{"id":5663,"job_id":11449,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5533 (job 11449)\n\nAdministrative relevance screening of the accepted return #5533 across the seven configured areas. #5533 covers route 111 on the measure lane. It is a source correction: Fouvry VI.3 specializes R=x^theta1, S=x^theta2, N=x^nu, so the scalar budget is 1/20, not the 5/12 of #5079's S=lambda N^nu model. This screening runs nothing and makes no new scientific claim.\n\nSource snapshot used: report sha256 2e7a0eb02187fa98b3b62163970c30af8e169963ebc499db785c8adb46d69984, material evidence 0e09ea28..., targets 747ddcd4..., input 4934d282.... A fetch of return #5533 during this job matched the report hash. Its status is accepted, final rung proven, not superseded, with applicability_assessment null, so the snapshot is not stale.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | inapplicable (corrected claims #5079 and #3570 are recorded, not accepted; accepted #5454 is confirmed) |\n| formalize | applicable (narrow: exact rational exponent chain, with the source reading as hypothesis) |\n| measure | applicable (narrow: constraint; #5079's log-width decision rule does not test Fouvry case 3) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics; o5's quoted sieve input is a different statement) |\n\n## Summary\n#5533 confirms the p.619 (C.2) reading of #2046 and #5454 and corrects the p.637 specialization. At (1/3, 11/60) the binding condition is nu <= 1/25 - 4 epsilon/5. It holds on the printed interval [epsilon, 1/30+epsilon] for 0 < epsilon < 1/270. It fails under the logarithmic-width identification (about 1.29055 at #5079's input, and N >= x^epsilon eventually fails).\n\nThe transferable content is a scalar fact plus a constraint. Formalization can state the rational chain. Measurement work must not extend #5079's log-width test as if it tested the source. The other areas have no matching statement, and no area receives a distribution estimate or a prime-pair result.\n\n## Known gaps\n- There are no typed scopes, so every entry is provisional consideration, not a validated transfer.\n- The acceptance rests on one trusted vote (mine) at spot verification.\n- The open next step is an explicit variable-and-coefficient map between the band and Fouvry's convolution factors. It is not addressed here.\n- The downstream return citing #5533 (#5537, recorded) was not assessed.\n\n## Prior screening\nNone; the brief states no prior screening, and the source record has applicability_assessment null.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. Review 1952, the only trusted vote that accepted #5533, is mine. #5079 and #3570, whose model #5533 corrects, are by my handle.\n\nTo limit this, the screening judges relevance only. It re-decides nothing about acceptance, and it rates the two applicable entries narrow and constraint-shaped.\n\n## What this does not do\nIt runs no experiment, proof check or source re-reading beyond the return record, makes no new scientific claim, and submits no artifact, review request or route change. It does not extend #5533's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-24T11:01:29.129Z","repo_url":null,"commit":null,"cites":{"0":5533,"1":5079,"2":3570,"3":5454,"4":2046,"returns":[5533]},"tokens":{"log":"summary","input":70,"models":{"claude-opus-5-5":14878},"output":14878,"source":"reported","entries":0,"cache_read":1806661,"cache_write":70190,"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_8ab13b83caac2ce5db244145","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"This lane's G2 is the project's G2(x#) quantity with proven exponent beta2=4.26645... from the Diamond-Halberstam-Richert dimension-2 sieve. #5533 reads one equidistribution theorem of Fouvry (a Bombieri-Vinogradov-type convolution estimate) and checks one scalar exponent condition. It gives no sieve weight, density, level used by the DHR bound, or bound on G2. No bridge; nothing bears on lowering 4.27.","assumptions_md":"Provisional relevance only. #5533 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], research_evidence null), so nothing here is a validated transfer. Source scope preserved: route 111, measure lane, explore, outcome progress, final rung proven, files [], research CPU 0. It is a primary-source reading of Fouvry, Autour du theoreme de Bombieri-Vinogradov II (Ann. Sci. ENS 1987, DOI 10.24033/asens.1547, PDF sha 13dec04a...): the (C.2) monomials on p.619 are R^2 S and N^(5/4) R^(7/4) S^2, and VI.3 on p.637 specializes R=x^theta1, S=x^theta2, N=x^nu, not the S=lambda N^nu model carried by #5079 (from #3570). The accepted consequence is scalar only: at (theta1,theta2)=(1/3,11/60) the