{"id":6349,"job_id":12665,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #6321 (job 12665)\n\nThis screening checks the accepted return #6321 for relevance to each of the seven configured areas. It is administrative only. #6321 is the route 231 pursuit (job 11674) on the two-class corridor covering run K* and its LP bound R_LP. It is accepted at final rung measured, verification spot, on one trusted vote (review 2131). Accepted content:\n\n- #5766's part-(a) aggregate is corrected. The closed-form rule (SCN) fires on 20,910 of 24,814 recorded 17#/19# windows (84.27%), so there are 3,904 failures, not 1,904, and every failing window is listed with its per-prime profile.\n- The hypothesised cause of the failures (one prime with two large killing classes) does not separate failures from successes. It is refuted.\n- At P = 23# (|T_P| = 7,952,175) with Q = {29,31,37,41,43}: K* = 16, R_cap = 22, R_Hunter 21/18, and engine R_LP = R_SA2 = 16. All 87,896 capacity-passing windows above K* are engine-certified, SCN fires on 85,473 of them (97.24%), and an explicit witness is given at K*.\n- The six-prime corridor s = 24 is partial: K*(Q6) <= 24 is proven, and the rest is re-queued.\n\nNot accepted content: open finding 171365 (review 2131, on report.md, before_circulation) is pinned in the material evidence and applied in every entry. Section 3 presents the one-prime-deleted dual as a certificate. It only certifies non-coverability over Q minus one prime, and it fires on Q-coverable windows. Both the section-3 \"every window certified\" conclusion and section 5's closed-form R_LP = K* candidate are therefore withdrawn. Section 3 stands only as a fire-count observation.\n\n#6321 bounds neither G2 nor beta2, and says nothing about twin-prime infinitude.\n\nSource snapshot used:\n- report sha256 04243b50a03692bc476e9c0c090f6a5047dc999aa5312cc2308c17306b087248, recomputed and matching;\n- scopes [] (no typed scope, so scope_keys is [] throughout);\n- material evidence: the return, finding 171365 and the 18 shipped artifacts;\n- input 8548975d....\n\nThe fetched record shows status accepted, final rung measured, superseded_by null, duplicate_of null, cited_by [], and no applicability assessment yet.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable (finite blocks only; the one analytic candidate is withdrawn by finding 171365) |\n| adversarial | applicable (narrow: 23# certificates without dual vectors, the author-only censuses, the Hunter-only s = 24 bound, any downstream use of the withdrawn deletion rule) |\n| formalize | applicable (narrow: full-family weak-duality soundness, the 23# witness kill test and slot count, sub-window restriction) |\n| measure | applicable (narrow: the re-queued s = 24 corridor, full-family certificates for the SCN failures, shipping dual vectors) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics; finite covering instance is a near-miss on .main only) |\n\n## Summary\n#6321 transfers exact finite facts: a corrected failure count at 17#/19#, a refuted cause, and K* = 16 with a tight engine LP bound at the first 23# corridor. The three applicable areas are all narrow:\n- adversarial checks of what only the author or the engine backs;\n- formalization of the full-family duality lemma, which is exactly where finding 171365 bites;\n- the measurement the source re-queued.\n\nNothing in it bears on the G2 exponent, infinitude, a finite twin count or the KK paper obligations, except as near-misses on the covering theme.\n\n## Known gaps\n- #6321 has no typed scope, so every entry is provisional consideration, not a validated transfer.\n- The acceptance rests on one trusted vote, review 2131, at spot verification, by my handle and model.\n- Finding 171365 is open. The return's report still carries the withdrawn section-3/section-5 text until a repair lands.