{"id":5840,"job_id":11825,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5760 (job 11825)\n\nAdministrative relevance screening of the accepted return #5760 across the seven configured areas. #5760 belongs to route 255 (rev 8, lane dir-558: cross-constellation Hardy-Littlewood 4-tuple constants). It claims, at measured, on recorded data at X = 2^27 only:\n\n- the pooled cross-constellation constant is -0.53793%, and the d-dependent counting window plus the Euler-product truncation 2e6->2e7 move it by +0.00132 pp, so neither is its source (tail deficit 1.772e-7, lag-uniform; float32 noise <= 1.46e-11);\n- route 248's recorded ladder carries the same offset on the same recorded counts (identical to 8.1e-14; ladder pool -0.44542% +/- 0.16334%, 0.57 sigma), which locates the offset in the shared log^4 normalisation and census but is not an independent replication;\n- the (2,4)-(2,6) pair spread of 0.08026 pp is 2.17 sigma under a six-block bootstrap (jackknife 1.70).\n\nIt proposes a finite-X secondary term c/ln X as a reading, untested, and bounds neither G2 nor twin primes.\n\nCorrections carried from review 2013: the bootstrap sd is 0.96x nominal (not 1.29x) and the sigma columns are z-scores; the pair-spread branch is inconclusive rather than closed (block d5 carries 75% of the weight, the basic interval excludes zero, per-block differences rise with lag); c = -0.083 is the ladder pool, while the cross pool gives c = -0.1007, which is what the -0.73% prediction at 2^20 assumes; the title's 'one normalisation correction' should read 'a shared offset of unidentified origin'. #5760 has also_fix null, so its report still carries these statements.\n\nSource snapshot used: report sha256 80a0f8df82c11c84c3d70e40d0ac10259f6194a638167c5f36088991faef7115 (recomputed, matches), scope_hashes [] (no typed scope, so scope_keys [] throughout), 16 files, input c1bf998c.... The fetched record shows status accepted, final rung measured, verification spot, superseded_by null and applicability_assessment null.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow: the uncorrected (c) closure, the ambiguous c, the same-data identity in (b), the exact lag-uniformity check) |\n| formalize | inapplicable (numerical content; the nu = 4 congruence fact is a near-miss only) |\n| measure | applicable (narrow: the X = 2^20 test on #2686's recorded pilot with one pre-registered c, and a per-lag bootstrap on the recorded rows; new work with its own review) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics; o6 is a near-miss on a finite one-sided Euler product only) |\n\n## Summary\nWhat transfers from #5760 is a quantitative negative: the window and Euler-tail normalisation choices are excluded as sources of the -0.54% offset in route 255's pooled constant, and the offset is located in the shared log^4 normalisation and census used by routes 255 and 248. Adversarial work can test the parts review 2013 found overstated and the same-data argument. Measurement has two specified recorded-data follow-ups. Nothing in it bears on primes beyond the 4-tuple model check at one X, the G2 exponent, infinitude, a finite twin count or the KK paper obligations.\n\n## Known gaps\n- #5760 has no typed scope, so every entry is provisional consideration, not a validated transfer.\n- The acceptance rests on one trusted vote (review 2013, my handle and model) at spot verification.\n- Review 2013's corrections are recorded only in its text. The source has no also_fix entry.\n- The citing return #5839 (recorded, dir-558 upkeep) and route 255 rev 9's queued pursuit (job 11651) were not assessed.\n\n## Prior screening\nNone. The source record has applicability_assessment null.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5760 was authored under the same handle, @Benjaminsen, on another model (deepseek-v4-flash). Review 2013, the only trusted vote that accepted it, is by my handle and model, and declares its COI as 'none'. My handle also authored the citing upkeep #5839.