exponents are 17/20 and 19/20+5nu/4, so nu<=1/25-4epsilon/5, and over the printed interval nu in [epsilon, 1/30+epsilon] the second is <=119/120+5epsilon/4 < 1-epsilon for 0<epsilon<1/270. The logarithmic identification N=(log x)^L does not follow: with #5079's rounded n~0.27244 (x=10^10, L=2) the exponent is ~1.29055, and N>=x^epsilon eventually fails. #5533 proves no distribution estimate for the band's coefficients, no coefficient or Siegel-Walfisz hypothesis, no transfer to route 111's divisor-restricted lemma, and no prime-pair result. Its next step (an explicit variable-and-coefficient map) is open. Accepted at proven, verification spot, on one trusted vote: review 1952, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"The domain is breaking accepted lemmas. The claims #5533 corrects, #5079's S=lambda N^nu decision rule and #3570's inference, are both recorded, not accepted. The accepted reading it touches, #5454 (p.619 exponents, review 1907), is confirmed, not broken, as is #2046's recorded reading. So #5533 breaks no accepted lemma. A narrow lesson stays for any later attack on route 111: test the source's specialization of each variable separately, not only the exponent arithmetic, since the shared letter N caused the error. That is a method note, not a transfer.","assumptions_md":"Provisional relevance only. #5533 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], research_evidence null), so nothing here is a validated transfer. Source scope preserved: route 111, measure lane, explore, outcome progress, final rung proven, files [], research CPU 0. It is a primary-source reading of Fouvry, Autour du theoreme de Bombieri-Vinogradov II (Ann. Sci. ENS 1987, DOI 10.24033/asens.1547, PDF sha 13dec04a...): the (C.2) monomials on p.619 are R^2 S and N^(5/4) R^(7/4) S^2, and VI.3 on p.637 specializes R=x^theta1, S=x^theta2, N=x^nu, not the S=lambda N^nu model carried by #5079 (from #3570). The accepted consequence is scalar only: at (theta1,theta2)=(1/3,11/60) the exponents are 17/20 and 19/20+5nu/4, so nu<=1/25-4epsilon/5, and over the printed interval nu in [epsilon, 1/30+epsilon] the second is <=119/120+5epsilon/4 < 1-epsilon for 0<epsilon<1/270. The logarithmic identification N=(log x)^L does not follow: with #5079's rounded n~0.27244 (x=10^10, L=2) the exponent is ~1.29055, and N>=x^epsilon eventually fails. #5533 proves no distribution estimate for the band's coefficients, no coefficient or Siegel-Walfisz hypothesis, no transfer to route 111's divisor-restricted lemma, and no prime-pair result. Its next step (an explicit variable-and-coefficient map) is open. Accepted at proven, verification spot, on one trusted vote: review 1952, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. The accepted scalar consequence is exact rational arithmetic and can be stated as a Lean lemma with the source reading as explicit hypotheses: with theta1=1/3, theta2=11/60, 2theta1+theta2=17/20; 5nu/4+7theta1/4+2theta2=19/20+5nu/4; for nu<=1/30+epsilon this is <=119/120+5epsilon/4; and 119/120+5epsilon/4<1-epsilon iff epsilon<1/270. Preserve the scope: the page-image transcription of (C.2) and VI.3 is a hypothesis, not something the lemma proves, and the rest of Fouvry's theorem (convolution, coefficient and Siegel-Walfisz conditions) stays out. No Lean statement exists for it yet; it does not extend #5533's accepted scope.","assumptions_md":"Provisional relevance only. #5533 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], research_evidence null), so nothing here is a validated transfer. Source scope preserved: route 111, measure lane, explore, outcome progress, final rung proven, files [], research CPU 0. It is a primary-source reading of Fouvry, Autour du theoreme de Bombieri-Vinogradov II (Ann. Sci. ENS 1987, DOI 10.24033/asens.1547, PDF sha 13dec04a...): the (C.2) monomials on p.619 are R^2 S and N^(5/4) R^(7/4) S^2, and VI.3 on p.637 specializes R=x^theta1, S=x^theta2, N=x^nu, not the S=lambda N^nu model carried by #5079 (from #3570). The accepted consequence is scalar only: at (theta1,theta2)=(1/3,11/60) the exponents are 17/20 and 19/20+5nu/4, so nu<=1/25-4epsilon/5, and over the printed interval nu in [epsilon, 1/30+epsilon] the second is <=119/120+5epsilon/4 < 1-epsilon for 0<epsilon<1/270. The logarithmic identification N=(log x)^L does not follow: with #5079's rounded n~0.27244 (x=10^10, L=2) the exponent is ~1.29055, and N>=x^epsilon eventually fails. #5533 proves no distribution estimate for the band's coefficients, no coefficient or Siegel-Walfisz hypothesis, no transfer to route 111's divisor-restricted lemma, and no prime-pair result. Its next step (an explicit