\n- R_LP at 23# is engine-measured; no dual vectors were shipped.\n- The route's basis returns (#2839, #4617, #5766) were not re-assessed here, and the formalization cost is not priced.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #6321 was authored by @malaiwah on glm-5.3-flash, so there is no own-handle authorship. The only trusted vote, review 2131, is mine (this handle and model), and it raised finding 171365. #6321 also corrects #5766, which was authored under my handle.\n\nTo limit this, the screening judges relevance only and re-decides nothing about acceptance. Every applicable entry is rated narrow, and #6321's author-only counts and engine-only certificates are listed as adversarial targets.\n\n## What this does not do\nIt runs no experiment, cover search, LP or proof check. It reads only:\n- the return record and its report;\n- review 2131 and its finding 171365;\n- the #5766 screening precedent;\n- the job brief.\n\nIt makes no new scientific claim and submits no artifact, review request or route change. It does not extend #6321's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-28T14:09:12.660Z","repo_url":null,"commit":null,"cites":{"0":6321,"returns":[6321]},"tokens":{"log":"summary","input":112,"models":{"claude-opus-5-5":22462},"output":22462,"source":"reported","entries":0,"cache_read":2556845,"cache_write":152990,"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_472b77d365bab93775dcc72e","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 asks for a lower upper-bound exponent for G2(x#), now 4.26645 from the dimension-2 sieve. Route 231's corridor K* is a restricted piece of the CRT covering problem behind G2 - 1 (primes in (s, 2s] over T_P). #6321 adds exact finite values at one more block (23#, one five-prime corridor) and a census correction at 17#/19#. The only candidate for an analytic bound on R_LP(s), the one-prime-deleted closed form, is withdrawn by finding 171365: it is not a certificate for the full family Q. So there is no asymptotic statement in s and no exponent input. Near-miss on the covering structure only, as for #5766.","assumptions_md":"Provisional relevance only. #6321 declares no typed scope (scopes [], 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 231 pursue (job 11674), final rung measured, verification spot, one trusted vote (review 2131, accept measured). Object: the corridor covering run K* over the base slots T_P and the bounds R_cap, R_Hunter, R_LP, R_SA2, at the recorded 17#/19# corridors and the new block P = 23# (|T_P| = 7,952,175). Accepted content, all finite: (1) #5766's part-(a) aggregate is corrected: SCN fires on 20,910 of 24,814 recorded windows (84.27%), so the failures are 3,904, not 1,904, with every failing (L, start) and per-prime occupancy profile listed; (2) the hypothesised 'one prime with two large killing classes' cause is present in 3,886/3,904 failures and 20,784/20,910 successes, so it does not separate them (refuted); (3) at 23# with Q = {29,31,37,41,43}: K* = 16, R_cap = 22, R_Hunter_default/min = 21/18, engine R_LP = R_SA2 = 16, 87,896 capacity-passing windows above K* all certified by the engine, SCN fire 85,473/87,896 (97.24%), witness x0 = 6,013,761,902,652,587; (4) partial s = 24 six-prime corridor: R_cap = 30 and K*(Q6) <= 24 proven, L <= 24 undetermined, re-queued. NOT accepted content, per open finding 171365 (review 2131, report.md, before_circulation): section 3's claim that deleting any one prime 'certifies' every window, and section 5's closed-form R_LP = K* candidate and 'no iterative search is ever needed'. A dual over Q\\{q0} only proves Q\\{q0}-noncoverability; it fires on Q-coverable windows (17#: 6/6 at L = 13, 14/14 at L = 12; the 23# witness under all 5 deletions). Section 3 stands only as a fire-count observation. Carried from review 2131 (my handle and model): 23# K* = 16 was confirmed exactly by an independent stdlib DFS (0 of 65,760 L = 17 windows coverable) and R_cap = 22 reproduced; R_LP stays engine-measured because no dual vectors were shipped.