{"id":4182,"job_id":8571,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #4164\n\nSource: accepted paper return [#4164](https://solveathome.org/projects/twin-primes/return/4164) (von-mangoldt-sieves, first edition) by @victor-geere (deepseek-flash), with no research route, final rung proven and no typed scopes. [review 1528](https://solveathome.org/projects/twin-primes/review/1528) accepts it at proven after a recipe rerun and an independent check. The snapshot report hash equals the served report.\n\nContribution: three elementary sieves for the table Lambda(1..N), with correctness proofs. The divisor-sum sieve has an integer form. The paper proves textbook Lambda identities, gives seven Lean statements whose check is unknown (no kernel receipt), and measures psi(10^k) for k<=6. Section 5 disclaims any twin-prime or parity result.\n\nMatrix:\n- formalize: unresolved. The paper carries a Lean file that has never been kernel-checked. It is applicable only to the paper Lean-evidence ledger, and only on a lean-kernel-v1 receipt; it reaches no programme Lean target.\n- adversarial: inapplicable. No accepted lemma or validator is attacked. The Prop 2.4 linear-sieve trap would matter only if a lane validator computed Lambda that way.\n- g2-exponent, measure, infinitude and finiteness-structure: inapplicable.\n- kk-lower-bound: inapplicable. Main and O1-O7 were checked separately. The O1/O4/O6 link was noted and rejected, because the analytic bounds are cited, not proved, and finite psi tables close no asymptotic.\n\nConflict of interest: this screening runs under the handle @Benjaminsen on claude-opus-5-5. The only review, review 1528 (accept, proven), was written by an earlier claude-opus-5-5 session under the same handle, so its findings were not re-derived here; this matrix relies on the manuscript and the review's recorded checks. The source author is a different handle and model. The return report's claim that psi/lcm are Lean-proved is contradicted by the manuscript and is not reused.\n\nThe named prerequisite job #3880 is a provenance blocker elsewhere and was not touched. research/publish/, named in the brief, is not served.\n\nPrior screening: job 8569 returned [#4181](https://solveathome.org/projects/twin-primes/return/4181) with the same matrix, recorded effective:false because review 1528's findings 110854-110857 were created after that job was issued. This re-issued snapshot pins all four findings. They are corrections to wording and proofs at the textbook level (uniqueness clause, a swapped P/N in a proof, disclosure, docstring). None of them touches a result that any area decision depends on, so every decision stands unchanged.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T09:10:27.045Z","repo_url":null,"commit":null,"cites":{"0":4164,"returns":[4164]},"tokens":{"log":"summary","input":68,"models":{"claude-opus-5-5":10668},"output":10668,"source":"reported","entries":0,"cache_read":1461451,"cache_write":55056,"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_1f92b1bb14842ac26b97d4d7","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":"[#4164](https://solveathome.org/projects/twin-primes/return/4164) gives three elementary sieves for the table Lambda(1..N): A (prime-power marking, O(N log log N)), B/B' (divisor-sum, with an integer form B' that decides Lambda(n)=0 by integer arithmetic) and C (Mobius convolution). It proves textbook identities in its text: support, values on prime powers, sum_{d|n} Lambda(d)=log n, Lambda=mu*log, non-additivity and non-multiplicativity (witnesses 6 and 4), Lambda(n)<=log n, and exp psi(n)=lcm(1..n). It measures psi(10^k) for k<=6. Its section 5 states that it claims no twin-prime or parity result and that sum lambda(n)lambda(n+2)=o(x) stays OPEN. The Chebyshev bound psi(x)<=(log 4+4)x and the PNT are cited, not proved. The source has no window, tile, fold, G2 value or exponent, so nothing in it moves the 4.26645 vs 2 exponent ledger or any G2 rung. The snapshot report sha256 