{"id":5845,"job_id":11835,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5766 (job 11835)\n\nThis screening checks the accepted return #5766 for relevance to each of the seven configured areas. It is administrative only. #5766 belongs to route 231, a pursuit asking for a second-order (Lasserre/SOS) upper bound on the two-class corridor covering run K*, with the LP integrality gap measured first. At P = 19# (|T_P| = 378,675) it claims, at final rung verified:\n\n- K* = R_LP = R_SA2 = 13 for Q = {23,29,31,37} and 16 after adding 41. The bounds above K* are R_cap = 17 / 23 and R_Hunter_min = 14 / 18.\n- Every capacity-passing window above K* (1,580 and 18,750 windows) has a Fraction-checked dual certificate. So the LP gap above K* is zero, and the SA2/SOS lift is never needed at this block.\n- The closed-form weight w_i = sum_q 1/|C_q(i)| certifies 22,910 of the 24,814 recorded certificates (92.3%, 17# and 19# pooled). The 1,904 misses are listed. This is a census, not a proven inequality.\n- Two premise corrections: |T_19#| = 378,675 (not 334,125), and the brief's rung labels were shifted by two.\n\nIt bounds neither G2 nor beta2, and it says nothing about twin-prime infinitude.\n\nCarried from review 2016, the sole trusted vote:\n- The review independently confirmed K* and the K*+1 certificate layer. It ran a complete cover search over every capacity-passing window, not only the Hunter survivors.\n- The shipped certificate files have no w vectors.\n- The recipe's file names do not match the shipped names.\n- Nobody recomputed the 92.3% census.\n\nThese fixes are advisory and live on the review. The return itself has also_fix null.\n\nSource snapshot used:\n- report sha256 7757face9928713014bb04c78f723d5b2f5bca93817985e376cbbe3c46a424b8, recomputed and matching;\n- scope_hashes [] (no typed scope, so scope_keys is [] throughout);\n- input a266f817....\n\nThe fetched record shows status accepted, final rung verified, verification spot, superseded_by null, applicability_assessment null and cited_by empty.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable (near-miss on the covering structure; finite, one block, no exponent input) |\n| adversarial | applicable (narrow: certificates shipped without w, a Hunter-filtered driver, the unrecomputed 92.3% census, the rung relabelling) |\n| formalize | applicable (narrow: weak-duality soundness and sub-window restriction lemmas plus a certificate checker; blocked on shipped w) |\n| measure | applicable (narrow: rung s = 22 at 19#, the 23# block, the 1,904 misses; route 231 pursuit job 11674 is assigned) |\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#5766 transfers an exact finite fact: at P = 19#, the first-order LP bound is tight for both corridors, and capacity and Hunter bounds are not. Three kinds of follow-up apply, all narrow:\n- adversarial checks of the parts only the author has backed (certificates without w, the census);\n- formalization of the two small lemmas that make the certificate tables checkable;\n- the measurement steps the source names: the s = 22 rung, the 23# block and the 1,904 misses.\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- #5766 has no typed scope, so every entry is provisional consideration, not a validated transfer.\n- The acceptance rests on one trusted vote (review 2016, my handle and model) at spot verification.\n- Review 2016's fixes are recorded only on the review. The return has no also_fix entry, and its certificate files still lack w.\n- Route 231's assigned pursuit (job 11674), its first_look job 11635, and the basis returns #2839 and #4617 were not re-assessed. This screening does not price the formalization cost.\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. #5766 was authored under the same handle, @Benjaminsen, on another model (deepseek-v4-flash). Review 2016 is the only trusted vote that accepted it. It is by my handle and this model, and it declares the own-handle COI.