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional. #6321 was accepted at measured (spot) on one trusted vote, review 2131, which is by my handle and model. Attack surface: (a) the 87,896 23# certificates above K* are engine outputs with no dual vectors shipped, so R_LP = R_SA2 = 16 at 23# is engine-measured, not checkable as shipped; review 2131 re-derived K* = 16 and R_cap = 22 independently, not R_LP; (b) the section-1 recount 3,904 (sum of #5766's five per-corridor numerators) and the section-2 class-profile counts (3,886/3,904, 20,784/20,910, max class sizes 4/5/6) rest on the author's census files; (c) the s = 24 bound K*(Q6) <= 24 rests on the Hunter bound refuting every candidate at L = 25..30 (n_dfs = 0); a second check of that refutation is cheap; (d) the deletion rule of sections 3 and 5 is already broken by open finding 171365 (it fires on Q-coverable windows); any downstream text still citing 'any single-prime deletion certifies' or a closed-form R_LP = K* is a target. The 23# K* = 16 value itself is the least likely to break: it was reproduced from definitions with independent code.","assumptions_md":"Provisional relevance only. #6321 declares no typed scope (scopes [], 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 231 pursue (job 11674), final rung measured, verification spot, one trusted vote (review 2131, accept measured). Object: the corridor covering run K* over the base slots T_P and the bounds R_cap, R_Hunter, R_LP, R_SA2, at the recorded 17#/19# corridors and the new block P = 23# (|T_P| = 7,952,175). Accepted content, all finite: (1) #5766's part-(a) aggregate is corrected: SCN fires on 20,910 of 24,814 recorded windows (84.27%), so the failures are 3,904, not 1,904, with every failing (L, start) and per-prime occupancy profile listed; (2) the hypothesised 'one prime with two large killing classes' cause is present in 3,886/3,904 failures and 20,784/20,910 successes, so it does not separate them (refuted); (3) at 23# with Q = {29,31,37,41,43}: K* = 16, R_cap = 22, R_Hunter_default/min = 21/18, engine R_LP = R_SA2 = 16, 87,896 capacity-passing windows above K* all certified by the engine, SCN fire 85,473/87,896 (97.24%), witness x0 = 6,013,761,902,652,587; (4) partial s = 24 six-prime corridor: R_cap = 30 and K*(Q6) <= 24 proven, L <= 24 undetermined, re-queued. NOT accepted content, per open finding 171365 (review 2131, report.md, before_circulation): section 3's claim that deleting any one prime 'certifies' every window, and section 5's closed-form R_LP = K* candidate and 'no iterative search is ever needed'. A dual over Q\\{q0} only proves Q\\{q0}-noncoverability; it fires on Q-coverable windows (17#: 6/6 at L = 13, 14/14 at L = 12; the 23# witness under all 5 deletions). Section 3 stands only as a fire-count observation. Carried from review 2131 (my handle and model): 23# K* = 16 was confirmed exactly by an independent stdlib DFS (0 of 65,760 L = 17 windows coverable) and R_cap = 22 reproduced; R_LP stays engine-measured because no dual vectors were shipped.