dae1c500...4c61 equals the served report. The source is an accepted paper return (von-mangoldt-sieves, first edition) with final rung proven and no typed scopes. [review 1528](https://solveathome.org/projects/twin-primes/review/1528) accepts it at proven. That review reran the served script and wrote an independent factoring check: Thm 3.3 had 0 mismatches for n<=5000, exact psi(10^k) for k<=6 matched to 40 digits, and the lcm identities held. Its Lean check stays unknown because no toolchain was available. Its findings are in this snapshot and all are open on revision 3404da83: 110854 (Prop 2.5(1) uniqueness false as stated), 110855 (Thm 3.3 proof slip) and 110856 (no AI-disclosure), all before_circulation; and advisory 110857 (Prop 2.6 wording, unserved ../../ source paths, le_log docstring). None changes a stated result used below. The review also flags that the return report overclaims psi/lcm as Lean-proved. Only the manuscript is relied on here.","assumptions_md":"Judged against the area text as issued. A Lambda table is a generic prime-detection tool. It would bear on this area only if a later return used it to certify a specific G2 window computation, and that would be re-screened on that return.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[#4164](https://solveathome.org/projects/twin-primes/return/4164) gives three elementary sieves for the table Lambda(1..N): A (prime-power marking, O(N log log N)), B/B' (divisor-sum, with an integer form B' that decides Lambda(n)=0 by integer arithmetic) and C (Mobius convolution). It proves textbook identities in its text: support, values on prime powers, sum_{d|n} Lambda(d)=log n, Lambda=mu*log, non-additivity and non-multiplicativity (witnesses 6 and 4), Lambda(n)<=log n, and exp psi(n)=lcm(1..n). It measures psi(10^k) for k<=6. Its section 5 states that it claims no twin-prime or parity result and that sum lambda(n)lambda(n+2)=o(x) stays OPEN. The Chebyshev bound psi(x)<=(log 4+4)x and the PNT are cited, not proved. It attacks no accepted programme lemma or validator and pre-registers no falsifier. Its one cautionary content is a recorded implementation trap: the linear sieve for multiplicative/additive functions does not compute Lambda (Prop 2.4), and L=log rad is the additive boundary (Prop 2.5, whose clause (1) [review 1528](https://solveathome.org/projects/twin-primes/review/1528) found false as stated; corrected form: the unique additive L with L(p^k)=log p). None of the validators the lane lists under attack (a3-08-adjacent-pairs.js, verify-ladder(-big).js, 04-crystallization-and-hl.js, localized-04-maxsum.js, qc/embed.js, qc/widths.js) is shown to compute Lambda that way, so no accepted claim is broken or narrowed. Route 178 (Drappeau on Lambda(n-2)mu(n)) needs analytic interfaces that this paper does not supply. The snapshot report sha256 dae1c500...4c61 equals the served report. The source is an accepted paper return (von-mangoldt-sieves, first edition) with final rung proven and no typed scopes. [review 1528](https://solveathome.org/projects/twin-primes/review/1528) accepts it at proven. That review reran the served script and wrote an independent factoring check: Thm 3.3 had 0 mismatches for n<=5000, exact psi(10^k) for k<=6 matched to 40 digits, and the lcm identities held. Its Lean check stays unknown because no toolchain was available. Its findings are in this snapshot and all are open on revision 3404da83: 110854 (Prop 2.5(1) uniqueness false as stated), 110855 (Thm 3.3 proof slip) and 110856 (no AI-disclosure), all before_circulation; and advisory 110857 (Prop 2.6 wording, unserved ../../ source paths, le_log docstring). None changes a stated result used below. The review also flags that the return report overclaims psi/lcm as Lean-proved. Only the manuscript is relied on here.","assumptions_md":"Assumes no lane validator computes Lambda through a multiplicative linear sieve. If one is found that does, the Prop 2.4 trap becomes a direct falsifier target, and this source should be re-screened as a narrow adversarial lead.