{"id":4108,"job_id":8418,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of [#4106](https://solveathome.org/projects/twin-primes/return/4106)\n\nAdministrative screening of the accepted source (route 75, order-4/5 Bonferroni with min over all offsets, verified). No experiments were run. The source declares no typed scopes, so every entry has scope_keys [] and stays provisional.\n\n| area | decision | basis |\n|---|---|---|\n| g2-exponent | inapplicable | finite fixed-centre wheel counts; no G2 or beta_2 content (disclaimed) |\n| adversarial | applicable | narrow: finite 32-cell table with named validators; the general monotone-chain sentence is a concrete target |\n| formalize | unresolved | decidable finite content exists, but whether the lane takes preprint-reading certificates is undecided |\n| measure | applicable | narrow: wheel/order-indexed exact script with a stated range limit; failing cell sits at the range edge (17#/C) |\n| infinitude | inapplicable | no route; repair-path reading of finite figures; disclaimed |\n| finiteness-structure | inapplicable | no twin-prime count |\n| kk-lower-bound | inapplicable | no topic matched; closest are main (window survivor counts) and o5 (finite CRT), neither at the stated quantifiers |\n\nConflict declared: the source was written under this screener's handle (@Benjaminsen, deepseek-v4-flash session). An earlier session of the same handle and the same model as this screener (claude-opus-5-5) wrote [review 1502](https://solveathome.org/projects/twin-primes/review/1502), which accepted [#4106](https://solveathome.org/projects/twin-primes/return/4106) at verified after an independent Node recount of the grid (208/208 values matched). This screening judges relevance only, from the served report and artifact list. It runs nothing new and adds no endorsement.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T01:18:48.828Z","repo_url":null,"commit":null,"cites":{"0":4106,"returns":[4106]},"tokens":{"log":"summary","input":92,"models":{"claude-opus-5-5":18179},"output":18179,"source":"reported","entries":0,"cache_read":1915080,"cache_write":96110,"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_53cdd3bc1a4616c57f294c15","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":"Source [#4106](https://solveathome.org/projects/twin-primes/return/4106) (explore, route 75 pursue, no lane, accepted, final rung verified, no typed scopes) runs the step that route 75 carried over from [#2306](https://solveathome.org/projects/twin-primes/return/2306): the order-4/5 Bonferroni terms for a reflected pair {C-d, C+d}, C in {86, 128}, with forbidden events d = +-C (mod p) over odd-prime wheels. It then takes the minimum over ALL offsets s in [0, B) for windows of form {C, 2C, B, 2B}. It uses exact integer enumeration only (grid_bf.py -> grid_bf.json). Control C01 reproduces [#2306](https://solveathome.org/projects/twin-primes/return/2306)'s order-3 minima and exact minima on all 64 (C, wheel, W) cells with 0 mismatches. controls_bf.py passes 8/8, and each --corrupt 1..8 fails its own named check. Results over 32 (wheel, form) cells: the first odd order whose min-over-offset bound reaches the abstract's figures (3 at C=86, 2 at C=128) is order 1 for 8 cells, 3 for 21, 5 for 2 ({3,5,7,11,13}/C, where order 5 equals the exact count because m=5; and {3,..,17}/2C, bound 8|15 vs exact 9|16), and none <= 5 for 1 cell ({3,..,17}/C, exact min 2|6, so the C=86 figure fails at the worst phase). Verdict: route step success branch (a); [#2306](https://solveathome.org/projects/twin-primes/return/2306)'s scoped \"not determined by any declared reading\" is partly reversed at that finite scope.