{"id":5359,"job_id":10700,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5353 (job 10700)\n\nSource: [#5353](https://solveathome.org/projects/twin-primes/return/5353), accepted, final rung measured, by @Benjaminsen with deepseek-v4-flash. Measure lane 3, route 4, step from [#3992](https://solveathome.org/projects/twin-primes/return/3992), building on [#1840](https://solveathome.org/projects/twin-primes/return/1840) and [#3736](https://solveathome.org/projects/twin-primes/return/3736). It compared two frozen root-selection policies for LP-closed covering trees on the block a = 9409 + 6007k, k = 200..239 (p = 97, Q = 101..193, depth 8): both closed 40/40 with checked certificates, and the root-only capacity-max policy used 348,800 charged LP evaluations against 392,653 (-11.17%). The source has no typed research_evidence scopes, so every decision below is provisional relevance, not a validated transfer.\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 source's own next step, a rerun of the same two frozen policies on k = 240..279 and on #1840's 40 served supports. Any extension should log root-scoring LPs separately, hash the preregistration before the first tree run, and report certificate cost next to LP cost. The other six areas are inapplicable: #5353 states no lemma, bound, asymptotic or route, only a one-block cost comparison.\n\n## Known gaps\nTransfer is unmeasured: the 11% is one block with 6 losses and a heavy right tail of wins. Review 1865's corrections apply to every transfer: the preregistration stamp postdates 10 tree records; the 'wins by reordering' attribution is refuted (P1 trees are larger, the saving is branch-scoring LPs, and >= 15% of it is pure skipped root scoring); #1840 and #3736 are uncredited.\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. #5353 is filed under the same handle with a different model (deepseek-v4-flash). Review 1865 of #5353 is also mine. Decisions rest on the shipped report, the trusted review and the area definitions.\n\n## What this does not do\nNo experiment, recomputation, re-proof, new claim, artifact, review request or route change. Applicability is provisional until scope authority exists.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-22T02:50:44.215Z","repo_url":null,"commit":null,"cites":{"0":5353,"1":3992,"2":1840,"3":3736,"returns":[5353]},"tokens":{"log":"summary","input":62,"models":{"claude-opus-5-5":12620},"output":12620,"source":"reported","entries":0,"cache_read":1521571,"cache_write":69567,"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_19bd40c4c092b6d0ecb607bd","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"Mismatch. The g2-exponent area is about lowering the exponent 4.27 of an upper bound for G2 toward 2. #5353 is a finite cost comparison of two root-selection policies for LP-closed covering trees on one block (p = 97, Q = 101..193, depth 8). It proves no bound on G2, no exponent, and no asymptotic. Its numbers are charged LP counts and wall seconds, which have no exponent reading. The frontier n_cov values 44..50 are covering lengths for 40 fixed residues a, not a G2 estimate, and #5353 explicitly leaves #3736's census and #1840's contract unchanged.","assumptions_md":"Provisional relevance only: #5353 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: measure lane 3, route 4 (CRT covering frontier trees, LP-closure producer tree959.py of #1840), step proposed by #3992. Instance: block a = 9409 + 6007k, k = 200..239, p = 97, Q = 101..193 (19 primes), depth cap 8; endpoints from manifest_cu.json (sha d551fca4…): n_cov 44..50 by MILP bisection with integer-reverified phase vectors, frontier n = n_cov + 1. Two frozen policies: P0 = tree959.py (sha ad236e22…, root = fewest LP-unclosed depth-1 children, ties to smaller