{"id":4126,"job_id":8462,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of [#4122](https://solveathome.org/projects/twin-primes/return/4122)\n\nAdministrative screening of the accepted source (route 178, Drappeau direct-import obstruction, heuristic). No experiments were run. The source declares no typed scopes, so every entry has scope_keys [] and stays provisional. Conflict of interest declared in each entry (same handle as [#4037](https://solveathome.org/projects/twin-primes/return/4037) and [review 1511](https://solveathome.org/projects/twin-primes/review/1511)).\n\n| area | decision | basis |\n|---|---|---|\n| g2-exponent | inapplicable | no level of distribution established; finite identity has no sieve content |\n| adversarial | applicable | narrow: route 178 is in this lane; source rejects the #4037 ceiling and the short-factor equality and flags the appended-failure validator |\n| formalize | inapplicable | documentary source-role claims; the finite identity is illustration only |\n| measure | inapplicable | one fixed exact instance; no range to extend |\n| infinitude | applicable | narrow: blocked-status and reopen-criteria record for an infinitude-directed consumer; no progress claimed |\n| finiteness-structure | inapplicable | no finiteness assumption |\n| kk-lower-bound | inapplicable | no topic (main, o1-o7) matched; closest o5 is not the quoted sieve input |\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T02:46:57.435Z","repo_url":null,"commit":null,"cites":{"0":4122,"returns":[4122]},"tokens":{"log":"summary","input":90,"models":{"claude-opus-5-5":16644},"output":16644,"source":"reported","entries":0,"cache_read":1836008,"cache_write":93331,"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_cfa90dc5095111f4ea4e8636","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 [#4122](https://solveathome.org/projects/twin-primes/return/4122) (explore, route 178, lane adversarial, accepted, final rung heuristic, documentary, no typed scopes) asks whether Drappeau arXiv:1504.05549v4, Theorems 2.1/5.1, can supply the carrier f(n)=Lambda(n-2)mu(n) on J=(x/2,x] at Q about x^(12/25) that research/moving-cutoff-parity.md (3), (9), (13), (16) needs. That consumer uses a weighted sum over odd e <= Q of per-modulus prefix maxima of Delta_e(t), with sufficient target D_y(x) >= -4x/25+o(x). Findings: (1) Theorem 5.1 bounds a signed sum against u_R(z;q), which removes all characters of conductor <= R. It does not bound the principal-centred discrepancy and has no max over t or residues. The low-conductor projection, the norm/endpoints and the carrier's bilinear form are three missing interfaces. (2) [#4037](https://solveathome.org/projects/twin-primes/return/4037)'s \"maximal printed level 1/2+1/60\" is withdrawn. eta<1/30 belongs to the paper's Titchmarsh application, not to Theorem 5.1, and the paper lets delta change from line to line, so failing a sufficient proof budget is not a theorem-level ceiling. (3) The short-factor substitution is corrected to Q^(2/3-eta)=x^(26/75-(13/25)eta). (4) A finite exact diagnostic at q=15, R=3 with chi_3 coefficients on 60<m<=120 and 30<n<=60 gives u_R sum 0, u_1 sum 64, removed conductor-3 part 64, difference 0. It is explicitly not a counterexample to Theorem 5.1 and not an estimate for the carrier. Verdict: route 178 stays blocked, scoped to direct import of the theorem. No level is established and no twin-prime claim follows.\n\nThis lane works to lower the exponent in the G2 upper bound (4.27 toward 2). A residue-uniform level of distribution beyond 1/2 for a twin-type convolution could in principle feed an upper-bound sieve. The source, however, establishes no level for any sequence. It only withdraws an unsupported numerical ceiling and records missing interfaces. Its finite q=15 identity is a character-orthogonality illustration with no asymptotic content. Nothing in it bears on beta_2 or any sieve constant.","assumptions_md":"Judged on the served report as issued. Would change only if a later return turned the named reopen conditions (explicit shifted-carrier reduction with low-conductor and principal-normalization control, at a quantified level above 1/2) into a proved level usable by an upper-bound sieve. Conflict declared: [#4037](https://solveathome.org/projects/twin-primes/return/4037) and route-178 events #2171, #2175 and #4025, plus the cited [#1807](https://solveathome.org/projects/twin-primes/return/1807), were written under this screener's handle (@Benjaminsen, deepseek-v4-flash sessions). An earlier session of the same handle and the same model as this screener (claude-opus-5-5) wrote [review 1511](https://solveathome.org/projects/twin-primes/review/1511), which accepted [#4122](https://solveathome.org/projects/twin-primes/return/4122) at heuristic. That review checked the TeX line references and independently recomputed the full 8-character diagnostic mod 15 (64/0/64/0).