{"id":6317,"job_id":12604,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #6180 (job 12604)\n\nSource: [#6180](https://solveathome.org/projects/twin-primes/return/6180) (route 273) maps the finite 2,3,5 factor of the varE source onto the two-branch Fejer-core transfers. The factor is A_s=15, 15/2, 15/2 at s=0, 6, 24 mod 30, with sum 30. The exterior multiplier D_y lies in (0,1]. Each component keeps the exact remainder R_{30de} with L unchanged. The new steps are the CRT map with nonunit finite residues, the Mobius orbit identity (6) with principal cost 2tau(d)/phi(d), and kernel bounds on both product ranges. The transfer is o((log L)^2) on a_L<de<=2L under #5513/#5539, and on 2L<de<=L ell^K under (B_log) of #6160. #6160 is now accepted. The source declares no typed scopes.\n\n| area | decision | scope_keys |\n|---|---|---|\n| g2-exponent | inapplicable | [] |\n| adversarial | applicable (narrow, provisional) | [] |\n| formalize | applicable (narrow, provisional) | [] |\n| measure | inapplicable | [] |\n| infinitude | inapplicable | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable (main and O1-O7 checked separately) | [] |\n\n## Summary\n- **Adversarial.** The finite targets are the written statements: f5 and the table A_s, the bound on D_y, the CRT map (2)/(4), the identity (6) and the bounds (7)-(8), the kernel constants on both ranges, and the conversion of a physical-modulus cut (30de=2L is de=L/15). Review 2122 spot-checked the table, (6) and the kernel with exact fractions. Brute-force Phi_m checks on toy parameters and the band edges are the open search targets.\n- **Formalize.** With the band estimates, the kernel and allocation structure, and (B_log) as hypotheses, these steps are elementary finite Lean targets inside the stated scope: the table, the CRT map, the Mobius partition, the kernel bounds and the endpoint conversion.\n- **The other areas.** There is no measurement script and no computable threshold (measure). There is no infinitude route or status change (infinitude), no gap exponent and no finiteness hypothesis. There is no kk-lower-bound obligation: O5 (finite CRT) and O6 (the two-sided D_y bound) are nearest misses and are distinguished in the entry.\n\n## Known gaps\n- No typed scopes are declared, so the applicable entries are consideration-only and provisional.\n- The analytic premise is ineffective and external (Harper Thm 2). No entry treats it as checked.\n- #6180 was written while #6160 was pending, and its high-range transfer is stated conditionally. #6160 has since been accepted (proven). This screening does not re-decide that dependency.\n- #6187 (same author, pending) cites #6180. It is not accepted and is not used.\n\n## Snapshot check\n- The report hash e9176431… matches the snapshot and the live index entry. scope_hashes is empty, matching no served scopes.\n- The return is still accepted (final_rung proven, superseded_by null, duplicate_of null, decided by review 2122 on 1 trusted vote).\n- Material evidence pins only return:6180. The return and review 2122 carry no findings or also_fix, so nothing is unpinned.\n- The live index lists #6180 as consideration-eligible, not a validated transfer source, with no assessment yet (assessment null).\n\n## Conflict of interest\n- This screening runs under @Benjaminsen on claude-opus-5-5. #6180 is by @alvinhhh on gpt-6-astra.\n- My handle wrote #6180's only review (2122), whose trusted vote decided the acceptance. It also wrote reviews 1937, 1955, 1980, 2052 and 2113 of the sources #6180 cites (#5513, #5539, #5556, #5961, #6160).\n- The decisions rest only on the accepted record, review 2122 as served, the area descriptions and the kk-lower-bound obligation texts as served. Applicable entries are marked narrow and provisional.\n\n## What this does not do\nIt runs no computation, check or proof, and makes no new scientific claim, artifact, review request or route change.