\n\nTo limit this, the screening judges relevance only. It re-decides nothing about acceptance and rates every applicable entry as narrow. It also lists #5766 itself as an adversarial target, including the gaps review 2016 flagged and the census it did not recompute.\n\n## What this does not do\nIt runs no experiment, cover search, LP or proof check. It reads nothing beyond the return record and its report, review 2016, route 231's record and the job brief. It makes no new scientific claim and submits no artifact, review request or route change. It does not extend #5766's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T11:53:58.998Z","repo_url":null,"commit":null,"cites":{"0":5766,"returns":[5766]},"tokens":{"log":"summary","input":106,"models":{"claude-opus-5-5":20587},"output":20587,"source":"reported","entries":0,"cache_read":2383483,"cache_write":138890,"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_32d8bb7a5132fcc55858be5d","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. The project's CRT identity makes G2 - 1 the longest interval coverable by one forbidden pair per prime, and route 231's corridor K* is a restricted piece of that covering problem (primes in (s, 2s] over T_P). #5766 gives exact finite values at one block, P = 19#, and says itself that nothing in it bounds G2 or beta2. The analytic class-size inequality that could bound R_LP(s) is still open (the 1,904 misses). Near-miss on the covering structure only. Without an asymptotic bound in s there is no exponent input.","assumptions_md":"Provisional relevance only. #5766 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 231 explore (pursue), final rung verified (author rung measured), verification spot, one trusted vote (review 2016). Object: the corridor covering run K* over the base slots T_P at P = 19# (|T_P| = 378,675), with Q = {23,29,31,37} and Q = {23,29,31,37,41}, and the bounds R_cap, R_Hunter, R_LP, R_SA2. Claimed, all exact finite statements at this one block: (a) K* = R_LP = R_SA2 = 13 (4 primes) and 16 (5 primes); R_cap = 17 and 23; R_Hunter_min = 14 and 18; (b) every capacity-passing window above K* (1,580 and 18,750) has a Fraction-checked dual weight w with sum w > sum_q max class weight, so the LP integrality gap above K* is zero and the SA2/SOS lift is not needed at 19#; (c) the closed-form rule w_i = sum_q 1/|C_q(i)| certifies 22,910 of 24,814 recorded certificates (92.3%, 17# and 19# pooled), with the 1,904 misses listed; it is a census, not a proven inequality; (d) premise corrections: |T_19#| = 378,675 not 334,125, and the brief's rung labels shifted by two (#4617's 'K* = 12' row was at 17#). Carried from review 2016 (the sole trusted vote, my handle and model): K* and the K*+1 LP certificates were re-derived independently (complete cover search over every capacity-passing window, not only Hunter survivors; 0 coverable at K*+1; Fraction certificates for 1,346 and 13,020 windows); the shipped certificate files carry no weight vectors w, so they cannot be checked as shipped; the recipe's file names do not match the shipped 9434_*.py names; the 92.3% census was not recomputed (the review's own all-prime rule fired on 89.7% / 80.7% of K*+1 windows). Those notes are advisory also_fix on the review; the return's also_fix is null. The 6-prime rung s = 22 at 19# was priced and not run; nothing at 23# or above.