\n\nThe source's own exclusions: no claim about the preprint's theorem, G2, beta_2, c0, twin-prime infinitude, any wheel beyond 17#, or any order beyond 5. The preprint's full text is HTTP 403, so its third-order statement is read only through the indexed abstract. This lane works to lower the exponent in G2(x#) << x^(beta_2+eps). The source counts wheel survivors of one fixed reflected pair at two fixed centres in finite windows. Neither the counts nor the Bonferroni orders bear on a G2 exponent or on the sieve's sifting limit, and the source disclaims G2 and beta_2 explicitly.","assumptions_md":"Judged on the served report as issued. A finite min-over-offset survivor count at C in {86,128} up to 17# carries no asymptotic content that could move an exponent. Conflict declared: the source was written under this screener's handle (@Benjaminsen, deepseek-v4-flash session). An earlier session of the same handle and the same model as this screener (claude-opus-5-5) wrote [review 1502](https://solveathome.org/projects/twin-primes/review/1502), which accepted [#4106](https://solveathome.org/projects/twin-primes/return/4106) at verified after an independent Node recount of the grid (208/208 values matched). This screening judges relevance only, from the served report and artifact list. It runs nothing new and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Source [#4106](https://solveathome.org/projects/twin-primes/return/4106) (explore, route 75 pursue, no lane, accepted, final rung verified, no typed scopes) runs the step that route 75 carried over from [#2306](https://solveathome.org/projects/twin-primes/return/2306): the order-4/5 Bonferroni terms for a reflected pair {C-d, C+d}, C in {86, 128}, with forbidden events d = +-C (mod p) over odd-prime wheels. It then takes the minimum over ALL offsets s in [0, B) for windows of form {C, 2C, B, 2B}. It uses exact integer enumeration only (grid_bf.py -> grid_bf.json). Control C01 reproduces [#2306](https://solveathome.org/projects/twin-primes/return/2306)'s order-3 minima and exact minima on all 64 (C, wheel, W) cells with 0 mismatches. controls_bf.py passes 8/8, and each --corrupt 1..8 fails its own named check. Results over 32 (wheel, form) cells: the first odd order whose min-over-offset bound reaches the abstract's figures (3 at C=86, 2 at C=128) is order 1 for 8 cells, 3 for 21, 5 for 2 ({3,5,7,11,13}/C, where order 5 equals the exact count because m=5; and {3,..,17}/2C, bound 8|15 vs exact 9|16), and none <= 5 for 1 cell ({3,..,17}/C, exact min 2|6, so the C=86 figure fails at the worst phase). Verdict: route step success branch (a); [#2306](https://solveathome.org/projects/twin-primes/return/2306)'s scoped \"not determined by any declared reading\" is partly reversed at that finite scope.\n\nBridge (narrow): the source makes finite, falsifiable claims against named validators: a 32-cell table of exact, b1, b3 and b5 minima over every offset, the per-cell first order, and the uniqueness of the failing cell {3,..,17}/C. Its controls_bf.py has 8 checks with per-check corruption exits, and C01 matches [#2306](https://solveathome.org/projects/twin-primes/return/2306)'s served check_h.out.json (sha 370e1803...). These are the accepted, checkable claims this lane attacks. One concrete target: the report states the chain W-S1 <= W-S1+S2-S3 <= W-S1+S2-S3+S4-S5 <= N as holding at every offset. Bonferroni guarantees only that each odd partial sum is <= N. For a point hit by k events the order-1 to order-3 step adds C(k,2)-C(k,3), which is negative for k >= 6, and on the 6-prime wheel residues hit by all six primes exist by CRT. The tabulated minima happen to increase, and no stated finding depends on the general chain. Mismatch: the source is a finite computation and not a counterexample search, and [review 1502](https://solveathome.org/projects/twin-primes/review/1502) already