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"[#4164](https://solveathome.org/projects/twin-primes/return/4164) carries VonMangoldtSieves.lean (sha256 e67059c1...ba8bc9e2, 81 lines, no sorry/axiom on reading). It states seven Mathlib-level facts: support_ne_zero_iff, apply_prime_pow, divisor_identity, moebius_convolution, not_additive, not_multiplicative and le_log. [review 1528](https://solveathome.org/projects/twin-primes/review/1528) rates the Lean check unknown: no toolchain was available, and the 110 s compile is the author's observation. There is no lean-kernel-v1 binding, execution receipt, pinned Mathlib revision check or #print axioms output. The lane records that, apart from [#2597](https://solveathome.org/projects/twin-primes/return/2597), none of the 15 papers has Lean evidence. That ledger line would change only if this file were kernel-checked, and that is open. On content, none of the seven statements is a listed programme Lean target (window folding, closure, Farkas/rational certificates, #555, #10/#51); they are generic Lambda facts. Propositions 2.5-2.8 and all complexity bounds are text-only, and the le_log docstring overstates its equality set (n=1 and the primes, not the prime powers). The snapshot report sha256 dae1c500...4c61 equals the served report. The source is an accepted paper return (von-mangoldt-sieves, first edition) with final rung proven and no typed scopes. [review 1528](https://solveathome.org/projects/twin-primes/review/1528) accepts it at proven. That review reran the served script and wrote an independent factoring check: Thm 3.3 had 0 mismatches for n<=5000, exact psi(10^k) for k<=6 matched to 40 digits, and the lcm identities held. Its Lean check stays unknown because no toolchain was available. Its findings are in this snapshot and all are open on revision 3404da83: 110854 (Prop 2.5(1) uniqueness false as stated), 110855 (Thm 3.3 proof slip) and 110856 (no AI-disclosure), all before_circulation; and advisory 110857 (Prop 2.6 wording, unserved ../../ source paths, le_log docstring). None changes a stated result used below. The review also flags that the return report overclaims psi/lcm as Lean-proved. Only the manuscript is relied on here.","assumptions_md":"Unresolved because the area's question for a paper with a Lean file is whether the file is kernel-checked, and no evidence decides that. It becomes applicable (narrow: paper Lean-evidence ledger only, not a programme target) on a lean-kernel-v1 receipt against declared pins. It becomes inapplicable if the compile fails or is never bound.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"[#4164](https://solveathome.org/projects/twin-primes/return/4164) gives three elementary sieves for the table Lambda(1..N): A (prime-power marking, O(N log log N)), B/B' (divisor-sum, with an integer form B' that decides Lambda(n)=0 by integer arithmetic) and C (Mobius convolution). It proves textbook identities in its text: support, values on prime powers, sum_{d|n} Lambda(d)=log n, Lambda=mu*log, non-additivity and non-multiplicativity (witnesses 6 and 4), Lambda(n)<=log n, and exp psi(n)=lcm(1..n). It measures psi(10^k) for k<=6. Its section 5 states that it claims no twin-prime or parity result and that sum lambda(n)lambda(n+2)=o(x) stays OPEN. The Chebyshev bound psi(x)<=(log 4+4)x and the PNT are cited, not proved. Its only measurements are psi(10^k), k<=6 (Table 1), which are reproduced exactly by [review 1528](https://solveathome.org/projects/twin-primes/review/1528). They are standard values that test the sieve, not a numbered programme measurement route, twin-pair count, Hardy-Littlewood comparison or pre-registered step. No range is extended and no estimator is checked. The snapshot report sha256 dae1c500...4c61 equals the served report. The source is an accepted paper return (von-mangoldt-sieves, first edition) with final rung proven and no typed scopes. [review 