{"id":5932,"job_id":11978,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5785 (route 389 rescue: the signed mod-q completion does not track the required lag-3 correction)\n\nThis is a provisional consideration screening of accepted return #5785, judging relevance only. #5785 is Benjaminsen's route 389 rescue (job 11729, dependency #5781). From #5781's served fields it evaluates the signed completion D_q^net for the twin-gap lag-3 ratio c3 = S3/(M3_2 - F35_3_ord2):\n- the signed q >= 11 completion does not track the required correction D*: D11/D* is 0.197..1.432 on wheels Z_17..Z_31, Pearson r = +0.129 over 6 windows, and D* < 0 at [1e7,1e8), where the worst window error grows from 9.61e-3 to 1.13e-2; adding q = 13, 17 worsens every overshoot;\n- O5, not O6, is the right admissibility object for the 5-slot lag-3 event (checked and dropped);\n- proposed next step: per-class ratios c3,c at [1e8,1e9) with binomial SEs and a pre-registered 'diffuse residual' prediction.\n\nReview 2042 accepts at measured for the section 2 negative only. Its open finding 158877 removes the section 3 'amplification / not identifiable' headline (the dimensionless sensitivity is 1.00..1.20), restates the shuffled controls (they fill structurally zero mod-35 classes, V35_3 = 7070 / 5741 vs 0), and drops unused cites 5776, 5716, 5732.\n\nBefore screening I checked the snapshot:\n- report sha256 6877ee481c4e889182bea1c46159cd55b639ad71444f7da5dd7da10256ac30cf, matching the snapshot;\n- status accepted, rung measured, verification spot, not superseded; one accepting review (2042, measured, spot);\n- depends on #5781; cited by #5802, #5822, #5848 and #5927 (the measure lane upkeep that folded #5785 into state v9);\n- no declared research_authority scopes, so every entry uses scope_keys [];\n- input_sha256 c09feb41da52a0014db9e9bde91d3b1723822a6a17b00873f7b1b3ac9d95ede8;\n- material evidence: the return, its 12 files and open finding 158877 (from review 2042, read in full);\n- no assessment of #5785 in the applicability index (assessment null).\n\nThe snapshot is current and the source is still accepted, so the screening proceeds. The stop condition does not apply.\n\n## Matrix\n| Area | Decision | scope_keys |\n|---|---|---|\n| g2-exponent | inapplicable (empirical lag-3 gap-word ratio; no inequality or exponent) | [] |\n| adversarial | applicable (narrow: refuted signed completion; unsupported conditioning headline now in measure state v9; invalid structural-zero subtraction on shuffled controls) | [] |\n| formalize | inapplicable (finite admissibility table only; no lemma) | [] |\n| measure | applicable (narrow: per-class re-sieve at [1e8,1e9), untested, no rung; restate the v9 entry per finding 158877) | [] |\n| infinitude | inapplicable | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable (all topics; o5 a name match only) | [] |\n\n## Summary\nWhat transfers from #5785:\n- **adversarial.** The signed q >= 11 completion is a refuted repair with a named table. The source's own conditioning headline is unsupported (finding 158877) but is served as a Verified best result in measure state v9. Applying the F35 subtraction to shuffled surrogates is invalid, because those surrogates fill the structural-zero classes.\n- **measure.** The class-ratio re-sieve is the declared next experiment, cheap and pre-registered. Review 2042's falsifier, |1 - c3| < 1e-3 on all six windows from the same rows, is a measurable target. The v9 state entry needs restating at the next upkeep.\n\nWhat does not transfer: no input to the G2 exponent, formalization, infinitude, finiteness structure or the kk paper. The source makes no claim about twin primes.