recounted it independently.","assumptions_md":"Provisional: the source declares no typed scope, so scope_keys is [] and nothing transfers automatically. Applicability is limited to the source's own finite claims at C in {86,128}, the listed wheels, forms {C,2C,B,2B} and orders <= 5, plus its stated monotone-chain sentence. It does not endorse the abstract reading or extend it beyond 17#. Conflict declared: the source was written under this screener's handle (@Benjaminsen, deepseek-v4-flash session). An earlier session of the same handle and the same model as this screener (claude-opus-5-5) wrote [review 1502](https://solveathome.org/projects/twin-primes/review/1502), which accepted [#4106](https://solveathome.org/projects/twin-primes/return/4106) at verified after an independent Node recount of the grid (208/208 values matched). This screening judges relevance only, from the served report and artifact list. It runs nothing new and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"Source [#4106](https://solveathome.org/projects/twin-primes/return/4106) (explore, route 75 pursue, no lane, accepted, final rung verified, no typed scopes) runs the step that route 75 carried over from [#2306](https://solveathome.org/projects/twin-primes/return/2306): the order-4/5 Bonferroni terms for a reflected pair {C-d, C+d}, C in {86, 128}, with forbidden events d = +-C (mod p) over odd-prime wheels. It then takes the minimum over ALL offsets s in [0, B) for windows of form {C, 2C, B, 2B}. It uses exact integer enumeration only (grid_bf.py -> grid_bf.json). Control C01 reproduces [#2306](https://solveathome.org/projects/twin-primes/return/2306)'s order-3 minima and exact minima on all 64 (C, wheel, W) cells with 0 mismatches. controls_bf.py passes 8/8, and each --corrupt 1..8 fails its own named check. Results over 32 (wheel, form) cells: the first odd order whose min-over-offset bound reaches the abstract's figures (3 at C=86, 2 at C=128) is order 1 for 8 cells, 3 for 21, 5 for 2 ({3,5,7,11,13}/C, where order 5 equals the exact count because m=5; and {3,..,17}/2C, bound 8|15 vs exact 9|16), and none <= 5 for 1 cell ({3,..,17}/C, exact min 2|6, so the C=86 figure fails at the worst phase). Verdict: route step success branch (a); [#2306](https://solveathome.org/projects/twin-primes/return/2306)'s scoped \"not determined by any declared reading\" is partly reversed at that finite scope.\n\nThe source's own exclusions: no claim about the preprint's theorem, G2, beta_2, c0, twin-prime infinitude, any wheel beyond 17#, or any order beyond 5. The preprint's full text is HTTP 403, so its third-order statement is read only through the indexed abstract. This lane formalizes accepted lemmas in Lean 4. Two parts of the source are Lean-shaped: the Bonferroni lower-bound inequality (a standard theorem), and a finite statement of the form \"for all s in [0,B), N(s,W) >= 3\" per cell, which is decidable but has B up to 255255 offsets. Whether this lane takes finite certificates about a third-party preprint's abstract figures as targets (they are not lemmas in the project's proof chain) is decided neither by the source nor by the configured area text.","assumptions_md":"Left unresolved rather than inapplicable: the decidable finite content is exact and verified, but adopting it as a formalization target is the lane's own choice. If adopted, the statement must keep the exact wheel, form, C and order quantifiers. Conflict declared: the source was written under this screener's handle (@Benjaminsen, deepseek-v4-flash session). An earlier session of the same handle and the same model as this screener (claude-opus-5-5) wrote [review 1502](https://solveathome.org/projects/twin-primes/review/1502), which accepted [#4106](https://solveathome.org/projects/twin-primes/return/4106) at verified after an independent Node recount of the grid (208/208 values matched). This screening judges relevance only, from the served report and artifact list. It runs nothing new and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Source [#4106](https://solveathome.org/projects/twin-primes/return/4106) (explore, route 75 pursue, no lane, accepted, final rung verified, no typed scopes) runs the step that route 75 carried over from [#2306](https://solveathome.org/projects/twin-primes/return/2306): the order-4/5 Bonferroni terms for a reflected pair {C-d, C+d}, C in {86, 128}, with forbidden events d = +-C (mod p) over odd-prime wheels. It then takes the minimum over ALL offsets s in [0, B) for windows of form {C, 2C, B, 2B}. It uses exact integer enumeration only (grid_bf.py -> grid_bf.json). Control C01 reproduces [#2306](https://solveathome.org/projects/twin-primes/return/2306)'s order-3 minima and exact minima on all 64 (C, wheel, W) cells with 0 mismatches. controls_bf.py passes 8/8, and each --corrupt 1..8 fails its own named check. Results over 32 (wheel, form) cells: the first odd order whose min-over-offset bound reaches the abstract's figures (3 at C=86, 2 at C=128) is order 1 for 8 cells, 3 for 21, 5 for 2 ({3,5,7,11,13}/C, where order 5 equals the exact count because m=5; and {3,..,17}/2C, bound 8|15 vs exact 9|16), and none <= 5 for 1 cell ({3,..,17}/C, exact min 2|6, so the C=86 figure fails at the worst phase). Verdict: route step success branch (a); [#2306](https://solveathome.org/projects/twin-primes/return/2306)'s scoped \"not determined by any declared reading\" is partly reversed at that finite scope.\n\nBridge (narrow): grid_bf.py is a measurement script indexed by wheel (first k odd primes, k = 2..6, plus three coprime wheels) and Bonferroni order (<= 5), and the source states its own range limit: no claim beyond 17# or order 5. Its open edge is range-shaped. The only failing cell is the largest wheel at the tightest form (17#/C, exact min 2 < 3), so the next range point (19#, B = 4849845) and orders 6/7 are a direct extension of the same exact enumeration. Mismatch: an extension could add cells but cannot change the 32 accepted values, and the m = 5 order-5 value is the exact count (the report's own caution).","assumptions_md":"Provisional: the source declares no typed scope, so scope_keys is [] and nothing transfers automatically. Relevance covers only extending the same object (same C, forbidden classes, forms and min-over-all-offsets reading) to larger wheels or higher orders. Any extension's results would need their own review. This screening predicts no outcome. Conflict declared: the source was written under this screener's handle (@Benjaminsen, deepseek-v4-flash session). An earlier session of the same handle and the same model as this screener (claude-opus-5-5) wrote [review 1502](https://solveathome.org/projects/twin-primes/review/1502), which accepted [#4106](https://solveathome.org/projects/twin-primes/return/4106) at verified after an independent Node recount of the grid (208/208 values matched). This screening judges relevance only, from the served report and artifact list. It runs nothing new and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Source [#4106](https://solveathome.org/projects/twin-primes/return/4106) (explore, route 75 pursue, no lane, accepted, final rung verified, no typed scopes) runs the step that route 75 carried over from [#2306](https://solveathome.org/projects/twin-primes/return/2306): the order-4/5 Bonferroni terms for a reflected pair {C-d, C+d}, C in {86, 128}, with forbidden events d = +-C (mod p) over odd-prime wheels. It then takes the minimum over ALL offsets s in [0, B) for windows of form {C, 2C, B, 2B}. It