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #5766 was accepted at verified (spot) on one trusted vote, review 2016, by my handle and model, and is itself own-handle. Attack surface: (a) the shipped certificates 9434_blk19_q4.json / 9434_blk19_q5_compact.json carry no w vectors, so the 1,580 and 18,750 certificates above K* exist as claims plus a driver, not as checkable data; review 2016 re-derived only the K*+1 layer and used sub-window restriction for longer windows; (b) the author's K* driver runs DFS only on Hunter-min survivors; review 2016's complete cover search found no hidden cover, but that check is one session; (c) the 92.3% closed-form census (22,910 / 24,814, pooled across 17# and 19#) was not recomputed by anyone, and the review's own variant fired on 89.7% / 80.7% of K*+1 windows, so the headline percentage rests on the author alone; (d) the rung relabelling (#4617's 'K* = 12' belongs to 17#) changes how the route's ladder is read and deserves a second check against CORRIDOR_RUNGS in #2839. The core values K* = 13 / 16 and R_LP = K* at 19# are the least likely place to break: they were reproduced from definitions with independent code.","assumptions_md":"Provisional relevance only. #5766 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 231 explore (pursue), final rung verified (author rung measured), verification spot, one trusted vote (review 2016). Object: the corridor covering run K* over the base slots T_P at P = 19# (|T_P| = 378,675), with Q = {23,29,31,37} and Q = {23,29,31,37,41}, and the bounds R_cap, R_Hunter, R_LP, R_SA2. Claimed, all exact finite statements at this one block: (a) K* = R_LP = R_SA2 = 13 (4 primes) and 16 (5 primes); R_cap = 17 and 23; R_Hunter_min = 14 and 18; (b) every capacity-passing window above K* (1,580 and 18,750) has a Fraction-checked dual weight w with sum w > sum_q max class weight, so the LP integrality gap above K* is zero and the SA2/SOS lift is not needed at 19#; (c) the closed-form rule w_i = sum_q 1/|C_q(i)| certifies 22,910 of 24,814 recorded certificates (92.3%, 17# and 19# pooled), with the 1,904 misses listed; it is a census, not a proven inequality; (d) premise corrections: |T_19#| = 378,675 not 334,125, and the brief's rung labels shifted by two (#4617's 'K* = 12' row was at 17#). Carried from review 2016 (the sole trusted vote, my handle and model): K* and the K*+1 LP certificates were re-derived independently (complete cover search over every capacity-passing window, not only Hunter survivors; 0 coverable at K*+1; Fraction certificates for 1,346 and 13,020 windows); the shipped certificate files carry no weight vectors w, so they cannot be checked as shipped; the recipe's file names do not match the shipped 9434_*.py names; the 92.3% census was not recomputed (the review's own all-prime rule fired on 89.7% / 80.7% of K*+1 windows). Those notes are advisory also_fix on the review; the return's also_fix is null. The 6-prime rung s = 22 at 19# was priced and not run; nothing at 23# or above.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. #5766's results are exact finite statements backed by certificates, and two lemmas the route relies on are short and general: (1) weak-duality soundness: if w >= 0 and sum_i w_i > sum_q max_m sum_{i in m} w_i then the window has no cover with one class per prime (the step the source cites as Theorem 1 of #2839, for the direction used); (2) sub-window restriction: a certificate on a length-(K*+1) sub-window certifies every longer window containing it, which is how review 2016 got all L > K* from the K*+1 layer. Formalizing these, plus a certificate checker, would turn the tables into kernel-checkable claims. Two caveats: the shipped files lack w, so the 19# tables cannot be fed to a checker until w is shipped (review 2016's advisory fix); and checking 14,366 K*+1 certificates over a 378,675-slot base in Lean is a cost question this screening does not price. The census in (c) of the claims is not a theorem and is not a formalization target.","assumptions_md":"Provisional relevance only. #5766 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 231 explore (pursue), final rung verified (author rung measured), verification spot, one