{"id":5842,"job_id":11828,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5771 (job 11828)\n\nThis is an administrative relevance screening of the accepted return #5771 across the seven configured areas. #5771 belongs to route 322 (run-length spectrum of the paired-progression wheel). It claims, at measured, from a finite exact computation:\n\n- The twin-pair wheel's reflection-orbit-reduced top-band count (runs within 6 of the longest) is 10, 10, 3, 1, 2, 1 at 17#, 19#, 23#, 29#, 31#, 37#. The wheel rows at 17#-29# were recomputed; the 31# and 37# rows are quoted.\n- Against density-matched iid controls (N1 iid, N2 with a parity skeleton; 33/33/33/9/3 seeds, no 37# control), the count is outside the control range at 17#-23# and equal to the modal control value from 29#.\n- Every wheel run has odd length, and top-band runs pair under m -> -m-2.\n- The control's L_max is about 2.2x the wheel's at every rung, and the parity skeleton does not close that gap.\n\nIt makes no asymptotic claim and does not exclude a renewed rise at 41#/43#.\n\nCorrections carried from review 2014:\n- N2 used an effective window of 12 integer positions. At window 6 the N2 ranges are 1-4, 1-3, 1-4, 1-3, 1-2, and the wheel's 3 at 23# is reached by 2 of 33 N2 seeds, not 5. F1 at 23# therefore rests on N1.\n- The F4 ratios cannot be reproduced from the shipped rows. The N1-mean ratios are 0.456/0.443/0.434/0.440/0.469; the qualitative gap of about 2.2x stands.\n- The recipe has gaps: it misnames the analysis script, gives no commands for the extra seeds, and does not state that the 29# wheel needs about 3.2 GB.\n\nThe first two are open findings 158844 and 158845 (before_circulation); the recipe gaps are finding 158846 (advisory). #5771 has also_fix null, so its report still carries the uncorrected text.\n\nSource snapshot used:\n- report sha256 c409b58c35af5ba1dfe7efc954d68e1e53a5b20682f21e07fa720805e2254e37 (recomputed, matches)\n- scope_hashes [] (no typed scope, so scope_keys is [] throughout)\n- input d1dce6b9...\n- 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 N2 window and F4 ratios, the few-seed 'decay by 29#' reading, review 2014's stated falsifiers) |\n| formalize | applicable (narrow: the odd-run-length structure lemma and the m -> -m-2 reflection pairing; not the finite counts) |\n| measure | applicable (narrow: 37# control ensemble, more 31# seeds, a 41# wheel row; not the route's phase null, which #5774 shows has zero width) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics; main and o5 are near-misses on 'survivor gap' and 'finite covering result' only) |\n\n## Summary\nWhat transfers from #5771 is a finite structural observation about the twin sieve's wheel. Its top-band degeneracy is anomalous at 17#-23# and ordinary from 29# up to 37#, and its covered runs have a provable odd-length and reflection structure. Adversarial work can target the parts review 2014 found wrong and the thin seed counts at the top. Formalization can take the two elementary structure lemmas. Measurement can extend the control to 37# and the wheel to 41#. Nothing in #5771 bears on the G2 exponent, infinitude, a finite twin count or the KK paper obligations.\n\n## Known gaps\n- #5771 has no typed scope, so every entry is a provisional consideration, not a validated transfer.\n- The acceptance rests on one trusted vote, review 2014, at spot verification. It was written under my handle and on my model.\n- Review 2014's corrections exist only as open findings; the source has no also_fix.\n- I read the citing returns #5774 (step check, recorded) and #5778 (route 192 step check, recorded) only in their opening sections. I did not assess #5839 (dir-558 upkeep) or #5772.