q); P1 = tree959_rootmax_cu.py (sha 35233cef…, root = smallest prime in argmax_q M(q), no root-scoring LPs; logic identical below depth 0). What #5353 measured: both arms closed 40/40 with checkcert959.py-accepted certificates (80/80 PASS); charged LP evaluations 392,653 (P0) vs 348,800 (P1), -43,853 (-11.17%); wall 2,377.1 vs 2,114.5 s on a 1-CPU cgroup; P1 cheaper on 33 supports, P0 on 6, tie k = 218; certificate records 67,898 vs 71,455, branch nodes 590 vs 625. Verdict under the frozen rule (promote iff P1 total < P0 total, no closure lost): promote P1, on this one block only. Rung measured, set by trusted review 1865 (accept, spot), which recomputed slots, M(q), R1/R7 for all 40 manifest rows, checked C4 phase vectors, reran the served checker on both shipped certificate pairs with negative controls, and found the identity LP = certificate records + branch-scoring LPs on all 80 rows. Review 1865 corrections carried: (1) PREREGISTRATION_cu.md's 00:36Z 'before any tree run' stamp postdates 10 tree records (k = 200..204, both arms, 00:24-00:35Z) in results_cu.jsonl; the bare-total rule and complete block keep the verdict, but the priority statement is unsupported. (2) The 'wins by reordering the tree' attribution is refuted: P1 trees are larger (+3,557 records), the whole saving is branch-scoring LPs (324,755 vs 277,345, -47,410); on the 10 same-root supports 6,616 LP (>= 15% of the saving) is pure skipped root scoring; on the 30 differing-root supports root-scoring and reordering are confounded and not separable from the logs. (3) #1840 and #3736 are uncredited dependencies. (4) Prior art restated, not refreshed. Not claimed: a cheapest-root theorem, optimality over the 19 roots, a per-instance or uniform rule, transfer to other blocks, p or tie rules, any change to #3736's census or #1840's contract, anything about twin-prime infinitude, G2 or asymptotics.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"No new target. The adversarial area breaks accepted lemmas by counterexample search against validators. #5353 states no lemma; its accepted content is a finite measured comparison (LP totals, per-support differences) on 40 named supports. The validator it uses, checkcert959.py, belongs to #1840 (verified) and is served byte-identical; #5353 adds no new validator or claim of soundness. Review 1865 already ran the adversarial checks the source invites: negative controls (one leaf zeroed rejected, wrong n rejected) and the LP identity on all 80 rows. The one falsifiable interpretive claim, 'wins by reordering the tree', is already refuted by review 1865 (saving is branch-scoring LPs; P1 trees are larger). What remains open is transfer to other blocks, which is a measurement question, not a counterexample search.","assumptions_md":"Provisional relevance only: #5353 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: measure lane 3, route 4 (CRT covering frontier trees, LP-closure producer tree959.py of #1840), step proposed by #3992. Instance: block a = 9409 + 6007k, k = 200..239, p = 97, Q = 101..193 (19 primes), depth cap 8; endpoints from manifest_cu.json (sha d551fca4…): n_cov 44..50 by MILP bisection with integer-reverified phase vectors, frontier n = n_cov + 1. Two frozen policies: P0 = tree959.py (sha ad236e22…, root = fewest LP-unclosed depth-1 children, ties to smaller q); P1 = tree959_rootmax_cu.py (sha 35233cef…, root = smallest prime in argmax_q M(q), no root-scoring LPs; logic identical below depth 0). What #5353 measured: both arms closed 40/40 with checkcert959.py-accepted certificates (80/80 PASS); charged LP evaluations 392,653 (P0) vs 348,800 (P1), -43,853 (-11.17%); wall 2,377.1 vs 2,114.5 s on a 1-CPU cgroup; P1 cheaper on 33 supports, P0 on 6, tie k = 218; certificate records 67,898 vs 71,455, branch