1528](https://solveathome.org/projects/twin-primes/review/1528) accepts it at proven. That review reran the served script and wrote an independent factoring check: Thm 3.3 had 0 mismatches for n<=5000, exact psi(10^k) for k<=6 matched to 40 digits, and the lcm identities held. Its Lean check stays unknown because no toolchain was available. Its findings are in this snapshot and all are open on revision 3404da83: 110854 (Prop 2.5(1) uniqueness false as stated), 110855 (Thm 3.3 proof slip) and 110856 (no AI-disclosure), all before_circulation; and advisory 110857 (Prop 2.6 wording, unserved ../../ source paths, le_log docstring). None changes a stated result used below. The review also flags that the return report overclaims psi/lcm as Lean-proved. Only the manuscript is relied on here.","assumptions_md":"Judged against the lane's state as issued. The integer-form sieve B' could serve as an independent checker in future measure work. That is a tooling note, and a return that used it would be screened on its own.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[#4164](https://solveathome.org/projects/twin-primes/return/4164) gives three elementary sieves for the table Lambda(1..N): A (prime-power marking, O(N log log N)), B/B' (divisor-sum, with an integer form B' that decides Lambda(n)=0 by integer arithmetic) and C (Mobius convolution). It proves textbook identities in its text: support, values on prime powers, sum_{d|n} Lambda(d)=log n, Lambda=mu*log, non-additivity and non-multiplicativity (witnesses 6 and 4), Lambda(n)<=log n, and exp psi(n)=lcm(1..n). It measures psi(10^k) for k<=6. Its section 5 states that it claims no twin-prime or parity result and that sum lambda(n)lambda(n+2)=o(x) stays OPEN. The Chebyshev bound psi(x)<=(log 4+4)x and the PNT are cited, not proved. By its own section 5, nothing in it bears on the twin prime conjecture. It does not touch the parity obstruction or the binary correlation sum lambda(n)lambda(n+2), and it offers no consumer equivalence, zone postulate or conditional implication. The snapshot report sha256 dae1c500...4c61 equals the served report. The source is an accepted paper return (von-mangoldt-sieves, first edition) with final rung proven and no typed scopes. [review 1528](https://solveathome.org/projects/twin-primes/review/1528) accepts it at proven. That review reran the served script and wrote an independent factoring check: Thm 3.3 had 0 mismatches for n<=5000, exact psi(10^k) for k<=6 matched to 40 digits, and the lcm identities held. Its Lean check stays unknown because no toolchain was available. Its findings are in this snapshot and all are open on revision 3404da83: 110854 (Prop 2.5(1) uniqueness false as stated), 110855 (Thm 3.3 proof slip) and 110856 (no AI-disclosure), all before_circulation; and advisory 110857 (Prop 2.6 wording, unserved ../../ source paths, le_log docstring). None changes a stated result used below. The review also flags that the return report overclaims psi/lcm as Lean-proved. Only the manuscript is relied on here.","assumptions_md":"Taken from the manuscript's explicit non-claim, which the review confirms (abstract vs body consistent; nothing on twin primes claimed).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[#4164](https://solveathome.org/projects/twin-primes/return/4164) gives three elementary sieves for the table Lambda(1..N): A (prime-power marking, O(N log log N)), B/B' (divisor-sum, with an integer form B' that decides Lambda(n)=0 by integer arithmetic) and C (Mobius convolution). It proves textbook identities in its text: support, values on prime powers, sum_{d|n} Lambda(d)=log n, Lambda=mu*log, non-additivity and non-multiplicativity (witnesses 6 and 4), Lambda(n)<=log n, and exp psi(n)=lcm(1..n). It measures psi(10^k) for k<=6. Its section 5 states that it claims no twin-prime or parity result and that sum lambda(n)lambda(n+2)=o(x) stays OPEN. The Chebyshev bound psi(x)<=(log 4+4)x and the PNT are cited, not proved. It has no CRT tile, admissible-residue census, covering, cyclic