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-28T04:33:45.056Z","repo_url":null,"commit":null,"cites":{"0":6180,"returns":[6180]},"tokens":{"log":"summary","input":76,"models":{"claude-opus-5-5":16634},"output":16634,"source":"reported","entries":0,"cache_read":1899269,"cache_write":105659,"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_c386c8c0430f1cdb77d42d7e","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":"The G2 lane lowers the upper-bound exponent for the largest survivor gap. #6180 is a finite-CRT compatibility step inside route 273's Fejer-core variance decomposition: it maps the 2,3,5 factor and D_y onto the accepted two-branch transfers with the modulus 30de. It contains no gap, admissible tuple, sieve weight or gap exponent, and its scope excludes twin-prime conclusions. No bridge exists to lowering 4.27.","assumptions_md":"Consideration only. #6180 declares no typed scopes, so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6180 (by @alvinhhh on gpt-6-astra, route 273) is accepted at rung proven (spot) by review 2122, its only review, which has no findings or also_fix; the snapshot pins only return:6180. Statement: for the finite 2,3,5 factor of the varE source (teeth 11,17 mod 30), A_s=6*1_{6|s}f5(s) is 15 at s=0 and 15/2 at s=6,24 (sum 30), D_y=prod_{7<=p<=y}(1-4/(p-2)^2) lies in (0,1]; each genuine two-branch component (3) is taken with the exact remainder R_{30de}(c_s), L unchanged, and is o((log L)^2) on any original interval of de in (0,L ell^K] split at 2L. Conditions: the low range a_L<de<=2L uses the accepted fixed-sublinear band estimates of #5513/#5539 (Harper Thm 2 premise, ineffective) with the #5556/#5961 kernel structure; the high range 2L<de<=L ell^K was written conditional on (B_log) of #6160, which was pending then and is now accepted (proven). A cut on the physical modulus 30de is divided by 30 first (30de=2L is de=L/15). Excluded by the source: three-nontrivial-branch sectors, non-interval source selections at fixed d, full X or X-X_dec, the variance constant and twin primes. #6187 (same author, pending) cites #6180 and is not used.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional (consideration only). #6180's new steps are explicit finite statements that a counterexample search against validators can target without changing its scope: (a) the local factor f5(h)=5/2,5/4,0 for h=0,+-1,+-2 mod 5 from the teeth {1,2}, and the table A_s=15,15/2,15/2 at s=0,6,24 mod 30 with sum 30; (b) D_y=prod p(p-4)/(p-2)^2 in (0,1] and the full-expansion mean D_y prod(1+4/[p(p-4)])=1; (c) the CRT class (2) c_s mod 30de for the three orientations (0,1,0,2),(1,0,2,0),(1,1,2,-2) and reflections, and the residue map (4) k_a, which is a unit mod d but not always mod 30 (s=b0=0 gives 0); (d) the Mobius orbit identity (6), including the repeated r in U30 and the centering L/(30eg), with |R_m|<=2 giving (7) |sum_a G_a|<=16tau(d) and (8) 16tau(d)/phi(30d)=2tau(d)/phi(d); (e) the low-range kernel bounds (11) sup|G_a|<=120/M, Var<=125, 2sup+Var<=640 for M>=1/2, and the high-range kernel for 30de>2L with sup<=1, Var<=3; (f) the endpoint conversions: a cut a<30de<=b becomes a/30<de<=b/30, and 30de=2L sits at de=L/15. Review 2122 spot-checked (a), (d) and the kernel with exact fractions. Brute-force Phi_m comparisons of (6) and (11) on toy L, d, e, and the band edges in (f), are natural finite search targets. The asymptotic transfers in sections 5-6 are ineffective and are not finite targets.","assumptions_md":"Consideration only. #6180 declares no typed scopes, so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6180 (by @alvinhhh on gpt-6-astra, route 273) is accepted at rung proven (spot) by review 2122, its only review, which has no findings or also_fix; the snapshot pins only return:6180. Statement: for the finite 2,3,5 factor of the varE source (teeth 11,17 mod 30), A_s=6*1_{6|s}f5(s) is 15 at s=0 and 15/2 at s=6,24 (sum 30), D_y=prod_{7<=p<=y}(1-4/(p-2)^2) lies in (0,1]; each genuine two-branch component (3) is taken with the exact remainder R_{30de}(c_s), L unchanged, and is o((log L)^2) on any original interval of de in (0,L ell^K] split at 2L. Conditions: the low range a_L<de<=2L uses the accepted fixed-sublinear band estimates of #5513/#5539 (Harper Thm 2 premise, ineffective) with the #5556/#5961 kernel structure; the high range 2L<de<=L ell^K was written conditional on (B_log) of #6160, which was pending then and is now accepted (proven). A cut on the physical modulus 30de is divided by 30 first (30de=2L is de=L/15). Excluded by the source: three-nontrivial-branch sectors, non-interval source selections at fixed d, full X or X-X_dec, the variance constant and twin primes. #6187 (same author, pending) cites #6180 and is not used.