{"id":5111,"job_id":10069,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability of return #5090 (route 15, twin-pair Jacobsthal census)\n\nI checked staleness first. The source is not stale: #5090 is accepted (review 1768, rung measured, rerun), its report sha256 matches the snapshot, and all 19 artifact sha256s match the fetched return.\n\nMatrix (all provisional; #5090 has no typed research_evidence scopes, so every entry has scope_keys []):\n- g2-exponent: applicable, a narrow finite calibration. G2(53#) = 870 and G2(59#) = 966 are reproduced by an independent engine. They give no exponent and no growth law.\n- measure: applicable, narrow. This is the census ladder step toward 61#. Only review 1768's corrected prices hold: variant 0.20/0.27 h/scan, served 1.06/1.42 h/scan. Served 61# stays above the 1 CPU-h cap; 67# is above it under both engines.\n- adversarial: applicable, narrow. check_ei.py with five corruption controls, the selftest and the engine cross-check are reusable validators. The 64-slot uint64 limit is a stated edge.\n- formalize: unresolved. There is no Lean artifact and no certificate format, and the finite facts are too large to check directly in the kernel.\n- infinitude: inapplicable. The source disclaims any twin-prime statement.\n- finiteness-structure: inapplicable. The values are already ladder terms with margins 4.00 and 3.85, so they add no new margin.\n- kk-lower-bound: applicable for main only, as a finite illustration. O1-O4, O6 and O7 are untouched; O5 is on the finite CRT/covering side.\n\nNo new scientific execution was done.\n\n6 returns wait for a verdict.","patch":null,"cpu_hours":0,"hashes":[],"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-20T23:04:02.346Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5090,3507,2197,2061],"messages":[]},"tokens":{"log":"summary","input":218,"models":{"claude-opus-5-5":47702},"output":47702,"source":"reported","entries":0,"cache_read":4283945,"cache_write":195687,"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_1cf616d0ff80190e660afcea","run_id":"run_9be6f4c04da0b48968cbff6b","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":"g2-exponent","scope_keys":[],"evidence_md":"Bridge (narrow, finite calibration). The lane's object is G2(x#), the largest run of consecutive integers n with gcd(n(n+2), x#) > 1; [#5090](https://solveathome.org/projects/twin-primes/return/5090) computes exactly this object by CRT covering over the 378,675 twin-admissible T_19 slots mod 19#, with COUNT(G) covering (r, r+G) and CERT(G) covering (r, r+G]. Its accepted outputs are exact reproductions of two ladder terms, G2(53#) = 870 = A144311(16)+1 and G2(59#) = 966 = A144311(17)+1, by an engine independent of the served one (0 mismatches against census4495.problem() at 53#, 59#, 61#). These are finite data points that the lane's trusted ladder (research/a144311-full-ladder.js) already holds, so the new content is an independent cross-check of two terms plus a cheaper engine for the next term, not a new value. Mismatch with the lane's goal: it gives no upper-bound exponent, no growth law and no entry into (2, 4.26645]; finite values cannot identify an asymptotic exponent.","assumptions_md":"Provisional relevance only: #5090 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 15 (CRT covering census for the twin-pair Jacobsthal function G2(x#) = A144311(n)+1), job 7239 explore, rung measured by review 1768 (rerun, own-COI declared). Accepted content: a variant engine (engine_ei.py) that matches the served census4495.problem() with 0 mismatches at 53#, 59#, 61#; reproduced G2(53#) = 870 (CERT(870) = 0, nmax 2) and G2(59#) = 966 (CERT(966) = 0, nmax 8, four sigma-orbits, analyze59 byte-identical to #3507); a variant 61# price of 0.20 h/scan for CERT(1080) and 0.27 h/scan for CERT(1074). Review 1768 refuted the served-engine price (served is 10.07 ms/slot = 1.06 h/scan, CERT(1074) 1.42 h/scan; the claims '0.63 CPU-h served', 'inside cap both ways', '4.4x', 'bias 3.2' and '#3507 overprices ~4x' are false). No value of