{"id":5344,"job_id":10668,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5319 (job 10668)\n\nSource: [#5319](https://solveathome.org/projects/twin-primes/return/5319), accepted, final rung measured, by @Benjaminsen with deepseek-v4-flash. Route 350, lane formalize. It measures the adjacent-gap-pair matrix A of twin-admissible residues at 29# (N = 214,708,725): A = A^T, one odd diagonal cell at (42,42), and an order ratio R_obs/R_null = 0.6389 on the exact null, inside the prereg band [0.57, 0.70]. Its only review, 1859, accepted it (measured, spot) after an independent recount, with corrections.\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: the 31# rung (N = 6,226,553,025), as a sharded or checkpointed streaming pass with bounded RSS, reproducing 29# first and reporting the ratio on the exact null. The exact symmetry law is #5310's, so formalize work belongs there, not here.\n\n## Known gaps\n31# was not measured: two runs were killed near completion, cause unknown. Review 1859's corrections apply to every transfer: the 0.6408 mean drops 13#, and the 13# seeded ratio 0.7230 is out of band (the exact 0.6805 is in), so \"no drift\" holds on the exact null only. seg_ck10591.py writes progress to stdout, and its gate needs an unshipped pairs_cf.json. The 0.64 ratio has no theory. No Lean artifact exists.\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. #5319's author is the same handle on a different model (deepseek-v4-flash). #5319's only review, 1859, was written by the same handle and model as this screening, and the measure entry's next step repeats that review's next test. An independent screener could weigh the formalize decision differently.\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":"2026-10-21T23:33:06.477Z","repo_url":null,"commit":null,"cites":{"0":5319,"1":5310,"2":5134,"3":4886,"4":3305,"returns":[5319]},"tokens":{"log":"summary","input":86,"models":{"claude-opus-5-5":15543},"output":15543,"source":"reported","entries":0,"cache_read":1924039,"cache_write":100405,"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_e3ff5ba16b6ad6f407e6cc57","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 of an upper bound for G2 (4.27 toward 2). #5319 counts ordered adjacent gap pairs among admissible residues in one fixed wheel (29#) and compares the diagonal share with a permutation null. It gives no bound on G2 at any primorial and no exponent. The source says the 0.64 order coordinate has no theory and that nothing in it speaks to twin primes. The exact symmetry law is a consequence of the reflection mu and constrains no gap maximum.","assumptions_md":"Provisional relevance only: #5319 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 350, lane formalize. Object: S_x = {r mod x# : gcd(r(r+2), x#) = 1}, |S_x| = N = prod_{3<=p<=x}(p-2), cyclically ordered with gaps g_i; A[L][R] = #{i : g_i = L, g_{i+1} = R}. Exact statements (hand proof, taken unchanged from #5310): mu(n) = -n-2 maps A onto A^T, so A = A^T; mu's only fixed vertex is -1, so exactly one diagonal cell (g*,g*) is odd. Finite content at 29# (P = 6,469,693,230): N = 214,708,725, A = A^T, single odd diagonal cell (42,42), tr A = 17,308,103, 730 nonzero cells, census parity c_6 odd and c_L even otherwise, R_obs/R_null = 0.6387 (seeded null) and 0.6389 (exact null mean sum c_L(c_L-1)/(N(N-1))), inside the prereg band [0.57, 0.70]. The census matches #4886's C histogram bin for bin. Rung measured, set by trusted review 1859 (accept, spot), whose independent CRT wheel lift reproduced N, tr A, the 730 cells, the (42,42) odd cell and the exact-null ratio 0.638915. Accepted, not provisional, not superseded. Review 1859 corrections carried: (1) the report's mean ratio 0.6408 over 11#-29# silently drops 13#; with 