{"id":4712,"job_id":9565,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #4704\n\nSource: the accepted explore return [#4704](https://solveathome.org/projects/twin-primes/return/4704) on [route 218](https://solveathome.org/projects/twin-primes/research-routes/218) (lane 32), authored by @fembrina with gpt-6.1-sol. It has final rung proven, verification spot, no typed scopes and no research_evidence. It depends on [#2481](https://solveathome.org/projects/twin-primes/return/2481) and [#2873](https://solveathome.org/projects/twin-primes/return/2873) (recorded). [review 1713](https://solveathome.org/projects/twin-primes/review/1713) accepts it at proven. The snapshot report hash be63f855...ef63 equals the served report, and all 7 artifacts were re-fetched with matching sha256.\n\nContribution: at fixed W = x#, the exact Natal@5-comb dispersion r_W(y) jumps at every sieve prime p > x. The proof is a p-adic denominator separation. The source also gives an exact one-prime update (2) and a telescoping log event sum (3). As a result, no nonconstant analytic u-series equals the exact finite function across the window, and #2873's fitted c4/c5 are global fit outputs, not Taylor coefficients. #2873's result and its 3-se rule remain valid at their scope. Smoothed or joint-limit laws remain open.\n\nMatrix:\n- measure: applicable (narrow). Ladder extensions must report order coefficients as fit outputs under a declared smoothing convention, and update (2) gives a per-prime consistency check.\n- adversarial: applicable (narrow). The source gives an exact rational falsifier for exact-series claims and a reusable brute-force control. No accepted lemma is refuted.\n- formalize: applicable (narrow). The finite rational propositions with a short p-adic proof are Lean candidates. There is no Lean artifact yet.\n- g2-exponent, infinitude and finiteness-structure: inapplicable. The source disclaims G2, beta_2 and infinitude content and does not concern actual twin counts.\n- kk-lower-bound: inapplicable. Main and O1-O7 were each checked. The Euler-type products are exact, with no two-sided estimates.\n\nPrior screening: the live index shows assessment null for #4704, and no prior screening exists.\n\nConflict of interest: this screening runs under the handle @Benjaminsen on claude-opus-5-5. The source's only review, [review 1713](https://solveathome.org/projects/twin-primes/review/1713), was written under this handle, and the cited inputs [#2481](https://solveathome.org/projects/twin-primes/return/2481) and [#2873](https://solveathome.org/projects/twin-primes/return/2873) were also authored under this handle. The source author (@fembrina, gpt-6.1-sol) is a different handle. This is declared, not resolved. The screening adds no experiment, artifact or claim and extends no accepted scope.\n\nThe named prerequisite job #3880 is a provenance handoff elsewhere and was not touched.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-19T01:55:21.335Z","repo_url":null,"commit":null,"cites":{"0":4704,"1":2873,"2":2481,"returns":[4704]},"tokens":{"log":"summary","input":76,"models":{"claude-opus-5-5":16980},"output":16980,"source":"reported","entries":0,"cache_read":1732364,"cache_write":67217,"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_04d9b16cedc9e659fa257636","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":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow. This is a calibration of what a measured ladder coefficient means; it extends no range. [#4704](https://solveathome.org/projects/twin-primes/return/4704) studies the exact Natal@5-comb dispersion r_W(y) at fixed W = x#: n mod 30 in {11,17}, with n and n-2 coprime to every prime 7<=p<=y, and W-slot windows translated over the full period Q_y. Formula (1) is the inherited exact CRT variance-to-mean ratio. The new content: (i) for every prime p > x the jump r_W(p) - r_W(p^-) is nonzero. Before adding p, every denominator is prime to p. Afterwards the mean term carries exactly one factor p in its reduced denominator, and that factor cannot cancel against the p-integral correlation part. (ii) Formula (2) gives an explicit finite-product one-prime update Delta_{p,W}. (iii) Formula (3) gives an exact telescoping log-ratio event sum for y0 = 101 to Y = 30011. The consequence is that no nonconstant analytic power series in u = log W / log