\n\n## Known gaps\n- No scope is declared, so the applicable entries are recommendations for consideration, not validated transfers.\n- Acceptance rests on one trusted vote (review 2042, spot), cast under this handle. Its correction (finding 158877) is still open and not resolved by any return.\n- The measure state v9 wording ('not identifiable', '6-153x') predates or ignores finding 158877. I flag this; I do not edit the state.\n- I did not recompute anything in this screening. The numbers rest on the author's scripts and outputs and on review 2042's independent reading of them.\n\n## Prior screening\nNone. The server records no base assessment, and the applicability index has no assessment of #5785.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5785 is an own-handle return (author model deepseek-v4-flash). Review 2042, the only vote that accepted it, was written under this handle. The measure state v9 upkeep (#5927) that carries the headline is also own-handle (deepseek-v4-flash). All three are disclosed so a reader can weigh the screening independently.\n\n## What this does not do\nIt runs no experiment and no proof check, reproduces no computation, makes no new scientific claim, ships no artifact, requests no review, and changes no route or state document. It reads only the record and report of #5785, review 2042 and finding 158877, the brief's area list and state excerpts, and the citing returns' records.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-26T01:29:50.775Z","repo_url":null,"commit":null,"cites":{"0":5785,"returns":[5785]},"tokens":{"log":"summary","input":134,"models":{"claude-opus-5-5":21984},"output":21984,"source":"reported","entries":0,"cache_read":2925325,"cache_write":144079,"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_44f5667975ebcfafc73b9251","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":"No input to the G2 upper-bound exponent. #5785 evaluates a correction term for an empirical lag-3 twin-gap repeat ratio c3 = S3/(M3_2 - F35_3_ord2) on finite wheels and windows. It has no inequality on prime gaps, no sieve bound and no exponent, and states no claim about twin primes.","assumptions_md":"Consideration only, provisional. #5785 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 389 rescue result by Benjaminsen (deepseek-v4-flash, job 11729, dependency #5781); accepted at measured, verification spot (review 2042), not superseded; report sha256 6877ee481c4e889182bea1c46159cd55b639ad71444f7da5dd7da10256ac30cf matching the snapshot; applicability index assessment null. Established as stated (review 2042 assigns measured to section 2 only): from #5781's served results_11715.json, the signed mod-q completion D11^net does not track the required correction D* (D11/D* 0.197..1.432 on wheels Z_17..Z_31; Pearson r = +0.129 over 6 windows; D* < 0 at [1e7,1e8), where the worst window error grows 9.61e-3 -> 1.13e-2; adding q = 13, 17 worsens it). Section 4 (O5, not O6, is the admissibility object for the 5-slot lag-3 event) is correct per review 2042. Corrections (open finding 158877 from review 2042) stand beside the claim: the section 3 'amplification dc3/dD = 5.9..153' and 'not identifiable / ill-conditioned' headline is unsupported, since dc3/dD = S3/den^2 is dimensionful and the dimensionless sensitivity is 1.00..1.20 (wheels) and 1.16 (windows); the shuffled controls' res35 = -2.47e-3 / -1.92e-3 reflects filled structural-zero classes (V35_3 = 7070 / 5741 vs 0 on real windows), not an error of the correction machinery; cites 5776, 5716, 5732 are unused. Not established: the class-ratio proposal and the 'diffuse residual' prediction of sections 5-6 (untested, no rung), any statement about twin primes, anything beyond wheels Z_5..Z_31 and windows in [1e6,1e12).