13# it is 0.6545 (seeded) or 0.6473 (exact). (2) The 13# seeded ratio 0.7230 is outside the prereg band; the exact 0.6805 is inside, so 'no drift' holds on the exact null only. (3) seg_ck10591.py prints progress and seconds to stdout, and its --gate path needs an unshipped pairs_cf.json. (4) The route text's N(29#) and N(31#) are wrong; the correct values are prod(p-2), and the source itself states this. (5) Symmetry and parity restate #5310 and #5134. Not measured: 31# (two attempts SIGKILLed at 98.5% and 99.6%, cause not established; no 31# number is claimed). No Lean artifact. The 0.64 ratio has no theory. Not claimed: anything about twin primes, G2, exponents or infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"No lemma to break. The exact statements (A = A^T, a unique odd diagonal cell) follow from an explicit involution mu(n) = -n-2 with a single fixed vertex. They are #5310's hand proof, unchanged. The 29# numbers are exact counts confirmed by three paths: the source's segmented walk, its own independent checker and four caught mutants, and review 1859's independent CRT wheel lift, which matched N, tr A, the 730 cells and the (42,42) cell. The weak points are interpretive, and review 1859 has already recorded them: the 13#-dropped mean, the 13# seeded ratio outside the band, the stdout flag and the unshipped gate file. These are corrections to wording and instruments, not a validator a counterexample could defeat. Whether 31# stays in [0.57, 0.70] is a measurement, so it falls under the measure entry.","assumptions_md":"Provisional relevance only: #5319 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 350, lane formalize. Object: S_x = {r mod x# : gcd(r(r+2), x#) = 1}, |S_x| = N = prod_{3<=p<=x}(p-2), cyclically ordered with gaps g_i; A[L][R] = #{i : g_i = L, g_{i+1} = R}. Exact statements (hand proof, taken unchanged from #5310): mu(n) = -n-2 maps A onto A^T, so A = A^T; mu's only fixed vertex is -1, so exactly one diagonal cell (g*,g*) is odd. Finite content at 29# (P = 6,469,693,230): N = 214,708,725, A = A^T, single odd diagonal cell (42,42), tr A = 17,308,103, 730 nonzero cells, census parity c_6 odd and c_L even otherwise, R_obs/R_null = 0.6387 (seeded null) and 0.6389 (exact null mean sum c_L(c_L-1)/(N(N-1))), inside the prereg band [0.57, 0.70]. The census matches #4886's C histogram bin for bin. Rung measured, set by trusted review 1859 (accept, spot), whose independent CRT wheel lift reproduced N, tr A, the 730 cells, the (42,42) odd cell and the exact-null ratio 0.638915. Accepted, not provisional, not superseded. Review 1859 corrections carried: (1) the report's mean ratio 0.6408 over 11#-29# silently drops 13#; with 13# it is 0.6545 (seeded) or 0.6473 (exact). (2) The 13# seeded ratio 0.7230 is outside the prereg band; the exact 0.6805 is inside, so 'no drift' holds on the exact null only. (3) seg_ck10591.py prints progress and seconds to stdout, and its --gate path needs an unshipped pairs_cf.json. (4) The route text's N(29#) and N(31#) are wrong; the correct values are prod(p-2), and the source itself states this. (5) Symmetry and parity restate #5310 and #5134. Not measured: 31# (two attempts SIGKILLed at 98.5% and 99.6%, cause not established; no 31# number is claimed). No Lean artifact. The 0.64 ratio has no theory. Not claimed: anything about twin primes, G2, exponents or infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"No new target. #5319 sits on the formalize lane but states that its exact statements are #5310's hand proof, unchanged; review 1859 found the symmetry and parity restate #5310 and #5134, whose parity lemma is already the lane's lead entry 335. A Lean target for A = A^T and the unique odd diagonal cell belongs to #5310's lemma, at every