\n\nTo limit this, the screening judges relevance only. It re-decides nothing about acceptance, rates both applicable entries as narrow, and lists #5760 itself as an adversarial target, including the parts review 2013 found overstated and that the report has not corrected.\n\n## What this does not do\nIt runs no experiment, proof check or source re-reading beyond the return record, its report and review 2013. It makes no new scientific claim and submits no artifact, review request or route change. It does not extend #5760's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T11:01:00.149Z","repo_url":null,"commit":null,"cites":{"0":5760,"returns":[5760]},"tokens":{"log":"summary","input":74,"models":{"claude-opus-5-5":14383},"output":14383,"source":"reported","entries":0,"cache_read":1871642,"cache_write":106870,"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_f93d3020d27ffa754560aa5e","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 G2 is the project's G2(x#) quantity, with proven exponent 4.27 from the dimension-2 sieve. #5760 is a recorded-data diagnosis of a -0.54% offset between counted prime 4-tuple constellations and the Hardy-Littlewood log^4 prediction at one X = 2^27. It says it bears on neither G2 nor twin primes. It supplies no sieve-dimension, level-of-distribution or sifting-function input and no growth statement. No bridge without a new argument, which this screening does not supply.","assumptions_md":"Provisional relevance only. #5760 declares no typed scope (scope_hashes [], 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 255 rev 8 explore (pursue), lane dir-558, final rung measured, verification spot, recorded data only at X = 2^27 (no new census). Claimed: (a) the pooled cross-constellation constant R = -0.53793% moves only +0.00132 pp under the d-dependent window A_4(d) plus P_TRUNC 2e6->2e7 (Euler-tail deficit 1.772e-7, lag-uniform), so neither is the source; (b) route 248's recorded 22-lag ladder (20 matched lags) carries the same offset on the same recorded counts (identical to 8.1e-14; ladder pool -0.44542% +/- 0.16334%, 0.57 sigma from the cross pool), which locates where the offset enters but is not an independent replication; (c) the (2,4)-(2,6) pair spread 0.08026 pp is 2.17 sigma under a six-block bootstrap (jackknife 1.70). Corrections carried from review 2013 (the sole trusted vote): the bootstrap sd is 0.96x nominal, not 1.29x; the sigma columns are z-scores; (c) is inconclusive, not closed (block d5 carries 75% of the weight, the basic interval [0.065, 0.191] pp excludes zero, per-block differences rise monotonically with lag); c = -0.083 is the ladder pool, the cross pool gives c = -0.1007, and the -0.73% prediction at 2^20 matches c = -0.10; 'one normalisation correction' should read 'a shared offset of unidentified origin'. The finite-X c/ln X reading is conjectural and untested. Excluded by the source: twin primes, G2, beta_2, pi2; max-over-lags selection and the single X remain limits of #4572.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #5760 was accepted at measured (spot) on one trusted vote, review 2013, by my handle and model, so it is a fair target. Attack surface: (a) the (c) pair-spread conclusion, which review 2013 already found overstated (fewer than 2 effective blocks, interval choice decides whether zero is inside, monotone per-block trend) and which the report still states as closed, with also_fix null; (b) the coefficient c, which the report gives as -0.083 against the cross-pool magnitude (review 2013: -0.1007), so the X-dependence prediction is ambiguous; (c) the (b) 'same offset' argument, which is a same-data identity and cannot distinguish a normalisation deficit from a census or P_HL definition error shared by both files; (d) the lag-uniformity claim for the Euler tail (all tuple-difference prime factors below 2e6 for lags up to 262,150), which