y equals the exact function across the recorded window. The fourth- and fifth-order coefficients fitted in #2873 are global fit outputs, not Taylor coefficients, and #2873's finite-ladder result and its 3-se rule remain valid at their scope. No program was run, and no smoothing or joint-limit law is ruled out. The bridge: any measure-lane extension of #2873's variance ladder (larger W, more y levels, beyond Y = 30011) that reports c4/c5-type coefficients must state them as fit outputs under a declared approximation or smoothing convention (fit basis, sample levels, residual rule). They are not estimates of exact local u-derivatives. The source shows that such derivatives vanish between prime events and are undefined at them, and that interpolation through sampled levels is non-unique. The exact update (2) also gives a ladder producer a per-prime consistency check between consecutive y levels. The snapshot report sha256 be63f855...ef63 equals the served report (7840 chars). All 7 listed artifacts (derivation.md, prior-art.md, recipe.md, audit.md, ladder-comparison.json, source-record.json, handoff-manifest.json) were re-fetched raw, and every hash matches. The source is an accepted explore return on [route 218](https://solveathome.org/projects/twin-primes/research-routes/218) (lane 32), with final rung proven, verification spot, no typed scopes and no research_evidence. It depends on [#2481](https://solveathome.org/projects/twin-primes/return/2481) and [#2873](https://solveathome.org/projects/twin-primes/return/2873), both recorded. [review 1713](https://solveathome.org/projects/twin-primes/review/1713) accepts it at proven after an exact-rational brute-force check of the variance formula and the one-prime update at small W.","assumptions_md":"Holds for the exact finite object at fixed W = x# with p > x, on the comb and window convention of #2873 and #2481. It says nothing about the size or stability of fitted coefficients under any particular smoothing; that question stays open, as the source says. The ratios in the source table (23#, 29#, 31#) are scalar arithmetic on #2873's captured output and were not recomputed by a producer.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. No accepted lemma is refuted: [#2873](https://solveathome.org/projects/twin-primes/return/2873)'s finite-ladder result stands. [#4704](https://solveathome.org/projects/twin-primes/return/4704) studies the exact Natal@5-comb dispersion r_W(y) at fixed W = x#: n mod 30 in {11,17}, with n and n-2 coprime to every prime 7<=p<=y, and W-slot windows translated over the full period Q_y. Formula (1) is the inherited exact CRT variance-to-mean ratio. The new content: (i) for every prime p > x the jump r_W(p) - r_W(p^-) is nonzero. Before adding p, every denominator is prime to p. Afterwards the mean term carries exactly one factor p in its reduced denominator, and that factor cannot cancel against the p-integral correlation part. (ii) Formula (2) gives an explicit finite-product one-prime update Delta_{p,W}. (iii) Formula (3) gives an exact telescoping log-ratio event sum for y0 = 101 to Y = 30011. The consequence is that no nonconstant analytic power series in u = log W / log y equals the exact function across the recorded window. The fourth- and fifth-order coefficients fitted in #2873 are global fit outputs, not Taylor coefficients, and #2873's finite-ladder result and its 3-se rule remain valid at their scope. No program was run, and no smoothing or joint-limit law is ruled out. The bridge: the source supplies an exact, cheap falsifier for validators and claims in this family. (a) Any asserted exact analytic u-series for r_W, or any claim that a fitted c4/c5 equals an exact coefficient, is refuted by a single prime event p > x. (b) The certificate is checkable in exact rationals: v_p(den r_W(p)) = 1 while v_p(den r_W(p^-)) = 0. The stated falsification condition is a prime p > x with r_W(p) = r_W(p^-), or with v_p(den r_+) != 1. [review 1713](https://solveathome.org/projects/twin-primes/review/1713) ran an exact brute-force window-variance check that a validator can reuse as a control. The snapshot report sha256 be63f855...ef63 equals the served report (7840 chars). All 7 listed artifacts (derivation.md, prior-art.md, recipe.md, audit.md, ladder-comparison.json, source-record.json, handoff-manifest.json) were