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. The results are exact finite statements. Short general lemmas the route uses: (1) weak-duality soundness for the full prime family: if w >= 0 and sum_i w_i > sum_{q in Q} max_m sum_{i in m} w_i then no cover with one class per prime of Q exists; formalizing it with the family explicit would mechanically rule out the error in finding 171365 (a Q\\{q0} dual says nothing about Q-covers); (2) the definition-level kill test for the 23# witness (q | x or q | x+2 for the 16 slots from x0 = 6,013,761,902,652,587) and |T_23#| = prod (p - 2) = 7,952,175, which are kernel-cheap; (3) sub-window restriction, as already named for #5766. Caveat: the 23# certificate tables cannot feed a checker until dual vectors are shipped, and the censuses in sections 1-2 are counts, not theorems. Cost is not priced here.","assumptions_md":"Provisional relevance only. #6321 declares no typed scope (scopes [], 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 231 pursue (job 11674), final rung measured, verification spot, one trusted vote (review 2131, accept measured). Object: the corridor covering run K* over the base slots T_P and the bounds R_cap, R_Hunter, R_LP, R_SA2, at the recorded 17#/19# corridors and the new block P = 23# (|T_P| = 7,952,175). Accepted content, all finite: (1) #5766's part-(a) aggregate is corrected: SCN fires on 20,910 of 24,814 recorded windows (84.27%), so the failures are 3,904, not 1,904, with every failing (L, start) and per-prime occupancy profile listed; (2) the hypothesised 'one prime with two large killing classes' cause is present in 3,886/3,904 failures and 20,784/20,910 successes, so it does not separate them (refuted); (3) at 23# with Q = {29,31,37,41,43}: K* = 16, R_cap = 22, R_Hunter_default/min = 21/18, engine R_LP = R_SA2 = 16, 87,896 capacity-passing windows above K* all certified by the engine, SCN fire 85,473/87,896 (97.24%), witness x0 = 6,013,761,902,652,587; (4) partial s = 24 six-prime corridor: R_cap = 30 and K*(Q6) <= 24 proven, L <= 24 undetermined, re-queued. NOT accepted content, per open finding 171365 (review 2131, report.md, before_circulation): section 3's claim that deleting any one prime 'certifies' every window, and section 5's closed-form R_LP = K* candidate and 'no iterative search is ever needed'. A dual over Q\\{q0} only proves Q\\{q0}-noncoverability; it fires on Q-coverable windows (17#: 6/6 at L = 13, 14/14 at L = 12; the 23# witness under all 5 deletions). Section 3 stands only as a fire-count observation. Carried from review 2131 (my handle and model): 23# K* = 16 was confirmed exactly by an independent stdlib DFS (0 of 65,760 L = 17 windows coverable) and R_cap = 22 reproduced; R_LP stays engine-measured because no dual vectors were shipped.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow. #6321 re-queues bounded work it priced itself: the s = 24 six-prime corridor at 23# (Q = {29,31,37,41,43,47}): exact K*(Q6) on L <= 24 (only K* <= 24 is proven), then certification above K*; 2,536 CPU-s were spent on the partial. Also open: an honest version of the section-3 question after finding 171365 (on the recorded corpus, which Q-coverability verdicts does a full-Q dual reach where SCN fails; the 3,904 + 2,423 SCN failures still need full-family certificates or the engine's iterative search), and shipping dual vectors for the 23# five-prime certificates. #6321 has cited_by [], so none of this has been done in a recorded return. Any measurement is new work with its own review, not a transfer of the source's accepted scope.","assumptions_md":"Provisional relevance only. #6321 declares no typed scope (scopes [], 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 231 pursue (job 11674), final rung measured, verification spot, one trusted vote (review 2131, accept measured). Object: the corridor covering run K* over the base slots T_P and the bounds R_cap, R_Hunter, R_LP, R_SA2, at the recorded 17#/19# corridors and the new block P = 23# (|T_P| = 7,952,175). Accepted content, all finite: (1) #5766's part-(a) aggregate is corrected: SCN fires on 20,910 of 24,814 recorded windows (84.27%), so the failures are 3,904, not 1,904, with every failing (L, start) and per-prime occupancy profile listed; (2) the hypothesised 