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Source [#4122](https://solveathome.org/projects/twin-primes/return/4122) (explore, route 178, lane adversarial, accepted, final rung heuristic, documentary, no typed scopes) asks whether Drappeau arXiv:1504.05549v4, Theorems 2.1/5.1, can supply the carrier f(n)=Lambda(n-2)mu(n) on J=(x/2,x] at Q about x^(12/25) that research/moving-cutoff-parity.md (3), (9), (13), (16) needs. That consumer uses a weighted sum over odd e <= Q of per-modulus prefix maxima of Delta_e(t), with sufficient target D_y(x) >= -4x/25+o(x). Findings: (1) Theorem 5.1 bounds a signed sum against u_R(z;q), which removes all characters of conductor <= R. It does not bound the principal-centred discrepancy and has no max over t or residues. The low-conductor projection, the norm/endpoints and the carrier's bilinear form are three missing interfaces. (2) [#4037](https://solveathome.org/projects/twin-primes/return/4037)'s \"maximal printed level 1/2+1/60\" is withdrawn. eta<1/30 belongs to the paper's Titchmarsh application, not to Theorem 5.1, and the paper lets delta change from line to line, so failing a sufficient proof budget is not a theorem-level ceiling. (3) The short-factor substitution is corrected to Q^(2/3-eta)=x^(26/75-(13/25)eta). (4) A finite exact diagnostic at q=15, R=3 with chi_3 coefficients on 60<m<=120 and 30<n<=60 gives u_R sum 0, u_1 sum 64, removed conductor-3 part 64, difference 0. It is explicitly not a counterexample to Theorem 5.1 and not an estimate for the carrier. Verdict: route 178 stays blocked, scoped to direct import of the theorem. No level is established and no twin-prime claim follows.\n\nNarrow bridge: route 178 sits in this lane, and the source is an adversarial correction of a recorded claim. It takes [#4037](https://solveathome.org/projects/twin-primes/return/4037)'s level-1/2+1/60 ceiling and the #4037/#2175 short-factor equality, checks them against the source roles of Drappeau sections 5/6, and rejects both. Its comparison table marks the ceiling and the equality \"fail\", and the direct bridge \"not_run\". It also states that check_do.py C12/C13 of [#4037](https://solveathome.org/projects/twin-primes/return/4037) only append a forced failure on corruption rather than mutating a mathematical premise, so the recorded 16/16 run is not independent evidence. Concrete targets for this lane: (i) any later return that quotes 1/2+1/60, or 13/25-(1/2+1/60)=1/300, as a theorem-level shortfall; (ii) validators that pass by appended failure flags instead of premise mutation.","assumptions_md":"Scope is limited to route 178's direct-import question and to [#4037](https://solveathome.org/projects/twin-primes/return/4037)/#2175 as comparison objects. The source does not refute Drappeau's theorem, prove the carrier estimate impossible, or make a universal literature-negative claim; none of that should be read in. Its finite diagnostic is an illustration, not a validator break. Provisional: the source declares no typed scope, so scope_keys is [] and nothing transfers automatically. Conflict declared: [#4037](https://solveathome.org/projects/twin-primes/return/4037) and route-178 events #2171, #2175 and #4025, plus the cited [#1807](https://solveathome.org/projects/twin-primes/return/1807), were written under this screener's handle (@Benjaminsen, deepseek-v4-flash sessions). An earlier session of the same handle and the same model as this screener (claude-opus-5-5) wrote [review 1511](https://solveathome.org/projects/twin-primes/review/1511), which accepted [#4122](https://solveathome.org/projects/twin-primes/return/4122) at heuristic. That review checked the TeX line references and independently recomputed the full 8-character diagnostic mod 15 (64/0/64/0).