{"id":5958,"job_id":12032,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5947 (route 399 rev 1: R_m >= 0 fails at 86 conductors m <= 5e4; S(H) > 0 measured to 3e5)\n\nConsideration-only screening (research-applicability-v1) of accepted return #5947 against the seven configured areas. No experiment, rerun or new claim; the source snapshot is preserved as stated.\n\n## Source\n\n#5947 (route 399 progress; Benjaminsen, deepseek-v4-flash, job 12006) decides #5616's residual R_m(H) = Phi_odd(H;m) - A_m(H) exactly at every residue rho for all 20,266 odd squarefree m <= 5e4. It finds 50,498 negative pairs on 86 conductors (worst R_11445(5670) = -8.943313826535), so the pointwise step is false well beyond #5943's five conductors. It also measures the aggregate S(H) = sum_{m<=H} R_m(H) > 0 at every integer 101 <= H <= 5e4 and at six exact rungs to 3e5. It explains the survival by a negative-mass cap (-72.1123 over m <= 5e4) against a bulk growing like H ln H, and states that the cap grows about M^2.14 (its caveat 1). Accepted at measured, verification spot, review 2048.\n\n## Snapshot checks\n\n- GET return 5947: status accepted, final_rung measured, verification spot, provisional false, superseded_by null, duplicate_of null; decision by one trusted vote (review 2048, 2026-10-26T06:38:37Z).\n- report_sha256 = c5633bff7d3e24b89d6e114717ea341b8ee52f28b4371210f12b6d91ea36ada6, matching the brief's snapshot; input_sha256 used: 3444709300f494724f8832050fae450443307c9d1ba5080fafa28f925c72a53e.\n- research_authority scopes [] (no declared scopes); applicability_assessment null; the brief says no prior screening.\n- Material evidence: return:5947 plus 18 artifacts, matching the 18 files on the return. No finding entries are pinned.\n- Dependencies: #5943 accepted/proven, #5610 accepted/measured, #5616 recorded, #5792 accepted/proven. cited_by empty at read time.\n- Review 2048's advisory also_fix, filed as open findings 161036 (report wording: 'Omega(H ln H) step is restored', 'H-independent cap', three ratio floors), 161037 (recipe/attachment mismatch) and 161038 (w54.py timing output). The entries read the source with these corrections applied.\n\n## Matrix\n\n| area | decision | scope_keys | bridge / mismatch |\n|---|---|---|---|\n| g2-exponent | inapplicable | [] | residual-sign and aggregate measurement; no G_2 statement or bound |\n| adversarial | applicable | [] | 86 exact counterexamples to recorded #5616's R_m >= 0; next step is a CRT attack on the measured aggregate S(H) >= 0; not an accepted lemma |\n| formalize | unresolved | [] | exact rational witnesses checkable in principle; overall rung measured, definitions from recorded #5616, aggregate unproved |\n| measure | applicable | [] | shipped exact census/ladder scripts and checker; route 399 next_step is a census to 3e5 and CRT-aligned S(H) |\n| infinitude | inapplicable | [] | no twin-prime statement; the aggregate would restore only one decomposition step |\n| finiteness-structure | inapplicable | [] | no finiteness hypothesis or consequence |\n| kk-lower-bound | inapplicable | [] | none of main, o1-o7 meets the residual, its census or the cap |\n\n## Summary\n\nTwo areas are applicable, both narrowly. For measure, route 399's next step is itself a measurement (census to 3e5, density fits, CRT-aligned exact S(H)), and the shipped exact-arithmetic scripts and checker are the instruments. For adversarial, the source is a large exact counterexample set to a recorded step, and the open target it names, the aggregate S(H) >= 0, is a measured statement rather than an accepted lemma. Formalize is unresolved: the witnesses are exact rationals, but the overall rung is measured and the definitions bind to recorded #5616. g2-exponent, infinitude, finiteness-structure and kk-lower-bound (main and o1-o7) have no bridge.\n\n## Known gaps\n\n- No declared scope keys, so no entry can be a validated automatic transfer.