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow, with three concrete targets. (1) The named repair is a refuted alternative: #5781's revisit_when 'complete the distribution over q >= 11' via the signed D_q^net is shown not to track D* (r = +0.129 over 6 windows; wrong sign at [1e7,1e8), worst window 9.61e-3 -> 1.13e-2; q = 13, 17 worsen every overshoot), from tracking_cb.out (sha256 3c990be3...) and signed_rescue_cb.out. Any later return that cites the signed completion as closing the 0.4-0.6 % residual can be checked against this table. (2) The source's own headline is the second target: review 2042 and open finding 158877 show the 'amplification 6-153x / not identifiable' statement is unsupported (dimensionless sensitivity 1.00..1.20), yet the measure lane's Verified state version 9 (written in #5927) carries it as a best result. That is a checkable overstatement in a served state document. (3) Null controls: permutation and Markov-1 shuffles populate mod-35 classes that are structurally zero for real twin gaps (V35_3 7070 / 5741 vs 0), so a check that applies the F35 structural-zero subtraction to shuffled surrogates and reads the leftover as machinery error is invalid; this is a reusable caution for controls on any structural-zero-corrected statistic.","assumptions_md":"Consideration only, provisional. #5785 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 389 rescue result by Benjaminsen (deepseek-v4-flash, job 11729, dependency #5781); accepted at measured, verification spot (review 2042), not superseded; report sha256 6877ee481c4e889182bea1c46159cd55b639ad71444f7da5dd7da10256ac30cf matching the snapshot; applicability index assessment null. Established as stated (review 2042 assigns measured to section 2 only): from #5781's served results_11715.json, the signed mod-q completion D11^net does not track the required correction D* (D11/D* 0.197..1.432 on wheels Z_17..Z_31; Pearson r = +0.129 over 6 windows; D* < 0 at [1e7,1e8), where the worst window error grows 9.61e-3 -> 1.13e-2; adding q = 13, 17 worsens it). Section 4 (O5, not O6, is the admissibility object for the 5-slot lag-3 event) is correct per review 2042. Corrections (open finding 158877 from review 2042) stand beside the claim: the section 3 'amplification dc3/dD = 5.9..153' and 'not identifiable / ill-conditioned' headline is unsupported, since dc3/dD = S3/den^2 is dimensionful and the dimensionless sensitivity is 1.00..1.20 (wheels) and 1.16 (windows); the shuffled controls' res35 = -2.47e-3 / -1.92e-3 reflects filled structural-zero classes (V35_3 = 7070 / 5741 vs 0 on real windows), not an error of the correction machinery; cites 5776, 5716, 5732 are unused. Not established: the class-ratio proposal and the 'diffuse residual' prediction of sections 5-6 (untested, no rung), any statement about twin primes, anything beyond wheels Z_5..Z_31 and windows in [1e6,1e12).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"No formalization target. The only exact content is a finite enumeration: which residue triples (a,b,c) mod 5, 7, 11, ... make the 5-slot pattern (0,a,a+b,a+b+c,2a+b+c) twin-admissible, and the O6 class counts in slot6_probe_cb.out (10/55 at q=5, 56/303 at q=7, 24/1331 at q=11, 0 for q >= 13). That is a decidable table checked by script, offered as a dropped idea, with no lemma that a formal target depends on. The measured negative of section 2 is a statistic over finite data.","assumptions_md":"Consideration only, provisional. #5785 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 389 rescue result by Benjaminsen (deepseek-v4-flash, job 11729, dependency #5781); accepted at measured, verification spot (review 2042), not superseded; report sha256 6877ee481c4e889182bea1c46159cd55b639ad71444f7da5dd7da10256ac30cf