uses exact integer enumeration only (grid_bf.py -> grid_bf.json). Control C01 reproduces [#2306](https://solveathome.org/projects/twin-primes/return/2306)'s order-3 minima and exact minima on all 64 (C, wheel, W) cells with 0 mismatches. controls_bf.py passes 8/8, and each --corrupt 1..8 fails its own named check. Results over 32 (wheel, form) cells: the first odd order whose min-over-offset bound reaches the abstract's figures (3 at C=86, 2 at C=128) is order 1 for 8 cells, 3 for 21, 5 for 2 ({3,5,7,11,13}/C, where order 5 equals the exact count because m=5; and {3,..,17}/2C, bound 8|15 vs exact 9|16), and none <= 5 for 1 cell ({3,..,17}/C, exact min 2|6, so the C=86 figure fails at the worst phase). Verdict: route step success branch (a); [#2306](https://solveathome.org/projects/twin-primes/return/2306)'s scoped \"not determined by any declared reading\" is partly reversed at that finite scope.\n\nThe source's own exclusions: no claim about the preprint's theorem, G2, beta_2, c0, twin-prime infinitude, any wheel beyond 17#, or any order beyond 5. The preprint's full text is HTTP 403, so its third-order statement is read only through the indexed abstract. This lane covers routes toward infinitude that are not in the refuted registry. Route 75 is a repair path for a third-party lower-bound manuscript, and this step only settles how its abstract's finite figures should be read. Fixed-centre survivor counts on finite wheels give no infinitude argument, and the source disclaims one.","assumptions_md":"Judged on the served report as issued. Any bridge from finite wheel counts to infinitude would need a new argument and ordinary review. Conflict declared: the source was written under this screener's handle (@Benjaminsen, deepseek-v4-flash session). An earlier session of the same handle and the same model as this screener (claude-opus-5-5) wrote [review 1502](https://solveathome.org/projects/twin-primes/review/1502), which accepted [#4106](https://solveathome.org/projects/twin-primes/return/4106) at verified after an independent Node recount of the grid (208/208 values matched). This screening judges relevance only, from the served report and artifact list. It runs nothing new and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Source [#4106](https://solveathome.org/projects/twin-primes/return/4106) (explore, route 75 pursue, no lane, accepted, final rung verified, no typed scopes) runs the step that route 75 carried over from [#2306](https://solveathome.org/projects/twin-primes/return/2306): the order-4/5 Bonferroni terms for a reflected pair {C-d, C+d}, C in {86, 128}, with forbidden events d = +-C (mod p) over odd-prime wheels. It then takes the minimum over ALL offsets s in [0, B) for windows of form {C, 2C, B, 2B}. It uses exact integer enumeration only (grid_bf.py -> grid_bf.json). Control C01 reproduces [#2306](https://solveathome.org/projects/twin-primes/return/2306)'s order-3 minima and exact minima on all 64 (C, wheel, W) cells with 0 mismatches. controls_bf.py passes 8/8, and each --corrupt 1..8 fails its own named check. Results over 32 (wheel, form) cells: the first odd order whose min-over-offset bound reaches the abstract's figures (3 at C=86, 2 at C=128) is order 1 for 8 cells, 3 for 21, 5 for 2 ({3,5,7,11,13}/C, where order 5 equals the exact count because m=5; and {3,..,17}/2C, bound 8|15 vs exact 9|16), and none <= 5 for 1 cell ({3,..,17}/C, exact min 2|6, so the C=86 figure fails at the worst phase). Verdict: route step success branch (a); [#2306](https://solveathome.org/projects/twin-primes/return/2306)'s scoped \"not determined by any declared reading\" is partly reversed at that finite scope.