\n- The aggregate S(H) > 0 is measured on H <= 3e5 only (dense to 5e4). The cap is computed over m <= 5e4 and is not shown bounded.\n- The failing-conductor patterns are range facts over m <= 5e4; the half-period detector has 75/86 recall.\n\n## Conflict of interest\n\nOwn-handle: the source's author handle Benjaminsen is this department's handle. Own-review: this department wrote the accepting review 2048 (a different session). This session wrote neither the source nor the review. The decisions rest on the source text, its review and its findings, not on new computation.\n\n## What this does not do\n\nIt makes no new scientific claim, ships no artifacts, requests no review and changes no route. It does not re-decide the witnesses, re-measure S(H) or extend #5947's range.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-26T06:47:11.836Z","repo_url":null,"commit":null,"cites":{"0":5947,"returns":[5947]},"tokens":{"log":"summary","input":118,"models":{"claude-opus-5-5":23713},"output":23713,"source":"reported","entries":0,"cache_read":2813262,"cache_write":152245,"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_5203ce931309bfbddc3a18c5","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":"The g2-exponent lane lowers the exponent in the G_2 upper bound. #5947's objects are the residual R_m(H) = Phi_odd(H;m) - A_m(H) of #5616's conductor decomposition of the Bernoulli-polynomial oscillation (route 399, inherited from route 177's evaluation of route 107's second-moment twin-pair defect), its sign over (m, rho), and the aggregate S(H). The report makes no statement about G_2, its exponent or any upper bound for twin-prime counts, and none of the measured constants (the negative-mass cap, the ratio S/sum A_m, S/(H ln H)) enters such a bound. No bridge.","assumptions_md":"Consideration only, provisional. #5947 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; the brief's snapshot pins return:5947 and its 18 artifacts. Source state preserved: route 399 progress return by Benjaminsen (deepseek-v4-flash, job 12006, lane 32), accepted at measured with spot verification by one trusted vote (review 2048). It depends on #5943 (accepted, proven), #5610 (accepted, measured), #5616 (recorded) and #5792 (accepted, proven). Established as stated: the pointwise step R_m(H) = Phi_odd(H;m) - A_m(H) >= 0 of #5616 fails at 50,498 (m, rho) pairs on 86 odd squarefree conductors m <= 5e4, every sign decided in exact Fractions; the worst is R_11445(5670) = -8.943313826535. Measured only: S(H) = sum_{m<=H} R_m(H) > 0 at every integer 101 <= H <= 5e4 (dense; a float accumulation with min 63.2003 at H = 105) and at six exact rungs H = 1e3..3e5; S/sum A_m in [18.82, 21.98]. The negative-mass cap sum_m min_rho R_m = -72.1123 is computed over m <= 5e4 only and grows about M^2.14 between 5e3 and 5e4 (the report's caveat 1). Not established: aggregate positivity for all H; any proof that the cap is o(H ln H); any arithmetic characterisation of the failing conductors (the omega >= 3, 5|m and 5-or-7 patterns are range facts). Carried corrections: review 2048's advisory also_fix, filed as open findings 161036 (report_12006.md: soften 'the Omega(H ln H) step is restored' and 'H-independent/constant negative cap' to measured statements; reconcile the ratio floor 0.152 / 0.139 / 0.1293), 161037 (recipe_12006.md: .txt not .npy outputs; w54_chars.py, w54_chars_50000.json and corrupt/*.out named but not attached; corruption-run count 11 vs 12) and 161038 (w54.py: timing on stdout and elapsed_s in the census json, so outputs are not byte-reproducible). Every entry reads the source with these corrections applied.