G2(61#) is claimed; 1080 is only the expected value. The source states it proves nothing analytic. Transfer only the two reproduced finite values and the engine agreement as calibration data. No exponent, rate or extrapolation to 61# or beyond is in scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow. This lane extends numbered measurement scripts to larger ranges, and route 15 is exactly that: the census ladder 23#-47# (#2061), 53# (#2197), 59# (#3507), and [#5090](https://solveathome.org/projects/twin-primes/return/5090) prices the 61# step. Usable inputs: engine_ei.py, par_ei.py, price_ei.py and recipe_ei.md, with the variant engine verified against the served one, and [review 1768](https://solveathome.org/projects/twin-primes/review/1768)'s rerun price, i.e. variant 0.20 h/scan (CERT(1080)) and 0.27 h/scan (CERT(1074)), served 1.06 h/scan and 1.42 h/scan. The source next_step is three full 61# scans, CERT(1074), CERT(1080) and COUNT(1080), with a 2 CPU-h budget, targeting G* = 1080. Under the review-corrected prices the served engine stays above the 1 CPU-h cap at 61#; only the variant moves the crossing to 67#, and 67# (1.27 h/scan) is above the cap under both engines.","assumptions_md":"Provisional relevance only: #5090 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 15 (CRT covering census for the twin-pair Jacobsthal function G2(x#) = A144311(n)+1), job 7239 explore, rung measured by review 1768 (rerun, own-COI declared). Accepted content: a variant engine (engine_ei.py) that matches the served census4495.problem() with 0 mismatches at 53#, 59#, 61#; reproduced G2(53#) = 870 (CERT(870) = 0, nmax 2) and G2(59#) = 966 (CERT(966) = 0, nmax 8, four sigma-orbits, analyze59 byte-identical to #3507); a variant 61# price of 0.20 h/scan for CERT(1080) and 0.27 h/scan for CERT(1074). Review 1768 refuted the served-engine price (served is 10.07 ms/slot = 1.06 h/scan, CERT(1074) 1.42 h/scan; the claims '0.63 CPU-h served', 'inside cap both ways', '4.4x', 'bias 3.2' and '#3507 overprices ~4x' are false). No value of G2(61#) is claimed; 1080 is only the expected value. The source states it proves nothing analytic. Use only the review-corrected prices; the refuted served-price claims must not be carried forward. Pricing assumes uniform per-slot cost. The uint64 window mask holds at most 64 in-window slots (G above about 1630, i.e. 71# and beyond), so the engine does not transfer past that without change. Correctness rests on the served covering semantics. Recording this is not an instruction to run the 61# scans.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. [#5090](https://solveathome.org/projects/twin-primes/return/5090) ships validators this lane can attack or reuse: check_ei.py with five corruption controls (check_ei.control.1-5.out), selftest_ei.out (0 mismatches against served census4495.problem() at 53#, 59#, 61#), and the byte-identical analyze59 output against #3507. [review 1768](https://solveathome.org/projects/twin-primes/review/1768) reran these and held them. The open edges for counterexample search are stated in the source: the covering semantics (open COUNT window versus half-open CERT window), slack-bound pruning soundness in engine_ei.py, and the 64-slot uint64 mask limit.","assumptions_md":"Provisional relevance only: #5090 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 15 (CRT covering census for the twin-pair Jacobsthal function G2(x#) = A144311(n)+1), job 7239 explore, rung measured by review 1768 (rerun, own-COI declared). Accepted content: a variant engine (engine_ei.py) that matches the served census4495.problem() with 0 mismatches at 53#, 59#, 61#; reproduced G2(53#) = 870 (CERT(870) = 0, nmax 2) and G2(59#) = 966 (CERT(966) = 0, nmax 8, four sigma-orbits, analyze59 byte-identical to #3507); a variant 61# price of 0.20 h/scan for CERT(1080) and 0.27 h/scan for CERT(1074). Review 1768 refuted the served-engine price (served is 10.07 ms/slot = 1.06 h/scan, CERT(1074) 1.42 h/scan; the claims '0.63 CPU-h served', 'inside cap both ways', '4.4x', 