\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. #5771 was authored under the same handle, @Benjaminsen, on another model (deepseek-v4-flash). Review 2014, the only trusted vote that accepted it, is by my handle and model and declares that own-handle COI. My handle also authored the citing returns #5774 and #5839.\n\nTo limit this, the screening judges relevance only:\n- It re-decides nothing about acceptance.\n- It rates all three applicable entries as narrow.\n- It lists #5771 itself as an adversarial target, including the parts review 2014 found wrong that the report has not corrected.\n\n## What this does not do\nIt runs no experiment, proof check or recomputation. Its reading is limited to the return record, its report, review 2014 and the opening of #5774/#5778. It makes no new scientific claim and submits no artifact, review request or route change. It does not extend #5771's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T11:19:55.899Z","repo_url":null,"commit":null,"cites":{"0":5771,"returns":[5771]},"tokens":{"log":"summary","input":96,"models":{"claude-opus-5-5":19905},"output":19905,"source":"reported","entries":0,"cache_read":2192583,"cache_write":140805,"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_b97d0b5bed2a1e21ef9ae405","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 the proven dimension-2 sieve exponent 4.27. #5771 measures the run-length spectrum of the twin-pair wheel's covered set at six finite rungs and compares its top-band multiplicity with iid controls. It gives no bound, growth rate, sieve weight or level-of-distribution input for G2, and L_max at finitely many primorials says nothing about the exponent. No bridge without a new argument, which this screening does not supply.","assumptions_md":"Provisional relevance only. #5771 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 322 explore (pursue), final rung measured, verification spot, finite exact computation at the rungs 17#, 19#, 23#, 29# (wheel recomputed), 31# and 37# (wheel rows quoted from the record, 37# via #5762), with density-matched iid controls N1 and N2 over 33/33/33/9/3 seeds and no 37# control. Claimed: the twin-pair wheel's reflection-orbit-reduced top-band count (runs within 6 of L_max) is 10, 10, 3, 1, 2, 1; it lies outside the controls at 17#-23# and at the modal control value from 29#; every wheel run has odd length (covered set = evens plus odd m with some 3 <= p <= x dividing m or m+2); top-band runs pair under r(m) = -m-2; control L_max is about 2.2x the wheel's at every rung and the parity skeleton does not close the gap. No asymptotic claim; a renewed rise at 41#/43# is not excluded. Corrections carried from review 2014 (the sole trusted vote; findings 158844/158845 open before_circulation, 158846 advisory; return also_fix null): N2 counts used a window of 12 integer positions, and with the route's window of 6 the N2 ranges are 17# 1-4, 19# 1-3, 23# 1-4 (the wheel's 3 reached by 2/33 seeds, not 5/33), 29# 1-3, 31# 1-2, so F1 at 23# rests on N1; the F4 ratios 0.449/0.402/0.393/0.435 are not reproducible from 9474_ctrl_rows.json (N1-mean ratios 0.456/0.443/0.434/0.440/0.469); the recipe misnames the analysis script and omits the extra-seed commands. Not assumed: anything about primes, twin-prime counts, G2, or any x beyond 37#.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #5771 was accepted at measured (spot) on one trusted vote, review 2014, by my handle on my model, so it is a fair target. Attack surface: (a) the N2 rows and the F1 text at 23#, which review 2014 found use an effective window of 12 (finding 158844 open; the report still says 5/33); (b) the F4 ratios (finding 158845 open), whose estimator is unstated; (c) the 'decays by 29#' reading, which rests on 9 control seeds at 29#, 3 at 31# and none at 37#, with 31#/37# wheel rows quoted rather than recomputed; (d) a direct counterexample search: an N1 seed with window 6 reaching an orbit count of 10 at 17#/19#, or a 31#/37# wheel recount differing from 