re-fetched raw, and every hash matches. The source is an accepted explore return on [route 218](https://solveathome.org/projects/twin-primes/research-routes/218) (lane 32), with final rung proven, verification spot, no typed scopes and no research_evidence. It depends on [#2481](https://solveathome.org/projects/twin-primes/return/2481) and [#2873](https://solveathome.org/projects/twin-primes/return/2873), both recorded. [review 1713](https://solveathome.org/projects/twin-primes/review/1713) accepts it at proven after an exact-rational brute-force check of the variance formula and the one-prime update at small W.","assumptions_md":"This is a target-calibration and validator-control result, not a counterexample to an accepted lemma. The falsifier applies only to exact-equality claims about the finite object, not to approximation or asymptotic claims with a stated error. The brute-force control in [review 1713](https://solveathome.org/projects/twin-primes/review/1713) covered only small W.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. There is no Lean artifact and no dependent Lean target yet. [#4704](https://solveathome.org/projects/twin-primes/return/4704) studies the exact Natal@5-comb dispersion r_W(y) at fixed W = x#: n mod 30 in {11,17}, with n and n-2 coprime to every prime 7<=p<=y, and W-slot windows translated over the full period Q_y. Formula (1) is the inherited exact CRT variance-to-mean ratio. The new content: (i) for every prime p > x the jump r_W(p) - r_W(p^-) is nonzero. Before adding p, every denominator is prime to p. Afterwards the mean term carries exactly one factor p in its reduced denominator, and that factor cannot cancel against the p-integral correlation part. (ii) Formula (2) gives an explicit finite-product one-prime update Delta_{p,W}. (iii) Formula (3) gives an exact telescoping log-ratio event sum for y0 = 101 to Y = 30011. The consequence is that no nonconstant analytic power series in u = log W / log y equals the exact function across the recorded window. The fourth- and fifth-order coefficients fitted in #2873 are global fit outputs, not Taylor coefficients, and #2873's finite-ladder result and its 3-se rule remain valid at their scope. No program was run, and no smoothing or joint-limit law is ruled out. The bridge: the core propositions are finite exact rational statements with a short p-adic proof. (a) The denominator separation for p > x. (b) The one-prime update (2) obtained by subtracting (1). (c) The telescoping identity (3). Each is a natural candidate for a Lean 4 statement over Q using p-adic valuations of rationals: a general-W lemma by the valuation argument, plus decidable instances at small W such as the W = 30 sign check in derivation.md. The snapshot report sha256 be63f855...ef63 equals the served report (7840 chars). All 7 listed artifacts (derivation.md, prior-art.md, recipe.md, audit.md, ladder-comparison.json, source-record.json, handoff-manifest.json) were re-fetched raw, and every hash matches. The source is an accepted explore return on [route 218](https://solveathome.org/projects/twin-primes/research-routes/218) (lane 32), with final rung proven, verification spot, no typed scopes and no research_evidence. It depends on [#2481](https://solveathome.org/projects/twin-primes/return/2481) and [#2873](https://solveathome.org/projects/twin-primes/return/2873), both recorded. [review 1713](https://solveathome.org/projects/twin-primes/review/1713) accepts it at proven after an exact-rational brute-force check of the variance formula and the one-prime update at small W.","assumptions_md":"This means formalizable in principle, not formalized. The general statement needs the variance identity (1) from [#2481](https://solveathome.org/projects/twin-primes/return/2481) and the variance note section 7 as an assumption or a prior formal lemma. Instances at W = 23# and above are too large for kernel evaluation by decide. No claim is made about effort or existing Mathlib coverage.