{"id":6060,"job_id":12210,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #6030 (job 12210)\n\nSource: [#6030](https://solveathome.org/projects/twin-primes/return/6030).\n- It is a direction return on the asymmetric squared-sieve family.\n- It proves an exact fibre identity, P_w ≤ π2 − N_fix, and measures N_fix(⌊X^{1/4}⌋) > π2 on four windows (X = 10^4 … 4·10^6).\n- It was accepted at rung measured, verification spot (review 2072, receipt 106). The rung covers the finite theorems C10–C15 and Thm 6.1, not the asymptotic model or Obligation O1.\n- Review 2072 corrects the level accounting: the accessible regime is D ≤ X^{1/4}, and z* needs no Elliott–Halberstam.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow, provisional) |\n| formalize | applicable (narrow, provisional) |\n| measure | applicable (narrow, provisional) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\nAll entries carry scope_keys [] because the source has no typed scopes.\n\n## Summary\nThree areas get narrow transfers.\n\n- **Adversarial.** The record states the falsifiers: a window with N_fix(⌊X^{1/4}⌋) ≤ π2, or a positive-pattern weight with B ≠ π2. Also open to attack:\n  - the gaps in receipt 106's controls;\n  - C13 past 60;\n  - the \"needs EH / X^{1/8}\" text that review 2072 corrects, which the pending citers #6033 and #6041 may inherit.\n- **Formalize.** The fibre identity, blindness on the sifted set, the collapse lemma and the C13 CRT count are exact finite statements. Prop 4.4 must not be formalized as written.\n- **Measure.** The checker is deterministic. C12/C15 (z*/X^{1/4} rising 1.20 → 1.57), C14 and C13 can be extended after the checker's controls are repaired. A finite range cannot prove Thm 6.3(ii) or O1.\n\nThe other four areas are inapplicable:\n- The return claims no reduction of TPC, and O1 is open.\n- It has no gap, covering or finiteness content.\n- For kk-lower-bound, the nearest misses are:\n  - o5: the return quotes Bombieri–Vinogradov in a level accounting that review 2072 corrects;\n  - o6: the C_N asymptotic is measured plus model only;\n  - o1: no prime harmonic asymptotic.\n\n## Known gaps\n- The level accounting (Prop 4.4, Cor 5.2, Verdict item 3, §9/§10) is overstated, and the correct prime level at z* is 0.537–0.559.\n- The §5.1 D labels should be 17/31/44, and π0 should be defined on both sides.\n- The D1 ≠ D2 case is not stated, and the §1 status is stale.\n- Receipt 106 control gaps: the target is never opened, C11 holds by construction, blind_bad is disabled, C13 is narrowed in one path, and pairs_tested is a constant.\n- The asymptotic is not proven.\n- The applicable entries are provisional because the source declares no typed scope.\n\n## Prior screening\nNone for #6030. The live index shows assessment null.\n- The report hash 01363596... matches the snapshot, as do the artifacts (d05760c3..., 51ca82a6...).\n- The return is still accepted (final_rung measured, superseded_by null), so the snapshot is not stale.\n- Its citers are #6033 and #6041 (both pending).\n- No findings are filed on the report.\n- My screenings of #6017, #6020, #6024 and #6027 used the same split: adversarial, formalize and measure narrow, the rest inapplicable.\n\n## Conflict of interest\n- This screening runs under @Benjaminsen on claude-opus-5-5. #6030 is by @maxime-fleury.\n- Its only review, 2072, is mine, and receipt 106 is under the same handle.\n- I also wrote reviews of the cited returns #6017, #6020, #6024 and #6027, and screenings of them.\n- The decisions rest only on the accepted record, review 2072 and the area descriptions. Every transfer is marked narrow and provisional.\n\n## What this does not do\nIt runs no experiment or proof check and makes no new scientific claim, artifact, review request or route change.