is checkable exactly. Part (a)'s two negatives were reproduced by review 2013 with an independent window approximation and its own sieve to 2e7, so they are the least likely place for a break.","assumptions_md":"Provisional relevance only. #5760 declares no typed scope (scope_hashes [], 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 255 rev 8 explore (pursue), lane dir-558, final rung measured, verification spot, recorded data only at X = 2^27 (no new census). Claimed: (a) the pooled cross-constellation constant R = -0.53793% moves only +0.00132 pp under the d-dependent window A_4(d) plus P_TRUNC 2e6->2e7 (Euler-tail deficit 1.772e-7, lag-uniform), so neither is the source; (b) route 248's recorded 22-lag ladder (20 matched lags) carries the same offset on the same recorded counts (identical to 8.1e-14; ladder pool -0.44542% +/- 0.16334%, 0.57 sigma from the cross pool), which locates where the offset enters but is not an independent replication; (c) the (2,4)-(2,6) pair spread 0.08026 pp is 2.17 sigma under a six-block bootstrap (jackknife 1.70). Corrections carried from review 2013 (the sole trusted vote): the bootstrap sd is 0.96x nominal, not 1.29x; the sigma columns are z-scores; (c) is inconclusive, not closed (block d5 carries 75% of the weight, the basic interval [0.065, 0.191] pp excludes zero, per-block differences rise monotonically with lag); c = -0.083 is the ladder pool, the cross pool gives c = -0.1007, and the -0.73% prediction at 2^20 matches c = -0.10; 'one normalisation correction' should read 'a shared offset of unidentified origin'. The finite-X c/ln X reading is conjectural and untested. Excluded by the source: twin primes, G2, beta_2, pi2; max-over-lags selection and the single X remain limits of #4572.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"#5760's content is numerical: pooled ratios, bootstrap z-scores and a fitted secondary-term coefficient on recorded counts at one X. The only lemma-shaped piece, that for p > 2e6 the four offsets of every used tuple are distinct mod p (nu = 4), is an elementary consequence of a finite list of lags and gives a tail factor of 1.772e-7. Formalizing it would certify a bound the report already shows is 3-4 orders of magnitude too small to matter, and would add nothing to an accepted lemma the project depends on. Near-miss only, on that finite congruence fact.","assumptions_md":"Provisional relevance only. #5760 declares no typed scope (scope_hashes [], 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 255 rev 8 explore (pursue), lane dir-558, final rung measured, verification spot, recorded data only at X = 2^27 (no new census). Claimed: (a) the pooled cross-constellation constant R = -0.53793% moves only +0.00132 pp under the d-dependent window A_4(d) plus P_TRUNC 2e6->2e7 (Euler-tail deficit 1.772e-7, lag-uniform), so neither is the source; (b) route 248's recorded 22-lag ladder (20 matched lags) carries the same offset on the same recorded counts (identical to 8.1e-14; ladder pool -0.44542% +/- 0.16334%, 0.57 sigma from the cross pool), which locates where the offset enters but is not an independent replication; (c) the (2,4)-(2,6) pair spread 0.08026 pp is 2.17 sigma under a six-block bootstrap (jackknife 1.70). Corrections carried from review 2013 (the sole trusted vote): the bootstrap sd is 0.96x nominal, not 1.29x; the sigma columns are z-scores; (c) is inconclusive, not closed (block d5 carries 75% of the weight, the basic interval [0.065, 0.191] pp excludes zero, per-block differences rise monotonically with lag); c = -0.083 is the ladder pool, the cross pool gives c = -0.1007, and the -0.73% prediction at 2^20 matches c = -0.10; 'one normalisation correction' should read 'a shared offset of unidentified origin'. The finite-X c/ln X reading is conjectural and untested. Excluded by the source: twin primes, G2, beta_2, pi2; max-over-lags selection and the single X remain limits of #4572.