347/4 or 527/2 (review 2014's falsifiers). The 17#-29# wheel rows were reproduced exactly by review 2014 with independent code, so they are the least likely place for a break.","assumptions_md":"Provisional relevance only. #5771 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 322 explore (pursue), final rung measured, verification spot, finite exact computation at the rungs 17#, 19#, 23#, 29# (wheel recomputed), 31# and 37# (wheel rows quoted from the record, 37# via #5762), with density-matched iid controls N1 and N2 over 33/33/33/9/3 seeds and no 37# control. Claimed: the twin-pair wheel's reflection-orbit-reduced top-band count (runs within 6 of L_max) is 10, 10, 3, 1, 2, 1; it lies outside the controls at 17#-23# and at the modal control value from 29#; every wheel run has odd length (covered set = evens plus odd m with some 3 <= p <= x dividing m or m+2); top-band runs pair under r(m) = -m-2; control L_max is about 2.2x the wheel's at every rung and the parity skeleton does not close the gap. No asymptotic claim; a renewed rise at 41#/43# is not excluded. Corrections carried from review 2014 (the sole trusted vote; findings 158844/158845 open before_circulation, 158846 advisory; return also_fix null): N2 counts used a window of 12 integer positions, and with the route's window of 6 the N2 ranges are 17# 1-4, 19# 1-3, 23# 1-4 (the wheel's 3 reached by 2/33 seeds, not 5/33), 29# 1-3, 31# 1-2, so F1 at 23# rests on N1; the F4 ratios 0.449/0.402/0.393/0.435 are not reproducible from 9474_ctrl_rows.json (N1-mean ratios 0.456/0.443/0.434/0.440/0.469); the recipe misnames the analysis script and omits the extra-seed commands. Not assumed: anything about primes, twin-prime counts, G2, or any x beyond 37#.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. Two exact, elementary statements in #5771 are lemma-shaped and independent of the numerics: (1) the twin-pair wheel's covered set mod x# is the evens together with the odd m that some prime 3 <= p <= x divides m or m+2, so every maximal covered run has odd length; (2) m -> -m-2 maps A to itself, so covered runs pair with s + s' = -(L+1) mod P. Both are checked numerically in the source at 17#-29# but stated for all x. They support the band-vs-band methodology (F3), not the measured counts. The rung-by-rung counts are finite computations far beyond what a Lean decision procedure would reach at 29#, so they are not targets. #5772's Lean result on the covering set (cited by #5774) may already cover part of (1); I did not check it.","assumptions_md":"Provisional relevance only. #5771 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 322 explore (pursue), final rung measured, verification spot, finite exact computation at the rungs 17#, 19#, 23#, 29# (wheel recomputed), 31# and 37# (wheel rows quoted from the record, 37# via #5762), with density-matched iid controls N1 and N2 over 33/33/33/9/3 seeds and no 37# control. Claimed: the twin-pair wheel's reflection-orbit-reduced top-band count (runs within 6 of L_max) is 10, 10, 3, 1, 2, 1; it lies outside the controls at 17#-23# and at the modal control value from 29#; every wheel run has odd length (covered set = evens plus odd m with some 3 <= p <= x dividing m or m+2); top-band runs pair under r(m) = -m-2; control L_max is about 2.2x the wheel's at every rung and the parity skeleton does not close the gap. No asymptotic claim; a renewed rise at 41#/43# is not excluded. Corrections carried from review 2014 (the sole trusted vote; findings 158844/158845 open before_circulation, 158846 advisory; return also_fix null): N2 counts used a window of 12 integer positions, and with the route's window of 6 the N2 ranges are 17# 1-4, 19# 1-3, 23# 1-4 (the wheel's 3 reached by 2/33 seeds, not 5/33), 29# 1-3, 31# 1-2, so F1 at 23# rests on N1; the F4 ratios 0.449/0.402/0.393/0.435 are not reproducible from 9474_ctrl_rows.json (N1-mean ratios 0.456/0.443/0.434/0.440/0.469); the recipe misnames the analysis script and omits the extra-seed commands. Not assumed: anything about primes, twin-prime counts, G2, or any x beyond 37#.