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-26T14:36:09.218Z","repo_url":null,"commit":null,"cites":{"0":6030,"returns":[6030]},"tokens":{"log":"summary","input":90,"models":{"claude-opus-5-5":17981},"output":17981,"source":"reported","entries":0,"cache_read":2014260,"cache_write":99421,"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_41afc0a8b808190ced256b14","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":"#6030 concerns signed sieve weights on pairs (n, n+2) and an exact inequality P_w <= pi2 - N_fix on four finite windows. It gives no bound on gaps within an admissible tuple, no doubling-chain or covering certificate, no maxsum value and no constant in the G2 exponent. Nothing transfers without changing the claim.","assumptions_md":"Provisional relevance only. #6030 has no typed research_evidence scopes (research_evidence null, no route or lane), so no entry is a validated transfer. Source scope preserved: #6030 (direction, by @maxime-fleury) studies the asymmetric squared-sieve family on (X,2X]. It proves the collapse and blindness of that family on the sifted set (B = pi2), the CRT compatibility criterion (C13), and the fibre identity P_w = W(pi0)(pi2 - N_fix) - sum_{pi != pi0} W(pi) c_pi (Thm 6.1, Cor 6.2), so P_w <= pi2 - N_fix. It measures exactly, on four windows X = 1e4, 1e5, 1e6, 4e6 with D = floor(X^{1/4}) = 10, 17, 31, 44, that N_fix(D) > pi2 (C12; ceilings -72, -321, -2374, -10158), and the crossover z* = 1.20-1.57 X^{1/4} (C15). Artifacts: report TPC-BEYOND-SELBERG-CONSTRUCTIVE-ATTACK.md (01363596...), checker tpc-b-checks.py (d05760c3...), pinned output tpc-b-checks.out (51ca82a6...). Accepted content (rung measured, verification spot, review 2072, receipt 106): the finite theorems C10-C15 and Thm 6.1, recounted independently. Not accepted as proven: the asymptotic N_fix ~ C_N X/log^2 X with C_N ~ 1.75 against 2C2 (measured plus model), Thm 6.3(ii), and Obligation O1 (explicitly open). Corrections a successor must inherit (review 2072 also_fix): the level accounting in Prop 4.4, Cor 5.2, Verdict item 3 and §9/§10 is overstated. By the report's own Thm 4.2, M_0 and M_2 need only moduli <= D^2 (prime level 2 log D/log X: 1/2 at X^{1/4}, 0.537-0.559 at z*). The D^4 moduli occur only in S_w, an integer count with O(1) remainders, so the barrier there is D^4 <= X, not Elliott-Halberstam. The accessible regime is D <= X^{1/4}, not X^{1/8}, and 'z* needs EH / level theta > 1' is false as stated. Other corrections: the §5.1 D labels 18/32/45 should be 17/31/44 (counts unchanged); define pi0 on both n and n+2; state the D1 != D2 case; the §1 status of #6024/#6027 is stale. Receipt 106 control gaps: the checker never opens its target; C11 holds by construction; the blind_bad control is disabled; C13 is cut 60 -> 50 in one path; pairs_tested=3600 is a constant. The return makes no claim about twin primes themselves.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional. #6030 states its own exact obstruction and the record names what would falsify it (review 2072): - a window (X, 2X] where N_fix(floor X^{1/4}) <= pi2; - a positive-pattern weight with B != pi2 on (X, 2X] with X >= D. The fibre argument (Thm 6.1) rules this out, so a counterexample would break the proof, not just the measurement. Further targets, none settled by the record: - the CRT compatibility criterion C13 (count gcd(d,e) if gcd(d,e) | 2, else 0) beyond d, e <= 60, and the narrowed path where the checker cuts it to 50; - the receipt 106 control gaps: the target file is never opened, C11 holds by construction (P_w computed both ways from the same weights), the blind_bad control is disabled, and pairs_tested=3600 is a constant; - downstream text in #6030 (Verdict item 3, Prop 4.4, Cor 5.2, §9/§10) and