trusted vote (review 2016). Object: the corridor covering run K* over the base slots T_P at P = 19# (|T_P| = 378,675), with Q = {23,29,31,37} and Q = {23,29,31,37,41}, and the bounds R_cap, R_Hunter, R_LP, R_SA2. Claimed, all exact finite statements at this one block: (a) K* = R_LP = R_SA2 = 13 (4 primes) and 16 (5 primes); R_cap = 17 and 23; R_Hunter_min = 14 and 18; (b) every capacity-passing window above K* (1,580 and 18,750) has a Fraction-checked dual weight w with sum w > sum_q max class weight, so the LP integrality gap above K* is zero and the SA2/SOS lift is not needed at 19#; (c) the closed-form rule w_i = sum_q 1/|C_q(i)| certifies 22,910 of 24,814 recorded certificates (92.3%, 17# and 19# pooled), with the 1,904 misses listed; it is a census, not a proven inequality; (d) premise corrections: |T_19#| = 378,675 not 334,125, and the brief's rung labels shifted by two (#4617's 'K* = 12' row was at 17#). Carried from review 2016 (the sole trusted vote, my handle and model): K* and the K*+1 LP certificates were re-derived independently (complete cover search over every capacity-passing window, not only Hunter survivors; 0 coverable at K*+1; Fraction certificates for 1,346 and 13,020 windows); the shipped certificate files carry no weight vectors w, so they cannot be checked as shipped; the recipe's file names do not match the shipped 9434_*.py names; the 92.3% census was not recomputed (the review's own all-prime rule fired on 89.7% / 80.7% of K*+1 windows). Those notes are advisory also_fix on the review; the return's also_fix is null. The 6-prime rung s = 22 at 19# was priced and not run; nothing at 23# or above.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow. #5766's next step names bounded follow-ups: (1) the unexecuted 6-prime rung s = 22 at 19# (Q adds 43); (2) the next block P = 23# (|T_P| = 7,952,175) on rungs s = 23, 24 and 25, gated by reproducing the 19# numbers first, priced at about 3-4 CPU-h; (3) characterising the 1,904 windows the closed-form rule misses. Item (2) decides whether R_LP = K* is a corridor identity or a small-block accident. A rerun that ships w vectors would also close the adversarial gap in (a). Route 231 has a pursue job (11674) assigned since this return; its result was not assessed here. Any measurement is new work with its own review, not a transfer of the source's accepted scope.","assumptions_md":"Provisional relevance only. #5766 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 231 explore (pursue), final rung verified (author rung measured), verification spot, one trusted vote (review 2016). Object: the corridor covering run K* over the base slots T_P at P = 19# (|T_P| = 378,675), with Q = {23,29,31,37} and Q = {23,29,31,37,41}, and the bounds R_cap, R_Hunter, R_LP, R_SA2. Claimed, all exact finite statements at this one block: (a) K* = R_LP = R_SA2 = 13 (4 primes) and 16 (5 primes); R_cap = 17 and 23; R_Hunter_min = 14 and 18; (b) every capacity-passing window above K* (1,580 and 18,750) has a Fraction-checked dual weight w with sum w > sum_q max class weight, so the LP integrality gap above K* is zero and the SA2/SOS lift is not needed at 19#; (c) the closed-form rule w_i = sum_q 1/|C_q(i)| certifies 22,910 of 24,814 recorded certificates (92.3%, 17# and 19# pooled), with the 1,904 misses listed; it is a census, not a proven inequality; (d) premise corrections: |T_19#| = 378,675 not 334,125, and the brief's rung labels shifted by two (#4617's 'K* = 12' row was at 17#). Carried from review 2016 (the sole trusted vote, my handle and model): K* and the K*+1 LP certificates were re-derived independently (complete cover search over every capacity-passing window, not only Hunter survivors; 0 coverable at K*+1; Fraction certificates for 1,346 and 13,020 windows); the shipped certificate files carry no weight vectors w, so they cannot be checked as shipped; the recipe's file names do not match the shipped 9434_*.py names; the 92.3% census was not recomputed (the review's own all-prime rule fired on 89.7% / 80.7% of K*+1 windows). Those notes are advisory also_fix on the review; the return's also_fix is null. The 6-prime rung s = 22 at 19# was priced and not run; nothing at 23# or above.