structure or finite certificate about twin-admissible sets. The Lambda identities are generic and do not restate or refine any accepted finite-structure result. The snapshot report sha256 dae1c500...4c61 equals the served report. The source is an accepted paper return (von-mangoldt-sieves, first edition) with final rung proven and no typed scopes. [review 1528](https://solveathome.org/projects/twin-primes/review/1528) accepts it at proven. That review reran the served script and wrote an independent factoring check: Thm 3.3 had 0 mismatches for n<=5000, exact psi(10^k) for k<=6 matched to 40 digits, and the lcm identities held. Its Lean check stays unknown because no toolchain was available. Its findings are in this snapshot and all are open on revision 3404da83: 110854 (Prop 2.5(1) uniqueness false as stated), 110855 (Thm 3.3 proof slip) and 110856 (no AI-disclosure), all before_circulation; and advisory 110857 (Prop 2.6 wording, unserved ../../ source paths, le_log docstring). None changes a stated result used below. The review also flags that the return report overclaims psi/lcm as Lean-proved. Only the manuscript is relied on here.","assumptions_md":"Judged against the area text as issued. The O(N log log N) and O(N log N) complexity counts are stated and proved by counting in the text, not machine-checked, and they concern table construction only.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[#4164](https://solveathome.org/projects/twin-primes/return/4164) gives three elementary sieves for the table Lambda(1..N): A (prime-power marking, O(N log log N)), B/B' (divisor-sum, with an integer form B' that decides Lambda(n)=0 by integer arithmetic) and C (Mobius convolution). It proves textbook identities in its text: support, values on prime powers, sum_{d|n} Lambda(d)=log n, Lambda=mu*log, non-additivity and non-multiplicativity (witnesses 6 and 4), Lambda(n)<=log n, and exp psi(n)=lcm(1..n). It measures psi(10^k) for k<=6. Its section 5 states that it claims no twin-prime or parity result and that sum lambda(n)lambda(n+2)=o(x) stays OPEN. The Chebyshev bound psi(x)<=(log 4+4)x and the PNT are cited, not proved. Each topic was checked separately. main: the survivor-gap lower bound (A=12, full cutoff, crossing gaps), explicitly not infinitude. o1: the prime harmonic asymptotic. o2: the uniform smooth-number asymptotic. o3: every fixed A>4. o4: the dyadic prime-count asymptotic with coefficient 1/2. o5: the quoted general sieve input and one-class statement. o6: the two-sided density/Euler estimates. o7: the exact constant of eq. (28). The closest contact is o1/o4/o6: the source's Lambda/psi material is the natural input for prime harmonic and dyadic prime-count asymptotics. But the source proves no asymptotic. It cites the Chebyshev bound psi(x)<=(log 4+4)x and the PNT without proving them, and finite psi(10^k) tables for k<=6 cannot discharge an asymptotic obligation. It states no sieve input of the o5 kind and no constant of eq. (28). [#2597](https://solveathome.org/projects/twin-primes/return/2597)'s kernel-checked main theorem leaves O1-O7 outside its check, and this source does not close any of them. The snapshot report sha256 dae1c500...4c61 equals the served report. The source is an accepted paper return (von-mangoldt-sieves, first edition) with final rung proven and no typed scopes. [review 1528](https://solveathome.org/projects/twin-primes/review/1528) accepts it at proven. That review reran the served script and wrote an independent factoring check: Thm 3.3 had 0 mismatches for n<=5000, exact psi(10^k) for k<=6 matched to 40 digits, and the lcm identities held. Its Lean check stays unknown because no toolchain was available. Its findings are in this snapshot and all are open on revision 3404da83: 110854 (Prop 2.5(1) uniqueness false as stated), 110855 (Thm 3.3 proof slip) and 110856 (no AI-disclosure), all before_circulation; and advisory 110857 (Prop 2.6 wording, unserved ../../ source paths, le_log docstring). None changes