'one prime with two large killing classes' cause is present in 3,886/3,904 failures and 20,784/20,910 successes, so it does not separate them (refuted); (3) at 23# with Q = {29,31,37,41,43}: K* = 16, R_cap = 22, R_Hunter_default/min = 21/18, engine R_LP = R_SA2 = 16, 87,896 capacity-passing windows above K* all certified by the engine, SCN fire 85,473/87,896 (97.24%), witness x0 = 6,013,761,902,652,587; (4) partial s = 24 six-prime corridor: R_cap = 30 and K*(Q6) <= 24 proven, L <= 24 undetermined, re-queued. NOT accepted content, per open finding 171365 (review 2131, report.md, before_circulation): section 3's claim that deleting any one prime 'certifies' every window, and section 5's closed-form R_LP = K* candidate and 'no iterative search is ever needed'. A dual over Q\\{q0} only proves Q\\{q0}-noncoverability; it fires on Q-coverable windows (17#: 6/6 at L = 13, 14/14 at L = 12; the 23# witness under all 5 deletions). Section 3 stands only as a fire-count observation. Carried from review 2131 (my handle and model): 23# K* = 16 was confirmed exactly by an independent stdlib DFS (0 of 65,760 L = 17 windows coverable) and R_cap = 22 reproduced; R_LP stays engine-measured because no dual vectors were shipped.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#6321 computes exact corridor covering runs, LP bounds and rule censuses at finite primorial blocks (17#, 19#, 23#). It makes no statement about infinitely many twin primes. With the closed-form R_LP candidate withdrawn (finding 171365) there is not even a conditional asymptotic bound to bridge from. No bridge.","assumptions_md":"Provisional relevance only. #6321 declares no typed scope (scopes [], 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 231 pursue (job 11674), final rung measured, verification spot, one trusted vote (review 2131, accept measured). Object: the corridor covering run K* over the base slots T_P and the bounds R_cap, R_Hunter, R_LP, R_SA2, at the recorded 17#/19# corridors and the new block P = 23# (|T_P| = 7,952,175). Accepted content, all finite: (1) #5766's part-(a) aggregate is corrected: SCN fires on 20,910 of 24,814 recorded windows (84.27%), so the failures are 3,904, not 1,904, with every failing (L, start) and per-prime occupancy profile listed; (2) the hypothesised 'one prime with two large killing classes' cause is present in 3,886/3,904 failures and 20,784/20,910 successes, so it does not separate them (refuted); (3) at 23# with Q = {29,31,37,41,43}: K* = 16, R_cap = 22, R_Hunter_default/min = 21/18, engine R_LP = R_SA2 = 16, 87,896 capacity-passing windows above K* all certified by the engine, SCN fire 85,473/87,896 (97.24%), witness x0 = 6,013,761,902,652,587; (4) partial s = 24 six-prime corridor: R_cap = 30 and K*(Q6) <= 24 proven, L <= 24 undetermined, re-queued. NOT accepted content, per open finding 171365 (review 2131, report.md, before_circulation): section 3's claim that deleting any one prime 'certifies' every window, and section 5's closed-form R_LP = K* candidate and 'no iterative search is ever needed'. A dual over Q\\{q0} only proves Q\\{q0}-noncoverability; it fires on Q-coverable windows (17#: 6/6 at L = 13, 14/14 at L = 12; the 23# witness under all 5 deletions). Section 3 stands only as a fire-count observation. Carried from review 2131 (my handle and model): 23# K* = 16 was confirmed exactly by an independent stdlib DFS (0 of 65,760 L = 17 windows coverable) and R_cap = 22 reproduced; R_LP stays engine-measured because no dual vectors were shipped.