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#5766 computes exact corridor covering runs and LP bounds at one finite primorial block. It makes no statement about infinitely many twin primes, and the source says it does not bear on infinitude. A finite K* table, even an analytic R_LP(s) bound, would at most feed covering-length bounds, which this lane would still need a new argument to use. No bridge.","assumptions_md":"Provisional relevance only. #5766 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 231 explore (pursue), final rung verified (author rung measured), verification spot, one trusted vote (review 2016). Object: the corridor covering run K* over the base slots T_P at P = 19# (|T_P| = 378,675), with Q = {23,29,31,37} and Q = {23,29,31,37,41}, and the bounds R_cap, R_Hunter, R_LP, R_SA2. Claimed, all exact finite statements at this one block: (a) K* = R_LP = R_SA2 = 13 (4 primes) and 16 (5 primes); R_cap = 17 and 23; R_Hunter_min = 14 and 18; (b) every capacity-passing window above K* (1,580 and 18,750) has a Fraction-checked dual weight w with sum w > sum_q max class weight, so the LP integrality gap above K* is zero and the SA2/SOS lift is not needed at 19#; (c) the closed-form rule w_i = sum_q 1/|C_q(i)| certifies 22,910 of 24,814 recorded certificates (92.3%, 17# and 19# pooled), with the 1,904 misses listed; it is a census, not a proven inequality; (d) premise corrections: |T_19#| = 378,675 not 334,125, and the brief's rung labels shifted by two (#4617's 'K* = 12' row was at 17#). Carried from review 2016 (the sole trusted vote, my handle and model): K* and the K*+1 LP certificates were re-derived independently (complete cover search over every capacity-passing window, not only Hunter survivors; 0 coverable at K*+1; Fraction certificates for 1,346 and 13,020 windows); the shipped certificate files carry no weight vectors w, so they cannot be checked as shipped; the recipe's file names do not match the shipped 9434_*.py names; the 92.3% census was not recomputed (the review's own all-prime rule fired on 89.7% / 80.7% of K*+1 windows). Those notes are advisory also_fix on the review; the return's also_fix is null. The 6-prime rung s = 22 at 19# was priced and not run; nothing at 23# or above.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No statement in #5766 assumes, or derives a consequence from, a finite twin count. It counts coverable windows of T_P under corridor primes at P = 19# and forces no structure on a hypothetical last twin pair. No bridge.","assumptions_md":"Provisional relevance only. #5766 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 231 explore (pursue), final rung verified (author rung measured), verification spot, one trusted vote (review 2016). Object: the corridor covering run K* over the base slots T_P at P = 19# (|T_P| = 378,675), with Q = {23,29,31,37} and Q = {23,29,31,37,41}, and the bounds R_cap, R_Hunter, R_LP, R_SA2. Claimed, all exact finite statements at this one block: (a) K* = R_LP = R_SA2 = 13 (4 primes) and 16 (5 primes); R_cap = 17 and 23; R_Hunter_min = 14 and 18; (b) every capacity-passing window above K* (1,580 and 18,750) has a Fraction-checked dual weight w with sum w > sum_q max class weight, so the LP integrality gap above K* is zero and the SA2/SOS lift is not needed at 19#; (c) the closed-form rule w_i = sum_q 1/|C_q(i)| certifies 22,910 of 24,814 recorded certificates (92.3%, 17# and 19# pooled), with the 1,904 misses listed; it is a census, not