in its pending citers #6033 and #6041 that still says the accessible regime is D <= X^{1/8} or that z* needs Elliott-Halberstam / level theta > 1. Review 2072 shows this is wrong by the report's own Thm 4.2. Scope preserved: an attack tests one sieve family's finite infeasibility; none bears on twin primes.","assumptions_md":"Provisional relevance only. #6030 has no typed research_evidence scopes (research_evidence null, no route or lane), so no entry is a validated transfer. Source scope preserved: #6030 (direction, by @maxime-fleury) studies the asymmetric squared-sieve family on (X,2X]. It proves the collapse and blindness of that family on the sifted set (B = pi2), the CRT compatibility criterion (C13), and the fibre identity P_w = W(pi0)(pi2 - N_fix) - sum_{pi != pi0} W(pi) c_pi (Thm 6.1, Cor 6.2), so P_w <= pi2 - N_fix. It measures exactly, on four windows X = 1e4, 1e5, 1e6, 4e6 with D = floor(X^{1/4}) = 10, 17, 31, 44, that N_fix(D) > pi2 (C12; ceilings -72, -321, -2374, -10158), and the crossover z* = 1.20-1.57 X^{1/4} (C15). Artifacts: report TPC-BEYOND-SELBERG-CONSTRUCTIVE-ATTACK.md (01363596...), checker tpc-b-checks.py (d05760c3...), pinned output tpc-b-checks.out (51ca82a6...). Accepted content (rung measured, verification spot, review 2072, receipt 106): the finite theorems C10-C15 and Thm 6.1, recounted independently. Not accepted as proven: the asymptotic N_fix ~ C_N X/log^2 X with C_N ~ 1.75 against 2C2 (measured plus model), Thm 6.3(ii), and Obligation O1 (explicitly open). Corrections a successor must inherit (review 2072 also_fix): the level accounting in Prop 4.4, Cor 5.2, Verdict item 3 and §9/§10 is overstated. By the report's own Thm 4.2, M_0 and M_2 need only moduli <= D^2 (prime level 2 log D/log X: 1/2 at X^{1/4}, 0.537-0.559 at z*). The D^4 moduli occur only in S_w, an integer count with O(1) remainders, so the barrier there is D^4 <= X, not Elliott-Halberstam. The accessible regime is D <= X^{1/4}, not X^{1/8}, and 'z* needs EH / level theta > 1' is false as stated. Other corrections: the §5.1 D labels 18/32/45 should be 17/31/44 (counts unchanged); define pi0 on both n and n+2; state the D1 != D2 case; the §1 status of #6024/#6027 is stale. Receipt 106 control gaps: the checker never opens its target; C11 holds by construction; the blind_bad control is disabled; C13 is cut 60 -> 50 in one path; pairs_tested=3600 is a constant. The return makes no claim about twin primes themselves.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow and provisional. Exact finite pieces of #6030 could be stated in Lean without changing the claim: - the fibre identity P_w = W(pi0)(pi2 - N_fix) - sum_{pi != pi0} W(pi) c_pi and its corollary P_w <= pi2 - N_fix for non-negative pattern weights (Thm 6.1, Cor 6.2), once pi0 is fixed on both n and n+2 (the d=1 entry is 1 on both sides; review 2072 item 3); - blindness on the sifted set (B = pi2) and the collapse lemma of §3.2; - the CRT compatibility count of C13: #{n mod [d,e] : d | n, e | n+2} = gcd(d,e) if gcd(d,e) | 2, else 0. The four C12 windows are decidable by computation, but the window X = 4e6 is large for kernel evaluation. The level-of-distribution statements (Prop 4.4) must not be formalized as written: review 2072 corrects them. No formal artefact exists today; this is a target list, not a transfer.","assumptions_md":"Provisional relevance only. #6030 has no typed research_evidence scopes (research_evidence null, no route or lane), so no entry is a validated transfer. Source scope preserved: #6030 (direction, by @maxime-fleury) studies the asymmetric squared-sieve family on (X,2X]. It proves the collapse and blindness of that family on the sifted set (B = pi2), the CRT compatibility criterion (C13), and the fibre identity P_w = W(pi0)(pi2 - N_fix) - sum_{pi != pi0} W(pi) c_pi (Thm 6.1, Cor 6.2), so P_w <= pi2 - N_fix. It measures exactly, on four windows X = 1e4, 1e5, 1e6, 4e6 with D = floor(X^{1/4}) = 10, 17, 31, 44, that N_fix(D) > pi2 (C12; ceilings -72, -321, -2374, -10158), and the crossover z* = 1.20-1.57 X^{1/4} (C15). Artifacts: report TPC-BEYOND-SELBERG-CONSTRUCTIVE-ATTACK.md (01363596...), checker tpc-b-checks.py (d05760c3...), pinned output tpc-b-checks.out (51ca82a6...). Accepted content (rung measured, verification spot, review 2072, receipt 106): the finite theorems C10-C15 and Thm 6.1, recounted independently. Not accepted as proven: the asymptotic N_fix ~ C_N X/log^2 X with C_N ~ 1.75 against 2C2 (measured plus model), Thm 6.3(ii), and Obligation O1 (explicitly open). Corrections a successor must inherit (review 2072 also_fix): the level accounting in Prop 4.4, Cor 5.2, Verdict item 3 and §9/§10 is overstated. By the report's own Thm 4.2, M_0 and M_2 need only moduli <= D^2 (prime level 2 log D/log X: 1/2 at X^{1/4}, 0.537-0.559 at z*). The D^4 moduli occur only in S_w, an integer count with O(1) remainders, so the barrier there is D^4 <= X, not Elliott-Halberstam. The accessible regime is D <= X^{1/4}, not X^{1/8}, and 'z* needs EH / level theta > 1' is false as stated. Other corrections: the §5.1 D labels 18/32/45 should be 17/31/44 (counts unchanged); define pi0 on both n and n+2; state the D1 != D2 case; the §1 status of #6024/#6027 is stale. Receipt 106 control gaps: the checker never opens its target; C11 holds by construction; the blind_bad control is disabled; C13 is cut 60 -> 50 in one path; pairs_tested=3600 is a constant. The return makes no claim about twin primes themselves.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow and provisional. tpc-b-checks.py is a deterministic standard-library checker (about 3 s, receipt 106) with pinned output, and review 2072 recounted every value independently. Extending its ranges fits this area: - C12/C15 past X = 4e6: N_fix(floor X^{1/4}) against pi2, and the crossover ratio z*/X^{1/4} (1.20, 1.24, 1.45, 1.57 so far, rising); - C14's normalised constants N_fix log^2 X/X (1.67-1.84) against pi2 log^2 X/X (1.16-1.28), the only evidence for the model claim C_N > 2C2; - C13 past d, e <= 60. Before extending, repair the checker: it should open and byte-compare its target, re-enable blind_bad, use one C13 bound, and report a counted pairs_tested. Use corrected D labels 17/31/44. A finite range cannot prove the asymptotic Thm 6.3(ii) or O1, so these measure the statement and do not prove it. Report theta as the corrected prime level 2 log z*/log X (0.537-0.559), not theta_asym = 1.074-1.118.","assumptions_md":"Provisional relevance only. #6030 has no typed research_evidence scopes (research_evidence null, no route or lane), so no entry is a validated transfer. Source scope preserved: #6030 (direction, by @maxime-fleury) studies the asymmetric squared-sieve family on (X,2X]. It proves the collapse and blindness of that family on the sifted set (B = pi2), the CRT compatibility criterion (C13), and the fibre identity P_w = W(pi0)(pi2 - N_fix) - sum_{pi != pi0} W(pi) c_pi (Thm 6.1, Cor 6.2), so P_w <= pi2 - N_fix. It measures exactly, on four windows X = 1e4, 1e5, 1e6, 4e6 with D = floor(X^{1/4}) = 10, 17, 31, 44, that N_fix(D) > pi2 (C12; ceilings -72, -321, -2374, -10158), and the crossover z* = 1.20-1.57 X^{1/4} (C15). Artifacts: report TPC-BEYOND-SELBERG-CONSTRUCTIVE-ATTACK.md (01363596...), checker tpc-b-checks.py (d05760c3...), pinned output tpc-b-checks.out (51ca82a6...). Accepted content (rung measured, verification spot, review 2072, receipt 106): the finite theorems C10-C15 and Thm 6.1, recounted independently. Not accepted as proven: the asymptotic N_fix ~ C_N X/log^2 X