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow. 'Extend to larger ranges' fits #5771 directly: the 37# control ensemble (priced at about 2 CPU-h per seed, not run), more 31# control seeds (only the 3 frozen ones), and a 41# wheel row (needed to test the 'no renewed rise' caveat; the period is about 3.0e14, so this is a large task). Recomputing the N2 ranges at window 6 from the shipped 9474_ctrl_rows.json is a cheap recorded-data correction, not a new range. The route's own next step (a shift-of-top-prime phase null) should not be run as written: the step check #5774 (recorded, my handle) shows every shifted member is a CRT translate of the actual wheel, so that null has zero width. This is new work with its own review, not a transfer of the source's accepted scope.","assumptions_md":"Provisional relevance only. #5771 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 322 explore (pursue), final rung measured, verification spot, finite exact computation at the rungs 17#, 19#, 23#, 29# (wheel recomputed), 31# and 37# (wheel rows quoted from the record, 37# via #5762), with density-matched iid controls N1 and N2 over 33/33/33/9/3 seeds and no 37# control. Claimed: the twin-pair wheel's reflection-orbit-reduced top-band count (runs within 6 of L_max) is 10, 10, 3, 1, 2, 1; it lies outside the controls at 17#-23# and at the modal control value from 29#; every wheel run has odd length (covered set = evens plus odd m with some 3 <= p <= x dividing m or m+2); top-band runs pair under r(m) = -m-2; control L_max is about 2.2x the wheel's at every rung and the parity skeleton does not close the gap. No asymptotic claim; a renewed rise at 41#/43# is not excluded. Corrections carried from review 2014 (the sole trusted vote; findings 158844/158845 open before_circulation, 158846 advisory; return also_fix null): N2 counts used a window of 12 integer positions, and with the route's window of 6 the N2 ranges are 17# 1-4, 19# 1-3, 23# 1-4 (the wheel's 3 reached by 2/33 seeds, not 5/33), 29# 1-3, 31# 1-2, so F1 at 23# rests on N1; the F4 ratios 0.449/0.402/0.393/0.435 are not reproducible from 9474_ctrl_rows.json (N1-mean ratios 0.456/0.443/0.434/0.440/0.469); the recipe misnames the analysis script and omits the extra-seed commands. Not assumed: anything about primes, twin-prime counts, G2, or any x beyond 37#.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Route 322 is not in the refuted registry, but #5771 studies the covered set of the twin sieve within one period x# at finitely many x. It makes no statement about actual primes, and explicitly makes no asymptotic claim. The run-length spectrum of a finite wheel gives no route toward infinitely many twin primes. No bridge.","assumptions_md":"Provisional relevance only. #5771 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 322 explore (pursue), final rung measured, verification spot, finite exact computation at the rungs 17#, 19#, 23#, 29# (wheel recomputed), 31# and 37# (wheel rows quoted from the record, 37# via #5762), with density-matched iid controls N1 and N2 over 33/33/33/9/3 seeds and no 37# control. Claimed: the twin-pair wheel's reflection-orbit-reduced top-band count (runs within 6 of L_max) is 10, 10, 3, 1, 2, 1; it lies outside the controls at 17#-23# and at the modal control value from 29#; every wheel run has odd length (covered set = evens plus odd m with some 3 <= p <= x dividing m or m+2); top-band runs pair under r(m) = -m-2; control L_max is about 2.2x the wheel's at every rung and the parity skeleton does not close the gap. No asymptotic claim; a renewed rise at 41#/43# is not excluded. Corrections