02\",\"artifact:5358:2eb282739e5fd0f50d0fdcc11ecefa149ef1a431bb15292933fc7450b5cfb71e\":\"2eb282739e5fd0f50d0fdcc11ecefa149ef1a431bb15292933fc7450b5cfb71e\",\"artifact:5358:44ce5905693dc272a36232e00fbaf9960bcae83d37edce1f34bf747168fdbb10\":\"44ce5905693dc272a36232e00fbaf9960bcae83d37edce1f34bf747168fdbb10\",\"artifact:5358:4d442e602049444ff7fc952b314965c4a89b929cbf7799d080ffdaeeaa42063d\":\"4d442e602049444ff7fc952b314965c4a89b929cbf7799d080ffdaeeaa42063d\",\"artifact:5358:4d7dd563456f05aab431ca743feeb961cee4d9150999bd83c59813b39c600656\":\"4d7dd563456f05aab431ca743feeb961cee4d9150999bd83c59813b39c600656\",\"artifact:5358:622f65a5739a58d9eefb4d4e8ca005a7b8b60818a3b13d85147cf2e126ec99e7\":\"622f65a5739a58d9eefb4d4e8ca005a7b8b60818a3b13d85147cf2e126ec99e7\",\"artifact:5358:65aff82fd5949a86ba34e7b82a7c4dc8d3a63d314ea7424a2718adba7a442243\":\"65aff82fd5949a86ba34e7b82a7c4dc8d3a63d314ea7424a2718adba7a442243\",\"artifact:5358:7adaed5cd3b79e3691ad7885573f1d4f2d154ad238bd1e3cc24a9c6f1785611d\":\"7adaed5cd3b79e3691ad7885573f1d4f2d154ad238bd1e3cc24a9c6f1785611d\",\"artifact:5358:af8e6df0462187aa8f783a9845ab8ef44ccd58712439cfa9b32bcb5523460a14\":\"af8e6df0462187aa8f783a9845ab8ef44ccd58712439cfa9b32bcb5523460a14\",\"artifact:5358:bf3ceebb53850b3ab34940089020ddeeb35c197357a0767f86875ffb82ded788\":\"bf3ceebb53850b3ab34940089020ddeeb35c197357a0767f86875ffb82ded788\",\"artifact:5358:c109f40b58108664ea0eca8aaa2e48a09a13bba62d8946c30e37322c0d47aa25\":\"c109f40b58108664ea0eca8aaa2e48a09a13bba62d8946c30e37322c0d47aa25\",\"artifact:5358:cdf7b757f894c4c6012e3b640c6557799d80b277d3ed17e64f3b8505ed95bac9\":\"cdf7b757f894c4c6012e3b640c6557799d80b277d3ed17e64f3b8505ed95bac9\",\"artifact:5358:d2e5c48a1020ef85aa0442137ea4e6402a151f8c4955bbc678f182d1781a6a51\":\"d2e5c48a1020ef85aa0442137ea4e6402a151f8c4955bbc678f182d1781a6a51\",\"artifact:5358:d88926e06a6090b8676810d565236447d3da639adbeb233f06c7b06fd0dcd1a4\":\"d88926e06a6090b8676810d565236447d3da639adbeb233f06c7b06fd0dcd1a4\",\"artifact:5358:db1aaaf698047919b6e027843363dc71c7f10bc2307f842444cd06a884a304b8\":\"db1aaaf698047919b6e027843363dc71c7f10bc2307f842444cd06a884a304b8\",\"artifact:5358:dff50e0b08fe9687d7444f6d98325ac56ff10f135b034d51a1a5e5ac9a95d595\":\"dff50e0b08fe9687d7444f6d98325ac56ff10f135b034d51a1a5e5ac9a95d595\",\"artifact:5358:ef0a11eb584ac9cc5705a60bbe90366134eb0a19e6b07a2987ce59beab83464d\":\"ef0a11eb584ac9cc5705a60bbe90366134eb0a19e6b07a2987ce59beab83464d\",\"artifact:5358:f57c374f8ad028610c3a8e2ab1e8e565af098d4a501ea5df4b7e418228eaf2c1\":\"f57c374f8ad028610c3a8e2ab1e8e565af098d4a501ea5df4b7e418228eaf2c1\"},\"sha256\":\"b34159b95e5bb1a236baee13361ac579c0b675b7995e09977487c2d6bb5af479\"},\"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:5358,input_sha256:\"a893ab6c93d4200aa0383236e0b8a73756441743441aae3710b678e6a5e15809\",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/5372/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"8066176b5fb9ae5d0dc28245ff84bcd2456a4bac069326ddc248372a940bed06","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}