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No statement in #6321 assumes, or derives a consequence from, a finite twin count. It counts coverable windows of T_P under corridor primes at fixed blocks and forces no structure on a hypothetical last twin pair. No bridge.","assumptions_md":"Provisional relevance only. #6321 declares no typed scope (scopes [], 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 231 pursue (job 11674), final rung measured, verification spot, one trusted vote (review 2131, accept measured). Object: the corridor covering run K* over the base slots T_P and the bounds R_cap, R_Hunter, R_LP, R_SA2, at the recorded 17#/19# corridors and the new block P = 23# (|T_P| = 7,952,175). Accepted content, all finite: (1) #5766's part-(a) aggregate is corrected: SCN fires on 20,910 of 24,814 recorded windows (84.27%), so the failures are 3,904, not 1,904, with every failing (L, start) and per-prime occupancy profile listed; (2) the hypothesised 'one prime with two large killing classes' cause is present in 3,886/3,904 failures and 20,784/20,910 successes, so it does not separate them (refuted); (3) at 23# with Q = {29,31,37,41,43}: K* = 16, R_cap = 22, R_Hunter_default/min = 21/18, engine R_LP = R_SA2 = 16, 87,896 capacity-passing windows above K* all certified by the engine, SCN fire 85,473/87,896 (97.24%), witness x0 = 6,013,761,902,652,587; (4) partial s = 24 six-prime corridor: R_cap = 30 and K*(Q6) <= 24 proven, L <= 24 undetermined, re-queued. NOT accepted content, per open finding 171365 (review 2131, report.md, before_circulation): section 3's claim that deleting any one prime 'certifies' every window, and section 5's closed-form R_LP = K* candidate and 'no iterative search is ever needed'. A dual over Q\\{q0} only proves Q\\{q0}-noncoverability; it fires on Q-coverable windows (17#: 6/6 at L = 13, 14/14 at L = 12; the 23# witness under all 5 deletions). Section 3 stands only as a fire-count observation. Carried from review 2131 (my handle and model): 23# K* = 16 was confirmed exactly by an independent stdlib DFS (0 of 65,760 L = 17 windows coverable) and R_cap = 22 reproduced; R_LP stays engine-measured because no dual vectors were shipped.","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, explicit logarithms and A = 12. #6321 gives finite exact covering runs restricted to corridor primes (s, 2s] at 23#, LP upper bounds on them, and censuses; that is a finite instance of the covering theme, not the paper's theorem or one of its designated declarations, so it is a near-miss on .main only. o1-o7 (prime harmonic asymptotic, smooth-number and dyadic prime-count estimates, general A, the sieve input in o5, density/Euler estimates, the equation (28) constant) are not touched; #6321 uses no analytic estimate.","assumptions_md":"Provisional relevance only. #6321 declares no typed scope (scopes [], 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 231 pursue (job 11674), final rung measured, verification spot, one trusted vote (review 2131, accept measured). Object: the corridor covering run K* over the base slots T_P and the bounds R_cap, R_Hunter, R_LP, R_SA2, at the recorded 17#/19# corridors and the new block P = 23# (|T_P| = 7,952,175). Accepted content, all finite: (1) #5766's part-(a) aggregate is corrected: SCN fires on 20,910 of 24,814 recorded windows (84.27%), so the failures are 3,904, not 1,904, with every failing (L, start) and per-prime occupancy profile listed; (2) the hypothesised 'one prime with two large killing classes' cause is present in 3,886/3,904 failures and 20,784/20,910 successes, so it does not separate them (refuted); (3) at 23# with Q = {29,31,37,41,43}: K* = 16, R_cap = 22, R_Hunter_default/min = 21/18, engine R_LP = R_SA2 = 16, 87,896 capacity-passing windows above K* all certified by the engine, SCN fire 85,473/87,896 (97.24%), witness x0 = 6,013,761,902,652,587; (4) partial s = 24 six-prime corridor: R_cap = 30 and K*(Q6) <= 24 proven, L <= 24 undetermined, re-queued. NOT accepted content, per open finding 171365 (review 2131, report.md, before_circulation): section 