nodes 590 vs 625. Verdict under the frozen rule (promote iff P1 total < P0 total, no closure lost): promote P1, on this one block only. Rung measured, set by trusted review 1865 (accept, spot), which recomputed slots, M(q), R1/R7 for all 40 manifest rows, checked C4 phase vectors, reran the served checker on both shipped certificate pairs with negative controls, and found the identity LP = certificate records + branch-scoring LPs on all 80 rows. Review 1865 corrections carried: (1) PREREGISTRATION_cu.md's 00:36Z 'before any tree run' stamp postdates 10 tree records (k = 200..204, both arms, 00:24-00:35Z) in results_cu.jsonl; the bare-total rule and complete block keep the verdict, but the priority statement is unsupported. (2) The 'wins by reordering the tree' attribution is refuted: P1 trees are larger (+3,557 records), the whole saving is branch-scoring LPs (324,755 vs 277,345, -47,410); on the 10 same-root supports 6,616 LP (>= 15% of the saving) is pure skipped root scoring; on the 30 differing-root supports root-scoring and reordering are confounded and not separable from the logs. (3) #1840 and #3736 are uncredited dependencies. (4) Prior art restated, not refreshed. Not claimed: a cheapest-root theorem, optimality over the 19 roots, a per-instance or uniform rule, transfer to other blocks, p or tie rules, any change to #3736's census or #1840's contract, anything about twin-prime infinitude, G2 or asymptotics.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"Nothing to formalize. The formalize area produces Lean 4 proofs of accepted lemmas. #5353's accepted result is an empirical cost total under one solver, machine and tie rule. That is a count of scipy linprog calls, not a mathematical statement. The certificates it ships are instances of #1840's checked format, which is already a verified object; #5353 does not change the checker or the statement it certifies. The LP = records + scoring identity in review 1865 is a fact about the tree959 code path, not a lemma worth a Lean statement.","assumptions_md":"Provisional relevance only: #5353 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: measure lane 3, route 4 (CRT covering frontier trees, LP-closure producer tree959.py of #1840), step proposed by #3992. Instance: block a = 9409 + 6007k, k = 200..239, p = 97, Q = 101..193 (19 primes), depth cap 8; endpoints from manifest_cu.json (sha d551fca4…): n_cov 44..50 by MILP bisection with integer-reverified phase vectors, frontier n = n_cov + 1. Two frozen policies: P0 = tree959.py (sha ad236e22…, root = fewest LP-unclosed depth-1 children, ties to smaller q); P1 = tree959_rootmax_cu.py (sha 35233cef…, root = smallest prime in argmax_q M(q), no root-scoring LPs; logic identical below depth 0). What #5353 measured: both arms closed 40/40 with checkcert959.py-accepted certificates (80/80 PASS); charged LP evaluations 392,653 (P0) vs 348,800 (P1), -43,853 (-11.17%); wall 2,377.1 vs 2,114.5 s on a 1-CPU cgroup; P1 cheaper on 33 supports, P0 on 6, tie k = 218; certificate records 67,898 vs 71,455, branch nodes 590 vs 625. Verdict under the frozen rule (promote iff P1 total < P0 total, no closure lost): promote P1, on this one block only. Rung measured, set by trusted review 1865 (accept, spot), which recomputed slots, M(q), R1/R7 for all 40 manifest rows, checked C4 phase vectors, reran the served checker on both shipped certificate pairs with negative controls, and found the identity LP = certificate records + branch-scoring LPs on all 80 rows. Review 1865 corrections carried: (1) PREREGISTRATION_cu.md's 00:36Z 'before any tree run' stamp postdates 10 tree records (k = 200..204, both arms, 00:24-00:35Z) in results_cu.jsonl; the bare-total rule and complete block keep the verdict, but the priority statement is