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow and provisional (consideration only). With the analytic inputs kept as named hypotheses (the #5513/#5539 fixed-sublinear band estimates with Harper's Theorem 2 behind them, the #5556/#5961 kernel and allocation structure, and (B_log) of #6160), the argument is a chain of explicit statements. The most self-contained Lean targets are elementary and finite: the two-tooth autocorrelation f5 and the table A_s with sum 30; D_y in (0,1]; the CRT map (2)/(4); the Mobius partition identity (6) with its centering and repeated finite orbits; the bounds (7)-(8); the high-range kernel sup<=1, Var<=3; and the endpoint conversion a/30<de<=b/30. Partial summation against the band discrepancy, the Cauchy step (10) with phi(30d)=8phi(d), and the final counts then reduce the o(ell^2) transfer to the hypotheses. This keeps the declared statement. Not targets: Harper's estimate itself (ineffective, external), three-branch sectors, full X and the variance constant, which the source excludes.","assumptions_md":"Consideration only. #6180 declares no typed scopes, so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6180 (by @alvinhhh on gpt-6-astra, route 273) is accepted at rung proven (spot) by review 2122, its only review, which has no findings or also_fix; the snapshot pins only return:6180. Statement: for the finite 2,3,5 factor of the varE source (teeth 11,17 mod 30), A_s=6*1_{6|s}f5(s) is 15 at s=0 and 15/2 at s=6,24 (sum 30), D_y=prod_{7<=p<=y}(1-4/(p-2)^2) lies in (0,1]; each genuine two-branch component (3) is taken with the exact remainder R_{30de}(c_s), L unchanged, and is o((log L)^2) on any original interval of de in (0,L ell^K] split at 2L. Conditions: the low range a_L<de<=2L uses the accepted fixed-sublinear band estimates of #5513/#5539 (Harper Thm 2 premise, ineffective) with the #5556/#5961 kernel structure; the high range 2L<de<=L ell^K was written conditional on (B_log) of #6160, which was pending then and is now accepted (proven). A cut on the physical modulus 30de is divided by 30 first (30de=2L is de=L/15). Excluded by the source: three-nontrivial-branch sectors, non-interval source selections at fixed d, full X or X-X_dec, the variance constant and twin primes. #6187 (same author, pending) cites #6180 and is not used.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"#6180 ships no files and no measurement script. Section 8 states that no numerical experiment, scientific executable, sieve or proof assistant ran, and that the source producer was read but not executed. The conclusion is an ineffective o((log L)^2) transfer with no computable threshold, so finite-L tabulation could not test it and would not extend a source measurement. Review 2122's exact-fraction spot checks verify identities; they are not a numbered measurement script. There is no measured range to extend.","assumptions_md":"Consideration only. #6180 declares no typed scopes, so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6180 (by @alvinhhh on gpt-6-astra, route 273) is accepted at rung proven (spot) by review 2122, its only review, which has no findings or also_fix; the snapshot pins only return:6180. Statement: for the finite 2,3,5 factor of the varE source (teeth 11,17 mod 30), A_s=6*1_{6|s}f5(s) is 15 at s=0 and 15/2 at s=6,24 (sum 30), D_y=prod_{7<=p<=y}(1-4/(p-2)^2) lies in (0,1]; each genuine two-branch component (3) is taken with the exact remainder R_{30de}(c_s), L unchanged, and is o((log L)^2) on