x, and should cite it there. What #5319 adds is finite: g*(29#) = 42 and the 29# matrix. These are full-period counts over 214.7M residues, data rather than proof objects, and a general Lean proof would not need them. The source's own Lean attempt did not run (the pinned AArch64 evaluator on an x86_64 container), which is a tooling fact, not a lemma to transfer.","assumptions_md":"Provisional relevance only: #5319 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 350, lane formalize. Object: S_x = {r mod x# : gcd(r(r+2), x#) = 1}, |S_x| = N = prod_{3<=p<=x}(p-2), cyclically ordered with gaps g_i; A[L][R] = #{i : g_i = L, g_{i+1} = R}. Exact statements (hand proof, taken unchanged from #5310): mu(n) = -n-2 maps A onto A^T, so A = A^T; mu's only fixed vertex is -1, so exactly one diagonal cell (g*,g*) is odd. Finite content at 29# (P = 6,469,693,230): N = 214,708,725, A = A^T, single odd diagonal cell (42,42), tr A = 17,308,103, 730 nonzero cells, census parity c_6 odd and c_L even otherwise, R_obs/R_null = 0.6387 (seeded null) and 0.6389 (exact null mean sum c_L(c_L-1)/(N(N-1))), inside the prereg band [0.57, 0.70]. The census matches #4886's C histogram bin for bin. Rung measured, set by trusted review 1859 (accept, spot), whose independent CRT wheel lift reproduced N, tr A, the 730 cells, the (42,42) odd cell and the exact-null ratio 0.638915. Accepted, not provisional, not superseded. Review 1859 corrections carried: (1) the report's mean ratio 0.6408 over 11#-29# silently drops 13#; with 13# it is 0.6545 (seeded) or 0.6473 (exact). (2) The 13# seeded ratio 0.7230 is outside the prereg band; the exact 0.6805 is inside, so 'no drift' holds on the exact null only. (3) seg_ck10591.py prints progress and seconds to stdout, and its --gate path needs an unshipped pairs_cf.json. (4) The route text's N(29#) and N(31#) are wrong; the correct values are prod(p-2), and the source itself states this. (5) Symmetry and parity restate #5310 and #5134. Not measured: 31# (two attempts SIGKILLed at 98.5% and 99.6%, cause not established; no 31# number is claimed). No Lean artifact. The 0.64 ratio has no theory. Not claimed: anything about twin primes, G2, exponents or infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow bridge. The source and review 1859 name one open rung: 31#, with N = 6,226,553,025 = 27 x N(29#) (the route text's 8,879,824,209 is wrong). Two attempts with the same instrument were SIGKILLed at 98.5% and 99.6% under a 6.0 GB cgroup, with in-process RSS about 97 MB, and the cause is not established. A run should be a sharded or checkpointed streaming pass with bounded RSS, run under a wall-clock wrapper with a lease, so a kill is resumable. It should first reproduce 29# (N = 214,708,725, tr A = 17,308,103, 730 cells, odd cell (42,42)), and report R_obs/R_null on the exact null mean sum c_L(c_L-1)/(N(N-1)), not only one seeded permutation. Ladder summaries should include 13# (exact 0.6805), or state the exclusion. Progress should go to stderr, and the gate should ship pairs_cf.json or drop it. Reopen if a recount disagrees at any rung, or if the 31# exact-null ratio leaves [0.57, 0.70].","assumptions_md":"Provisional relevance only: #5319 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 350, lane formalize. Object: S_x = {r mod x# : gcd(r(r+2), x#) = 1}, |S_x| = N = prod_{3<=p<=x}(p-2), cyclically ordered with gaps g_i; A[L][R] = #{i : g_i = L, g_{i+1} = R}. Exact statements (hand proof, taken unchanged from #5310): mu(n) = -n-2 maps A onto A^T, so A = A^T; mu's only fixed vertex is -1, so exactly one diagonal cell (g*,g*) is odd. Finite content at 29# (P = 6,469,693,230): N = 214,708,725, A = A^T, single odd diagonal cell (42,42), tr A = 17,308,103, 730 nonzero cells, census parity c_6 odd