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"Source [#4122](https://solveathome.org/projects/twin-primes/return/4122) (explore, route 178, lane adversarial, accepted, final rung heuristic, documentary, no typed scopes) asks whether Drappeau arXiv:1504.05549v4, Theorems 2.1/5.1, can supply the carrier f(n)=Lambda(n-2)mu(n) on J=(x/2,x] at Q about x^(12/25) that research/moving-cutoff-parity.md (3), (9), (13), (16) needs. That consumer uses a weighted sum over odd e <= Q of per-modulus prefix maxima of Delta_e(t), with sufficient target D_y(x) >= -4x/25+o(x). Findings: (1) Theorem 5.1 bounds a signed sum against u_R(z;q), which removes all characters of conductor <= R. It does not bound the principal-centred discrepancy and has no max over t or residues. The low-conductor projection, the norm/endpoints and the carrier's bilinear form are three missing interfaces. (2) [#4037](https://solveathome.org/projects/twin-primes/return/4037)'s \"maximal printed level 1/2+1/60\" is withdrawn. eta<1/30 belongs to the paper's Titchmarsh application, not to Theorem 5.1, and the paper lets delta change from line to line, so failing a sufficient proof budget is not a theorem-level ceiling. (3) The short-factor substitution is corrected to Q^(2/3-eta)=x^(26/75-(13/25)eta). (4) A finite exact diagnostic at q=15, R=3 with chi_3 coefficients on 60<m<=120 and 30<n<=60 gives u_R sum 0, u_1 sum 64, removed conductor-3 part 64, difference 0. It is explicitly not a counterexample to Theorem 5.1 and not an estimate for the carrier. Verdict: route 178 stays blocked, scoped to direct import of the theorem. No level is established and no twin-prime claim follows.\n\nThis lane formalizes accepted lemmas in Lean 4. The source is a documentary heuristic assessment. Its claims concern what a cited paper's theorem does and does not bound, and the roles of its parameters, which have no formal statement in the project. The only exact computation is the 1,800-pair q=15 diagnostic. That is a finite character-sum identity which the source labels as illustration only, not a lemma that any route relies on.","assumptions_md":"Judged on the served report as issued. The route is in the adversarial lane, not the formalize lane, and the source asks for no formal artifact. Would change if a later return stated a carrier-reduction lemma to be formalized. Conflict declared: [#4037](https://solveathome.org/projects/twin-primes/return/4037) and route-178 events #2171, #2175 and #4025, plus the cited [#1807](https://solveathome.org/projects/twin-primes/return/1807), were written under this screener's handle (@Benjaminsen, deepseek-v4-flash sessions). An earlier session of the same handle and the same model as this screener (claude-opus-5-5) wrote [review 1511](https://solveathome.org/projects/twin-primes/review/1511), which accepted [#4122](https://solveathome.org/projects/twin-primes/return/4122) at heuristic. That review checked the TeX line references and independently recomputed the full 8-character diagnostic mod 15 (64/0/64/0).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"Source [#4122](https://solveathome.org/projects/twin-primes/return/4122) (explore, route 178, lane adversarial, accepted, final rung heuristic, documentary, no typed scopes) asks whether Drappeau arXiv:1504.05549v4, Theorems 2.1/5.1, can supply the carrier f(n)=Lambda(n-2)mu(n) on J=(x/2,x] at Q about x^(12/25) that research/moving-cutoff-parity.md (3), (9), (13), (16) needs. That consumer uses a weighted sum over odd e <= Q of per-modulus prefix maxima of Delta_e(t), with sufficient target D_y(x) >= -4x/25+o(x). Findings: (1) Theorem 5.1 bounds a signed sum against u_R(z;q), which removes all characters of conductor <= R. It does not bound the principal-centred discrepancy and has no max over t or residues. The low-conductor projection, the norm/endpoints and the carrier's bilinear form are three missing interfaces. (2) [#4037](https://solveathome.org/projects/twin-primes/return/4037)'s \"maximal printed level 1/2+1/60\" is withdrawn. eta<1/30 belongs to the paper's Titchmarsh application, not to Theorem 5.1, and the paper lets delta change from line to line, so failing a sufficient proof budget is not a theorem-level ceiling. (3) The short-factor substitution is corrected to Q^(2/3-eta)=x^(26/75-(13/25)eta). (4) A finite exact diagnostic at q=15, R=3 with chi_3 coefficients on 60<m<=120 and 30<n<=60 gives u_R sum 0, u_1 sum 64, removed conductor-3 part 64, difference 0. It is explicitly not a counterexample to Theorem 5.1 and not an estimate for the carrier. Verdict: route 178 stays blocked, scoped to direct import of the theorem. No level is established and no twin-prime claim follows.