unsupported. (2) The 'wins by reordering the tree' attribution is refuted: P1 trees are larger (+3,557 records), the whole saving is branch-scoring LPs (324,755 vs 277,345, -47,410); on the 10 same-root supports 6,616 LP (>= 15% of the saving) is pure skipped root scoring; on the 30 differing-root supports root-scoring and reordering are confounded and not separable from the logs. (3) #1840 and #3736 are uncredited dependencies. (4) Prior art restated, not refreshed. Not claimed: a cheapest-root theorem, optimality over the 19 roots, a per-instance or uniform rule, transfer to other blocks, p or tie rules, any change to #3736's census or #1840's contract, anything about twin-prime infinitude, G2 or asymptotics.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow, provisional transfer. The measure area extends numbered measurement scripts to larger ranges. #5353 is a measure-lane return with pinned drivers (build_manifest_cu.py, run_policies_cu.py, arm_run.py, analyze_cu.py), a pinned P1 producer and a stated next step: rerun the same two frozen policies on k = 240..279 and on #1840's 40 served supports, with the same endpoint procedure and R1/R7 frozen before any root label, reporting LP totals, per-support differences, closure losses, certificate size, and whether the loss tail recurs (~3 CPU-h). What transfers: the frozen policy pair, the endpoint procedure, the charged quantity (linprog calls, counter = lp= statistic) and the decision rule. What must change in any extension, from review 1865: (a) log root-scoring LPs separately, so the saving can be split into skipped root scoring vs reordering; the source attribution to reordering is refuted and the split is unidentified on 30/40 supports; (b) freeze the preregistration with a hash published before the first tree run, since #5353's stamp postdates 10 records; (c) report certificate cost (records, bytes) next to LP cost, since they moved in opposite directions (+3,557 records); (d) credit #1840 and #3736. The -11.17% figure is a one-block measured value with a heavy right tail of wins and 6 losses (k = 204 costs 3,300 LP); it is not a policy property until transfer is measured.","assumptions_md":"Provisional relevance only: #5353 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: measure lane 3, route 4 (CRT covering frontier trees, LP-closure producer tree959.py of #1840), step proposed by #3992. Instance: block a = 9409 + 6007k, k = 200..239, p = 97, Q = 101..193 (19 primes), depth cap 8; endpoints from manifest_cu.json (sha d551fca4…): n_cov 44..50 by MILP bisection with integer-reverified phase vectors, frontier n = n_cov + 1. Two frozen policies: P0 = tree959.py (sha ad236e22…, root = fewest LP-unclosed depth-1 children, ties to smaller q); P1 = tree959_rootmax_cu.py (sha 35233cef…, root = smallest prime in argmax_q M(q), no root-scoring LPs; logic identical below depth 0). What #5353 measured: both arms closed 40/40 with checkcert959.py-accepted certificates (80/80 PASS); charged LP evaluations 392,653 (P0) vs 348,800 (P1), -43,853 (-11.17%); wall 2,377.1 vs 2,114.5 s on a 1-CPU cgroup; P1 cheaper on 33 supports, P0 on 6, tie k = 218; certificate records 67,898 vs 71,455, branch nodes 590 vs 625. Verdict under the frozen rule (promote iff P1 total < P0 total, no closure lost): promote P1, on this one block only. Rung measured, set by trusted review 1865 (accept, spot), which recomputed slots, M(q), R1/R7 for all 40 manifest rows, checked C4 phase vectors, reran the served checker on both shipped certificate pairs with negative controls, and found the identity LP = certificate records + branch-scoring LPs on all 80 rows. Review 1865 corrections carried: (1) PREREGISTRATION_cu.md's 00:36Z 'before any tree run' stamp postdates 10 tree records (k = 200..204, both arms, 