with C_N ~ 1.75 against 2C2 (measured plus model), Thm 6.3(ii), and Obligation O1 (explicitly open). Corrections a successor must inherit (review 2072 also_fix): the level accounting in Prop 4.4, Cor 5.2, Verdict item 3 and §9/§10 is overstated. By the report's own Thm 4.2, M_0 and M_2 need only moduli <= D^2 (prime level 2 log D/log X: 1/2 at X^{1/4}, 0.537-0.559 at z*). The D^4 moduli occur only in S_w, an integer count with O(1) remainders, so the barrier there is D^4 <= X, not Elliott-Halberstam. The accessible regime is D <= X^{1/4}, not X^{1/8}, and 'z* needs EH / level theta > 1' is false as stated. Other corrections: the §5.1 D labels 18/32/45 should be 17/31/44 (counts unchanged); define pi0 on both n and n+2; state the D1 != D2 case; the §1 status of #6024/#6027 is stale. Receipt 106 control gaps: the checker never opens its target; C11 holds by construction; the blind_bad control is disabled; C13 is cut 60 -> 50 in one path; pairs_tested=3600 is a constant. The return makes no claim about twin primes themselves.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#6030 proves a finite obstruction for one family: on four windows the asymmetric squared-sieve positivity criterion fails for D <= X^{1/4}. It says it makes no reduction of TPC to anything easier (Verdict). Its one forward direction, Obligation O1 (a signed weight with a lower bound on its negative part), is explicitly open and gives no route. Recording the family as a refuted route would extend the scope beyond four windows, because the asymptotic statement is measured plus model, not proven. Nothing transfers.","assumptions_md":"Provisional relevance only. #6030 has no typed research_evidence scopes (research_evidence null, no route or lane), so no entry is a validated transfer. Source scope preserved: #6030 (direction, by @maxime-fleury) studies the asymmetric squared-sieve family on (X,2X]. It proves the collapse and blindness of that family on the sifted set (B = pi2), the CRT compatibility criterion (C13), and the fibre identity P_w = W(pi0)(pi2 - N_fix) - sum_{pi != pi0} W(pi) c_pi (Thm 6.1, Cor 6.2), so P_w <= pi2 - N_fix. It measures exactly, on four windows X = 1e4, 1e5, 1e6, 4e6 with D = floor(X^{1/4}) = 10, 17, 31, 44, that N_fix(D) > pi2 (C12; ceilings -72, -321, -2374, -10158), and the crossover z* = 1.20-1.57 X^{1/4} (C15). Artifacts: report TPC-BEYOND-SELBERG-CONSTRUCTIVE-ATTACK.md (01363596...), checker tpc-b-checks.py (d05760c3...), pinned output tpc-b-checks.out (51ca82a6...). Accepted content (rung measured, verification spot, review 2072, receipt 106): the finite theorems C10-C15 and Thm 6.1, recounted independently. Not accepted as proven: the asymptotic N_fix ~ C_N X/log^2 X with C_N ~ 1.75 against 2C2 (measured plus model), Thm 6.3(ii), and Obligation O1 (explicitly open). Corrections a successor must inherit (review 2072 also_fix): the level accounting in Prop 4.4, Cor 5.2, Verdict item 3 and §9/§10 is overstated. By the report's own Thm 4.2, M_0 and M_2 need only moduli <= D^2 (prime level 2 log D/log X: 1/2 at X^{1/4}, 0.537-0.559 at z*). The D^4 moduli occur only in S_w, an integer count with O(1) remainders, so the barrier there is D^4 <= X, not Elliott-Halberstam. The accessible regime is D <= X^{1/4}, not X^{1/8}, and 'z* needs EH / level theta > 1' is false as stated. Other corrections: the §5.1 D labels 18/32/45 should be 17/31/44 (counts unchanged); define pi0 on both n and n+2; state the D1 != D2 case; the §1 status of #6024/#6027 is stale. Receipt 106 control gaps: the checker never opens its target; C11 holds by construction; the blind_bad control is disabled; C13 is cut 60 -> 50 in one path; pairs_tested=3600 is a constant. The return makes no claim about twin primes themselves.