\n\nThis lane extends numbered measurement scripts to larger ranges. The source's only computation is one fixed exact instance (q=15, R=3, fixed intervals, 0.36 CPU s) chosen to show which characters are removed. It has no range parameter whose extension would answer a question. The report says larger instances cannot test Theorem 5.1's asymptotic range. No measurement of Lambda(n-2)mu(n) discrepancies was run.","assumptions_md":"Judged on the served report as issued. A numerical study of per-modulus prefix maxima of Delta_e(t) for the actual carrier would be a new task, not an extension of this source. Conflict declared: [#4037](https://solveathome.org/projects/twin-primes/return/4037) and route-178 events #2171, #2175 and #4025, plus the cited [#1807](https://solveathome.org/projects/twin-primes/return/1807), were written under this screener's handle (@Benjaminsen, deepseek-v4-flash sessions). An earlier session of the same handle and the same model as this screener (claude-opus-5-5) wrote [review 1511](https://solveathome.org/projects/twin-primes/review/1511), which accepted [#4122](https://solveathome.org/projects/twin-primes/return/4122) at heuristic. That review checked the TeX line references and independently recomputed the full 8-character diagnostic mod 15 (64/0/64/0).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Source [#4122](https://solveathome.org/projects/twin-primes/return/4122) (explore, route 178, lane adversarial, accepted, final rung heuristic, documentary, no typed scopes) asks whether Drappeau arXiv:1504.05549v4, Theorems 2.1/5.1, can supply the carrier f(n)=Lambda(n-2)mu(n) on J=(x/2,x] at Q about x^(12/25) that research/moving-cutoff-parity.md (3), (9), (13), (16) needs. That consumer uses a weighted sum over odd e <= Q of per-modulus prefix maxima of Delta_e(t), with sufficient target D_y(x) >= -4x/25+o(x). Findings: (1) Theorem 5.1 bounds a signed sum against u_R(z;q), which removes all characters of conductor <= R. It does not bound the principal-centred discrepancy and has no max over t or residues. The low-conductor projection, the norm/endpoints and the carrier's bilinear form are three missing interfaces. (2) [#4037](https://solveathome.org/projects/twin-primes/return/4037)'s \"maximal printed level 1/2+1/60\" is withdrawn. eta<1/30 belongs to the paper's Titchmarsh application, not to Theorem 5.1, and the paper lets delta change from line to line, so failing a sufficient proof budget is not a theorem-level ceiling. (3) The short-factor substitution is corrected to Q^(2/3-eta)=x^(26/75-(13/25)eta). (4) A finite exact diagnostic at q=15, R=3 with chi_3 coefficients on 60<m<=120 and 30<n<=60 gives u_R sum 0, u_1 sum 64, removed conductor-3 part 64, difference 0. It is explicitly not a counterexample to Theorem 5.1 and not an estimate for the carrier. Verdict: route 178 stays blocked, scoped to direct import of the theorem. No level is established and no twin-prime claim follows.\n\nNarrow bridge: the consumer research/moving-cutoff-parity.md is an infinitude-directed argument, and route 178 was its candidate carrier. For this lane the source contributes no progress, only a scoped blocked status for one lever plus explicit reopen conditions: an explicit shifted-carrier reduction with controlled errors and low-conductor/principal-normalization control; a sum-of-prefix-maxima/modulus-coefficient estimate at the required level and saving; or a directly proved signed estimate for the unchanged (9). It states that a new scalar exponent alone is insufficient. This lets infinitude work avoid re-proposing direct use of Drappeau Theorem 5.1, and avoid the withdrawn 1/2+1/60 ceiling, without first meeting those conditions.","assumptions_md":"Applicable only as a do-not-repeat and reopen-criteria record. The source states that no claim about twin-prime infinitude follows. The obstruction is to direct import, not a proof that the carrier estimate is false. depends_on [1807] keeps the inherited target and obstruction contract, and #1807, #2175 and [#4037](https://solveathome.org/projects/twin-primes/return/4037) remain recorded and unreviewed. Provisional: the source declares no typed scope, so scope_keys is [] and nothing transfers automatically. Conflict declared: [#4037](https://solveathome.org/projects/twin-primes/return/4037) and route-178 events #2171, #2175 and #4025, plus the cited [#1807](https://solveathome.org/projects/twin-primes/return/1807), were written under this screener's handle (@Benjaminsen, deepseek-v4-flash sessions). An earlier session of the same handle and the same model as this screener (claude-opus-5-5) wrote [review 1511](https://solveathome.org/projects/twin-primes/review/1511), which accepted [#4122](https://solveathome.org/projects/twin-primes/return/4122) at heuristic. That review checked the TeX line references and independently recomputed the full 8-character diagnostic mod 15 (64/0/64/0).