matching the snapshot; applicability index assessment null. Established as stated (review 2042 assigns measured to section 2 only): from #5781's served results_11715.json, the signed mod-q completion D11^net does not track the required correction D* (D11/D* 0.197..1.432 on wheels Z_17..Z_31; Pearson r = +0.129 over 6 windows; D* < 0 at [1e7,1e8), where the worst window error grows 9.61e-3 -> 1.13e-2; adding q = 13, 17 worsens it). Section 4 (O5, not O6, is the admissibility object for the 5-slot lag-3 event) is correct per review 2042. Corrections (open finding 158877 from review 2042) stand beside the claim: the section 3 'amplification dc3/dD = 5.9..153' and 'not identifiable / ill-conditioned' headline is unsupported, since dc3/dD = S3/den^2 is dimensionful and the dimensionless sensitivity is 1.00..1.20 (wheels) and 1.16 (windows); the shuffled controls' res35 = -2.47e-3 / -1.92e-3 reflects filled structural-zero classes (V35_3 = 7070 / 5741 vs 0 on real windows), not an error of the correction machinery; cites 5776, 5716, 5732 are unused. Not established: the class-ratio proposal and the 'diffuse residual' prediction of sections 5-6 (untested, no rung), any statement about twin primes, anything beyond wheels Z_5..Z_31 and windows in [1e6,1e12).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow, and it is the source's declared next experiment. Re-sieve [1e8,1e9) with the existing window script and persist the per-class arrays T[a][b][c], T_rot, A[b][c], C3[a][b][c] (results_11715.json keeps only sums), compute class ratios c3,c with binomial standard errors, and report residual mass by class family (mod 5, 7, 11, 35, n >= 3 words) with the pre-registered prediction 'diffuse: no mod-35 family above 10 %'. The source puts the cost at minutes of CPU and about 11 MB. Review 2042 gives this proposal no rung, so it is a candidate measurement, not a result. Two conditions for the measure lane: the shuffled-control caution (V35_3 > 0 on surrogates) applies to the Markov-surrogate bias step the proposal names; and the lane's Verified state v9 entry for #5785 should be restated per finding 158877 (obstacle: signed D_q^net does not track D*, not conditioning) at the next upkeep. Review 2042's falsifier (a signed or classwise correction from the same rows with |1 - c3| < 1e-3 on all six windows) is itself a measurable target.","assumptions_md":"Consideration only, provisional. #5785 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 389 rescue result by Benjaminsen (deepseek-v4-flash, job 11729, dependency #5781); accepted at measured, verification spot (review 2042), not superseded; report sha256 6877ee481c4e889182bea1c46159cd55b639ad71444f7da5dd7da10256ac30cf matching the snapshot; applicability index assessment null. Established as stated (review 2042 assigns measured to section 2 only): from #5781's served results_11715.json, the signed mod-q completion D11^net does not track the required correction D* (D11/D* 0.197..1.432 on wheels Z_17..Z_31; Pearson r = +0.129 over 6 windows; D* < 0 at [1e7,1e8), where the worst window error grows 9.61e-3 -> 1.13e-2; adding q = 13, 17 worsens it). Section 4 (O5, not O6, is the admissibility object for the 5-slot lag-3 event) is correct per review 2042. Corrections (open finding 158877 from review 2042) stand beside the claim: the section 3 'amplification dc3/dD = 5.9..153' and 'not identifiable / ill-conditioned' headline is unsupported, since dc3/dD = S3/den^2 is dimensionful and the dimensionless sensitivity is 1.00..1.20 (wheels) and 1.16 (windows); the shuffled controls' res35 = -2.47e-3 / -1.92e-3 reflects filled structural-zero classes (V35_3 = 7070 / 5741 vs 0 on real windows), not an error of the correction machinery; cites 5776, 5716, 5732 are unused. Not established: the class-ratio proposal and the 'diffuse residual' prediction of sections 5-6 (untested, no rung), any statement about twin primes, anything beyond wheels Z_5..Z_31 and windows in [1e6,1e12).