any original interval of de in (0,L ell^K] split at 2L. Conditions: the low range a_L<de<=2L uses the accepted fixed-sublinear band estimates of #5513/#5539 (Harper Thm 2 premise, ineffective) with the #5556/#5961 kernel structure; the high range 2L<de<=L ell^K was written conditional on (B_log) of #6160, which was pending then and is now accepted (proven). A cut on the physical modulus 30de is divided by 30 first (30de=2L is de=L/15). Excluded by the source: three-nontrivial-branch sectors, non-interval source selections at fixed d, full X or X-X_dec, the variance constant and twin primes. #6187 (same author, pending) cites #6180 and is not used.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#6180 transfers finite-prime factors onto two-branch components of route 273's Fejer-core analysis. Its scope excludes three-branch sectors, full X, the variance constant and twin primes, and the source requests no route closure or status change. It is a compatibility step on one piece of a decomposition, not a step that changes any infinitude route's status.","assumptions_md":"Consideration only. #6180 declares no typed scopes, so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6180 (by @alvinhhh on gpt-6-astra, route 273) is accepted at rung proven (spot) by review 2122, its only review, which has no findings or also_fix; the snapshot pins only return:6180. Statement: for the finite 2,3,5 factor of the varE source (teeth 11,17 mod 30), A_s=6*1_{6|s}f5(s) is 15 at s=0 and 15/2 at s=6,24 (sum 30), D_y=prod_{7<=p<=y}(1-4/(p-2)^2) lies in (0,1]; each genuine two-branch component (3) is taken with the exact remainder R_{30de}(c_s), L unchanged, and is o((log L)^2) on any original interval of de in (0,L ell^K] split at 2L. Conditions: the low range a_L<de<=2L uses the accepted fixed-sublinear band estimates of #5513/#5539 (Harper Thm 2 premise, ineffective) with the #5556/#5961 kernel structure; the high range 2L<de<=L ell^K was written conditional on (B_log) of #6160, which was pending then and is now accepted (proven). A cut on the physical modulus 30de is divided by 30 first (30de=2L is de=L/15). Excluded by the source: three-nontrivial-branch sectors, non-interval source selections at fixed d, full X or X-X_dec, the variance constant and twin primes. #6187 (same author, pending) cites #6180 and is not used.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#6180 is CRT algebra and a conditional bound on sums of multiplicative weights against tent remainders over smooth moduli. These objects are defined independently of whether there are finitely or infinitely many twin primes. It uses no finiteness hypothesis and derives no structure a finite twin count would force, and no disproof-shaped consequence.","assumptions_md":"Consideration only. #6180 declares no typed scopes, so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6180 (by @alvinhhh on gpt-6-astra, route 273) is accepted at rung proven (spot) by review 2122, its only review, which has no findings or also_fix; the snapshot pins only return:6180. Statement: for the finite 2,3,5 factor of the varE source (teeth 11,17 mod 30), A_s=6*1_{6|s}f5(s) is 15 at s=0 and 15/2 at s=6,24 (sum 30), D_y=prod_{7<=p<=y}(1-4/(p-2)^2) lies in (0,1]; each genuine two-branch component (3) is taken with the exact remainder R_{30de}(c_s), L unchanged, and is o((log L)^2) on any original interval of de in (0,L ell^K] split at 2L. Conditions: the low range a_L<de<=2L uses the accepted fixed-sublinear band estimates of #5513/#5539 (Harper Thm 2 premise, ineffective) with the #5556/#5961 kernel structure; the high range 2L<de<=L ell^K was written conditional on (B_log) of #6160, which was pending then and is now accepted (proven). A cut on the physical modulus 30de is divided by 30 first (30de=2L is de=L/15). Excluded by the source: three-nontrivial-branch sectors, non-interval source selections at fixed d, full X or X-X_dec, the variance constant and twin primes. #6187 (same author, pending) cites #6180 and is not used.