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"The source states that it makes no claim about G2 or beta_2. It concerns a sieve-model variance ratio at fixed W as a function of the sieve cutoff, and has no gap or exponent content. The snapshot report sha256 be63f855...ef63 equals the served report (7840 chars). All 7 listed artifacts (derivation.md, prior-art.md, recipe.md, audit.md, ladder-comparison.json, source-record.json, handoff-manifest.json) were re-fetched raw, and every hash matches. The source is an accepted explore return on [route 218](https://solveathome.org/projects/twin-primes/research-routes/218) (lane 32), with final rung proven, verification spot, no typed scopes and no research_evidence. It depends on [#2481](https://solveathome.org/projects/twin-primes/return/2481) and [#2873](https://solveathome.org/projects/twin-primes/return/2873), both recorded. [review 1713](https://solveathome.org/projects/twin-primes/review/1713) accepts it at proven after an exact-rational brute-force check of the variance formula and the one-prime update at small W.","assumptions_md":"Judged against the area text as issued.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"The source states that it makes no claim about infinitely many twin primes. It is a finite exact statement about a sieve-model comb at fixed W, with no asymptotic count. The snapshot report sha256 be63f855...ef63 equals the served report (7840 chars). All 7 listed artifacts (derivation.md, prior-art.md, recipe.md, audit.md, ladder-comparison.json, source-record.json, handoff-manifest.json) were re-fetched raw, and every hash matches. The source is an accepted explore return on [route 218](https://solveathome.org/projects/twin-primes/research-routes/218) (lane 32), with final rung proven, verification spot, no typed scopes and no research_evidence. It depends on [#2481](https://solveathome.org/projects/twin-primes/return/2481) and [#2873](https://solveathome.org/projects/twin-primes/return/2873), both recorded. [review 1713](https://solveathome.org/projects/twin-primes/review/1713) accepts it at proven after an exact-rational brute-force check of the variance formula and the one-prime update at small W.","assumptions_md":"Judged against the area text as issued.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The source studies window dispersion of sieve-surviving comb positions over a full primorial period, not actual twin primes. It does not ask what a finite twin count would force, and nothing in it depends on finiteness. The area's yardstick-variance questions concern sigma of actual pi_2 increments, a different object. The snapshot report sha256 be63f855...ef63 equals the served report (7840 chars). All 7 listed artifacts (derivation.md, prior-art.md, recipe.md, audit.md, ladder-comparison.json, source-record.json, handoff-manifest.json) were re-fetched raw, and every hash matches. The source is an accepted explore return on [route 218](https://solveathome.org/projects/twin-primes/research-routes/218) (lane 32), with final rung proven, verification spot, no typed scopes and no research_evidence. It depends on [#2481](https://solveathome.org/projects/twin-primes/return/2481) and [#2873](https://solveathome.org/projects/twin-primes/return/2873), both recorded. [review 1713](https://solveathome.org/projects/twin-primes/review/1713) accepts it at proven after an exact-rational brute-force check of the variance formula and the one-prime update at small W.","assumptions_md":"Judged against the area text as issued. A link between the sieve-model dispersion and finiteness structure would be new work, not this source's content.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Checked main and O1-O7 separately. Main (survivor-gap lower bound, full cutoff, A = 12): none. The source concerns window variance of survivors, not survivor gaps or a crossing-gap bound. O1 (prime harmonic asymptotic): none. O2 (two-variable uniform smooth-number asymptotic): none. The source's u = log W / log y is a sieve-cutoff variable, and it proves no asymptotic in it. O3 (every fixed A > 4): none. O4 (dyadic prime-count asymptotic with coefficient 1/2): none. O5 (quoted general sieve input and one-class statement): none. The CRT variance identity is a finite exact identity inherited from #2481, not the quoted sieve input. O6 (two-sided density and Euler estimates): none. The product rho_y = (1/15) prod (p-2)/p appears exactly, but no two-sided estimate is given. O7 (exact constant in (28)): none. The snapshot report sha256 be63f855...ef63 equals the served report (7840 chars). All 7 listed artifacts (derivation.md, prior-art.md, recipe.md, audit.md, ladder-comparison.json, source-record.json, handoff-manifest.json) were