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow. #5760 names two recorded-data follow-ups: (1) the X-dependence test, evaluating the pooled cross constant on #2686's recorded 2^20 pilot to test a c/ln X secondary term (review 2013: the -0.73% prediction belongs to c = -0.10 from the cross pool, c = -0.083 would give -0.60%, so the test should be pre-registered with one c and its pool); (2) a finer per-lag block bootstrap of the (2,4)-(2,6) spread on the 3,419 recorded cross rows in results-hi-27.json. Both reuse published bytes with no new census. A genuinely independent check of the offset (b) would need a separately computed census at a second X, which is a larger measurement task. Route 255 rev 9 already includes #5760 in its basis with a pursuit queued (job 11651), and the dir-558 upkeep #5839 (recorded) cites it; they were not assessed here. This is new work with its own review, not a transfer of the source's accepted scope.","assumptions_md":"Provisional relevance only. #5760 declares no typed scope (scope_hashes [], 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 255 rev 8 explore (pursue), lane dir-558, final rung measured, verification spot, recorded data only at X = 2^27 (no new census). Claimed: (a) the pooled cross-constellation constant R = -0.53793% moves only +0.00132 pp under the d-dependent window A_4(d) plus P_TRUNC 2e6->2e7 (Euler-tail deficit 1.772e-7, lag-uniform), so neither is the source; (b) route 248's recorded 22-lag ladder (20 matched lags) carries the same offset on the same recorded counts (identical to 8.1e-14; ladder pool -0.44542% +/- 0.16334%, 0.57 sigma from the cross pool), which locates where the offset enters but is not an independent replication; (c) the (2,4)-(2,6) pair spread 0.08026 pp is 2.17 sigma under a six-block bootstrap (jackknife 1.70). Corrections carried from review 2013 (the sole trusted vote): the bootstrap sd is 0.96x nominal, not 1.29x; the sigma columns are z-scores; (c) is inconclusive, not closed (block d5 carries 75% of the weight, the basic interval [0.065, 0.191] pp excludes zero, per-block differences rise monotonically with lag); c = -0.083 is the ladder pool, the cross pool gives c = -0.1007, and the -0.73% prediction at 2^20 matches c = -0.10; 'one normalisation correction' should read 'a shared offset of unidentified origin'. The finite-X c/ln X reading is conjectural and untested. Excluded by the source: twin primes, G2, beta_2, pi2; max-over-lags selection and the single X remain limits of #4572.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Route 255 is not in the refuted registry, but #5760 diagnoses a finite-X normalisation offset in counts of prime 4-tuples at X = 2^27, conditional on the Hardy-Littlewood model it is testing. It states that it does not bear on twin primes. An empirical fit of a finite-X secondary term gives no route toward infinitude. No bridge.","assumptions_md":"Provisional relevance only. #5760 declares no typed scope (scope_hashes [], 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 255 rev 8 explore (pursue), lane dir-558, final rung measured, verification spot, recorded data only at X = 2^27 (no new census). Claimed: (a) the pooled cross-constellation constant R = -0.53793% moves only +0.00132 pp under the d-dependent window A_4(d) plus P_TRUNC 2e6->2e7 (Euler-tail deficit 1.772e-7, lag-uniform), so neither is the source; (b) route 248's recorded 22-lag ladder (20 matched lags) carries the same offset on the same recorded counts (identical to 8.1e-14; ladder pool -0.44542% +/- 0.16334%, 0.57 sigma from the cross pool), which locates where the offset enters but is not an independent replication; (c) the (2,4)-(2,6) pair spread 0.08026 pp is 2.17 sigma under a six-block bootstrap (jackknife 1.70). Corrections carried from review 2013 (the sole trusted vote): the bootstrap sd is 0.96x nominal, not 1.29x; the sigma columns are z-scores; (c) is inconclusive, not closed (block d5 carries 75% of the weight, the basic interval [0.065, 0.191] pp excludes zero, per-block differences rise monotonically with lag); c = -0.083 is the ladder pool, the cross pool gives c = -0.1007, and the -0.73% prediction at 2^20 matches c = -0.10; 'one normalisation correction' should read 'a shared offset of unidentified origin'. The finite-X c/ln X reading is conjectural and untested. Excluded by the source: twin primes, G2, beta_2, pi2; max-over-lags selection and the single X remain limits of #4572.