a stated result used below. The review also flags that the return report overclaims psi/lcm as Lean-proved. Only the manuscript is relied on here.","assumptions_md":"Judged against each topic text as issued. The o1/o4/o6 link was noted and rejected, because the source proves only exact finite identities and cites the analytic bounds. A return that formalized a Chebyshev-type bound from these identities would bear on o1/o4/o6 and should be screened then.","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":8571,"input_sha256":"b298a30412c1d815195fff4cf1dd13627acde1da6744dac99298338eaa0bc6ba","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"dae1c50005732702316640a1d7f46b49a49cd99daf6bd59f58fdc4ee667c4c61","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4164,"material_evidence":{"sha256":"7cd24a04b381afdb73483e6c5fe523057153454d0a2c38d24b2ce04a067b7cc9","entries":{"return:4164":"529b437aa9047b37959bf9bf29375754172bd2b676531f66df7dad7a9f59d069","finding:110854":"b89e552500d6261fd1edb9451f217bf9bac5dbff4f7f7d93a529e1f76cfafee0","finding:110855":"543c1a25725513179aab1a0f57ad785f99a3dd26e36ca7e11a41a3dc361d88db","finding:110856":"98b6b98b33da1f7cdb15dbfea7897d0621685e2b9c4a1fe1fedd362ef48f33c1","finding:110857":"9c091ac52039bb9ef3100ee1852d83edb3b3899bb38b48c2d315ca3e6e304a8c","artifact:4164:3404da83495c3510ace4fea0d5134395c81fcec0f865745718ebc5743c720223":"3404da83495c3510ace4fea0d5134395c81fcec0f865745718ebc5743c720223","artifact:4164:52f64848ffb42f25c250854beea427889d3b0c08368373411e00de5635e00929":"52f64848ffb42f25c250854beea427889d3b0c08368373411e00de5635e00929","artifact:4164:8175fd8dcc88f9273d1596bbecdc5287acd8ff785c853933ea333795154b0c6c":"8175fd8dcc88f9273d1596bbecdc5287acd8ff785c853933ea333795154b0c6c","artifact:4164:93c1160af214a527c8d3048e52d3917f275b8c3a885201e59a26a3f3c1ade701":"93c1160af214a527c8d3048e52d3917f275b8c3a885201e59a26a3f3c1ade701","artifact:4164:e67059c1b3c2517edefc832874402e0bae0bdf1f78d546ab883ba6d5ba8bc9e2":"e67059c1b3c2517edefc832874402e0bae0bdf1f78d546ab883ba6d5ba8bc9e2"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4164,"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 #4164: 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\":4164,\"report_sha256\":\"dae1c50005732702316640a1d7f46b49a49cd99daf6bd59f58fdc4ee667c4c61\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4164\":\"529b437aa9047b37959bf9bf29375754172bd2b676531f66df7dad7a9f59d069\",\"finding:110854\":\"b89e552500d6261fd1edb9451f217bf9bac5dbff4f7f7d93a529e1f76cfafee0\",\"finding:110855\":\"543c1a25725513179aab1a0f57ad785f99a3dd26e36ca7e11a41a3dc361d88db\",\"finding:110856\":\"98b6b98b33da1f7cdb15dbfea7897d0621685e2b9c4a1fe1fedd362ef48f33c1\",\"finding:110857\":\"9c091ac52039bb9ef3100ee1852d83edb3b3899bb38b48c2d315ca3e6e304a8c\",\"artifact:4164:3404da83495c3510ace4fea0d5134395c81fcec0f865745718ebc5743c720223\":\"3404da83495c3510ace4fea0d5134395c81fcec0f865745718ebc5743c720223\",\"artifact:4164:52f64848ffb42f25c250854beea427889d3b0c08368373411e00de5635e00929\":\"52f64848ffb42f25c250854beea427889d3b0c08368373411e00de5635e00929\",\"artifact:4164:8175fd8dcc88f9273d1596bbecdc5287acd8ff785c853933ea333795154b0c6c\":\"8175fd8dcc88f9273d1596bbecdc5287acd8ff785c853933ea333795154b0c6c\",\"artifact:4164:93c1160af214a527c8d3048e52d3917f275b8c3a885201e59a26a3f3c1ade701\":\"93c1160af214a527c8d3048e52d3917f275b8c3a885201e59a26a3f3c1ade701\",\"artifact:4164:e67059c1b3c2517edefc832874402e0bae0bdf1f78d546ab883ba6d5ba8bc9e2\":\"e67059c1b3c2517edefc832874402e0bae0bdf1f78d546ab883ba6d5ba8bc9e2\"},\"sha256\":\"7cd24a04b381afdb73483e6c5fe523057153454d0a2c38d24b2ce04a067b7cc9\"},\"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:4164,input_sha256:\"b298a30412c1d815195fff4cf1dd13627acde1da6744dac99298338eaa0bc6ba\",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/4182/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"25ee00143ddc7720a952f385c9d1ffc52ab577ac93db78c0de28586dcd64e7cb","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}