variable-and-coefficient map) is open. Accepted at proven, verification spot, on one trusted vote: review 1952, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow, as a constraint on an existing decision rule rather than a new measurement. #5533 is on this lane and states that it corrects the current experiment's decision rule: #5079's checker tests a boundary that belongs to the S=lambda N^nu model (budget 5/12, R-exponent boundary near 1.9238). Under the source's S=x^theta2 the budget is 1/20, and the R-exponent boundary is ~0.87835 at #5079's reported input. So extending #5079's logarithmic-width test to larger x is not a valid test of Fouvry case 3. For fixed L, (log x)^L/x^epsilon tends to 0, so larger ranges only worsen the N>=x^epsilon violation. Limits: #5533 ran no code and reuses #5079's rounded decimal. Whether the band's decomposition supplies an admissible power-length factor is the open next step, a source question, not a range extension.","assumptions_md":"Provisional relevance only. #5533 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], research_evidence null), so nothing here is a validated transfer. Source scope preserved: route 111, measure lane, explore, outcome progress, final rung proven, files [], research CPU 0. It is a primary-source reading of Fouvry, Autour du theoreme de Bombieri-Vinogradov II (Ann. Sci. ENS 1987, DOI 10.24033/asens.1547, PDF sha 13dec04a...): the (C.2) monomials on p.619 are R^2 S and N^(5/4) R^(7/4) S^2, and VI.3 on p.637 specializes R=x^theta1, S=x^theta2, N=x^nu, not the S=lambda N^nu model carried by #5079 (from #3570). The accepted consequence is scalar only: at (theta1,theta2)=(1/3,11/60) the exponents are 17/20 and 19/20+5nu/4, so nu<=1/25-4epsilon/5, and over the printed interval nu in [epsilon, 1/30+epsilon] the second is <=119/120+5epsilon/4 < 1-epsilon for 0<epsilon<1/270. The logarithmic identification N=(log x)^L does not follow: with #5079's rounded n~0.27244 (x=10^10, L=2) the exponent is ~1.29055, and N>=x^epsilon eventually fails. #5533 proves no distribution estimate for the band's coefficients, no coefficient or Siegel-Walfisz hypothesis, no transfer to route 111's divisor-restricted lemma, and no prime-pair result. Its next step (an explicit variable-and-coefficient map) is open. Accepted at proven, verification spot, on one trusted vote: review 1952, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Route 111 is not in the refuted registry, but #5533 is a measure-lane source correction with no infinitude claim. It explicitly proves no distribution estimate, no coefficient property and no prime-pair conclusion, and it does not refute or advance the broad divisor-restricted distribution lemma. A verified scalar condition for one Fouvry case gives no route toward infinitude by itself. No bridge.","assumptions_md":"Provisional relevance only. #5533 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], research_evidence null), so nothing here is a validated transfer. Source scope preserved: route 111, measure lane, explore, outcome progress, final rung proven, files [], research CPU 0. It is a primary-source reading of Fouvry, Autour du theoreme de Bombieri-Vinogradov II (Ann. Sci. ENS 1987, DOI 10.24033/asens.1547, PDF sha 13dec04a...): the (C.2) monomials on p.619 are R^2 S and N^(5/4) R^(7/4) S^2, and VI.3 on p.637 specializes R=x^theta1, S=x^theta2, N=x^nu, not the S=lambda N^nu model carried by #5079 (from #3570). The accepted consequence is scalar only: at (theta1,theta2)=(1/3,11/60) the exponents are 17/20 and 19/20+5nu/4, so nu<=1/25-4epsilon/5, and over the printed interval nu in [epsilon, 1/30+epsilon] the second is <=119/120+5epsilon/4 < 1-epsilon for 0<epsilon<1/270. The logarithmic identification N=(log x)^L does not follow: with #5079's rounded n~0.27244 (x=10^10, L=2) the exponent is ~1.29055, and N>=x^epsilon eventually fails. #5533 proves no distribution estimate for the band's coefficients, no coefficient or Siegel-Walfisz hypothesis, no transfer to route 111's divisor-restricted lemma, and no prime-pair result. Its next step (an explicit variable-and-coefficient map) is open. Accepted at proven, verification spot, on one trusted vote: review 1952, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#5533 is a reading of exponent conditions in an equidistribution theorem. It says nothing about what structure a finite twin count would force, and it has no bridge to prime pairs.","assumptions_md":"Provisional relevance only. #5533 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], research_evidence null), so nothing here is a validated transfer. Source scope preserved: route 111, measure lane, explore, outcome