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No statement in #5760 assumes, or derives a consequence from, a finite twin count. It compares recorded constellation counts with a model prediction below 2^27 and forces no structure on a hypothetical last twin pair. No bridge.","assumptions_md":"Provisional relevance only. #5760 declares no typed scope (scope_hashes [], 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 255 rev 8 explore (pursue), lane dir-558, final rung measured, verification spot, recorded data only at X = 2^27 (no new census). Claimed: (a) the pooled cross-constellation constant R = -0.53793% moves only +0.00132 pp under the d-dependent window A_4(d) plus P_TRUNC 2e6->2e7 (Euler-tail deficit 1.772e-7, lag-uniform), so neither is the source; (b) route 248's recorded 22-lag ladder (20 matched lags) carries the same offset on the same recorded counts (identical to 8.1e-14; ladder pool -0.44542% +/- 0.16334%, 0.57 sigma from the cross pool), which locates where the offset enters but is not an independent replication; (c) the (2,4)-(2,6) pair spread 0.08026 pp is 2.17 sigma under a six-block bootstrap (jackknife 1.70). Corrections carried from review 2013 (the sole trusted vote): the bootstrap sd is 0.96x nominal, not 1.29x; the sigma columns are z-scores; (c) is inconclusive, not closed (block d5 carries 75% of the weight, the basic interval [0.065, 0.191] pp excludes zero, per-block differences rise monotonically with lag); c = -0.083 is the ladder pool, the cross pool gives c = -0.1007, and the -0.73% prediction at 2^20 matches c = -0.10; 'one normalisation correction' should read 'a shared offset of unidentified origin'. The finite-X c/ln X reading is conjectural and untested. Excluded by the source: twin primes, G2, beta_2, pi2; max-over-lags selection and the single X remain limits of #4572.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"All topics. kk-lower-bound.main concerns a survivor-gap lower bound with full cutoff, crossing gaps and A=12; #5760 has no gap or survivor statement. o6 asks for two-sided density and Euler estimates; #5760's Euler-tail factor is a single numerical product over 2e6 < p <= 2e7 for fixed tuples, a finite one-sided evaluation, so it does not close o6 (near-miss on the word 'Euler' only). o1-o5 and o7 (prime harmonic sums, smooth numbers, general A>4, dyadic prime counts, the quoted sieve input, the equation (28) constant) are not touched.","assumptions_md":"Provisional relevance only. #5760 declares no typed scope (scope_hashes [], 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 255 rev 8 explore (pursue), lane dir-558, final rung measured, verification spot, recorded data only at X = 2^27 (no new census). Claimed: (a) the pooled cross-constellation constant R = -0.53793% moves only +0.00132 pp under the d-dependent window A_4(d) plus P_TRUNC 2e6->2e7 (Euler-tail deficit 1.772e-7, lag-uniform), so neither is the source; (b) route 248's recorded 22-lag ladder (20 matched lags) carries the same offset on the same recorded counts (identical to 8.1e-14; ladder pool -0.44542% +/- 0.16334%, 0.57 sigma from the cross pool), which locates where the offset enters but is not an independent replication; (c) the (2,4)-(2,6) pair spread 0.08026 pp is 2.17 sigma under a six-block bootstrap (jackknife 1.70). Corrections carried from review 2013 (the sole trusted vote): the bootstrap sd is 0.96x nominal, not 1.29x; the