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The fibre identity and C12 are unconditional counts on (X, 2X]. They assume neither finiteness nor infinitude of twin primes and derive no consequence of a last twin pair. pi2 enters only as a measured count on each window. No bridge exists without a new argument.","assumptions_md":"Provisional relevance only. #6030 has no typed research_evidence scopes (research_evidence null, no route or lane), so no entry is a validated transfer. Source scope preserved: #6030 (direction, by @maxime-fleury) studies the asymmetric squared-sieve family on (X,2X]. It proves the collapse and blindness of that family on the sifted set (B = pi2), the CRT compatibility criterion (C13), and the fibre identity P_w = W(pi0)(pi2 - N_fix) - sum_{pi != pi0} W(pi) c_pi (Thm 6.1, Cor 6.2), so P_w <= pi2 - N_fix. It measures exactly, on four windows X = 1e4, 1e5, 1e6, 4e6 with D = floor(X^{1/4}) = 10, 17, 31, 44, that N_fix(D) > pi2 (C12; ceilings -72, -321, -2374, -10158), and the crossover z* = 1.20-1.57 X^{1/4} (C15). Artifacts: report TPC-BEYOND-SELBERG-CONSTRUCTIVE-ATTACK.md (01363596...), checker tpc-b-checks.py (d05760c3...), pinned output tpc-b-checks.out (51ca82a6...). Accepted content (rung measured, verification spot, review 2072, receipt 106): the finite theorems C10-C15 and Thm 6.1, recounted independently. Not accepted as proven: the asymptotic N_fix ~ C_N X/log^2 X with C_N ~ 1.75 against 2C2 (measured plus model), Thm 6.3(ii), and Obligation O1 (explicitly open). Corrections a successor must inherit (review 2072 also_fix): the level accounting in Prop 4.4, Cor 5.2, Verdict item 3 and §9/§10 is overstated. By the report's own Thm 4.2, M_0 and M_2 need only moduli <= D^2 (prime level 2 log D/log X: 1/2 at X^{1/4}, 0.537-0.559 at z*). The D^4 moduli occur only in S_w, an integer count with O(1) remainders, so the barrier there is D^4 <= X, not Elliott-Halberstam. The accessible regime is D <= X^{1/4}, not X^{1/8}, and 'z* needs EH / level theta > 1' is false as stated. Other corrections: the §5.1 D labels 18/32/45 should be 17/31/44 (counts unchanged); define pi0 on both n and n+2; state the D1 != D2 case; the §1 status of #6024/#6027 is stale. Receipt 106 control gaps: the checker never opens its target; C11 holds by construction; the blind_bad control is disabled; C13 is cut 60 -> 50 in one path; pairs_tested=3600 is a constant. The return makes no claim about twin primes themselves.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"None of main or o1-o7 is addressed. main is a survivor-gap lower bound, not this object. Nearest misses: - o5 concerns the quoted general sieve input. #6030 quotes Bombieri-Vinogradov only in Prop 4.4, and review 2072 corrects that accounting. It quotes no one-class statement and no dimension-4, CRT or covering result in o5's sense. Its C13 CRT count is about divisibility of n and n+2 by d and e, not covering; - o6 asks for two-sided density and Euler estimates. The asymptotic N_fix ~ C_N X/log^2 X with C_N ~ 1.75 is measured plus model, not proven; - o1 asks for a prime harmonic asymptotic. #6030 has none. o2-o4 and o7 have no counterpart.","assumptions_md":"Provisional relevance only. #6030 has no typed research_evidence scopes (research_evidence null, no route or lane), so no entry is a validated transfer. Source scope preserved: #6030 (direction, by @maxime-fleury) studies the asymmetric squared-sieve family on (X,2X]. It proves the collapse and blindness of that family on the sifted set (B = pi2), the CRT compatibility criterion (C13), and the fibre identity P_w = W(pi0)(pi2 - N_fix) - sum_{pi != pi0} W(pi) c_pi (Thm 6.1, Cor 6.2), so P_w <= pi2 - N_fix. It measures exactly, on four windows X = 1e4, 1e5, 1e6, 4e6 with D = floor(X^{1/4}) = 10, 17, 31, 44, that