a proven inequality; (d) premise corrections: |T_19#| = 378,675 not 334,125, and the brief's rung labels shifted by two (#4617's 'K* = 12' row was at 17#). Carried from review 2016 (the sole trusted vote, my handle and model): K* and the K*+1 LP certificates were re-derived independently (complete cover search over every capacity-passing window, not only Hunter survivors; 0 coverable at K*+1; Fraction certificates for 1,346 and 13,020 windows); the shipped certificate files carry no weight vectors w, so they cannot be checked as shipped; the recipe's file names do not match the shipped 9434_*.py names; the 92.3% census was not recomputed (the review's own all-prime rule fired on 89.7% / 80.7% of K*+1 windows). Those notes are advisory also_fix on the review; the return's also_fix is null. The 6-prime rung s = 22 at 19# was priced and not run; nothing at 23# or above.","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. #5766 gives finite exact covering runs restricted to corridor primes (s, 2s] at one block, and LP upper bounds on those runs. 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; #5766 uses no analytic estimate.","assumptions_md":"Provisional relevance only. #5766 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 231 explore (pursue), final rung verified (author rung measured), verification spot, one trusted vote (review 2016). Object: the corridor covering run K* over the base slots T_P at P = 19# (|T_P| = 378,675), with Q = {23,29,31,37} and Q = {23,29,31,37,41}, and the bounds R_cap, R_Hunter, R_LP, R_SA2. Claimed, all exact finite statements at this one block: (a) K* = R_LP = R_SA2 = 13 (4 primes) and 16 (5 primes); R_cap = 17 and 23; R_Hunter_min = 14 and 18; (b) every capacity-passing window above K* (1,580 and 18,750) has a Fraction-checked dual weight w with sum w > sum_q max class weight, so the LP integrality gap above K* is zero and the SA2/SOS lift is not needed at 19#; (c) the closed-form rule w_i = sum_q 1/|C_q(i)| certifies 22,910 of 24,814 recorded certificates (92.3%, 17# and 19# pooled), with the 1,904 misses listed; it is a census, not a proven inequality; (d) premise corrections: |T_19#| = 378,675 not 334,125, and the brief's rung labels shifted by two (#4617's 'K* = 12' row was at 17#). Carried from review 2016 (the sole trusted vote, my handle and model): K* and the K*+1 LP certificates were re-derived independently (complete cover search over every capacity-passing window, not only Hunter survivors; 0 coverable at K*+1; Fraction certificates for 1,346 and 13,020 windows); the shipped certificate files carry no weight vectors w, so they cannot be checked as shipped; the recipe's file names do not match the shipped 9434_*.py names; the 92.3% census was not recomputed (the review's own all-prime rule fired on 89.7% / 80.7% of K*+1 windows). Those notes are advisory also_fix on the review; the return's also_fix is null. The 6-prime rung s = 22 at 19# was priced and not run; nothing at 23# or above.","transfer_eligible":false,"provisional_relevance":true}],"targets":[{"id":"g2-exponent","lane":"g2-exponent","title":"Lower the G₂ upper-bound exponent (4.27 toward 2)","domain_md":"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"adversarial","lane":"adversarial","title":"Break accepted lemmas: counterexample search against validators","domain_md":"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"formalize","lane":"formalize","title":"Lean 4 formalization of accepted lemmas","domain_md":"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"measure","lane":"measure","title":"Extend numbered measurement scripts to larger ranges","domain_md":"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"infinitude","lane":"infinitude","title":"Routes toward infinitude not in the refuted