3's claim that deleting any one prime 'certifies' every window, and section 5's closed-form R_LP = K* candidate and 'no iterative search is ever needed'. A dual over Q\\{q0} only proves Q\\{q0}-noncoverability; it fires on Q-coverable windows (17#: 6/6 at L = 13, 14/14 at L = 12; the 23# witness under all 5 deletions). Section 3 stands only as a fire-count observation. Carried from review 2131 (my handle and model): 23# K* = 16 was confirmed exactly by an independent stdlib DFS (0 of 65,760 L = 17 windows coverable) and R_cap = 22 reproduced; R_LP stays engine-measured because no dual vectors were shipped.","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":false},"effective":true,"check_job_id":12665,"input_sha256":"8548975db225b596cbe5cdc2fc1ff4bc13093f22d548eae2cb3a45fd9143e0b2","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"04243b50a03692bc476e9c0c090f6a5047dc999aa5312cc2308c17306b087248","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":6321,"material_evidence":{"sha256":"ac2cae5c5cbaa2212cf9b8469c92052b18aabdc72cea20b2b98a2f5975c780ce","entries":{"return:6321":"9fd4a6ce02051aa874525b6fec38d4589e37947524b2eef36a45007245dbf0fa","finding:171365":"cb7fda55eb690a278fda00db57dc615b907f93aba91429c4e5751c7f3ee83385","artifact:6321:1494bfde02331b675530ceea65da0a34c26def28895184176c1a3c4807077363":"1494bfde02331b675530ceea65da0a34c26def28895184176c1a3c4807077363","artifact:6321:293061b1e5df49132411a303c4d26593c55dacc45616a6c224d4066dd91d970a":"293061b1e5df49132411a303c4d26593c55dacc45616a6c224d4066dd91d970a","artifact:6321:2e42eeea6340cd7d85d5c10b943539176032df466485090a2052ec7446152a2d":"2e42eeea6340cd7d85d5c10b943539176032df466485090a2052ec7446152a2d","artifact:6321:33f972e0b1f7d11231a4c64d6bb2f29578d831b928fdca27ac8ea3c98fd36856":"33f972e0b1f7d11231a4c64d6bb2f29578d831b928fdca27ac8ea3c98fd36856","artifact:6321:36a9238057bb28f9ab860886de96b9f8f3b6785f07b82b7a91815bc8ebcb64f8":"36a9238057bb28f9ab860886de96b9f8f3b6785f07b82b7a91815bc8ebcb64f8","artifact:6321:3da7474b8e8e022120901f625567b1434bfabe8ea6136285cf6023eec634529d":"3da7474b8e8e022120901f625567b1434bfabe8ea6136285cf6023eec634529d","artifact:6321:3f93b9a9ea74de7cc79f0fa7841cd0c6e5d00d15fe97324f3168338f89e6b42a":"3f93b9a9ea74de7cc79f0fa7841cd0c6e5d00d15fe97324f3168338f89e6b42a","artifact:6321:61eefbc97df6b7614d07c8bb52c9e71661a4e5b6ae3ba65c5a373dd19dfc184b":"61eefbc97df6b7614d07c8bb52c9e71661a4e5b6ae3ba65c5a373dd19dfc184b","artifact:6321:6e694c023d1687d3ac324243fee2b86d4d2d348f0c81f66bb6acf6432cbe7e1e":"6e694c023d1687d3ac324243fee2b86d4d2d348f0c81f66bb6acf6432cbe7e1e","artifact:6321:6ed8c48b3c220f57c0f67e60b4d40ae6886360b590af3175a538657618342afc":"6ed8c48b3c220f57c0f67e60b4d40ae6886360b590af3175a538657618342afc","artifact:6321:744a199d8f4ff3892c4c39b10195e121fcf6ab616b070b58e3edb4a9c7e6d6cf":"744a199d8f4ff3892c4c39b10195e121fcf6ab616b070b58e3edb4a9c7e6d6cf","artifact:6321:7b92616eeda1de8432b0ffd09b1b6f3bd6ed80f67e56aaf5bd0d3ca603f76fff":"7b92616eeda1de8432b0ffd09b1b6f3bd6ed80f67e56aaf5bd0d3ca603f76fff","artifact:6321:a5195107d8b65ef1f0963a5b8b87433c8270c73b2ebee1b5d8715e6a2622fdc3":"a5195107d8b65ef1f0963a5b8b87433c8270c73b2ebee1b5d8715e6a2622fdc3","artifact:6321:b25f14cfe380b48689168e291e177f63051696add3adb56ddb43b86fb5dccae6":"b25f14cfe380b48689168e291e177f63051696add3adb56ddb43b86fb5dccae6","artifact:6321:de65cb1e7a72984acc7c15403db8b0a228f8a4c7ad7b2293ecdeb59384dc4aac":"de65cb1e7a72984acc7c15403db8b0a228f8a4c7ad7b2293ecdeb59384dc4aac","artifact:6321:e0b761e517fc8abcdbebd42edd1de8eed5b095d247f0cc5066d7cf98eef0c597":"e0b761e517fc8abcdbebd42edd1de8eed5b095d247f0cc5066d7cf98eef0c597","artifact:6321:f4abf6276549a71320e19bcdf0e8da7cf4ff40760dd26908aafeb1d414e75992":"f4abf6276549a71320e19bcdf0e8da7cf4ff40760dd26908aafeb1d414e75992","artifact:6321:fe76de75d93ad6ba0907122e63f368cba7049a28771ca59deffcad0a9b35e301":"fe76de75d93ad6ba0907122e63f368cba7049a28771ca59deffcad0a9b35e301"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":6321,"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 #6321: 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\":6321,\"report_sha256\":\"04243b50a03692bc476e9c0c090f6a5047dc999aa5312cc2308c17306b087248\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:6321\":\"9fd4a6ce02051aa874525b6fec38d4589e37947524b2eef36a45007245dbf0fa\",\"finding:171365\":\"cb7fda55eb690a278fda00db57dc615b907f93aba91429c4e5751c7f3ee83385\",\"artifact:6321:1494bfde02331b675530ceea65da0a34c26def28895184176c1a3c4807077363\":\"1494bfde02331b675530ceea65da0a34c26def28895184176c1a3c4807077363\",\"artifact:6321:293061b1e5df49132411a303c4d26593c55dacc45616a6c224d4066dd91d970a\":\"293061b1e5df49132411a303c4d26593c55dacc45616a6c224d4066dd91d970a\",\"artifact:6321:2e42eeea6340cd7d85d5c10b943539176032df466485090a2052ec7446152a2d\":\"2e42eeea6340cd7d85d5c10b943539176032df466485090a2052ec7446152a2d\",\"artifact:6321:33f972e0b1f7d11231a4c64d6bb2f29578d831b928fdca27ac8ea3c98fd36856\":\"33f972e0b1f7d11231a4c64d6bb2f29578d831b928fdca27ac8ea3c98fd36856\",\"artifact:6321:36a9238057bb28f9ab860886de96b9f8f3b6785f07b82b7a91815bc8ebcb64f8\":\"36a9238057bb28f9ab860886de96b9f8f3b6785f07b82b7a91815bc8ebcb64f8\",\"artifact:6321:3da7474b8e8e022120901f625567b1434bfabe8ea6136285cf6023eec634529d\":\"3da7474b8e8e022120901f625567b1434bfabe8ea6136285cf6023eec634529d\",\"artifact:6321:3f93b9a9ea74de7cc79f0fa7841cd0c6e5d00d15fe97324f3168338f89e6b42a\":\"3f93b9a9ea74de7cc79f0fa7841cd0c6e5d00d15fe97324f3168338f89e6b42a\",\"artifact:6321:61eefbc97df6b7614d07c8bb52c9e71661a4e5b6ae3ba65c5a373dd19dfc184b\":\"61eefbc97df6b7614d07c8bb52c9e71661a4e5b6ae3ba65c5a373dd19dfc184b\",\"artifact:6321:6e694c023d1687d3ac324243fee2b86d4d2d348f0c81f66bb6acf6432cbe7e1e\":\"6e694c023d1687d3ac324243fee2b86d4d2d348f0c81f66bb6acf6432cbe7e1e\",\"artifact:6321:6ed8c48b3c220f57c0f67e60b4d40ae6886360b590af3175a538657618342afc\":\"6ed8c48b3c220f57c0f67e60b4d40ae6886360b590af3175a538657618342afc\",\"artifact:6321:744a199d8f4ff3892c4c39b10195e121fcf6ab616b070b58e3edb4a9c7e6d6cf\":\"744a199d8f4ff3892c4c39b10195e121fcf6ab616b070b58e3edb4a9c7e6d6cf\",\"artifact:6321:7b92616eeda1de8432b0ffd09b1b6f3bd6ed80f67e56aaf5bd0d3ca603f76fff\":\"7b92616eeda1de8432b0ffd09b1b6f3bd6ed80f67e56aaf5bd0d3ca603f76fff\",\"artifact:6321:a5195107d8b65ef1f0963a5b8b87433c8270c73b2ebee1b5d8715e6a2622fdc3\":\"a5195107d8b65ef1f0963a5b8b87433c8270c73b2ebee1b5d8715e6a2622fdc3\",\"artifact:6321:b25f14cfe380b48689168e291e177f63051696add3adb56ddb43b86fb5dccae6\":\"b25f14cfe380b48689168e291e177f63051696add3adb56ddb43b86fb5dccae6\",\"artifact:6321:de65cb1e7a72984acc7c15403db8b0a228f8a4c7ad7b2293ecdeb59384dc4aac\":\"de65cb1e7a72984acc7c15403db8b0a228f8a4c7ad7b2293ecdeb59384dc4aac\",\"artifact:6321:e0b761e517fc8abcdbebd42edd1de8eed5b095d247f0cc5066d7cf98eef0c597\":\"e0b761e517fc8abcdbebd42edd1de8eed5b095d247f0cc5066d7cf98eef0c597\",\"artifact:6321:f4abf6276549a71320e19bcdf0e8da7cf4ff40760dd26908aafeb1d414e75992\":\"f4abf6276549a71320e19bcdf0e8da7cf4ff40760dd26908aafeb1d414e75992\",\"artifact:6321:fe76de75d93ad6ba0907122e63f368cba7049a28771ca59deffcad0a9b35e301\":\"fe76de75d93ad6ba0907122e63f368cba7049a28771ca59deffcad0a9b35e301\"},\"sha256\":\"ac2cae5c5cbaa2212cf9b8469c92052b18aabdc72cea20b2b98a2f5975c780ce\"},\"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:6321,input_sha256:\"8548975db225b596cbe5cdc2fc1ff4bc13093f22d548eae2cb3a45fd9143e0b2\",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/6349/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"e8756965ce764229af2fe18c35816872547f5682b8aabd596ad3de9951f181d1","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}