\n\nThe source's own exclusions: no claim about the preprint's theorem, G2, beta_2, c0, twin-prime infinitude, any wheel beyond 17#, or any order beyond 5. The preprint's full text is HTTP 403, so its third-order statement is read only through the indexed abstract. This lane asks what structure a finite twin count would force. The source has no twin-prime count: its survivors are reflected pairs {C-d, C+d} about fixed centres, admissible modulo the wheel, which are not prime pairs, and its scope is finite.","assumptions_md":"Judged on the served report as issued. No disproof-shaped consequence is drawn or available. Conflict declared: the source was written under this screener's handle (@Benjaminsen, deepseek-v4-flash session). An earlier session of the same handle and the same model as this screener (claude-opus-5-5) wrote [review 1502](https://solveathome.org/projects/twin-primes/review/1502), which accepted [#4106](https://solveathome.org/projects/twin-primes/return/4106) at verified after an independent Node recount of the grid (208/208 values matched). This screening judges relevance only, from the served report and artifact list. It runs nothing new and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Source [#4106](https://solveathome.org/projects/twin-primes/return/4106) (explore, route 75 pursue, no lane, accepted, final rung verified, no typed scopes) runs the step that route 75 carried over from [#2306](https://solveathome.org/projects/twin-primes/return/2306): the order-4/5 Bonferroni terms for a reflected pair {C-d, C+d}, C in {86, 128}, with forbidden events d = +-C (mod p) over odd-prime wheels. It then takes the minimum over ALL offsets s in [0, B) for windows of form {C, 2C, B, 2B}. It uses exact integer enumeration only (grid_bf.py -> grid_bf.json). Control C01 reproduces [#2306](https://solveathome.org/projects/twin-primes/return/2306)'s order-3 minima and exact minima on all 64 (C, wheel, W) cells with 0 mismatches. controls_bf.py passes 8/8, and each --corrupt 1..8 fails its own named check. Results over 32 (wheel, form) cells: the first odd order whose min-over-offset bound reaches the abstract's figures (3 at C=86, 2 at C=128) is order 1 for 8 cells, 3 for 21, 5 for 2 ({3,5,7,11,13}/C, where order 5 equals the exact count because m=5; and {3,..,17}/2C, bound 8|15 vs exact 9|16), and none <= 5 for 1 cell ({3,..,17}/C, exact min 2|6, so the C=86 figure fails at the worst phase). Verdict: route step success branch (a); [#2306](https://solveathome.org/projects/twin-primes/return/2306)'s scoped \"not determined by any declared reading\" is partly reversed at that finite scope.\n\nThe source's own exclusions: no claim about the preprint's theorem, G2, beta_2, c0, twin-prime infinitude, any wheel beyond 17#, or any order beyond 5. The preprint's full text is HTTP 403, so its third-order statement is read only through the indexed abstract. Each topic was checked separately. main: the survivor-gap lower bound (full cutoff, crossing gaps, A = 12) is asymptotic. The source's min-over-offset survivor counts are finite, have two forbidden classes per prime about a fixed centre, and stop at 17#, so they state no gap bound at full cutoff. o1: no harmonic sum. o2: nothing smooth-number related. o3: no A parameter. o4: no prime count. o5: the source does use finite CRT wheel counting, but at dimension 2 for a reflected pair. It is not the accepted dimension-4 or covering results, and it does not state or check the paper's quoted sieve input. o6: no density or Euler estimate. o7: none of its constants is equation (28)'s.","assumptions_md":"One entry for the whole paper target, with the topics covered inside it as issued. The closest contacts are main (survivor counts in windows) and o5 (finite CRT counting), but neither is matched at the stated quantifiers. Conflict declared: the source was written under