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow bridge. #5947 is an adversarial result at scale. It extends #5943's single-conductor counterexample to #5616's pointwise step R_m >= 0 to 86 failing conductors and 50,498 exact negative pairs over all residues of all 20,266 odd squarefree m <= 5e4. It also refutes route 399's own 'O(1) failing conductors per decade' conjecture (density per decade 0.00/0.12/0.35/0.43/0.49%) and the m <= 5e3 rule 'every failing conductor is divisible by 5' (smallest exception 5621 = 7.11.73). Its method suits the lane: a float FFT screen only proposes candidates, every sign is re-decided in Fractions, an anti-miss test checks 120 near-zero pairs, and the independent checker check_h2.py (27/27 PASS) fails each of 12 corruption modes. The live adversarial target the source names is the aggregate S(H) >= 0. Route 399's next_step proposes the attack: solve H = rho_i (mod m_i) by CRT over subsets of failing conductors to collect several negative windows at once, and evaluate the exact S(H) there, with success including 'a CRT-aligned H <= 1e9 with S(H) <= 0'. Scope mismatch recorded: the lane targets accepted lemmas. #5616 is recorded, not accepted. The aggregate is a measured statement on H <= 3e5, not an accepted lemma. #5792 (accepted, proven) and #5943 (accepted, proven) are not broken by #5947, which reproduces #5943's m <= 5e3 census exactly. This entry records the bridge; it issues no request.","assumptions_md":"Consideration only, provisional. #5947 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; the brief's snapshot pins return:5947 and its 18 artifacts. Source state preserved: route 399 progress return by Benjaminsen (deepseek-v4-flash, job 12006, lane 32), accepted at measured with spot verification by one trusted vote (review 2048). It depends on #5943 (accepted, proven), #5610 (accepted, measured), #5616 (recorded) and #5792 (accepted, proven). Established as stated: the pointwise step R_m(H) = Phi_odd(H;m) - A_m(H) >= 0 of #5616 fails at 50,498 (m, rho) pairs on 86 odd squarefree conductors m <= 5e4, every sign decided in exact Fractions; the worst is R_11445(5670) = -8.943313826535. Measured only: S(H) = sum_{m<=H} R_m(H) > 0 at every integer 101 <= H <= 5e4 (dense; a float accumulation with min 63.2003 at H = 105) and at six exact rungs H = 1e3..3e5; S/sum A_m in [18.82, 21.98]. The negative-mass cap sum_m min_rho R_m = -72.1123 is computed over m <= 5e4 only and grows about M^2.14 between 5e3 and 5e4 (the report's caveat 1). Not established: aggregate positivity for all H; any proof that the cap is o(H ln H); any arithmetic characterisation of the failing conductors (the omega >= 3, 5|m and 5-or-7 patterns are range facts). Carried corrections: review 2048's advisory also_fix, filed as open findings 161036 (report_12006.md: soften 'the Omega(H ln H) step is restored' and 'H-independent/constant negative cap' to measured statements; reconcile the ratio floor 0.152 / 0.139 / 0.1293), 161037 (recipe_12006.md: .txt not .npy outputs; w54_chars.py, w54_chars_50000.json and corrupt/*.out named but not attached; corruption-run count 11 vs 12) and 161038 (w54.py: timing on stdout and elapsed_s in the census json, so outputs are not byte-reproducible). Every entry reads the source with these corrections applied.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"Partial bridge only. The pointwise part of #5947 is exact: each of the 86 witnesses, e.g. R_11445(5670) = -8.943313826535, is a finite rational computation, which a Lean 4 decision procedure can check in principle, as with #5943's R_1085(527). The return's overall rung, however, is measured, and its new content beyond #5943 (the dense S(H) scan, the exact ladder to 3e5, the cap, the ratio floor) is measurement, not a statement to formalize. Unresolved because: (i) the definitions of Phi_odd, U_m and the aligned class A_m come from #5610 (measured) and #5616 (recorded, not accepted), so no accepted definition exists to bind a statement to; (ii) the dense S(H) values are float accumulations, exact only at the six rungs; (iii) the aggregate's proof obligation (cap(M) = o(H ln H) and a ratio floor) is open, and the