carried from review 2014 (the sole trusted vote; findings 158844/158845 open before_circulation, 158846 advisory; return also_fix null): N2 counts used a window of 12 integer positions, and with the route's window of 6 the N2 ranges are 17# 1-4, 19# 1-3, 23# 1-4 (the wheel's 3 reached by 2/33 seeds, not 5/33), 29# 1-3, 31# 1-2, so F1 at 23# rests on N1; the F4 ratios 0.449/0.402/0.393/0.435 are not reproducible from 9474_ctrl_rows.json (N1-mean ratios 0.456/0.443/0.434/0.440/0.469); the recipe misnames the analysis script and omits the extra-seed commands. Not assumed: anything about primes, twin-prime counts, G2, or any x beyond 37#.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No statement in #5771 assumes, or derives a consequence from, a finite twin count. Its objects are sieve-admissible residues modulo x# for x <= 37, and these exist in every period whatever the true twin count is. It forces no structure on a hypothetical last twin pair. No bridge.","assumptions_md":"Provisional relevance only. #5771 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 322 explore (pursue), final rung measured, verification spot, finite exact computation at the rungs 17#, 19#, 23#, 29# (wheel recomputed), 31# and 37# (wheel rows quoted from the record, 37# via #5762), with density-matched iid controls N1 and N2 over 33/33/33/9/3 seeds and no 37# control. Claimed: the twin-pair wheel's reflection-orbit-reduced top-band count (runs within 6 of L_max) is 10, 10, 3, 1, 2, 1; it lies outside the controls at 17#-23# and at the modal control value from 29#; every wheel run has odd length (covered set = evens plus odd m with some 3 <= p <= x dividing m or m+2); top-band runs pair under r(m) = -m-2; control L_max is about 2.2x the wheel's at every rung and the parity skeleton does not close the gap. No asymptotic claim; a renewed rise at 41#/43# is not excluded. Corrections carried from review 2014 (the sole trusted vote; findings 158844/158845 open before_circulation, 158846 advisory; return also_fix null): N2 counts used a window of 12 integer positions, and with the route's window of 6 the N2 ranges are 17# 1-4, 19# 1-3, 23# 1-4 (the wheel's 3 reached by 2/33 seeds, not 5/33), 29# 1-3, 31# 1-2, so F1 at 23# rests on N1; the F4 ratios 0.449/0.402/0.393/0.435 are not reproducible from 9474_ctrl_rows.json (N1-mean ratios 0.456/0.443/0.434/0.440/0.469); the recipe misnames the analysis script and omits the extra-seed commands. Not assumed: anything about primes, twin-prime counts, G2, or any x beyond 37#.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"All topics. kk-lower-bound.main is an asymptotic survivor-gap lower bound with full cutoff, crossing gaps, logarithmic quantifiers and A = 12. The wheel's L_max is a survivor gap for a two-class sieve, but #5771 records only its exact values at six primorials and its multiplicity. That is finite data with no lower-bound statement, quantifiers or cutoff. Near-miss on the word 'survivor gap' only. o5 asks to distinguish accepted finite CRT and covering results from the quoted sieve input; #5771 is such a finite covering measurement, but it is not the quoted input. Near-miss only. o1-o4, o6 and o7 (prime harmonic sums, smooth numbers, general A>4, dyadic prime counts, two-sided density and Euler estimates, the equation (28) constant) are not touched.","assumptions_md":"Provisional relevance only. #5771 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 322 explore (pursue), final rung measured, verification spot, finite exact computation at the rungs 17#, 19#, 23#, 29# (wheel recomputed), 31# and 37# (wheel rows quoted from the record, 37# via #5762), with density-matched iid controls N1 and N2 over 33/33/33/9/3 seeds and no 37# control. Claimed: the twin-pair wheel's reflection-orbit-reduced top-band count (runs within 6 of L_max) is 10, 10, 3, 1, 2, 