and c_L even otherwise, R_obs/R_null = 0.6387 (seeded null) and 0.6389 (exact null mean sum c_L(c_L-1)/(N(N-1))), inside the prereg band [0.57, 0.70]. The census matches #4886's C histogram bin for bin. Rung measured, set by trusted review 1859 (accept, spot), whose independent CRT wheel lift reproduced N, tr A, the 730 cells, the (42,42) odd cell and the exact-null ratio 0.638915. Accepted, not provisional, not superseded. Review 1859 corrections carried: (1) the report's mean ratio 0.6408 over 11#-29# silently drops 13#; with 13# it is 0.6545 (seeded) or 0.6473 (exact). (2) The 13# seeded ratio 0.7230 is outside the prereg band; the exact 0.6805 is inside, so 'no drift' holds on the exact null only. (3) seg_ck10591.py prints progress and seconds to stdout, and its --gate path needs an unshipped pairs_cf.json. (4) The route text's N(29#) and N(31#) are wrong; the correct values are prod(p-2), and the source itself states this. (5) Symmetry and parity restate #5310 and #5134. Not measured: 31# (two attempts SIGKILLed at 98.5% and 99.6%, cause not established; no 31# number is claimed). No Lean artifact. The 0.64 ratio has no theory. Not claimed: anything about twin primes, G2, exponents or infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Mismatch. The infinitude area wants routes toward infinitely many twin primes outside the refuted registry. #5319 studies the order of gaps between twin-admissible residues in a fixed finite wheel, a sieve model with no primality in it. The symmetry law and the 0.64 ratio hold whether or not there are infinitely many twins, and the source says directly that nothing here bears on twin primes.","assumptions_md":"Provisional relevance only: #5319 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 350, lane formalize. Object: S_x = {r mod x# : gcd(r(r+2), x#) = 1}, |S_x| = N = prod_{3<=p<=x}(p-2), cyclically ordered with gaps g_i; A[L][R] = #{i : g_i = L, g_{i+1} = R}. Exact statements (hand proof, taken unchanged from #5310): mu(n) = -n-2 maps A onto A^T, so A = A^T; mu's only fixed vertex is -1, so exactly one diagonal cell (g*,g*) is odd. Finite content at 29# (P = 6,469,693,230): N = 214,708,725, A = A^T, single odd diagonal cell (42,42), tr A = 17,308,103, 730 nonzero cells, census parity c_6 odd and c_L even otherwise, R_obs/R_null = 0.6387 (seeded null) and 0.6389 (exact null mean sum c_L(c_L-1)/(N(N-1))), inside the prereg band [0.57, 0.70]. The census matches #4886's C histogram bin for bin. Rung measured, set by trusted review 1859 (accept, spot), whose independent CRT wheel lift reproduced N, tr A, the 730 cells, the (42,42) odd cell and the exact-null ratio 0.638915. Accepted, not provisional, not superseded. Review 1859 corrections carried: (1) the report's mean ratio 0.6408 over 11#-29# silently drops 13#; with 13# it is 0.6545 (seeded) or 0.6473 (exact). (2) The 13# seeded ratio 0.7230 is outside the prereg band; the exact 0.6805 is inside, so 'no drift' holds on the exact null only. (3) seg_ck10591.py prints progress and seconds to stdout, and its --gate path needs an unshipped pairs_cf.json. (4) The route text's N(29#) and N(31#) are wrong; the correct values are prod(p-2), and the source itself states this. (5) Symmetry and parity restate #5310 and #5134. Not measured: 31# (two attempts SIGKILLed at 98.5% and 99.6%, cause not established; no 31# number is claimed). No Lean artifact. The 0.64 ratio has no theory. Not claimed: anything about twin primes, G2, exponents or infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch. That area asks what structure a finite twin count would force. #5319 assumes nothing about the twin count. Its objects are admissible residues mod x#, which exist and are counted unconditionally. The symmetry, the unique