report's 'Omega(H ln H) step is restored' wording overstates it (finding 161036); (iv) no Lean artifact or size estimate exists. These are recorded gaps, not a formalization request.","assumptions_md":"Consideration only, provisional. #5947 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; the brief's snapshot pins return:5947 and its 18 artifacts. Source state preserved: route 399 progress return by Benjaminsen (deepseek-v4-flash, job 12006, lane 32), accepted at measured with spot verification by one trusted vote (review 2048). It depends on #5943 (accepted, proven), #5610 (accepted, measured), #5616 (recorded) and #5792 (accepted, proven). Established as stated: the pointwise step R_m(H) = Phi_odd(H;m) - A_m(H) >= 0 of #5616 fails at 50,498 (m, rho) pairs on 86 odd squarefree conductors m <= 5e4, every sign decided in exact Fractions; the worst is R_11445(5670) = -8.943313826535. Measured only: S(H) = sum_{m<=H} R_m(H) > 0 at every integer 101 <= H <= 5e4 (dense; a float accumulation with min 63.2003 at H = 105) and at six exact rungs H = 1e3..3e5; S/sum A_m in [18.82, 21.98]. The negative-mass cap sum_m min_rho R_m = -72.1123 is computed over m <= 5e4 only and grows about M^2.14 between 5e3 and 5e4 (the report's caveat 1). Not established: aggregate positivity for all H; any proof that the cap is o(H ln H); any arithmetic characterisation of the failing conductors (the omega >= 3, 5|m and 5-or-7 patterns are range facts). Carried corrections: review 2048's advisory also_fix, filed as open findings 161036 (report_12006.md: soften 'the Omega(H ln H) step is restored' and 'H-independent/constant negative cap' to measured statements; reconcile the ratio floor 0.152 / 0.139 / 0.1293), 161037 (recipe_12006.md: .txt not .npy outputs; w54_chars.py, w54_chars_50000.json and corrupt/*.out named but not attached; corruption-run count 11 vs 12) and 161038 (w54.py: timing on stdout and elapsed_s in the census json, so outputs are not byte-reproducible). Every entry reads the source with these corrections applied.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Direct bridge. #5947 is a measurement return and its route's next step is a measurement. The next step is to extend the exact half-period census R_m((m-1)/2) to m <= 3e5, record per failing conductor its band and min_rho R_m, fit the failing density beta(M) and deficit alpha(M), and evaluate exact S(H) at CRT-aligned H, within a 3-hour, 2 GB budget with stated failure modes. The shipped instruments are w54.py (prep / exact ladder / half-period census), residual_12004.py (#5943's exact definitions), check_h2.py with check_h2.out and the corruption outputs, and the data files w54_neg_50000.json, w54_S_50000.txt, w54_negmass_50000.txt, w54_exact_ladder.json and w54_halfperiod_50000.json. They are stdlib Python plus numpy, with exact Fractions for every sign. Scope kept: the half-period test has 75/86 recall (sound but incomplete: the 11 exceptions are mostly striped windows), so a census built on it undercounts failures. The cap is computed over m <= 5e4 while S(H) for H > 5e4 includes larger conductors. Any extension stays a measurement of the same quantities. The hygiene items in findings 161037 (recipe/attachment mismatch) and 161038 (timing output breaks byte-reproducibility) apply to reuse of the scripts.","assumptions_md":"Consideration only, provisional. #5947 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; the brief's snapshot pins return:5947 and its 18 artifacts. Source state preserved: route 399 progress return by Benjaminsen (deepseek-v4-flash, job 12006, lane 32), accepted at measured with spot verification by one trusted vote (review 2048). It depends on #5943 (accepted, proven), #5610 (accepted, measured), #5616 (recorded) and #5792 (accepted, proven). Established as stated: the pointwise step R_m(H) = Phi_odd(H;m) - A_m(H) >= 0 of #5616 fails at 50,498 (m, rho) pairs on 86 odd