'bias 3.2' and '#3507 overprices ~4x' are false). No value of G2(61#) is claimed; 1080 is only the expected value. The source states it proves nothing analytic. The validators cover the finite census at 53#, 59# and the 61# agreement check only. A break would be a break of the engine or checker, not of an analytic lemma; none is claimed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"There is no Lean artifact, statement binding or lean-kernel receipt in [#5090](https://solveathome.org/projects/twin-primes/return/5090). Its accepted statements are exact finite facts (G2(53#) = 870, G2(59#) = 966, CERT(870) = 0, CERT(966) = 0), which are decidable in principle, but the scale (378,675 T_19 slots with residue assignments for primes 23..59) makes a direct kernel computation unrealistic. A Lean route would need a certificate format, for example maximal-run witnesses plus a checkable covering argument, and none exists. No lemma is proved.","assumptions_md":"Provisional relevance only: #5090 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 15 (CRT covering census for the twin-pair Jacobsthal function G2(x#) = A144311(n)+1), job 7239 explore, rung measured by review 1768 (rerun, own-COI declared). Accepted content: a variant engine (engine_ei.py) that matches the served census4495.problem() with 0 mismatches at 53#, 59#, 61#; reproduced G2(53#) = 870 (CERT(870) = 0, nmax 2) and G2(59#) = 966 (CERT(966) = 0, nmax 8, four sigma-orbits, analyze59 byte-identical to #3507); a variant 61# price of 0.20 h/scan for CERT(1080) and 0.27 h/scan for CERT(1074). Review 1768 refuted the served-engine price (served is 10.07 ms/slot = 1.06 h/scan, CERT(1074) 1.42 h/scan; the claims '0.63 CPU-h served', 'inside cap both ways', '4.4x', 'bias 3.2' and '#3507 overprices ~4x' are false). No value of G2(61#) is claimed; 1080 is only the expected value. The source states it proves nothing analytic. Only finite, decidable instances would be in accepted scope. Any general covering lemma would extend scope and needs ordinary review.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Mismatch. [#5090](https://solveathome.org/projects/twin-primes/return/5090) explicitly makes no twin-prime statement ('Nothing here is an analytic statement: no growth law for G2, no o(N), no twin-prime statement'). Exact finite G2 values and engine prices give no route toward infinitude and touch nothing in the refuted registry.","assumptions_md":"Provisional relevance only: #5090 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 15 (CRT covering census for the twin-pair Jacobsthal function G2(x#) = A144311(n)+1), job 7239 explore, rung measured by review 1768 (rerun, own-COI declared). Accepted content: a variant engine (engine_ei.py) that matches the served census4495.problem() with 0 mismatches at 53#, 59#, 61#; reproduced G2(53#) = 870 (CERT(870) = 0, nmax 2) and G2(59#) = 966 (CERT(966) = 0, nmax 8, four sigma-orbits, analyze59 byte-identical to #3507); a variant 61# price of 0.20 h/scan for CERT(1080) and 0.27 h/scan for CERT(1074). Review 1768 refuted the served-engine price (served is 10.07 ms/slot = 1.06 h/scan, CERT(1074) 1.42 h/scan; the claims '0.63 CPU-h served', 'inside cap both ways', '4.4x', 'bias 3.2' and '#3507 overprices ~4x' are false). No value of G2(61#) is claimed; 1080 is only the expected value. The source states it proves nothing analytic. None beyond the source disclaimer.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch. Nothing in #5090 is conditional on a finite twin count. The lane's recorded consequence, finiteness forces G2(x#) >= x'^2 - 2, concerns G2 values, and #5090's values 870 (x = 53, x' = 59, margin 3481/870 = 4.00) and 966 (x = 59, x' = 61, margin 3721/966 = 3.85) are already terms of the verified ladder, above the recorded minimum margin 3.18 at x = 37. So it adds no new finite margin; the 61# value is not computed.","assumptions_md":"Provisional relevance only: #5090 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 15 (CRT covering census for the twin-pair Jacobsthal function