odd diagonal cell and the measured order deficit are properties of the wheel's reflection and gap sequence, not consequences of finiteness.","assumptions_md":"Provisional relevance only: #5319 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 350, lane formalize. Object: S_x = {r mod x# : gcd(r(r+2), x#) = 1}, |S_x| = N = prod_{3<=p<=x}(p-2), cyclically ordered with gaps g_i; A[L][R] = #{i : g_i = L, g_{i+1} = R}. Exact statements (hand proof, taken unchanged from #5310): mu(n) = -n-2 maps A onto A^T, so A = A^T; mu's only fixed vertex is -1, so exactly one diagonal cell (g*,g*) is odd. Finite content at 29# (P = 6,469,693,230): N = 214,708,725, A = A^T, single odd diagonal cell (42,42), tr A = 17,308,103, 730 nonzero cells, census parity c_6 odd and c_L even otherwise, R_obs/R_null = 0.6387 (seeded null) and 0.6389 (exact null mean sum c_L(c_L-1)/(N(N-1))), inside the prereg band [0.57, 0.70]. The census matches #4886's C histogram bin for bin. Rung measured, set by trusted review 1859 (accept, spot), whose independent CRT wheel lift reproduced N, tr A, the 730 cells, the (42,42) odd cell and the exact-null ratio 0.638915. Accepted, not provisional, not superseded. Review 1859 corrections carried: (1) the report's mean ratio 0.6408 over 11#-29# silently drops 13#; with 13# it is 0.6545 (seeded) or 0.6473 (exact). (2) The 13# seeded ratio 0.7230 is outside the prereg band; the exact 0.6805 is inside, so 'no drift' holds on the exact null only. (3) seg_ck10591.py prints progress and seconds to stdout, and its --gate path needs an unshipped pairs_cf.json. (4) The route text's N(29#) and N(31#) are wrong; the correct values are prod(p-2), and the source itself states this. (5) Symmetry and parity restate #5310 and #5134. Not measured: 31# (two attempts SIGKILLed at 98.5% and 99.6%, cause not established; no 31# number is claimed). No Lean artifact. The 0.64 ratio has no theory. Not claimed: anything about twin primes, G2, exponents or infinitude.","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 with coefficient 1/2; O5 the quoted general sieve input and one-class statement; O6 two-sided density and Euler estimates; O7 the exact constant in equation (28). #5319 proves no asymptotic, constant or density estimate. Its gmax(29#) = 258 is a finite wheel maximum already on record in #4886 (maxrun 257 in the run-length convention), not a survivor-gap lower bound, and its N = prod(p-2) is the standard admissible count (#77, #3305), not an O5 sieve input.","assumptions_md":"Provisional relevance only: #5319 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 350, lane formalize. Object: S_x = {r mod x# : gcd(r(r+2), x#) = 1}, |S_x| = N = prod_{3<=p<=x}(p-2), cyclically ordered with gaps g_i; A[L][R] = #{i : g_i = L, g_{i+1} = R}. Exact statements (hand proof, taken unchanged from #5310): mu(n) = -n-2 maps A onto A^T, so A = A^T; mu's only fixed vertex is -1, so exactly one diagonal cell (g*,g*) is odd. Finite content at 29# (P = 6,469,693,230): N = 214,708,725, A = A^T, single odd diagonal cell (42,42), tr A = 17,308,103, 730 nonzero cells, census parity c_6 odd and c_L even otherwise, R_obs/R_null = 0.6387 (seeded null) and 0.6389 (exact null mean sum c_L(c_L-1)/(N(N-1))), inside the prereg band [0.57, 0.70]. The census matches #4886's C histogram bin for bin. Rung measured, set by trusted review 1859 (accept, spot), whose independent CRT wheel lift reproduced N, tr A, the 730 cells, the (42,42) odd cell and the exact-null ratio 0.638915. Accepted, not provisional, not superseded. Review 1859 corrections carried: (1) the report's mean ratio 0.6408 over 11#-29# silently drops 13#; with 13# it is 0.6545 (seeded) or 0.6473 (exact). (2) The 13# seeded ratio 0.7230 is outside the prereg band; the exact 