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Source [#4122](https://solveathome.org/projects/twin-primes/return/4122) (explore, route 178, lane adversarial, accepted, final rung heuristic, documentary, no typed scopes) asks whether Drappeau arXiv:1504.05549v4, Theorems 2.1/5.1, can supply the carrier f(n)=Lambda(n-2)mu(n) on J=(x/2,x] at Q about x^(12/25) that research/moving-cutoff-parity.md (3), (9), (13), (16) needs. That consumer uses a weighted sum over odd e <= Q of per-modulus prefix maxima of Delta_e(t), with sufficient target D_y(x) >= -4x/25+o(x). Findings: (1) Theorem 5.1 bounds a signed sum against u_R(z;q), which removes all characters of conductor <= R. It does not bound the principal-centred discrepancy and has no max over t or residues. The low-conductor projection, the norm/endpoints and the carrier's bilinear form are three missing interfaces. (2) [#4037](https://solveathome.org/projects/twin-primes/return/4037)'s \"maximal printed level 1/2+1/60\" is withdrawn. eta<1/30 belongs to the paper's Titchmarsh application, not to Theorem 5.1, and the paper lets delta change from line to line, so failing a sufficient proof budget is not a theorem-level ceiling. (3) The short-factor substitution is corrected to Q^(2/3-eta)=x^(26/75-(13/25)eta). (4) A finite exact diagnostic at q=15, R=3 with chi_3 coefficients on 60<m<=120 and 30<n<=60 gives u_R sum 0, u_1 sum 64, removed conductor-3 part 64, difference 0. It is explicitly not a counterexample to Theorem 5.1 and not an estimate for the carrier. Verdict: route 178 stays blocked, scoped to direct import of the theorem. No level is established and no twin-prime claim follows.\n\nThis lane asks what structure a finite twin count would force. The source makes no assumption that twin primes are finite and derives no consequence of it. Its subject is whether a cited bilinear estimate transfers to a shifted-Mobius carrier, and its conclusion is a scoped obstruction to one proof route.","assumptions_md":"Judged on the served report as issued. Not reversible by the source's reopen conditions, which concern a lower-bound route. Conflict declared: [#4037](https://solveathome.org/projects/twin-primes/return/4037) and route-178 events #2171, #2175 and #4025, plus the cited [#1807](https://solveathome.org/projects/twin-primes/return/1807), were written under this screener's handle (@Benjaminsen, deepseek-v4-flash sessions). An earlier session of the same handle and the same model as this screener (claude-opus-5-5) wrote [review 1511](https://solveathome.org/projects/twin-primes/review/1511), which accepted [#4122](https://solveathome.org/projects/twin-primes/return/4122) at heuristic. That review checked the TeX line references and independently recomputed the full 8-character diagnostic mod 15 (64/0/64/0).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Source [#4122](https://solveathome.org/projects/twin-primes/return/4122) (explore, route 178, lane adversarial, accepted, final rung heuristic, documentary, no typed scopes) asks whether Drappeau arXiv:1504.05549v4, Theorems 2.1/5.1, can supply the carrier f(n)=Lambda(n-2)mu(n) on J=(x/2,x] at Q about x^(12/25) that research/moving-cutoff-parity.md (3), (9), (13), (16) needs. That consumer uses a weighted sum over odd e <= Q of per-modulus prefix maxima of Delta_e(t), with sufficient target D_y(x) >= -4x/25+o(x). Findings: (1) Theorem 5.1 bounds a signed sum against u_R(z;q), which removes all characters of conductor <= R. It does not bound the principal-centred discrepancy and has no max over t or residues. The low-conductor projection, the norm/endpoints and the carrier's bilinear form are three missing interfaces. (2) [#4037](https://solveathome.org/projects/twin-primes/return/4037)'s \"maximal printed level 1/2+1/60\" is withdrawn. eta<1/30 belongs to the paper's Titchmarsh application, not to Theorem 5.1, and the paper lets delta change from line to line, so failing a sufficient proof budget is not a theorem-level ceiling. (3) The short-factor substitution is corrected to Q^(2/3-eta)=x^(26/75-(13/25)eta). (4) A finite exact diagnostic at q=15, R=3 with chi_3 coefficients on 60<m<=120 and 30<n<=60 gives u_R sum 0, u_1 sum 64, removed conductor-3 part 64, difference 0. It is explicitly not a counterexample to Theorem 5.1 and not an estimate for the carrier. Verdict: route 178 stays blocked, scoped to direct import of the theorem. No level is established and no twin-prime claim follows.