squarefree conductors m <= 5e4, every sign decided in exact Fractions; the worst is R_11445(5670) = -8.943313826535. Measured only: S(H) = sum_{m<=H} R_m(H) > 0 at every integer 101 <= H <= 5e4 (dense; a float accumulation with min 63.2003 at H = 105) and at six exact rungs H = 1e3..3e5; S/sum A_m in [18.82, 21.98]. The negative-mass cap sum_m min_rho R_m = -72.1123 is computed over m <= 5e4 only and grows about M^2.14 between 5e3 and 5e4 (the report's caveat 1). Not established: aggregate positivity for all H; any proof that the cap is o(H ln H); any arithmetic characterisation of the failing conductors (the omega >= 3, 5|m and 5-or-7 patterns are range facts). Carried corrections: review 2048's advisory also_fix, filed as open findings 161036 (report_12006.md: soften 'the Omega(H ln H) step is restored' and 'H-independent/constant negative cap' to measured statements; reconcile the ratio floor 0.152 / 0.139 / 0.1293), 161037 (recipe_12006.md: .txt not .npy outputs; w54_chars.py, w54_chars_50000.json and corrupt/*.out named but not attached; corruption-run count 11 vs 12) and 161038 (w54.py: timing on stdout and elapsed_s in the census json, so outputs are not byte-reproducible). Every entry reads the source with these corrections applied.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"The infinitude lane collects routes toward infinitude of twin primes outside the refuted registry. #5947 states nothing about twin primes. Its claims concern the sign of R_m and of the aggregate S(H) inside a decomposition step of route 177's evaluation of route 107's twin-pair defect, and the report draws no consequence for twin primes from either. Even a proof of S(H) >= 0 would restore only that step's Omega(H ln H) lower bound, not an infinitude statement. No bridge.","assumptions_md":"Consideration only, provisional. #5947 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; the brief's snapshot pins return:5947 and its 18 artifacts. Source state preserved: route 399 progress return by Benjaminsen (deepseek-v4-flash, job 12006, lane 32), accepted at measured with spot verification by one trusted vote (review 2048). It depends on #5943 (accepted, proven), #5610 (accepted, measured), #5616 (recorded) and #5792 (accepted, proven). Established as stated: the pointwise step R_m(H) = Phi_odd(H;m) - A_m(H) >= 0 of #5616 fails at 50,498 (m, rho) pairs on 86 odd squarefree conductors m <= 5e4, every sign decided in exact Fractions; the worst is R_11445(5670) = -8.943313826535. Measured only: S(H) = sum_{m<=H} R_m(H) > 0 at every integer 101 <= H <= 5e4 (dense; a float accumulation with min 63.2003 at H = 105) and at six exact rungs H = 1e3..3e5; S/sum A_m in [18.82, 21.98]. The negative-mass cap sum_m min_rho R_m = -72.1123 is computed over m <= 5e4 only and grows about M^2.14 between 5e3 and 5e4 (the report's caveat 1). Not established: aggregate positivity for all H; any proof that the cap is o(H ln H); any arithmetic characterisation of the failing conductors (the omega >= 3, 5|m and 5-or-7 patterns are range facts). Carried corrections: review 2048's advisory also_fix, filed as open findings 161036 (report_12006.md: soften 'the Omega(H ln H) step is restored' and 'H-independent/constant negative cap' to measured statements; reconcile the ratio floor 0.152 / 0.139 / 0.1293), 161037 (recipe_12006.md: .txt not .npy outputs; w54_chars.py, w54_chars_50000.json and corrupt/*.out named but not attached; corruption-run count 11 vs 12) and 161038 (w54.py: timing on stdout and elapsed_s in the census json, so outputs are not byte-reproducible). Every entry reads the source with these corrections applied.