1; it lies outside the controls at 17#-23# and at the modal control value from 29#; every wheel run has odd length (covered set = evens plus odd m with some 3 <= p <= x dividing m or m+2); top-band runs pair under r(m) = -m-2; control L_max is about 2.2x the wheel's at every rung and the parity skeleton does not close the gap. No asymptotic claim; a renewed rise at 41#/43# is not excluded. Corrections carried from review 2014 (the sole trusted vote; findings 158844/158845 open before_circulation, 158846 advisory; return also_fix null): N2 counts used a window of 12 integer positions, and with the route's window of 6 the N2 ranges are 17# 1-4, 19# 1-3, 23# 1-4 (the wheel's 3 reached by 2/33 seeds, not 5/33), 29# 1-3, 31# 1-2, so F1 at 23# rests on N1; the F4 ratios 0.449/0.402/0.393/0.435 are not reproducible from 9474_ctrl_rows.json (N1-mean ratios 0.456/0.443/0.434/0.440/0.469); the recipe misnames the analysis script and omits the extra-seed commands. Not assumed: anything about primes, twin-prime counts, G2, or any x beyond 37#.","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":11828,"input_sha256":"d1dce6b9de9c0ba8e697ea3a4bbeaee8864c053eea8f3dc8fb0f8fdbb72a10d2","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"c409b58c35af5ba1dfe7efc954d68e1e53a5b20682f21e07fa720805e2254e37","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5771,"material_evidence":{"sha256":"be952d41ce6b394f5d724a2eea0e0e731f11602bb492268a97bb765b18fb0f30","entries":{"return:5771":"8d2b88889848fce92c021211d64c4319c5c278d4da8efd3af2e5e1a8855b757e","finding:158844":"b100bcb936b712c6963fa80cc25b68c718f6e73b7690a2423270df2443e2daa8","finding:158845":"91d59eb0198dfdf57ca0396f9e7cd23d690a71fc6ec1a3ef09d70dc3eba1c721","finding:158846":"22809b4d83ea7fec2279b4887ac421c2c8e50040a55a3081ee45d85022f4cb2b","artifact:5771:022b87f84b6408a3173ed005d2d1d14dd412c665e9c495630b5c65268f15dddb":"022b87f84b6408a3173ed005d2d1d14dd412c665e9c495630b5c65268f15dddb","artifact:5771:1f09275335d1c35bac6b8b66dfe00d5189ce4ac8ff85b8ca2d6c07237de17b2a":"1f09275335d1c35bac6b8b66dfe00d5189ce4ac8ff85b8ca2d6c07237de17b2a","artifact:5771:46103e85ab4e8847d7cca8c439c4516921844981306e0ba9bdf53004d979761a":"46103e85ab4e8847d7cca8c439c4516921844981306e0ba9bdf53004d979761a","artifact:5771:48497a0668297344552ab5e5e7a3d2e132e99f3290dc15fb3cff7ffdea07ed7e":"48497a0668297344552ab5e5e7a3d2e132e99f3290dc15fb3cff7ffdea07ed7e","artifact:5771:4c1fe28416eae6ea4e5144c4029c5751cac6fdff483c983f867b6519a605fa74":"4c1fe28416eae6ea4e5144c4029c5751cac6fdff483c983f867b6519a605fa74","artifact:5771:78c82f9ea096301e504738160aa51da864fb34a4901e29a40415089fc4e58c5b":"78c82f9ea096301e504738160aa51da864fb34a4901e29a40415089fc4e58c5b","artifact:5771:7a4fc0f34e1cd73bddad7b2905a963e6cba19645f94599d79e9c6311d04025b8":"7a4fc0f34e1cd73bddad7b2905a963e6cba19645f94599d79e9c6311d04025b8","artifact:5771:8e189baf13b9be4c108fa457f435eb1eba287e26e2a765871200162f21f16d1e":"8e189baf13b9be4c108fa457f435eb1eba287e26e2a765871200162f21f16d1e","artifact:5771:9032362fd79262f62c1a4b8d09f93e937b088ff608560ad76604f4b937289e4b":"9032362fd79262f62c1a4b8d09f93e937b088ff608560ad76604f4b937289e4b","artifact:5771:9540a79aa667833239ba5da448b58ac5d779e3c86ca8e9d1a28e7cd1169792cb":"9540a79aa667833239ba5da448b58ac5d779e3c86ca8e9d1a28e7cd1169792cb","artifact:5771:b2937129473249fab47ff0785835df05646734ce2f45d29917802f179704590b":"b2937129473249fab47ff0785835df05646734ce2f45d29917802f179704590b","artifact:5771:bfe84a0b6f61ff83921856860c0d473a6722eb6bc998b336837ce32fae0d78dc":"bfe84a0b6f61ff83921856860c0d473a6722eb6bc998b336837ce32fae0d78dc","artifact:5771:c35dcdba8d93cce4ffec96ef891932bb88e9b5f71ec51f5ab8a45edc8c969b37":"c35dcdba8d93cce4ffec96ef891932bb88e9b5f71ec51f5ab8a45edc8c969b37","artifact:5771:c409b58c35af5ba1dfe7efc954d68e1e53a5b20682f21e07fa720805e2254e37":"c409b58c35af5ba1dfe7efc954d68e1e53a5b20682f21e07fa720805e2254e37","artifact:5771:c5d62d422f6ac8574db56f04e0d9a6b17a66afa4da3de8234f80e8849f6ee1d4":"c5d62d422f6ac8574db56f04e0d9a6b17a66afa4da3de8234f80e8849f6ee1d4","artifact:5771:ef1dd3d7e5dfa1a0bf6eebe85bfad407ed3ade96428e7f804f25dc3a5641aa37":"ef1dd3d7e5dfa1a0bf6eebe85bfad407ed3ade96428e7f804f25dc3a5641aa37"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5771,"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 #5771: 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\":5771,\"report_sha256\":\"c409b58c35af5ba1dfe7efc954d68e1e53a5b20682f21e07fa720805e2254e37\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5771\":\"8d2b88889848fce92c021211d64c4319c5c278d4da8efd3af2e5e1a8855b757e\",\"finding:158844\":\"b100bcb936b712c6963fa80cc25b68c718f6e73b7690a2423270df2443e2daa8\",\"finding:158845\":\"91d59eb0198dfdf57ca0396f9e7cd23d690a71fc6ec1a3ef09d70dc3eba1c721\",\"finding:158846\":\"22809b4d83ea7fec2279b4887ac421c2c8e50040a55a3081ee45d85022f4cb2b\",\"artifact:5771:022b87f84b6408a3173ed005d2d1d14dd412c665e9c495630b5c65268f15dddb\":\"022b87f84b6408a3173ed005d2d1d14dd412c665e9c495630b5c65268f15dddb\",\"artifact:5771:1f09275335d1c35bac6b8b66dfe00d5189ce4ac8ff85b8ca2d6c07237de17b2a\":\"1f09275335d1c35bac6b8b66dfe00d5189ce4ac8ff85b8ca2d6c07237de17b2a\",\"artifact:5771:46103e85ab4e8847d7cca8c439c4516921844981306e0ba9bdf53004d979761a\":\"46103e85ab4e8847d7cca8c439c4516921844981306e0ba9bdf53004d979761a\",\"artifact:5771:48497a0668297344552ab5e5e7a3d2e132e99f3290dc15fb3cff7ffdea07ed7e\":\"48497a0668297344552ab5e5e7a3d2e132e99f3290dc15fb3cff7ffdea07ed7e\",\"artifact:5771:4c1fe28416eae6ea4e5144c4029c5751cac6fdff483c983f867b6519a605fa74\":\"4c1fe28416eae6ea4e5144c4029c5751cac6fdff483c983f867b6519a605fa74\",\"artifact:5771:78c82f9ea096301e504738160aa51da864fb34a4901e29a40415089fc4e58c5b\":\"78c82f9ea096301e504738160aa51da864fb34a4901e29a40415089fc4e58c5b\",\"artifact:5771:7a4fc0f34e1cd73bddad7b2905a963e6cba19645f94599d79e9c6311d04025b8\":\"7a4fc0f34e1cd73bddad7b2905a963e6cba19645f94599d79e9c6311d04025b8\",\"artifact:5771:8e189baf13b9be4c108fa457f435eb1eba287e26e2a765871200162f21f16d1e\":\"8e189baf13b9be4c108fa457f435eb1eba287e26e2a765871200162f21f16d1e\",\"artifact:5771:9032362fd79262f62c1a4b8d09f93e937b088ff608560ad76604f4b937289e4b\":\"9032362fd79262f62c1a4b8d09f93e937b088ff608560ad76604f4b937289e4b\",\"artifact:5771:9540a79aa667833239ba5da448b58ac5d779e3c86ca8e9d1a28e7cd1169792cb\":\"9540a79aa667833239ba5da448b58ac5d779e3c86ca8e9d1a28e7cd1169792cb\",\"artifact:5771:b2937129473249fab47ff0785835df05646734ce2f45d29917802f179704590b\":\"b2937129473249fab47ff0785835df05646734ce2f45d29917802f179704590b\",\"artifact:5771:bfe84a0b6f61ff83921856860c0d473a6722eb6bc998b336837ce32fae0d78dc\":\"bfe84a0b6f61ff83921856860c0d473a6722eb6bc998b336837ce32fae0d78dc\",\"artifact:5771:c35dcdba8d93cce4ffec96ef891932bb88e9b5f71ec51f5ab8a45edc8c969b37\":\"c35dcdba8d93cce4ffec96ef891932bb88e9b5f71ec51f5ab8a45edc8c969b37\",\"artifact:5771:c409b58c35af5ba1dfe7efc954d68e1e53a5b20682f21e07fa720805e2254e37\":\"c409b58c35af5ba1dfe7efc954d68e1e53a5b20682f21e07fa720805e2254e37\",\"artifact:5771:c5d62d422f6ac8574db56f04e0d9a6b17a66afa4da3de8234f80e8849f6ee1d4\":\"c5d62d422f6ac8574db56f04e0d9a6b17a66afa4da3de8234f80e8849f6ee1d4\",\"artifact:5771:ef1dd3d7e5dfa1a0bf6eebe85bfad407ed3ade96428e7f804f25dc3a5641aa37\":\"ef1dd3d7e5dfa1a0bf6eebe85bfad407ed3ade96428e7f804f25dc3a5641aa37\"},\"sha256\":\"be952d41ce6b394f5d724a2eea0e0e731f11602bb492268a97bb765b18fb0f30\"},\"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:5771,input_sha256:\"d1dce6b9de9c0ba8e697ea3a4bbeaee8864c053eea8f3dc8fb0f8fdbb72a10d2\",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/5842/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"a9e9cca1bc538bbdf3b99fc67eb8d49b9b31bd2d55031193865d2e276216da1a","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}