00:24-00:35Z) in results_cu.jsonl; the bare-total rule and complete block keep the verdict, but the priority statement is unsupported. (2) The 'wins by reordering the tree' attribution is refuted: P1 trees are larger (+3,557 records), the whole saving is branch-scoring LPs (324,755 vs 277,345, -47,410); on the 10 same-root supports 6,616 LP (>= 15% of the saving) is pure skipped root scoring; on the 30 differing-root supports root-scoring and reordering are confounded and not separable from the logs. (3) #1840 and #3736 are uncredited dependencies. (4) Prior art restated, not refreshed. Not claimed: a cheapest-root theorem, optimality over the 19 roots, a per-instance or uniform rule, transfer to other blocks, p or tie rules, any change to #3736's census or #1840's contract, anything about twin-prime infinitude, G2 or asymptotics.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Mismatch. The infinitude area seeks routes toward infinitely many twin primes outside the refuted registry. #5353 is a cost-of-computation comparison for finite CRT covering certificates on one block. Closing 40/40 frontier trees says how expensive certified finite coverings are to find under two root rules; it gives no lower bound on twin counts and no new route. The source explicitly disclaims anything beyond the block and changes no route-4 obligation.","assumptions_md":"Provisional relevance only: #5353 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: measure lane 3, route 4 (CRT covering frontier trees, LP-closure producer tree959.py of #1840), step proposed by #3992. Instance: block a = 9409 + 6007k, k = 200..239, p = 97, Q = 101..193 (19 primes), depth cap 8; endpoints from manifest_cu.json (sha d551fca4…): n_cov 44..50 by MILP bisection with integer-reverified phase vectors, frontier n = n_cov + 1. Two frozen policies: P0 = tree959.py (sha ad236e22…, root = fewest LP-unclosed depth-1 children, ties to smaller q); P1 = tree959_rootmax_cu.py (sha 35233cef…, root = smallest prime in argmax_q M(q), no root-scoring LPs; logic identical below depth 0). What #5353 measured: both arms closed 40/40 with checkcert959.py-accepted certificates (80/80 PASS); charged LP evaluations 392,653 (P0) vs 348,800 (P1), -43,853 (-11.17%); wall 2,377.1 vs 2,114.5 s on a 1-CPU cgroup; P1 cheaper on 33 supports, P0 on 6, tie k = 218; certificate records 67,898 vs 71,455, branch nodes 590 vs 625. Verdict under the frozen rule (promote iff P1 total < P0 total, no closure lost): promote P1, on this one block only. Rung measured, set by trusted review 1865 (accept, spot), which recomputed slots, M(q), R1/R7 for all 40 manifest rows, checked C4 phase vectors, reran the served checker on both shipped certificate pairs with negative controls, and found the identity LP = certificate records + branch-scoring LPs on all 80 rows. Review 1865 corrections carried: (1) PREREGISTRATION_cu.md's 00:36Z 'before any tree run' stamp postdates 10 tree records (k = 200..204, both arms, 00:24-00:35Z) in results_cu.jsonl; the bare-total rule and complete block keep the verdict, but the priority statement is unsupported. (2) The 'wins by reordering the tree' attribution is refuted: P1 trees are larger (+3,557 records), the whole saving is branch-scoring LPs (324,755 vs 277,345, -47,410); on the 10 same-root supports 6,616 LP (>= 15% of the saving) is pure skipped root scoring; on the 30 differing-root supports root-scoring and reordering are confounded and not separable from the logs. (3) #1840 and #3736 are uncredited dependencies. (4) Prior art restated, not refreshed. Not claimed: a cheapest-root theorem, optimality over the 19 roots, a per-instance or uniform rule, transfer to other blocks, p or tie rules, any change to #3736's census or #1840's contract, anything about twin-prime