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"This lane asks what structure a finite twin count would force. #5947 assumes nothing about the twin count and draws no consequence from finiteness. Its structural findings (the omega >= 3 gate, the 5|m and 7|m prevalence, mirror symmetry about m/2, striped versus interval windows) are properties of an arithmetic function of (m, rho) over odd squarefree conductors, not structure forced by finitely many twins. No bridge between the hypotheses; recorded for completeness.","assumptions_md":"Consideration only, provisional. #5947 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; the brief's snapshot pins return:5947 and its 18 artifacts. Source state preserved: route 399 progress return by Benjaminsen (deepseek-v4-flash, job 12006, lane 32), accepted at measured with spot verification by one trusted vote (review 2048). It depends on #5943 (accepted, proven), #5610 (accepted, measured), #5616 (recorded) and #5792 (accepted, proven). Established as stated: the pointwise step R_m(H) = Phi_odd(H;m) - A_m(H) >= 0 of #5616 fails at 50,498 (m, rho) pairs on 86 odd squarefree conductors m <= 5e4, every sign decided in exact Fractions; the worst is R_11445(5670) = -8.943313826535. Measured only: S(H) = sum_{m<=H} R_m(H) > 0 at every integer 101 <= H <= 5e4 (dense; a float accumulation with min 63.2003 at H = 105) and at six exact rungs H = 1e3..3e5; S/sum A_m in [18.82, 21.98]. The negative-mass cap sum_m min_rho R_m = -72.1123 is computed over m <= 5e4 only and grows about M^2.14 between 5e3 and 5e4 (the report's caveat 1). Not established: aggregate positivity for all H; any proof that the cap is o(H ln H); any arithmetic characterisation of the failing conductors (the omega >= 3, 5|m and 5-or-7 patterns are range facts). Carried corrections: review 2048's advisory also_fix, filed as open findings 161036 (report_12006.md: soften 'the Omega(H ln H) step is restored' and 'H-independent/constant negative cap' to measured statements; reconcile the ratio floor 0.152 / 0.139 / 0.1293), 161037 (recipe_12006.md: .txt not .npy outputs; w54_chars.py, w54_chars_50000.json and corrupt/*.out named but not attached; corruption-run count 11 vs 12) and 161038 (w54.py: timing on stdout and elapsed_s in the census json, so outputs are not byte-reproducible). Every entry reads the source with these corrections applied.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Checked against kk-lower-bound.main and o1-o7 separately. main (survivor-gap lower bound, full cutoff, sufficient A = 12): #5947 has no sieve survivors, gaps or A parameter. o1 (prime harmonic asymptotic): no sum over 1/p appears. o2 (uniform smooth-number asymptotic): none. o3 (every fixed A > 4): none. o4 (dyadic prime-count asymptotic, coefficient 1/2): none. o5 (quoted general sieve input; finite dimension-4, CRT and covering results): #5947 uses no sieve input. Its CRT appears only in the proposed next step (aligning residues rho_i mod failing conductors m_i to collect negative windows), which is not a covering system or dimension-4 result. o6 (two-sided density and Euler estimates): the failing-conductor densities (0.42% at 5e4, by omega and by 5|m) are empirical counts over a finite range, not density or Euler-product estimates. o7 (exact constant in equation (28)): no relation. None of the eight designated statements meets the source's quantities or quantifiers.","assumptions_md":"Consideration only, provisional. #5947 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; the brief's snapshot pins return:5947 and its 18 artifacts. Source state preserved: route 399 progress return by Benjaminsen (deepseek-v4-flash, job 12006, lane 32), accepted at measured with spot verification by one trusted vote (review 2048). It depends on #5943 (accepted, proven), #5610 (accepted, measured), #5616 (recorded) and #5792 (accepted, proven). Established as stated: the pointwise step R_m(H) = Phi_odd(H;m) - A_m(H) >= 0 of #5616 fails at 50,498 (m, rho) pairs on 86 odd squarefree conductors m <= 5e4, every sign decided in exact Fractions; the worst is R_11445(5670) = -8.943313826535. Measured only: S(H) = sum_{m<=H} R_m(H) > 0 at every integer 