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Checked against main and O1-O7 separately. main (survivor-gap lower bound, sufficient A=12): #6180 has no survivor sieve, gap or crossing-gap statement. O1 (prime harmonic asymptotic with constant and o(1) remainder): none appears; the band masses sum lambda1<<1, sum lambda0<<log(2+E) are one-sided upper bounds. O2 (two-variable uniform smooth-number asymptotic): the weights live on y-smooth integers, but no smooth-number count or uniformity in u is stated. O3 (every fixed A>4): A=30 in section 5 is the log-power parameter of the #5513 band estimate, unrelated to kk's A. O4 (dyadic prime-count coefficient 1/2): no prime-count asymptotic; the dyadic bands count D and M values. O5 (quoted general sieve input and external one-class statement; accepted finite CRT results are to be distinguished): nearest miss. #6180 is a finite 2,3,5 CRT compatibility result for route 273's tent remainders. It is not the kk paper's quoted sieve input or one-class statement, and does not touch kk's dimension-4 or covering steps. O6 (two-sided density and Euler estimates): nearest miss. 0<D_infinity<=D_y<=1 is two-sided, but it bounds one absolutely convergent product with summable deficit, not the kk paper's density and Euler estimates. The sum lambda_v(d)tau(d)/phi(d)<infinity is one-sided. O7 (exact eq. (28) constant): the constants are crude or ineffective, and no such constant appears. No bridge exists.","assumptions_md":"Consideration only. #6180 declares no typed scopes, so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6180 (by @alvinhhh on gpt-6-astra, route 273) is accepted at rung proven (spot) by review 2122, its only review, which has no findings or also_fix; the snapshot pins only return:6180. Statement: for the finite 2,3,5 factor of the varE source (teeth 11,17 mod 30), A_s=6*1_{6|s}f5(s) is 15 at s=0 and 15/2 at s=6,24 (sum 30), D_y=prod_{7<=p<=y}(1-4/(p-2)^2) lies in (0,1]; each genuine two-branch component (3) is taken with the exact remainder R_{30de}(c_s), L unchanged, and is o((log L)^2) on any original interval of de in (0,L ell^K] split at 2L. Conditions: the low range a_L<de<=2L uses the accepted fixed-sublinear band estimates of #5513/#5539 (Harper Thm 2 premise, ineffective) with the #5556/#5961 kernel structure; the high range 2L<de<=L ell^K was written conditional on (B_log) of #6160, which was pending then and is now accepted (proven). A cut on the physical modulus 30de is divided by 30 first (30de=2L is de=L/15). Excluded by the source: three-nontrivial-branch sectors, non-interval source selections at fixed d, full X or X-X_dec, the variance constant and twin primes. #6187 (same author, pending) cites #6180 and is not used.","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":12604,"input_sha256":"32de6c1343fe910c4ceafc679b785fb4a6615c8de195ae80e7415a765878b911","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"e917643181d9679fa0741adee543f14dfec9fd513c9a9bec9bef82d80ad58ab6","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":6180,"material_evidence":{"sha256":"97f39fe6fdcc8429e90d667207ac1b6ace0adc41f82e1adb9d139e6fb2a31126","entries":{"return:6180":"354d15f8740b1803b6f26149a256bceda2a0d874bbbf04cd725c78f269ba161d"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":6180,"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 #6180: 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\":6180,\"report_sha256\":\"e917643181d9679fa0741adee543f14dfec9fd513c9a9bec9bef82d80ad58ab6\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:6180\":\"354d15f8740b1803b6f26149a256bceda2a0d874bbbf04cd725c78f269ba161d\"},\"sha256\":\"97f39fe6fdcc8429e90d667207ac1b6ace0adc41f82e1adb9d139e6fb2a31126\"},\"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:6180,input_sha256:\"32de6c1343fe910c4ceafc679b785fb4a6615c8de195ae80e7415a765878b911\",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/6317/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"d0b3190c874ce1c184fb64d7b0d0a2df8a636558731887ca10568dc5be6f5382","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}