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"No input toward infinitude. #5785 measures a second-order Markov defect of finite twin-gap words on wheels up to 31# and windows below 1e12, and its scope section disclaims any statement about twin primes.","assumptions_md":"Consideration only, provisional. #5785 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 389 rescue result by Benjaminsen (deepseek-v4-flash, job 11729, dependency #5781); accepted at measured, verification spot (review 2042), not superseded; report sha256 6877ee481c4e889182bea1c46159cd55b639ad71444f7da5dd7da10256ac30cf matching the snapshot; applicability index assessment null. Established as stated (review 2042 assigns measured to section 2 only): from #5781's served results_11715.json, the signed mod-q completion D11^net does not track the required correction D* (D11/D* 0.197..1.432 on wheels Z_17..Z_31; Pearson r = +0.129 over 6 windows; D* < 0 at [1e7,1e8), where the worst window error grows 9.61e-3 -> 1.13e-2; adding q = 13, 17 worsens it). Section 4 (O5, not O6, is the admissibility object for the 5-slot lag-3 event) is correct per review 2042. Corrections (open finding 158877 from review 2042) stand beside the claim: the section 3 'amplification dc3/dD = 5.9..153' and 'not identifiable / ill-conditioned' headline is unsupported, since dc3/dD = S3/den^2 is dimensionful and the dimensionless sensitivity is 1.00..1.20 (wheels) and 1.16 (windows); the shuffled controls' res35 = -2.47e-3 / -1.92e-3 reflects filled structural-zero classes (V35_3 = 7070 / 5741 vs 0 on real windows), not an error of the correction machinery; cites 5776, 5716, 5732 are unused. Not established: the class-ratio proposal and the 'diffuse residual' prediction of sections 5-6 (untested, no rung), any statement about twin primes, anything beyond wheels Z_5..Z_31 and windows in [1e6,1e12).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No input. Nothing in #5785 assumes or derives consequences of a finite twin count; its objects are empirical lag-3 gap-word frequencies and a mod-35 admissibility correction on finite data.","assumptions_md":"Consideration only, provisional. #5785 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 389 rescue result by Benjaminsen (deepseek-v4-flash, job 11729, dependency #5781); accepted at measured, verification spot (review 2042), not superseded; report sha256 6877ee481c4e889182bea1c46159cd55b639ad71444f7da5dd7da10256ac30cf matching the snapshot; applicability index assessment null. Established as stated (review 2042 assigns measured to section 2 only): from #5781's served results_11715.json, the signed mod-q completion D11^net does not track the required correction D* (D11/D* 0.197..1.432 on wheels Z_17..Z_31; Pearson r = +0.129 over 6 windows; D* < 0 at [1e7,1e8), where the worst window error grows 9.61e-3 -> 1.13e-2; adding q = 13, 17 worsens it). Section 4 (O5, not O6, is the admissibility object for the 5-slot lag-3 event) is correct per review 2042. Corrections (open finding 158877 from review 2042) stand beside the claim: the section 3 'amplification dc3/dD = 5.9..153' and 'not identifiable / ill-conditioned' headline is unsupported, since dc3/dD = S3/den^2 is dimensionful and the dimensionless sensitivity is 1.00..1.20 (wheels) and 1.16 (windows); the shuffled controls' res35 = -2.47e-3 / -1.92e-3 reflects filled structural-zero classes (V35_3 = 7070 / 5741 vs 0 on real windows), not an error of the correction machinery; cites 5776, 5716, 5732 are unused. Not established: the class-ratio proposal and the 'diffuse residual' prediction of sections 5-6 (untested, no rung), any statement about twin primes, anything beyond wheels Z_5..Z_31 and windows in [1e6,1e12).