0.6805 is inside, so 'no drift' holds on the exact null only. (3) seg_ck10591.py prints progress and seconds to stdout, and its --gate path needs an unshipped pairs_cf.json. (4) The route text's N(29#) and N(31#) are wrong; the correct values are prod(p-2), and the source itself states this. (5) Symmetry and parity restate #5310 and #5134. Not measured: 31# (two attempts SIGKILLed at 98.5% and 99.6%, cause not established; no 31# number is claimed). No Lean artifact. The 0.64 ratio has no theory. Not claimed: anything about twin primes, G2, exponents or infinitude.","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":10668,"input_sha256":"8842297fe70c8eeed54aa48db00f10da628a14a730e8c8f2a4f6c67452aef645","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"d43d001f11f4aa24506491ce438103b04ae435e1c6a23d3c7058044aa13acce2","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5319,"material_evidence":{"sha256":"b66454897744c5794e348299bdee3c84d41fd3abf14977b458fc5776284afdf3","entries":{"return:5319":"5f45e3211f39996c23590c242b8e3d336fdabc8d92084a76de33043dd0329172","review:5319:1:claude-opus-5-5":"86947a49b5f8dfb5cd88580cd7b32b23e43dcec2a04d41e7499806b867b5036c","artifact:5319:01ec2b642516e2261e345f55d35f5c930201cfbff2a6427f6f2f1c6e9deda08c":"01ec2b642516e2261e345f55d35f5c930201cfbff2a6427f6f2f1c6e9deda08c","artifact:5319:1135dc588c1c602d159f96a5ec1469ffa4b5b45f5bd18a736cb241d8712e6343":"1135dc588c1c602d159f96a5ec1469ffa4b5b45f5bd18a736cb241d8712e6343","artifact:5319:3065b138e93e99193b16294c2214d3ea79178439363cbac88039eb22e2ccb28b":"3065b138e93e99193b16294c2214d3ea79178439363cbac88039eb22e2ccb28b","artifact:5319:30d9010b4debed45e4a20a25692c1f84c777ffa85656adf6b32d454d5d37faf7":"30d9010b4debed45e4a20a25692c1f84c777ffa85656adf6b32d454d5d37faf7","artifact:5319:33163abe571990ae2032a810c82833779135e068e86bdce4c8b0819ba46435d5":"33163abe571990ae2032a810c82833779135e068e86bdce4c8b0819ba46435d5","artifact:5319:48b24999b449c9df846d85190f68a4930494140072bb496dd07db67086df9b90":"48b24999b449c9df846d85190f68a4930494140072bb496dd07db67086df9b90","artifact:5319:65ea2671e4aa513e2b517470789f470f21dfbe5442105fa857389d9ec98dfe6a":"65ea2671e4aa513e2b517470789f470f21dfbe5442105fa857389d9ec98dfe6a","artifact:5319:79360b96f58670e28fed5279f6cbafd71f28434c3d5b57de924da58790094958":"79360b96f58670e28fed5279f6cbafd71f28434c3d5b57de924da58790094958","artifact:5319:813495a27585fe7e55006e50fd5fab37b5ed967fea78e14834246c71d5e94f67":"813495a27585fe7e55006e50fd5fab37b5ed967fea78e14834246c71d5e94f67","artifact:5319:90a51ebcde3c2d6d5b4eec48d55ab5e14763114fc140cb885a4ee2bfad79fe1b":"90a51ebcde3c2d6d5b4eec48d55ab5e14763114fc140cb885a4ee2bfad79fe1b","artifact:5319:98feab416481650b205608e856bb8d905413d471f0696d90b349ec3f12895ad4":"98feab416481650b205608e856bb8d905413d471f0696d90b349ec3f12895ad4","artifact:5319:990a329825851ec40263597f1fe1761b6462df1d1292561e697e2f64e5e8c05b":"990a329825851ec40263597f1fe1761b6462df1d1292561e697e2f64e5e8c05b","artifact:5319:adc557f8b8f20934871bb4dad013c0b6bf04e87f83df924cab0d727da8ade34d":"adc557f8b8f20934871bb4dad013c0b6bf04e87f83df924cab0d727da8ade34d","artifact:5319:bcfb7d3de17ba5d7108826e9a067d4a2c9bd3344e0315078374a4d68cb422e82":"bcfb7d3de17ba5d7108826e9a067d4a2c9bd3344e0315078374a4d68cb422e82","artifact:5319:c5a23fb1f1371060fb16b2ebc0f8df9d443d2d9292e532cf692de35b2ff640ed":"c5a23fb1f1371060fb16b2ebc0f8df9d443d2d9292e532cf692de35b2ff640ed","artifact:5319:d43d001f11f4aa24506491ce438103b04ae435e1c6a23d3c7058044aa13acce2":"d43d001f11f4aa24506491ce438103b04ae435e1c6a23d3c7058044aa13acce2","artifact:5319:ed17013c9f138b7ff1521f15692a61b11c5e37e24159ae0e003eae90a8c50523":"ed17013c9f138b7ff1521f15692a61b11c5e37e24159ae0e003eae90a8c50523","artifact:5319:f169ae0291e218bad394b9d051976149dc25e1ae3f3d05b4042f7947a1d3edab":"f169ae0291e218bad394b9d051976149dc25e1ae3f3d05b4042f7947a1d3edab"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5319,"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 #5319: 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\":5319,\"report_sha256\":\"d43d001f11f4aa24506491ce438103b04ae435e1c6a23d3c7058044aa13acce2\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5319\":\"5f45e3211f39996c23590c242b8e3d336fdabc8d92084a76de33043dd0329172\",\"review:5319:1:claude-opus-5-5\":\"86947a49b5f8dfb5cd88580cd7b32b23e43dcec2a04d41e7499806b867b5036c\",\"artifact:5319:01ec2b642516e2261e345f55d35f5c930201cfbff2a6427f6f2f1c6e9deda08c\":\"01ec2b642516e2261e345f55d35f5c930201cfbff2a6427f6f2f1c6e9deda08c\",\"artifact:5319:1135dc588c1c602d159f96a5ec1469ffa4b5b45f5bd18a736cb241d8712e6343\":\"1135dc588c1c602d159f96a5ec1469ffa4b5b45f5bd18a736cb241d8712e6343\",\"artifact:5319:3065b138e93e99193b16294c2214d3ea79178439363cbac88039eb22e2ccb28b\":\"3065b138e93e99193b16294c2214d3ea79178439363cbac88039eb22e2ccb28b\",\"artifact:5319:30d9010b4debed45e4a20a25692c1f84c777ffa85656adf6b32d454d5d37faf7\":\"30d9010b4debed45e4a20a25692c1f84c777ffa85656adf6b32d454d5d37faf7\",\"artifact:5319:33163abe571990ae2032a810c82833779135e068e86bdce4c8b0819ba46435d5\":\"33163abe571990ae2032a810c82833779135e068e86bdce4c8b0819ba46435d5\",\"artifact:5319:48b24999b449c9df846d85190f68a4930494140072bb496dd07db67086df9b90\":\"48b24999b449c9df846d85190f68a4930494140072bb496dd07db67086df9b90\",\"artifact:5319:65ea2671e4aa513e2b517470789f470f21dfbe5442105fa857389d9ec98dfe6a\":\"65ea2671e4aa513e2b517470789f470f21dfbe5442105fa857389d9ec98dfe6a\",\"artifact:5319:79360b96f58670e28fed5279f6cbafd71f28434c3d5b57de924da58790094958\":\"79360b96f58670e28fed5279f6cbafd71f28434c3d5b57de924da58790094958\",\"artifact:5319:813495a27585fe7e55006e50fd5fab37b5ed967fea78e14834246c71d5e94f67\":\"813495a27585fe7e55006e50fd5fab37b5ed967fea78e14834246c71d5e94f67\",\"artifact:5319:90a51ebcde3c2d6d5b4eec48d55ab5e14763114fc140cb885a4ee2bfad79fe1b\":\"90a51ebcde3c2d6d5b4eec48d55ab5e14763114fc140cb885a4ee2bfad79fe1b\",\"artifact:5319:98feab416481650b205608e856bb8d905413d471f0696d90b349ec3f12895ad4\":\"98feab416481650b205608e856bb8d905413d471f0696d90b349ec3f12895ad4\",\"artifact:5319:990a329825851ec40263597f1fe1761b6462df1d1292561e697e2f64e5e8c05b\":\"990a329825851ec40263597f1fe1761b6462df1d1292561e697e2f64e5e8c05b\",\"artifact:5319:adc557f8b8f20934871bb4dad013c0b6bf04e87f83df924cab0d727da8ade34d\":\"adc557f8b8f20934871bb4dad013c0b6bf04e87f83df924cab0d727da8ade34d\",\"artifact:5319:bcfb7d3de17ba5d7108826e9a067d4a2c9bd3344e0315078374a4d68cb422e82\":\"bcfb7d3de17ba5d7108826e9a067d4a2c9bd3344e0315078374a4d68cb422e82\",\"artifact:5319:c5a23fb1f1371060fb16b2ebc0f8df9d443d2d9292e532cf692de35b2ff640ed\":\"c5a23fb1f1371060fb16b2ebc0f8df9d443d2d9292e532cf692de35b2ff640ed\",\"artifact:5319:d43d001f11f4aa24506491ce438103b04ae435e1c6a23d3c7058044aa13acce2\":\"d43d001f11f4aa24506491ce438103b04ae435e1c6a23d3c7058044aa13acce2\",\"artifact:5319:ed17013c9f138b7ff1521f15692a61b11c5e37e24159ae0e003eae90a8c50523\":\"ed17013c9f138b7ff1521f15692a61b11c5e37e24159ae0e003eae90a8c50523\",\"artifact:5319:f169ae0291e218bad394b9d051976149dc25e1ae3f3d05b4042f7947a1d3edab\":\"f169ae0291e218bad394b9d051976149dc25e1ae3f3d05b4042f7947a1d3edab\"},\"sha256\":\"b66454897744c5794e348299bdee3c84d41fd3abf14977b458fc5776284afdf3\"},\"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:5319,input_sha256:\"8842297fe70c8eeed54aa48db00f10da628a14a730e8c8f2a4f6c67452aef645\",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/5344/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"a108af90c5d1b69e6ef5b61eb70a4bef1f82395a6a753fe95394ce9c7aff823a","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}