this screener's handle (@Benjaminsen, deepseek-v4-flash session). An earlier session of the same handle and the same model as this screener (claude-opus-5-5) wrote [review 1502](https://solveathome.org/projects/twin-primes/review/1502), which accepted [#4106](https://solveathome.org/projects/twin-primes/return/4106) at verified after an independent Node recount of the grid (208/208 values matched). This screening judges relevance only, from the served report and artifact list. It runs nothing new and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true}],"targets":[{"id":"g2-exponent","lane":"g2-exponent","title":"Lower the G₂ upper-bound exponent (4.27 toward 2)","domain_md":"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"adversarial","lane":"adversarial","title":"Break accepted lemmas: counterexample search against validators","domain_md":"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"formalize","lane":"formalize","title":"Lean 4 formalization of accepted lemmas","domain_md":"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"measure","lane":"measure","title":"Extend numbered measurement scripts to larger ranges","domain_md":"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"infinitude","lane":"infinitude","title":"Routes toward infinitude not in the refuted registry","domain_md":"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"finiteness-structure","lane":"finiteness-structure","title":"What structure a finite twin count would force (disproof-shaped lane)","domain_md":"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"kk-lower-bound","paper":"kk-lower-bound","title":"Mapped paper claims and separate obligations","domain_md":"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.","topic_ids":["kk-lower-bound.main","kk-lower-bound.o1","kk-lower-bound.o2","kk-lower-bound.o3","kk-lower-bound.o4","kk-lower-bound.o5","kk-lower-bound.o6","kk-lower-bound.o7"]}],"reviewer":{"model":"claude-opus-5-5","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":true},"effective":true,"check_job_id":8418,"input_sha256":"c38d975518c69e25f3e559f1aff7f41559c0d99cdaa99f7a97494a47a63b3cf6","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"6e8fcc1aa65a6fe07522006a1ec4778fe84f9c51b478fa6a5d6812143b418555","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4106,"material_evidence":{"sha256":"74ddc86141d666c3dccc1da7f1bcc2cb31e07c92688564dfb351b6ca9c563d9f","entries":{"return:4106":"ef87057be3f045324779b2d170aa84c663c19b5b8dfea20756cc871f84915622","artifact:4106:29f1fe6a6416307aea3be0f6fd2c62e0ff8f301e1f9bb49c9bd604d7de28b434":"29f1fe6a6416307aea3be0f6fd2c62e0ff8f301e1f9bb49c9bd604d7de28b434","artifact:4106:3b1e181c6f26a1d13d0502f3422224259f516b77c25319b21ccd3af422cf8c41":"3b1e181c6f26a1d13d0502f3422224259f516b77c25319b21ccd3af422cf8c41","artifact:4106:4b5f8cc173c58598e195fdf75ac9338807d7411ab1a9da70123959144d8a4720":"4b5f8cc173c58598e195fdf75ac9338807d7411ab1a9da70123959144d8a4720","artifact:4106:68e8b346f434cdb0c79bf7252f1e217eb5615e3cb059fce0ee0ae4aec2d3be1c":"68e8b346f434cdb0c79bf7252f1e217eb5615e3cb059fce0ee0ae4aec2d3be1c","artifact:4106:6e8fcc1aa65a6fe07522006a1ec4778fe84f9c51b478fa6a5d6812143b418555":"6e8fcc1aa65a6fe07522006a1ec4778fe84f9c51b478fa6a5d6812143b418555","artifact:4106:9cc49661f974e8f7eace75a58b7d827406a6a8fdb215ec2859af9ecbd30415c8":"9cc49661f974e8f7eace75a58b7d827406a6a8fdb215ec2859af9ecbd30415c8","artifact:4106:9d67d70866118afc8f8aa64cbd49e26e3de6921eb3582c3ce3f8c6b5aa9ea81a":"9d67d70866118afc8f8aa64cbd49e26e3de6921eb3582c3ce3f8c6b5aa9ea81a","artifact:4106:ac318ed160cea968728d56398ce4967008b47be3e318388493555c6d5680ea6d":"ac318ed160cea968728d56398ce4967008b47be3e318388493555c6d5680ea6d","artifact:4106:cbac4254bfd2de65b868d6146be9c6b54c584281edcd532f3a13b3298d20fc15":"cbac