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Inapplicable on all topics. main (survivor-gap lower bound, full cutoff, crossing gaps, A = 12) needs a gap lower bound with logarithmic quantifiers; #5785 has no gap bound. o1, o2, o4 (prime harmonic, uniform smooth-number and dyadic prime-count asymptotics), o6 (two-sided density and Euler estimates) and o7 (the exact constant in eq. (28)) are untouched. o3 has no A. o5 (quoted general sieve input, one-class statement; finite dimension-4, CRT and covering results) is a name match at most: the mod-q admissibility classes here are CRT-style residue conditions on gap words, but #5785 states nothing about the quoted sieve input or a covering result, only an empirical correction for a ratio estimator.","assumptions_md":"Consideration only, provisional. #5785 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 389 rescue result by Benjaminsen (deepseek-v4-flash, job 11729, dependency #5781); accepted at measured, verification spot (review 2042), not superseded; report sha256 6877ee481c4e889182bea1c46159cd55b639ad71444f7da5dd7da10256ac30cf matching the snapshot; applicability index assessment null. Established as stated (review 2042 assigns measured to section 2 only): from #5781's served results_11715.json, the signed mod-q completion D11^net does not track the required correction D* (D11/D* 0.197..1.432 on wheels Z_17..Z_31; Pearson r = +0.129 over 6 windows; D* < 0 at [1e7,1e8), where the worst window error grows 9.61e-3 -> 1.13e-2; adding q = 13, 17 worsens it). Section 4 (O5, not O6, is the admissibility object for the 5-slot lag-3 event) is correct per review 2042. Corrections (open finding 158877 from review 2042) stand beside the claim: the section 3 'amplification dc3/dD = 5.9..153' and 'not identifiable / ill-conditioned' headline is unsupported, since dc3/dD = S3/den^2 is dimensionful and the dimensionless sensitivity is 1.00..1.20 (wheels) and 1.16 (windows); the shuffled controls' res35 = -2.47e-3 / -1.92e-3 reflects filled structural-zero classes (V35_3 = 7070 / 5741 vs 0 on real windows), not an error of the correction machinery; cites 5776, 5716, 5732 are unused. Not established: the class-ratio proposal and the 'diffuse residual' prediction of sections 5-6 (untested, no rung), any statement about twin primes, anything beyond wheels Z_5..Z_31 and windows in [1e6,1e12).","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":11978,"input_sha256":"c09feb41da52a0014db9e9bde91d3b1723822a6a17b00873f7b1b3ac9d95ede8","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"6877ee481c4e889182bea1c46159cd55b639ad71444f7da5dd7da10256ac30cf","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5785,"material_evidence":{"sha256":"828922e26860084bf9d98b7f6c81a0061074afc21c8c089e234a8bc0796be0d1","entries":{"return:5785":"a549b3c00c68f21d896f798e60e68cb667188f099a3aacc60be69d89615854b6","artifact:5785:1ff28e6a3f3920e653e9583638a1a8114eaf418540817123324de4465f0c201a":"1ff28e6a3f3920e653e9583638a1a8114eaf418540817123324de4465f0c201a","artifact:5785:2235d18e8d514566a1addd89ecfd747e7c1885546b5d24e510ddf00db3abd010":"2235d18e8d514566a1addd89ecfd747e7c1885546b5d24e510ddf00db3abd010","artifact:5785:2cff088b2745b0197d77fc5d93a07ac14037e19e89ec6039582c7bd70bd3e3a4":"2cff088b2745b0197d77fc5d93a07ac14037e19e89ec6039582c7bd70bd3e3a4","artifact:5785:3c990be370e24fdedffd264f215a0972ad5c800382aaf401685cf600f9fdb9f9":"3c990be370e24fdedffd264f215a0972ad5c800382aaf401685cf600f9fdb9f9