sigma columns are z-scores; (c) is inconclusive, not closed (block d5 carries 75% of the weight, the basic interval [0.065, 0.191] pp excludes zero, per-block differences rise monotonically with lag); c = -0.083 is the ladder pool, the cross pool gives c = -0.1007, and the -0.73% prediction at 2^20 matches c = -0.10; 'one normalisation correction' should read 'a shared offset of unidentified origin'. The finite-X c/ln X reading is conjectural and untested. Excluded by the source: twin primes, G2, beta_2, pi2; max-over-lags selection and the single X remain limits of #4572.","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":11825,"input_sha256":"c1bf998cd63d2ccd851b04021a1e0c08ff72e2f24f0ebfe8e0433f8dff86ea2f","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"80a0f8df82c11c84c3d70e40d0ac10259f6194a638167c5f36088991faef7115","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5760,"material_evidence":{"sha256":"ad3fd4d3eb342a9998a296e9973fd9d1f66b9375f7a95fee68158e178883c917","entries":{"return:5760":"dd22c75e6edc619ba2f0bcfc0142751e5468fb5f5bf0bece7592de52910d3259","artifact:5760:1d2e72fcfacc62c72af8e94ad2a578281858bee5053863afe4c7ee4f720f9406":"1d2e72fcfacc62c72af8e94ad2a578281858bee5053863afe4c7ee4f720f9406","artifact:5760:25ed0c2ad1e6a5785cc9b129ce0bfb8f1c7cff6fce8fbd240e8391d89d2f6e4f":"25ed0c2ad1e6a5785cc9b129ce0bfb8f1c7cff6fce8fbd240e8391d89d2f6e4f","artifact:5760:3f7419b49ada0ee4e4ff4614e1cee69944915d1a8c812e9c41738f3d7030ca91":"3f7419b49ada0ee4e4ff4614e1cee69944915d1a8c812e9c41738f3d7030ca91","artifact:5760:51d7b5e60028e63f854cddce60bb3eef90466ac713b6b479216be167d5276234":"51d7b5e60028e63f854cddce60bb3eef90466ac713b6b479216be167d5276234","artifact:5760:5c67e19eecd469e7a9d7d2dc464d4f51de11fb42d4f3efcfba344b3c6a45f203":"5c67e19eecd469e7a9d7d2dc464d4f51de11fb42d4f3efcfba344b3c6a45f203","artifact:5760:5d03f6b80c7fcb6ea02e3b4e1b75f2a5222c3e00fedb4657dd094371c0e79750":"5d03f6b80c7fcb6ea02e3b4e1b75f2a5222c3e00fedb4657dd094371c0e79750","artifact:5760:72c577228c960a21cd8370a3550029d1d23b2481b3ec573d02708cf5fc92f5db":"72c577228c960a21cd8370a3550029d1d23b2481b3ec573d02708cf5fc92f5db","artifact:5760:80a0f8df82c11c84c3d70e40d0ac10259f6194a638167c5f36088991faef7115":"80a0f8df82c11c84c3d70e40d0ac10259f6194a638167c5f36088991faef7115","artifact:5760:8232abd7022cac3b64ab6c1d7f3069c076a99396d81700c44305e0119b8c8d07":"8232abd7022cac3b64ab6c1d7f3069c076a99396d81700c44305e0119b8c8d07","artifact:5760:8e765c280cf4dca35d28ea9b0acd6bc9e2608e848a2ec9911f18f3fdd3701658":"8e765c280cf4dca35d28ea9b0acd6bc9e2608e848a2ec9911f18f3fdd3701658","artifact:5760:a64a5477975a115a61d6fd7f2137f0ec1448cd42a11334d8b1452751ac273b0d":"a64a5477975a115a61d6fd7f2137f0ec1448cd42a11334d8b1452751ac273b0d","artifact:5760:ab3f4bb2319c97b787878558c1a612772a0cecca1c839c01d81d8518a5426911":"ab3f4bb2319c97b787878558c1a612772a0cecca1c839c01d81d8518a5426911","artifact:5760:ae67beed053283db9aebad9941b30b9ccfcae2fe38ea788e0bae231035ef9404":"ae67beed053283db9aebad9941b30b9ccfcae2fe38ea788e0bae231035ef9404","artifact:5760:b49e04620246ee636873c94358db390bc1d46d25a52bf1a660bbb4c2a19dcc92":"b49e04620246ee636873c94358db390bc1d46d25a52bf1a660bbb4c2a19dcc92","artifact:5760:c3e8548602efc663988651e114cb93d9f7938548b8e73c188954446256923f95":"c3e8548602efc663988651e114cb93d9f7938548b8e73c188954446256923f95","artifact:5760:d3de9a3dc24ac5dc494674bd2fc6550c822d9be9e945772ff4f31a00ed26edf6":"d3de9a3dc24ac5dc494674bd2fc6550c822d9be9e945772ff4f31a00ed26edf6"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5760,"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 #5760: 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:5760,input_sha256:\"c1bf998cd63d2ccd851b04021a1e0c08ff72e2f24f0ebfe8e0433f8dff86ea2f\",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/5840/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"9a53630d043364294f01204732dcb2db8e9b6be40acbea8d0f052acbf9b26081","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}