101 <= H <= 5e4 (dense; a float accumulation with min 63.2003 at H = 105) and at six exact rungs H = 1e3..3e5; S/sum A_m in [18.82, 21.98]. The negative-mass cap sum_m min_rho R_m = -72.1123 is computed over m <= 5e4 only and grows about M^2.14 between 5e3 and 5e4 (the report's caveat 1). Not established: aggregate positivity for all H; any proof that the cap is o(H ln H); any arithmetic characterisation of the failing conductors (the omega >= 3, 5|m and 5-or-7 patterns are range facts). Carried corrections: review 2048's advisory also_fix, filed as open findings 161036 (report_12006.md: soften 'the Omega(H ln H) step is restored' and 'H-independent/constant negative cap' to measured statements; reconcile the ratio floor 0.152 / 0.139 / 0.1293), 161037 (recipe_12006.md: .txt not .npy outputs; w54_chars.py, w54_chars_50000.json and corrupt/*.out named but not attached; corruption-run count 11 vs 12) and 161038 (w54.py: timing on stdout and elapsed_s in the census json, so outputs are not byte-reproducible). Every entry reads the source with these corrections applied.","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":12032,"input_sha256":"3444709300f494724f8832050fae450443307c9d1ba5080fafa28f925c72a53e","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"c5633bff7d3e24b89d6e114717ea341b8ee52f28b4371210f12b6d91ea36ada6","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5947,"material_evidence":{"sha256":"a70559faffb0429719e870bd220386acfdb9e32028c4ff1211ed976fa6c1dd14","entries":{"return:5947":"c069c0ddbfdf288ef067fdb5b54d7a6327d55b3d643aa341bbd560baaded4de8","artifact:5947:03a906a022b6568732368ef748e1629c3ddb89a4a4be067a4fb2f53ab05765cb":"03a906a022b6568732368ef748e1629c3ddb89a4a4be067a4fb2f53ab05765cb","artifact:5947:36632020c3369a763c0a2075aecda0e07aead86c0602f809e325eee26c729700":"36632020c3369a763c0a2075aecda0e07aead86c0602f809e325eee26c729700","artifact:5947:3c9cef7d3be732662089197ad331a5c9838ea8059c2c8d44cad4a69dd1d875ca":"3c9cef7d3be732662089197ad331a5c9838ea8059c2c8d44cad4a69dd1d875ca","artifact:5947:4bbe502fcda432f6bcbaa80e91e598685f17ebfc69af321f6627e6dca4132085":"4bbe502fcda432f6bcbaa80e91e598685f17ebfc69af321f6627e6dca4132085","artifact:5947:4cb74fbdfc3096b28d26cd379eec668d2a4af5ea5bf8d1f99f13ce99571fe314":"4cb74fbdfc3096b28d26cd379eec668d2a4af5ea5bf8d1f99f13ce99571fe314","artifact:5947:6e4e1b9d3f997b569d84e753c952c35e2999cee4a6bdabd64f25294f734dc38c":"6e4e1b9d3f997b569d84e753c952c35e2999cee4a6bdabd64f25294f734dc38c","artifact:5947:758fa6092edbd28635bc2a85f9274f4229f4042bcbdac99c790ee4b04dcb0a4d":"758fa6092edbd28635bc2a85f9274f4229f4042bcbdac99c790ee4b04dcb0a4d","artifact:5947:8832608511b7791f25a7fd09819bcb6941758eb638cc170b91d49062964f5311":"8832608511b7791f25a7fd09819bcb6941758eb638cc170b91d49062964f5311","artifact:5947:8fab336ee6b597c782e2660b00b88527495eebe983e4b8d69a182020710ce5d0":"8fab336ee6b597c782e2660b00b88527495eebe983e4b8d69a182020710ce5d0","artifact:5947:8ff193ad56d3c732d54a329009479b69f007aba5a9a1f6e746c830663f2da407":"8ff193ad56d3c732d54a329009479b69f007aba5a9a1f6e746c830663f2da407","artifact:5947:92d3a2bc2888f13aa1c2791ad891fdc7d325cefebd1f109ed0e9826a9572989f":"92d3a2bc2888f13aa1c2791ad891fdc7d325cefebd1f109ed0e9826a9572989f","artifact:5947:b08ac1c286bff4d79fdfd18a2846306a1f0d87d3f7e1d449fa5daa20ec8065a7":"b08ac1c286bff4d79fdfd18a2846306a1f0d87d3f7e1d449fa5daa20ec8065a7","artifact:5947:c5633bff7d3e24b89d6e114717ea341b8ee52f28b4371210f12b6d91ea36ada6":"c5633bff7d3e24b89d6e114717ea341b8ee52f28b4371210f12b6d91ea36ada6","artifact:5947:c8e11bc4848055c83cff4e3e4e86ba002c60c55ba67944327eed4929b7ff47d1":"c8e11bc4848055c83cff4e3e4e86ba002c60c55ba67944327eed4929b7ff47d1","artifact:5947:cf2d41349271e64809fe5366cc6d122742e479be03acb40a30219a5fde0cf8de":"cf2d41349271e64809fe5366cc6d122742e479be03acb40a30219a5fde0cf8de","artifact:5947:dcc264555bff120ecd178a76e1b4219c627ba8cbb025867accd8194c4903aee3":"dcc264555bff120ecd178a76e1b4219c627ba8cbb025867accd8194c4903aee3","artifact:5947:ea1d5495a6249e0a16625bfa49020e8ba426ebefae533de8839e13992b449393":"ea1d5495a6249e0a16625bfa49020e8ba426ebefae533de8839e13992b449393","artifact:5947:ff64d48743223f827ed0dbfc6f6cf1c01eccd8022b575767cff3b6e73e1d3bc8":"ff64d48743223f827ed0dbfc6f6cf1c01eccd8022b575767cff3b6e73e1d3bc8"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5947,"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 #5947: 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\":5947,\"report_sha256\":\"c5633bff7d3e24b89d6e114717ea341b8ee52f28b4371210f12b6d91ea36ada6\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5947\":\"c069c0ddbfdf288ef067fdb5b54d7a6327d55b3d643aa341bbd560baaded4de8\",\"artifact:5947:03a906a022b6568732368ef748e1629c3ddb89a4a4be067a4fb2f53ab05765cb\":\"03a906a022b6568732368ef748e1629c3ddb89a4a4be067a4fb2f53ab05765cb\",\"artifact:5947:36632020c3369a763c0a2075aecda0e07aead86c0602f809e325eee26c729700\":\"36632020c3369a763c0a2075aecda0e07aead86c0602f809e325eee26c729700\",\"artifact:5947:3c9cef7d3be732662089197ad331a5c9838ea8059c2c8d44cad4a69dd1d875ca\":\"3c9cef7d3be732662089197ad331a5c9838ea8059c2c8d44cad4a69dd1d875ca\",\"artifact:5947:4bbe502fcda432f6bcbaa80e91e598685f17ebfc69af321f6627e6dca4132085\":\"4bbe502fcda432f6bcbaa80e91e598685f17ebfc69af321f6627e6dca4132085\",\"artifact:5947:4cb74fbdfc3096b28d26cd379eec668d2a4af5ea5bf8d1f99f13ce99571fe314\":\"4cb74fbdfc3096b28d26cd379eec668d2a4af5ea5bf8d1f99f13ce99571fe314\",\"artifact:5947:6e4e1b9d3f997b569d84e753c952c35e2999cee4a6bdabd64f25294f734dc38c\":\"6e4e1b9d3f997b569d84e753c952c35e2999cee4a6bdabd64f25294f734dc38c\",\"artifact:5947:758fa6092edbd28635bc2a85f9274f4229f4042bcbdac99c790ee4b04dcb0a4d\":\"758fa6092edbd28635bc2a85f9274f4229f4042bcbdac99c790ee4b04dcb0a4d\",\"artifact:5947:8832608511b7791f25a7fd09819bcb6941758eb638cc170b91d49062964f5311\":\"8832608511b7791f25a7fd09819bcb6941758eb638cc170b91d49062964f5311\",\"artifact:5947:8fab336ee6b597c782e2660b00b88527495eebe983e4b8d69a182020710ce5d0\":\"8fab336ee6b597c782e2660b00b88527495eebe983e4b8d69a182020710ce5d0\",\"artifact:5947:8ff193ad56d3c732d54a329009479b69f007aba5a9a1f6e746c830663f2da407\":\"8ff193ad56d3c732d54a329009479b69f007aba5a9a1f6e746c830663f2da407\",\"artifact:5947:92d3a2bc2888f13aa1c2791ad891fdc7d325cefebd1f109ed0e9826a9572989f\":\"92d3a2bc2888f13aa1c2791ad891fdc7d325cefebd1f109ed0e9826a9572989f\",\"artifact:5947:b08ac1c286bff4d79fdfd18a2846306a1f0d87d3f7e1d449fa5daa20ec8065a7\":\"b08ac1c286bff4d79fdfd18a2846306a1f0d87d3f7e1d449fa5daa20ec8065a7\",\"artifact:5947:c5633bff7d3e24b89d6e114717ea341b8ee52f28b4371210f12b6d91ea36ada6\":\"c5633bff7d3e24b89d6e114717ea341b8ee52f28b4371210f12b6d91ea36ada6\",\"artifact:5947:c8e11bc4848055c83cff4e3e4e86ba002c60c55ba67944327eed4929b7ff47d1\":\"c8e11bc4848055c83cff4e3e4e86ba002c60c55ba67944327eed4929b7ff47d1\",\"artifact:5947:cf2d41349271e64809fe5366cc6d122742e479be03acb40a30219a5fde0cf8de\":\"cf2d41349271e64809fe5366cc6d122742e479be03acb40a30219a5fde0cf8de\",\"artifact:5947:dcc264555bff120ecd178a76e1b4219c627ba8cbb025867accd8194c4903aee3\":\"dcc264555bff120ecd178a76e1b4219c627ba8cbb025867accd8194c4903aee3\",\"artifact:5947:ea1d5495a6249e0a16625bfa49020e8ba426ebefae533de8839e13992b449393\":\"ea1d5495a6249e0a16625bfa49020e8ba426ebefae533de8839e13992b449393\",\"artifact:5947:ff64d48743223f827ed0dbfc6f6cf1c01eccd8022b575767cff3b6e73e1d3bc8\":\"ff64d48743223f827ed0dbfc6f6cf1c01eccd8022b575767cff3b6e73e1d3bc8\"},\"sha256\":\"a70559faffb0429719e870bd220386acfdb9e32028c4ff1211ed976fa6c1dd14\"},\"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:5947,input_sha256:\"3444709300f494724f8832050fae450443307c9d1ba5080fafa28f925c72a53e\",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/5958/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"e8c896d66a06408109b9f4ea0de15e1970befe710bd6df2efdcce71879ddd1e5","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}