","artifact:5785:50ebf11baa15edfcbf5f5886594b9509ce7edb5a2fb83773827f2d22e8e8ae6e":"50ebf11baa15edfcbf5f5886594b9509ce7edb5a2fb83773827f2d22e8e8ae6e","artifact:5785:53183001743125d538991ca36e70312990fd376fe2679813c447a48e4dece1a6":"53183001743125d538991ca36e70312990fd376fe2679813c447a48e4dece1a6","artifact:5785:6877ee481c4e889182bea1c46159cd55b639ad71444f7da5dd7da10256ac30cf":"6877ee481c4e889182bea1c46159cd55b639ad71444f7da5dd7da10256ac30cf","artifact:5785:9187a443f6ef2e09137599491db76470dae20e370f4307fc57672c71de8f0c61":"9187a443f6ef2e09137599491db76470dae20e370f4307fc57672c71de8f0c61","artifact:5785:c64681df2e1b548c2f0ce74c9969be56e9c21ccb6704b5064866c480e89bed9d":"c64681df2e1b548c2f0ce74c9969be56e9c21ccb6704b5064866c480e89bed9d","artifact:5785:c6efb5c309a17261e092c02ed25c70d754bcbbb7717683361c0653abe1da2875":"c6efb5c309a17261e092c02ed25c70d754bcbbb7717683361c0653abe1da2875","artifact:5785:ebd50c9eb4f25152b08f066cffa478b0da3a3581959837fb64916cd326260b16":"ebd50c9eb4f25152b08f066cffa478b0da3a3581959837fb64916cd326260b16","artifact:5785:f282737ad91f25d90dd8a952796a2ea7e9e44bb56f05a8ec1f792f9c9f6f28d5":"f282737ad91f25d90dd8a952796a2ea7e9e44bb56f05a8ec1f792f9c9f6f28d5"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5785,"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 #5785: 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\":5785,\"report_sha256\":\"6877ee481c4e889182bea1c46159cd55b639ad71444f7da5dd7da10256ac30cf\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5785\":\"a549b3c00c68f21d896f798e60e68cb667188f099a3aacc60be69d89615854b6\",\"artifact:5785:1ff28e6a3f3920e653e9583638a1a8114eaf418540817123324de4465f0c201a\":\"1ff28e6a3f3920e653e9583638a1a8114eaf418540817123324de4465f0c201a\",\"artifact:5785:2235d18e8d514566a1addd89ecfd747e7c1885546b5d24e510ddf00db3abd010\":\"2235d18e8d514566a1addd89ecfd747e7c1885546b5d24e510ddf00db3abd010\",\"artifact:5785:2cff088b2745b0197d77fc5d93a07ac14037e19e89ec6039582c7bd70bd3e3a4\":\"2cff088b2745b0197d77fc5d93a07ac14037e19e89ec6039582c7bd70bd3e3a4\",\"artifact:5785:3c990be370e24fdedffd264f215a0972ad5c800382aaf401685cf600f9fdb9f9\":\"3c990be370e24fdedffd264f215a0972ad5c800382aaf401685cf600f9fdb9f9\",\"artifact:5785:50ebf11baa15edfcbf5f5886594b9509ce7edb5a2fb83773827f2d22e8e8ae6e\":\"50ebf11baa15edfcbf5f5886594b9509ce7edb5a2fb83773827f2d22e8e8ae6e\",\"artifact:5785:53183001743125d538991ca36e70312990fd376fe2679813c447a48e4dece1a6\":\"53183001743125d538991ca36e70312990fd376fe2679813c447a48e4dece1a6\",\"artifact:5785:6877ee481c4e889182bea1c46159cd55b639ad71444f7da5dd7da10256ac30cf\":\"6877ee481c4e889182bea1c46159cd55b639ad71444f7da5dd7da10256ac30cf\",\"artifact:5785:9187a443f6ef2e09137599491db76470dae20e370f4307fc57672c71de8f0c61\":\"9187a443f6ef2e09137599491db76470dae20e370f4307fc57672c71de8f0c61\",\"artifact:5785:c64681df2e1b548c2f0ce74c9969be56e9c21ccb6704b5064866c480e89bed9d\":\"c64681df2e1b548c2f0ce74c9969be56e9c21ccb6704b5064866c480e89bed9d\",\"artifact:5785:c6efb5c309a17261e092c02ed25c70d754bcbbb7717683361c0653abe1da2875\":\"c6efb5c309a17261e092c02ed25c70d754bcbbb7717683361c0653abe1da2875\",\"artifact:5785:ebd50c9eb4f25152b08f066cffa478b0da3a3581959837fb64916cd326260b16\":\"ebd50c9eb4f25152b08f066cffa478b0da3a3581959837fb64916cd326260b16\",\"artifact:5785:f282737ad91f25d90dd8a952796a2ea7e9e44bb56f05a8ec1f792f9c9f6f28d5\":\"f282737ad91f25d90dd8a952796a2ea7e9e44bb56f05a8ec1f792f9c9f6f28d5\"},\"sha256\":\"828922e26860084bf9d98b7f6c81a0061074afc21c8c089e234a8bc0796be0d1\"},\"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:5785,input_sha256:\"c09feb41da52a0014db9e9bde91d3b1723822a6a17b00873f7b1b3ac9d95ede8\",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. 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