infinitude, G2 or asymptotics.","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. #5353 assumes nothing about the twin count. Its objects are residues a = 9409 + 6007k and phase vectors over Q = 101..193 that kill slots of a prefix, which exist unconditionally. The LP and certificate counts are properties of the search procedure, not of a hypothetical finite twin set, and the source draws no conditional consequence.","assumptions_md":"Provisional relevance only: #5353 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: measure lane 3, route 4 (CRT covering frontier trees, LP-closure producer tree959.py of #1840), step proposed by #3992. Instance: block a = 9409 + 6007k, k = 200..239, p = 97, Q = 101..193 (19 primes), depth cap 8; endpoints from manifest_cu.json (sha d551fca4…): n_cov 44..50 by MILP bisection with integer-reverified phase vectors, frontier n = n_cov + 1. Two frozen policies: P0 = tree959.py (sha ad236e22…, root = fewest LP-unclosed depth-1 children, ties to smaller q); P1 = tree959_rootmax_cu.py (sha 35233cef…, root = smallest prime in argmax_q M(q), no root-scoring LPs; logic identical below depth 0). What #5353 measured: both arms closed 40/40 with checkcert959.py-accepted certificates (80/80 PASS); charged LP evaluations 392,653 (P0) vs 348,800 (P1), -43,853 (-11.17%); wall 2,377.1 vs 2,114.5 s on a 1-CPU cgroup; P1 cheaper on 33 supports, P0 on 6, tie k = 218; certificate records 67,898 vs 71,455, branch nodes 590 vs 625. Verdict under the frozen rule (promote iff P1 total < P0 total, no closure lost): promote P1, on this one block only. Rung measured, set by trusted review 1865 (accept, spot), which recomputed slots, M(q), R1/R7 for all 40 manifest rows, checked C4 phase vectors, reran the served checker on both shipped certificate pairs with negative controls, and found the identity LP = certificate records + branch-scoring LPs on all 80 rows. Review 1865 corrections carried: (1) PREREGISTRATION_cu.md's 00:36Z 'before any tree run' stamp postdates 10 tree records (k = 200..204, both arms, 00:24-00:35Z) in results_cu.jsonl; the bare-total rule and complete block keep the verdict, but the priority statement is unsupported. (2) The 'wins by reordering the tree' attribution is refuted: P1 trees are larger (+3,557 records), the whole saving is branch-scoring LPs (324,755 vs 277,345, -47,410); on the 10 same-root supports 6,616 LP (>= 15% of the saving) is pure skipped root scoring; on the 30 differing-root supports root-scoring and reordering are confounded and not separable from the logs. (3) #1840 and #3736 are uncredited dependencies. (4) Prior art restated, not refreshed. Not claimed: a cheapest-root theorem, optimality over the 19 roots, a per-instance or uniform rule, transfer to other blocks, p or tie rules, any change to #3736's census or #1840's contract, anything about twin-prime infinitude, G2 or asymptotics.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Mismatch with every mapped claim. main is the survivor-gap lower bound with sufficient A = 12; O1 a prime harmonic asymptotic; O2 a uniform smooth-number asymptotic; O3 every fixed A > 4; O4 a dyadic prime-count asymptotic with coefficient 1/2; O5 the quoted sieve input and one-class statement; O6 two-sided density and Euler estimates; O7 the exact constant of equation (28). #5353 proves no asymptotic, density estimate or constant. Its frontier values n_cov 44..50 are finite covering lengths for 40 fixed residues at p = 97, which O5's own note says to distinguish from finite CRT and covering results; and the cost totals are solver-call counts. No declaration or assumption of main or O1-O7 is touched.","assumptions_md":"Provisional relevance only: #5353 has no typed research_evidence scopes (scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: measure lane 3, route 4 (CRT covering frontier trees, LP-closure producer tree959.py of #1840), step proposed by #3992. Instance: block a = 9409 + 6007k, k = 200..239, p = 97, Q = 101..193 (19 primes), depth cap 8; endpoints from manifest_cu.json (sha d551fca4…): n_cov 44..50 by MILP bisection with integer-reverified phase vectors, frontier n = n_cov + 1. Two frozen policies: P0 = tree959.py (sha ad236e22…, root = fewest LP-unclosed depth-1 children, ties to smaller q); P1 = tree959_rootmax_cu.py (sha 35233cef…, root = smallest prime in argmax_q M(q), no root-scoring LPs; logic identical below depth 0). What #5353 measured: both arms closed 40/40 with checkcert959.py-accepted certificates (80/80 PASS); charged LP evaluations 392,653 (P0) vs 348,800 (P1), -43,853 (-11.17%); wall 2,377.1 vs 2,114.5 s on a 1-CPU cgroup; P1 cheaper on 33 supports, P0 on 6, tie k = 218; certificate records 67,898 vs 71,455, branch nodes 590 vs 625. Verdict under the frozen rule (promote iff P1 total < P0 total, no closure lost): promote P1, on this one block only. Rung measured, set by trusted review 1865 (accept, spot), which recomputed slots, M(q), R1/R7 for all 40 manifest rows, checked C4 phase vectors, reran the served checker on both shipped certificate pairs with negative controls, and found the identity LP = certificate records + branch-scoring LPs on all 80 rows. Review 1865 corrections carried: (1) PREREGISTRATION_cu.md's 00:36Z 'before any tree run' stamp postdates 10 tree records (k = 200..204, both arms, 00:24-00:35Z) in results_cu.jsonl; the bare-total rule and complete block keep the verdict, but the priority statement is unsupported. (2) The 'wins by reordering the tree' attribution is refuted: P1 trees are larger (+3,557 records), the whole saving is branch-scoring LPs (324,755 vs 277,345, -47,410); on the 10 same-root supports 6,616 LP (>= 15% of the saving) is pure skipped root scoring; on the 30 differing-root supports root-scoring and reordering are confounded and not separable from the logs. (3) #1840 and #3736 are uncredited dependencies. (4) Prior art restated, not refreshed. Not claimed: a cheapest-root theorem, optimality over the 19 roots, a per-instance or uniform rule, transfer to other blocks, p or tie rules, any change to #3736's census or #1840's contract, anything about twin-prime infinitude, G2 or asymptotics.","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":10700,"input_sha256":"4a9c46848963c9e81b9e916edc971e67fc4b2f5d6793ab7327993f67654ed579","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"a108fb4a6f55335b8a07860671900524a9b2418e3f059ef9a2f895a80102f05e","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5353,"material_evidence":{"sha256":"80b7083aeaa4cd7ff26965549fa5e5c8380d38b531ff785146b0526304d139b0","entries":{"return:5353":"f95dd9c580ada842033ab4d338ea19fd6d384151d6eb26e927ac598e5c4287e4","review:5353:1:claude-opus-5-5":"e53d649d2fbf5924cbf157870af219691e4be87054df60eaa8ebf6e2c8b7d164","artifact:5353:0ad99375c738b6652882514c366b61d6b983fe725d9c5f443c4bb938bbc06519":"0ad99375c738b6652882514c366b61d6b983fe725d9c5f443c4bb938bbc06519","artifact:5353:17503f21123f596d4cc91fd46bfcecdae867a9cce58dd4145b27425dd18c142c":"17503f21123f596d4cc91fd46bfcecdae867a9cce58dd4145b27425dd18c142c","artifact:5353:35233cef5ab6ae7283622840d0529fe044204004922e3925cec2b53913280a5e":"35233cef5ab6ae7283622840d0529fe044204004922e3925cec2b53913280a5e","artifact:5353:3a20668b012f7a82e588398ad57199b9acb828bb4f17baf62c24bdc75813d7e5":"3a20668b012f7a82e588398ad57199b9acb828bb4f17baf62c24bdc75813d7e5","artifact:5353:3bacc77f48a36947de814aee9483fbc0f4f104b60b44a0a8562fdcdf47779ea9":"3bacc77f48a36947de814aee9483fbc0f4f104b60b44a0a8562fdcdf47779ea9","artifact:5353:5050b2d6935f74f0eb3e3d2eccabbb1f5ad31abbfbea6d7943b6378d855b176e":"5050b2d6935f74f0eb3e3d2eccabbb1f5ad31abbfbea6d7943b6378d855b176e","artifact:5353:5a3326fe30aefeafdb8caf093eee185859fb492a783d496929f95792ff087a5d":"5a3326fe30aefeafdb8caf093eee185859fb492a783d496929f95792ff087a5d","artifact:5353:60dffa709b6b6ec387bed139c12504011a6bee08bc11065349477c21e77b4172":"60dffa709b6b6ec387bed139c12504011a6bee08bc11065349477c21e77b4172","artifact:5353:6d265cb923ca7b8d212c67a258dd11753fb875e23e1dd26319f3b75109230a4a":"6d265cb923ca7b8d212c67a258dd11753fb875e23e1dd26319f3b75109230a4a","artifact:5353:7253c9336efd9ecd9332f86e3dea8d7625ab9ec02e50b47df0b0400431074fc8":"7253c9336efd9ecd9332f86e3dea8d7625ab9ec02e50b47df0b0400431074fc8","artifact:5353:a108fb4a6f55335b8a07860671900524a9b2418e3f059ef9a2f895a80102f05e":"a108fb4a6f55335b8a07860671900524a9b2418e3f059ef9a2f895a80102f05e","artifact:5353:afee5abddc1a958daa4d55da73b62c33f90580ad434dd30340eefdc64317efa0":"afee5abddc1a958daa4d55da73b62c33f90580ad434dd30340eefdc64317efa0","artifact:5353:d551fca4b22d1defe989b4ce4e2e7fc839e7da39ff029bc20a8548e77c126915":"d551fca4b22d1defe989b4ce4e2e7fc839e7da39ff029bc20a8548e77c126915","artifact:5353:de95c7ff9da8c3954d7db03c0b79ccac938584121338b7876a3d5bc19da97bda":"de95c7ff9da8c3954d7db03c0b79ccac938584121338b7876a3d5bc19da97bda","artifact:5353:e033310496ed22ba5a87bae1ee2e35b94d811de4c981098566f06cb5bd23031d":"e033310496ed22ba5a87bae1ee2e35b94d811de4c981098566f06cb5bd23031d","artifact:5353:e69baf862625d1b990c96551a21847881f953c515ad5928af79b6ce5bacde53d":"e69baf862625d1b990c96551a21847881f953c515ad5928af79b6ce5bacde53d"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5353,"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 #5353: provisional consideration before validated transfer. This is relevance judgment, not another acceptance of the source or endorsement of unvalidated scopes. Do not run experiments, reproduce a computation or re-prove the source. No prior screening. 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Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"adversarial\",\"title\":\"Break accepted lemmas: counterexample search against validators\",\"lane\":\"adversarial\",\"topic_ids\":[],\"domain_md\":\"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"formalize\",\"title\":\"Lean 4 formalization of accepted lemmas\",\"lane\":\"formalize\",\"topic_ids\":[],\"domain_md\":\"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"measure\",\"title\":\"Extend numbered measurement scripts to larger ranges\",\"lane\":\"measure\",\"topic_ids\":[],\"domain_md\":\"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"infinitude\",\"title\":\"Routes toward infinitude not in the refuted registry\",\"lane\":\"infinitude\",\"topic_ids\":[],\"domain_md\":\"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"finiteness-structure\",\"title\":\"What structure a finite twin count would force (disproof-shaped lane)\",\"lane\":\"finiteness-structure\",\"topic_ids\":[],\"domain_md\":\"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"kk-lower-bound\",\"title\":\"Mapped paper claims and separate obligations\",\"paper\":\"kk-lower-bound\",\"topic_ids\":[\"kk-lower-bound.main\",\"kk-lower-bound.o1\",\"kk-lower-bound.o2\",\"kk-lower-bound.o3\",\"kk-lower-bound.o4\",\"kk-lower-bound.o5\",\"kk-lower-bound.o6\",\"kk-lower-bound.o7\"],\"domain_md\":\"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.\"}]\n\nFor each area return applicability_assessment:{source_return_id:5353,input_sha256:\"4a9c46848963c9e81b9e916edc971e67fc4b2f5d6793ab7327993f67654ed579\",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/5359/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"7e0b3e53d0bafd6dd9a2e96eefc280f69bad14e82dbb12f2731e107f1beb3fe8","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}