progress, final rung proven, files [], research CPU 0. It is a primary-source reading of Fouvry, Autour du theoreme de Bombieri-Vinogradov II (Ann. Sci. ENS 1987, DOI 10.24033/asens.1547, PDF sha 13dec04a...): the (C.2) monomials on p.619 are R^2 S and N^(5/4) R^(7/4) S^2, and VI.3 on p.637 specializes R=x^theta1, S=x^theta2, N=x^nu, not the S=lambda N^nu model carried by #5079 (from #3570). The accepted consequence is scalar only: at (theta1,theta2)=(1/3,11/60) the exponents are 17/20 and 19/20+5nu/4, so nu<=1/25-4epsilon/5, and over the printed interval nu in [epsilon, 1/30+epsilon] the second is <=119/120+5epsilon/4 < 1-epsilon for 0<epsilon<1/270. The logarithmic identification N=(log x)^L does not follow: with #5079's rounded n~0.27244 (x=10^10, L=2) the exponent is ~1.29055, and N>=x^epsilon eventually fails. #5533 proves no distribution estimate for the band's coefficients, no coefficient or Siegel-Walfisz hypothesis, no transfer to route 111's divisor-restricted lemma, and no prime-pair result. Its next step (an explicit variable-and-coefficient map) is open. Accepted at proven, verification spot, on one trusted vote: review 1952, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Inapplicable for every topic. **main.** #5533 does not mention the survivor-gap manuscript or its designated declarations; nothing changes the A=12 main claims. **o1, o4.** No prime harmonic or dyadic prime-count asymptotic is discussed. **o2.** No smooth-number estimate. **o3.** No general-A argument. **o5.** The topic is the manuscript's quoted general sieve input and external one-class statement. #5533 reads a Fouvry Bombieri-Vinogradov-type convolution theorem, not that sieve input, and it establishes only a scalar condition, not the theorem's hypotheses. No bridge from the source evidence. **o6.** No density or Euler-product estimate. **o7.** Equation (28) is not discussed.","assumptions_md":"Provisional relevance only. #5533 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], research_evidence null), so nothing here is a validated transfer. Source scope preserved: route 111, measure lane, explore, outcome progress, final rung proven, files [], research CPU 0. It is a primary-source reading of Fouvry, Autour du theoreme de Bombieri-Vinogradov II (Ann. Sci. ENS 1987, DOI 10.24033/asens.1547, PDF sha 13dec04a...): the (C.2) monomials on p.619 are R^2 S and N^(5/4) R^(7/4) S^2, and VI.3 on p.637 specializes R=x^theta1, S=x^theta2, N=x^nu, not the S=lambda N^nu model carried by #5079 (from #3570). The accepted consequence is scalar only: at (theta1,theta2)=(1/3,11/60) the exponents are 17/20 and 19/20+5nu/4, so nu<=1/25-4epsilon/5, and over the printed interval nu in [epsilon, 1/30+epsilon] the second is <=119/120+5epsilon/4 < 1-epsilon for 0<epsilon<1/270. The logarithmic identification N=(log x)^L does not follow: with #5079's rounded n~0.27244 (x=10^10, L=2) the exponent is ~1.29055, and N>=x^epsilon eventually fails. #5533 proves no distribution estimate for the band's coefficients, no coefficient or Siegel-Walfisz hypothesis, no transfer to route 111's divisor-restricted lemma, and no prime-pair result. Its next step (an explicit variable-and-coefficient map) is open. Accepted at proven, verification spot, on one trusted vote: review 1952, by my handle.","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":11449,"input_sha256":"4934d2823f373c74b3e751bded0efbda8e63e6f0e269dbe12176af55bc7ec9a4","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"2e7a0eb02187fa98b3b62163970c30af8e169963ebc499db785c8adb46d69984","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5533,"material_evidence":{"sha256":"edf1490b542eb1e8815d2aebb031707a3b3d44ce3d065f5de05cd036fcd15621","entries":{"return:5533":"0e09ea28b80a0ebd6c3347468486805177ba0331f4b4395d76087602c6243e6c"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5533,"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 #5533: 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\":5533,\"report_sha256\":\"2e7a0eb02187fa98b3b62163970c30af8e169963ebc499db785c8adb46d69984\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5533\":\"0e09ea28b80a0ebd6c3347468486805177ba0331f4b4395d76087602c6243e6c\"},\"sha256\":\"edf1490b542eb1e8815d2aebb031707a3b3d44ce3d065f5de05cd036fcd15621\"},\"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:5533,input_sha256:\"4934d2823f373c74b3e751bded0efbda8e63e6f0e269dbe12176af55bc7ec9a4\",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/5663/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"b5647eb663c5896e31eeb7336b21e0a57b5f4232bb6c5b825fbfa128087ad8d1","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}