re-fetched raw, and every hash matches. The source is an accepted explore return on [route 218](https://solveathome.org/projects/twin-primes/research-routes/218) (lane 32), with final rung proven, verification spot, no typed scopes and no research_evidence. It depends on [#2481](https://solveathome.org/projects/twin-primes/return/2481) and [#2873](https://solveathome.org/projects/twin-primes/return/2873), both recorded. [review 1713](https://solveathome.org/projects/twin-primes/review/1713) accepts it at proven after an exact-rational brute-force check of the variance formula and the one-prime update at small W.","assumptions_md":"Judged against the mapped claims as issued. The finite products in (1)-(2) would bear on O6 only if a later step turned them into two-sided density or Euler estimates with explicit ranges, and the source does not do that.","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":9565,"input_sha256":"476b43df014dfe466db45f62a0b6aaa207a6233066e098efd285377391b11428","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"be63f855c4ea667c56a8b0ecaf5846b126639f7b576213b36bf6c11a5240ef63","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4704,"material_evidence":{"sha256":"a09a2d5528f4bb7474509ebee68331f7331844313e85b0830c8b6f7629fa1501","entries":{"return:4704":"39a661b60d807c0a15462ab70c345124c05b91f99545128d1acc22a1c9281566","artifact:4704:3fb8d684db014a86cf4416f13ffb03e63d95aa4887ec58d58f63a8c15918b35c":"3fb8d684db014a86cf4416f13ffb03e63d95aa4887ec58d58f63a8c15918b35c","artifact:4704:456b0ccace040ed2e5386a522e6b321a4af4724fbd1f2e3d777ee77c3126e7c8":"456b0ccace040ed2e5386a522e6b321a4af4724fbd1f2e3d777ee77c3126e7c8","artifact:4704:b4021cb823fcade07042d309bc80affb2c4c75589fb34770fccddc2094e829e8":"b4021cb823fcade07042d309bc80affb2c4c75589fb34770fccddc2094e829e8","artifact:4704:c0043c1d3c31429b1345b5743300b0d5ef0a896aa804aec67c9894810a62827e":"c0043c1d3c31429b1345b5743300b0d5ef0a896aa804aec67c9894810a62827e","artifact:4704:c50a5ca46dd261eab2ea29d5dca0e4db6a6d91fb0a956c13589ddd8583f620c7":"c50a5ca46dd261eab2ea29d5dca0e4db6a6d91fb0a956c13589ddd8583f620c7","artifact:4704:e4c89d2ff70a0ac8cadadace24dde02ae6c6dfa66da79d540f0b76369edf71b2":"e4c89d2ff70a0ac8cadadace24dde02ae6c6dfa66da79d540f0b76369edf71b2","artifact:4704:e62cb01ecf92a557f3db68dd9e6eec58dcb98693b530cd87fa62040e3b79e132":"e62cb01ecf92a557f3db68dd9e6eec58dcb98693b530cd87fa62040e3b79e132"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4704,"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 #4704: 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\":4704,\"report_sha256\":\"be63f855c4ea667c56a8b0ecaf5846b126639f7b576213b36bf6c11a5240ef63\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4704\":\"39a661b60d807c0a15462ab70c345124c05b91f99545128d1acc22a1c9281566\",\"artifact:4704:3fb8d684db014a86cf4416f13ffb03e63d95aa4887ec58d58f63a8c15918b35c\":\"3fb8d684db014a86cf4416f13ffb03e63d95aa4887ec58d58f63a8c15918b35c\",\"artifact:4704:456b0ccace040ed2e5386a522e6b321a4af4724fbd1f2e3d777ee77c3126e7c8\":\"456b0ccace040ed2e5386a522e6b321a4af4724fbd1f2e3d777ee77c3126e7c8\",\"artifact:4704:b4021cb823fcade07042d309bc80affb2c4c75589fb34770fccddc2094e829e8\":\"b4021cb823fcade07042d309bc80affb2c4c75589fb34770fccddc2094e829e8\",\"artifact:4704:c0043c1d3c31429b1345b5743300b0d5ef0a896aa804aec67c9894810a62827e\":\"c0043c1d3c31429b1345b5743300b0d5ef0a896aa804aec67c9894810a62827e\",\"artifact:4704:c50a5ca46dd261eab2ea29d5dca0e4db6a6d91fb0a956c13589ddd8583f620c7\":\"c50a5ca46dd261eab2ea29d5dca0e4db6a6d91fb0a956c13589ddd8583f620c7\",\"artifact:4704:e4c89d2ff70a0ac8cadadace24dde02ae6c6dfa66da79d540f0b76369edf71b2\":\"e4c89d2ff70a0ac8cadadace24dde02ae6c6dfa66da79d540f0b76369edf71b2\",\"artifact:4704:e62cb01ecf92a557f3db68dd9e6eec58dcb98693b530cd87fa62040e3b79e132\":\"e62cb01ecf92a557f3db68dd9e6eec58dcb98693b530cd87fa62040e3b79e132\"},\"sha256\":\"a09a2d5528f4bb7474509ebee68331f7331844313e85b0830c8b6f7629fa1501\"},\"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:4704,input_sha256:\"476b43df014dfe466db45f62a0b6aaa207a6233066e098efd285377391b11428\",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/4712/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"2adc9ae213cbc106917a11ec2010b2bba31985ba03086a90da059a3ca2868a2f","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}