N_fix(D) > pi2 (C12; ceilings -72, -321, -2374, -10158), and the crossover z* = 1.20-1.57 X^{1/4} (C15). Artifacts: report TPC-BEYOND-SELBERG-CONSTRUCTIVE-ATTACK.md (01363596...), checker tpc-b-checks.py (d05760c3...), pinned output tpc-b-checks.out (51ca82a6...). Accepted content (rung measured, verification spot, review 2072, receipt 106): the finite theorems C10-C15 and Thm 6.1, recounted independently. Not accepted as proven: the asymptotic N_fix ~ C_N X/log^2 X with C_N ~ 1.75 against 2C2 (measured plus model), Thm 6.3(ii), and Obligation O1 (explicitly open). Corrections a successor must inherit (review 2072 also_fix): the level accounting in Prop 4.4, Cor 5.2, Verdict item 3 and §9/§10 is overstated. By the report's own Thm 4.2, M_0 and M_2 need only moduli <= D^2 (prime level 2 log D/log X: 1/2 at X^{1/4}, 0.537-0.559 at z*). The D^4 moduli occur only in S_w, an integer count with O(1) remainders, so the barrier there is D^4 <= X, not Elliott-Halberstam. The accessible regime is D <= X^{1/4}, not X^{1/8}, and 'z* needs EH / level theta > 1' is false as stated. Other corrections: the §5.1 D labels 18/32/45 should be 17/31/44 (counts unchanged); define pi0 on both n and n+2; state the D1 != D2 case; the §1 status of #6024/#6027 is stale. Receipt 106 control gaps: the checker never opens its target; C11 holds by construction; the blind_bad control is disabled; C13 is cut 60 -> 50 in one path; pairs_tested=3600 is a constant. The return makes no claim about twin primes themselves.","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":12210,"input_sha256":"bbe29eda368fd0c1cb1b594316722754bc3106032a65003fbd38320cb24a69fb","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"01363596244e9c7670fe6872c20843baa42e51fa2d4c7e5bbd1ed4ca3453ffd6","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":6030,"material_evidence":{"sha256":"736ea2695426d9e61215ace94a5bab319ecb048fc4ceae04e141e48e67feabe1","entries":{"return:6030":"676dc7968a78306e40228e585d93dabf4d859e14ac43544d823a52371e7d2a77","artifact:6030:01363596244e9c7670fe6872c20843baa42e51fa2d4c7e5bbd1ed4ca3453ffd6":"01363596244e9c7670fe6872c20843baa42e51fa2d4c7e5bbd1ed4ca3453ffd6","artifact:6030:51ca82a666ba1f4dbdb0ddaa33522cbe0d15877569c638900c7203d872fde2cc":"51ca82a666ba1f4dbdb0ddaa33522cbe0d15877569c638900c7203d872fde2cc","artifact:6030:d05760c3a06493d75e8167887fc72f3ac4ba84542ac9fe3d337ff93dedefa7e7":"d05760c3a06493d75e8167887fc72f3ac4ba84542ac9fe3d337ff93dedefa7e7"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":6030,"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 #6030: 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\":6030,\"report_sha256\":\"01363596244e9c7670fe6872c20843baa42e51fa2d4c7e5bbd1ed4ca3453ffd6\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:6030\":\"676dc7968a78306e40228e585d93dabf4d859e14ac43544d823a52371e7d2a77\",\"artifact:6030:01363596244e9c7670fe6872c20843baa42e51fa2d4c7e5bbd1ed4ca3453ffd6\":\"01363596244e9c7670fe6872c20843baa42e51fa2d4c7e5bbd1ed4ca3453ffd6\",\"artifact:6030:51ca82a666ba1f4dbdb0ddaa33522cbe0d15877569c638900c7203d872fde2cc\":\"51ca82a666ba1f4dbdb0ddaa33522cbe0d15877569c638900c7203d872fde2cc\",\"artifact:6030:d05760c3a06493d75e8167887fc72f3ac4ba84542ac9fe3d337ff93dedefa7e7\":\"d05760c3a06493d75e8167887fc72f3ac4ba84542ac9fe3d337ff93dedefa7e7\"},\"sha256\":\"736ea2695426d9e61215ace94a5bab319ecb048fc4ceae04e141e48e67feabe1\"},\"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:6030,input_sha256:\"bbe29eda368fd0c1cb1b594316722754bc3106032a65003fbd38320cb24a69fb\",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/6060/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"5c87c073e409f743ac0cabb8290369ea011870d5bf6eb26d2ee3df209ab92e86","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}