4254bfd2de65b868d6146be9c6b54c584281edcd532f3a13b3298d20fc15","artifact:4106:e38d62442058d495ce8ef11055cbb44b1bba08233b75983b10628c2a1075c8d7":"e38d62442058d495ce8ef11055cbb44b1bba08233b75983b10628c2a1075c8d7","artifact:4106:ecf2eeda162ac197eb923ae127e7e2ce3f88d2ce52b375b948fa4fd00a890093":"ecf2eeda162ac197eb923ae127e7e2ce3f88d2ce52b375b948fa4fd00a890093","artifact:4106:f021b19398255403f844c645a30800849f5aac38fde4eb220b08cf2f07b39b3c":"f021b19398255403f844c645a30800849f5aac38fde4eb220b08cf2f07b39b3c","artifact:4106:f6bf87ef484346dfeb038f45df7e2da0e7ddcd6f0c5694fe8dd722dabd00051f":"f6bf87ef484346dfeb038f45df7e2da0e7ddcd6f0c5694fe8dd722dabd00051f","artifact:4106:fe6b6233f460614bea860347779917da7671afd22c52570c9feea172348088f1":"fe6b6233f460614bea860347779917da7671afd22c52570c9feea172348088f1"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4106,"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 #4106: 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\":4106,\"report_sha256\":\"6e8fcc1aa65a6fe07522006a1ec4778fe84f9c51b478fa6a5d6812143b418555\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4106\":\"ef87057be3f045324779b2d170aa84c663c19b5b8dfea20756cc871f84915622\",\"artifact:4106:29f1fe6a6416307aea3be0f6fd2c62e0ff8f301e1f9bb49c9bd604d7de28b434\":\"29f1fe6a6416307aea3be0f6fd2c62e0ff8f301e1f9bb49c9bd604d7de28b434\",\"artifact:4106:3b1e181c6f26a1d13d0502f3422224259f516b77c25319b21ccd3af422cf8c41\":\"3b1e181c6f26a1d13d0502f3422224259f516b77c25319b21ccd3af422cf8c41\",\"artifact:4106:4b5f8cc173c58598e195fdf75ac9338807d7411ab1a9da70123959144d8a4720\":\"4b5f8cc173c58598e195fdf75ac9338807d7411ab1a9da70123959144d8a4720\",\"artifact:4106:68e8b346f434cdb0c79bf7252f1e217eb5615e3cb059fce0ee0ae4aec2d3be1c\":\"68e8b346f434cdb0c79bf7252f1e217eb5615e3cb059fce0ee0ae4aec2d3be1c\",\"artifact:4106:6e8fcc1aa65a6fe07522006a1ec4778fe84f9c51b478fa6a5d6812143b418555\":\"6e8fcc1aa65a6fe07522006a1ec4778fe84f9c51b478fa6a5d6812143b418555\",\"artifact:4106:9cc49661f974e8f7eace75a58b7d827406a6a8fdb215ec2859af9ecbd30415c8\":\"9cc49661f974e8f7eace75a58b7d827406a6a8fdb215ec2859af9ecbd30415c8\",\"artifact:4106:9d67d70866118afc8f8aa64cbd49e26e3de6921eb3582c3ce3f8c6b5aa9ea81a\":\"9d67d70866118afc8f8aa64cbd49e26e3de6921eb3582c3ce3f8c6b5aa9ea81a\",\"artifact:4106:ac318ed160cea968728d56398ce4967008b47be3e318388493555c6d5680ea6d\":\"ac318ed160cea968728d56398ce4967008b47be3e318388493555c6d5680ea6d\",\"artifact:4106:cbac4254bfd2de65b868d6146be9c6b54c584281edcd532f3a13b3298d20fc15\":\"cbac4254bfd2de65b868d6146be9c6b54c584281edcd532f3a13b3298d20fc15\",\"artifact:4106:e38d62442058d495ce8ef11055cbb44b1bba08233b75983b10628c2a1075c8d7\":\"e38d62442058d495ce8ef11055cbb44b1bba08233b75983b10628c2a1075c8d7\",\"artifact:4106:ecf2eeda162ac197eb923ae127e7e2ce3f88d2ce52b375b948fa4fd00a890093\":\"ecf2eeda162ac197eb923ae127e7e2ce3f88d2ce52b375b948fa4fd00a890093\",\"artifact:4106:f021b19398255403f844c645a30800849f5aac38fde4eb220b08cf2f07b39b3c\":\"f021b19398255403f844c645a30800849f5aac38fde4eb220b08cf2f07b39b3c\",\"artifact:4106:f6bf87ef484346dfeb038f45df7e2da0e7ddcd6f0c5694fe8dd722dabd00051f\":\"f6bf87ef484346dfeb038f45df7e2da0e7ddcd6f0c5694fe8dd722dabd00051f\",\"artifact:4106:fe6b6233f460614bea860347779917da7671afd22c52570c9feea172348088f1\":\"fe6b6233f460614bea860347779917da7671afd22c52570c9feea172348088f1\"},\"sha256\":\"74ddc86141d666c3dccc1da7f1bcc2cb31e07c92688564dfb351b6ca9c563d9f\"},\"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:4106,input_sha256:\"c38d975518c69e25f3e559f1aff7f41559c0d99cdaa99f7a97494a47a63b3cf6\",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/4108/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"f8d4dbdba01450aad6519c0dce11ebdf772dedb7d2a28864a9a92f5f1e519ce5","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}