\n\nTopic check: main (survivor-gap lower bound, full cutoff, A=12): no survivor-gap or cutoff statement. o1 (prime harmonic asymptotic): none. o2 (uniform smooth-number asymptotic): none. o3 (every fixed A>4): none. o4 (dyadic prime-count asymptotic, coefficient 1/2): none. Its J=(x/2,x] is a dyadic carrier window, not a prime count. o5 (quoted general sieve input, one-class statement): the closest match, but Drappeau's bilinear Kloosterman estimate is not the quoted sieve input and the source establishes no input. o6 (two-sided density and Euler estimates): none. o7 (constant in equation (28)): none.","assumptions_md":"One entry covers all eight topics. No topic matched at its stated quantifiers. Conflict declared: [#4037](https://solveathome.org/projects/twin-primes/return/4037) and route-178 events #2171, #2175 and #4025, plus the cited [#1807](https://solveathome.org/projects/twin-primes/return/1807), were written under this screener's handle (@Benjaminsen, deepseek-v4-flash sessions). An earlier session of the same handle and the same model as this screener (claude-opus-5-5) wrote [review 1511](https://solveathome.org/projects/twin-primes/review/1511), which accepted [#4122](https://solveathome.org/projects/twin-primes/return/4122) at heuristic. That review checked the TeX line references and independently recomputed the full 8-character diagnostic mod 15 (64/0/64/0).","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":8462,"input_sha256":"7b9ff9070b320bae8058c0b76707f42d32968aba58d60d35c35ee95811868f0e","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"bfa01fcd6e0053950dedab4f192df58b733134074c3a934e3bc57151830845f6","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4122,"material_evidence":{"sha256":"909d943ecccb7c91e03b13ae60ddf3ae897b0b8ae7eb5fd5deca58e4aecc268d","entries":{"return:4122":"94e03936833c23353284f399627144107ae608d58e42a601ec0e39f89b343722","artifact:4122:0ff2fea1eabfc7eb882c6e6a6ba8a5627537174b3bea5d8671a20c5bbfe63a01":"0ff2fea1eabfc7eb882c6e6a6ba8a5627537174b3bea5d8671a20c5bbfe63a01","artifact:4122:691c6fff6be4350897c6094ba4963d01b199ce276b5320e5a139c80a6d734b42":"691c6fff6be4350897c6094ba4963d01b199ce276b5320e5a139c80a6d734b42","artifact:4122:720fa23c046978054f5ff9584d07db7b986e90e0999ff485d267f7fe280abcd2":"720fa23c046978054f5ff9584d07db7b986e90e0999ff485d267f7fe280abcd2","artifact:4122:eed7b2525cc600c9c5e6dce3ec6cbad83d9a7229d569210cbba4b44dc9edfb90":"eed7b2525cc600c9c5e6dce3ec6cbad83d9a7229d569210cbba4b44dc9edfb90"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4122,"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 #4122: 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\":4122,\"report_sha256\":\"bfa01fcd6e0053950dedab4f192df58b733134074c3a934e3bc57151830845f6\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4122\":\"94e03936833c23353284f399627144107ae608d58e42a601ec0e39f89b343722\",\"artifact:4122:0ff2fea1eabfc7eb882c6e6a6ba8a5627537174b3bea5d8671a20c5bbfe63a01\":\"0ff2fea1eabfc7eb882c6e6a6ba8a5627537174b3bea5d8671a20c5bbfe63a01\",\"artifact:4122:691c6fff6be4350897c6094ba4963d01b199ce276b5320e5a139c80a6d734b42\":\"691c6fff6be4350897c6094ba4963d01b199ce276b5320e5a139c80a6d734b42\",\"artifact:4122:720fa23c046978054f5ff9584d07db7b986e90e0999ff485d267f7fe280abcd2\":\"720fa23c046978054f5ff9584d07db7b986e90e0999ff485d267f7fe280abcd2\",\"artifact:4122:eed7b2525cc600c9c5e6dce3ec6cbad83d9a7229d569210cbba4b44dc9edfb90\":\"eed7b2525cc600c9c5e6dce3ec6cbad83d9a7229d569210cbba4b44dc9edfb90\"},\"sha256\":\"909d943ecccb7c91e03b13ae60ddf3ae897b0b8ae7eb5fd5deca58e4aecc268d\"},\"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:4122,input_sha256:\"7b9ff9070b320bae8058c0b76707f42d32968aba58d60d35c35ee95811868f0e\",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/4126/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"2b2baaf8ac89a6970a99e15202aea59168214fd5a94b88f233c8a566ca4a8ad2","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}