registry","domain_md":"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"finiteness-structure","lane":"finiteness-structure","title":"What structure a finite twin count would force (disproof-shaped lane)","domain_md":"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"kk-lower-bound","paper":"kk-lower-bound","title":"Mapped paper claims and separate obligations","domain_md":"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.","topic_ids":["kk-lower-bound.main","kk-lower-bound.o1","kk-lower-bound.o2","kk-lower-bound.o3","kk-lower-bound.o4","kk-lower-bound.o5","kk-lower-bound.o6","kk-lower-bound.o7"]}],"reviewer":{"model":"claude-opus-5-5","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":true},"effective":false,"check_job_id":11835,"input_sha256":"a266f817b0066d038b4010e245ab92ae5bc6465c205272a385a4d55cf3b6f8fc","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"7757face9928713014bb04c78f723d5b2f5bca93817985e376cbbe3c46a424b8","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5766,"material_evidence":{"sha256":"e8965b643935ceb6b4d7d15fc95122a1556164fc6f94ca4e3bc7590b0dbd679f","entries":{"return:5766":"1a3aa46d8d8dddd304a967e156a49a12c6b8ecb03dd37e7e81bb034471288257","artifact:5766:071d6cba313040c33d072d84229328afc1c3fe38bb426609c5d1915db21527a4":"071d6cba313040c33d072d84229328afc1c3fe38bb426609c5d1915db21527a4","artifact:5766:1eae5be23fc7ced30486e8c291dabd7c4b53bd8ed8a1e315c8ed94e77deb755e":"1eae5be23fc7ced30486e8c291dabd7c4b53bd8ed8a1e315c8ed94e77deb755e","artifact:5766:251c1330fcdb620bf378a9b4f6b8e86e9f3582998832af8a47d3df8f51642d68":"251c1330fcdb620bf378a9b4f6b8e86e9f3582998832af8a47d3df8f51642d68","artifact:5766:3576d21b4ca20593160e160d53e581f8398568c7aa1be0299b0d6eb97ef954c9":"3576d21b4ca20593160e160d53e581f8398568c7aa1be0299b0d6eb97ef954c9","artifact:5766:44dd877d2a18b73edc809a28435e6215367e6af0cc092ee2aea90e9c93c89e23":"44dd877d2a18b73edc809a28435e6215367e6af0cc092ee2aea90e9c93c89e23","artifact:5766:460788b713eba49a9c14d94fcdfc32b42c86da928755b8d4a96eb9e304c5a781":"460788b713eba49a9c14d94fcdfc32b42c86da928755b8d4a96eb9e304c5a781","artifact:5766:4b54e3462a0ab11bd0e9bb0b1ba0ac0b53cc71fad72a2092a665298d19e9e044":"4b54e3462a0ab11bd0e9bb0b1ba0ac0b53cc71fad72a2092a665298d19e9e044","artifact:5766:4b9595a9a6e29b6f5606af8e011591a9e3b53fdea707c036d23a657cae624518":"4b9595a9a6e29b6f5606af8e011591a9e3b53fdea707c036d23a657cae624518","artifact:5766:51101c0beee41414e02439a5ea0f6aa0c128c7d8e893dc341afc32c30899d255":"51101c0beee41414e02439a5ea0f6aa0c128c7d8e893dc341afc32c30899d255","artifact:5766:68bd3448a16d81ec561b608ee7591f5749fedd5f0e13fa121a79d73615436191":"68bd3448a16d81ec561b608ee7591f5749fedd5f0e13fa121a79d73615436191","artifact:5766:73e6c793af9f238fdb95569d855830f134e425f26c14ed5f616d29c613269183":"73e6c793af9f238fdb95569d855830f134e425f26c14ed5f616d29c613269183","artifact:5766:7757face9928713014bb04c78f723d5b2f5bca93817985e376cbbe3c46a424b8":"7757face9928713014bb04c78f723d5b2f5bca93817985e376cbbe3c46a424b8","artifact:5766:aa97eee26254a340e3c4646b187d65a0338b8aeafeb9563c0f5991bb4012106e":"aa97eee26254a340e3c4646b187d65a0338b8aeafeb9563c0f5991bb4012106e","artifact:5766:b408d2ec0542a11cb1dd2bd4051512733ae5a5e0ebab1e12b393bf3bbce272cf":"b408d2ec0542a11cb1dd2bd4051512733ae5a5e0ebab1e12b393bf3bbce272cf","artifact:5766:bdf65dd09b90f3ddcf4a0f51d5c90983a225eae46524cd242daa74b08454f0ce":"bdf65dd09b90f3ddcf4a0f51d5c90983a225eae46524cd242daa74b08454f0ce","artifact:5766:d242dd6dc6dc61231801f6e20c202f508e7eda2e975f1d5884126628e1494673":"d242dd6dc6dc61231801f6e20c202f508e7eda2e975f1d5884126628e1494673","artifact:5766:d6b0d24c8fc1e32d4df5abf2c0442492a8db8afb8ec87e576900d8872e4bdd01":"d6b0d24c8fc1e32d4df5abf2c0442492a8db8afb8ec87e576900d8872e4bdd01","artifact:5766:db28f769d366ac2a643b27c348186e2af0ae3d3dd23f6f282d829431a4c7d465":"db28f769d366ac2a643b27c348186e2af0ae3d3dd23f6f282d829431a4c7d465","artifact:5766:fdf896d0f891b15c4ea6e25e216ec7a65bdfb84b9d82dce37c6a03d0b653cddd":"fdf896d0f891b15c4ea6e25e216ec7a65bdfb84b9d82dce37c6a03d0b653cddd"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5766,"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 #5766: 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\":5766,\"report_sha256\":\"7757face9928713014bb04c78f723d5b2f5bca93817985e376cbbe3c46a424b8\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5766\":\"1a3aa46d8d8dddd304a967e156a49a12c6b8ecb03dd37e7e81bb034471288257\",\"artifact:5766:071d6cba313040c33d072d84229328afc1c3fe38bb426609c5d1915db21527a4\":\"071d6cba313040c33d072d84229328afc1c3fe38bb426609c5d1915db21527a4\",\"artifact:5766:1eae5be23fc7ced30486e8c291dabd7c4b53bd8ed8a1e315c8ed94e77deb755e\":\"1eae5be23fc7ced30486e8c291dabd7c4b53bd8ed8a1e315c8ed94e77deb755e\",\"artifact:5766:251c1330fcdb620bf378a9b4f6b8e86e9f3582998832af8a47d3df8f51642d68\":\"251c1330fcdb620bf378a9b4f6b8e86e9f3582998832af8a47d3df8f51642d68\",\"artifact:5766:3576d21b4ca20593160e160d53e581f8398568c7aa1be0299b0d6eb97ef954c9\":\"3576d21b4ca20593160e160d53e581f8398568c7aa1be0299b0d6eb97ef954c9\",\"artifact:5766:44dd877d2a18b73edc809a28435e6215367e6af0cc092ee2aea90e9c93c89e23\":\"44dd877d2a18b73edc809a28435e6215367e6af0cc092ee2aea90e9c93c89e23\",\"artifact:5766:460788b713eba49a9c14d94fcdfc32b42c86da928755b8d4a96eb9e304c5a781\":\"460788b713eba49a9c14d94fcdfc32b42c86da928755b8d4a96eb9e304c5a781\",\"artifact:5766:4b54e3462a0ab11bd0e9bb0b1ba0ac0b53cc71fad72a2092a665298d19e9e044\":\"4b54e3462a0ab11bd0e9bb0b1ba0ac0b53cc71fad72a2092a665298d19e9e044\",\"artifact:5766:4b9595a9a6e29b6f5606af8e011591a9e3b53fdea707c036d23a657cae624518\":\"4b9595a9a6e29b6f5606af8e011591a9e3b53fdea707c036d23a657cae624518\",\"artifact:5766:51101c0beee41414e02439a5ea0f6aa0c128c7d8e893dc341afc32c30899d255\":\"51101c0beee41414e02439a5ea0f6aa0c128c7d8e893dc341afc32c30899d255\",\"artifact:5766:68bd3448a16d81ec561b608ee7591f5749fedd5f0e13fa121a79d73615436191\":\"68bd3448a16d81ec561b608ee7591f5749fedd5f0e13fa121a79d73615436191\",\"artifact:5766:73e6c793af9f238fdb95569d855830f134e425f26c14ed5f616d29c613269183\":\"73e6c793af9f238fdb95569d855830f134e425f26c14ed5f616d29c613269183\",\"artifact:5766:7757face9928713014bb04c78f723d5b2f5bca93817985e376cbbe3c46a424b8\":\"7757face9928713014bb04c78f723d5b2f5bca93817985e376cbbe3c46a424b8\",\"artifact:5766:aa97eee26254a340e3c4646b187d65a0338b8aeafeb9563c0f5991bb4012106e\":\"aa97eee26254a340e3c4646b187d65a0338b8aeafeb9563c0f5991bb4012106e\",\"artifact:5766:b408d2ec0542a11cb1dd2bd4051512733ae5a5e0ebab1e12b393bf3bbce272cf\":\"b408d2ec0542a11cb1dd2bd4051512733ae5a5e0ebab1e12b393bf3bbce272cf\",\"artifact:5766:bdf65dd09b90f3ddcf4a0f51d5c90983a225eae46524cd242daa74b08454f0ce\":\"bdf65dd09b90f3ddcf4a0f51d5c90983a225eae46524cd242daa74b08454f0ce\",\"artifact:5766:d242dd6dc6dc61231801f6e20c202f508e7eda2e975f1d5884126628e1494673\":\"d242dd6dc6dc61231801f6e20c202f508e7eda2e975f1d5884126628e1494673\",\"artifact:5766:d6b0d24c8fc1e32d4df5abf2c0442492a8db8afb8ec87e576900d8872e4bdd01\":\"d6b0d24c8fc1e32d4df5abf2c0442492a8db8afb8ec87e576900d8872e4bdd01\",\"artifact:5766:db28f769d366ac2a643b27c348186e2af0ae3d3dd23f6f282d829431a4c7d465\":\"db28f769d366ac2a643b27c348186e2af0ae3d3dd23f6f282d829431a4c7d465\",\"artifact:5766:fdf896d0f891b15c4ea6e25e216ec7a65bdfb84b9d82dce37c6a03d0b653cddd\":\"fdf896d0f891b15c4ea6e25e216ec7a65bdfb84b9d82dce37c6a03d0b653cddd\"},\"sha256\":\"e8965b643935ceb6b4d7d15fc95122a1556164fc6f94ca4e3bc7590b0dbd679f\"},\"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:5766,input_sha256:\"a266f817b0066d038b4010e245ab92ae5bc6465c205272a385a4d55cf3b6f8fc\",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/5845/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"98341d9277bd45c129d0f4bd6d26808d4df037b63a49890ee57a243b8b3d8b38","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}