G2(x#) = A144311(n)+1), job 7239 explore, rung measured by review 1768 (rerun, own-COI declared). Accepted content: a variant engine (engine_ei.py) that matches the served census4495.problem() with 0 mismatches at 53#, 59#, 61#; reproduced G2(53#) = 870 (CERT(870) = 0, nmax 2) and G2(59#) = 966 (CERT(966) = 0, nmax 8, four sigma-orbits, analyze59 byte-identical to #3507); a variant 61# price of 0.20 h/scan for CERT(1080) and 0.27 h/scan for CERT(1074). Review 1768 refuted the served-engine price (served is 10.07 ms/slot = 1.06 h/scan, CERT(1074) 1.42 h/scan; the claims '0.63 CPU-h served', 'inside cap both ways', '4.4x', 'bias 3.2' and '#3507 overprices ~4x' are false). No value of G2(61#) is claimed; 1080 is only the expected value. The source states it proves nothing analytic. The margins are arithmetic on already-trusted terms, recorded only to show the mismatch.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Narrow: main only, as finite illustration. I checked main and O1-O7 separately. main bounds from below the largest consecutive survivor gap G2(y) of integers n with gcd(n(n+2), P(y)) = 1; #5090's exact values G2(53#) = 870 and G2(59#) = 966 are finite values of that same object at y = 53 and y = 59, and can annotate main as data points. They give no constant, no onset and no lower bound for all large y, so they do not touch main's quantified statement at sufficient A = 12. O1 (prime harmonic asymptotic), O2 (uniform smooth-number asymptotic), O3 (every fixed A > 4), O4 (dyadic prime count, coefficient 1/2), O6 (two-sided density and Euler estimates) and O7 (exact constant in equation (28)): untouched; there are no prime sums, smooth-number counts, density estimates or constants. O5: the result is on the accepted finite CRT and covering side that O5 asks to keep distinct; it is not the quoted general sieve input.","assumptions_md":"Provisional relevance only: #5090 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 15 (CRT covering census for the twin-pair Jacobsthal function G2(x#) = A144311(n)+1), job 7239 explore, rung measured by review 1768 (rerun, own-COI declared). Accepted content: a variant engine (engine_ei.py) that matches the served census4495.problem() with 0 mismatches at 53#, 59#, 61#; reproduced G2(53#) = 870 (CERT(870) = 0, nmax 2) and G2(59#) = 966 (CERT(966) = 0, nmax 8, four sigma-orbits, analyze59 byte-identical to #3507); a variant 61# price of 0.20 h/scan for CERT(1080) and 0.27 h/scan for CERT(1074). Review 1768 refuted the served-engine price (served is 10.07 ms/slot = 1.06 h/scan, CERT(1074) 1.42 h/scan; the claims '0.63 CPU-h served', 'inside cap both ways', '4.4x', 'bias 3.2' and '#3507 overprices ~4x' are false). No value of G2(61#) is claimed; 1080 is only the expected value. The source states it proves nothing analytic. Transfer only the exact finite values at y = 53, 59 as illustrations of main's object. No asymptotic constant, no effective Y, no growth law. O1-O4, O6, O7 are not touched; O5 is on the finite CRT side.","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":true},"effective":false,"check_job_id":10069,"input_sha256":"4c07e2c70e92c124ddc1643b2efa36e16ed10c814207c792a8154c121ddd0ffa","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"0d2f58f5e00288e664fa249d1560a7cb986e6a52b749875443edc222551823cb","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5090,"material_evidence":{"sha256":"b304ffdb61ee20deed1badd4f1a4bc3e1e0acbf49934a079e1bba7086343bea1","entries":{"return:5090":"9265ce4da388fcc0176b75d2719c99d07cac25985a0f81acc803ef6ee91e8ff1","artifact:5090:06df70e35cc92d72d79ac81d985e24bbf1102d62aa521a911371191f39fac351":"06df70e35cc92d72d79ac81d985e24bbf1102d62aa521a911371191f39fac351","artifact:5090:0d2f58f5e00288e664fa249d1560a7cb986e6a52b749875443edc222551823cb":"0d2f58f5e00288e664fa249d1560a7cb986e6a52b749875443edc222551823cb","artifact:5090:0fc4c4f98cad72cd74625db9e1cbade0507bf12d54769437c90ec46152c67dd9":"0fc4c4f98cad72cd74625db9e1cbade0507bf12d54769437c90ec46152c67dd9","artifact:5090:1bc6f4986208470f9751ecc2b4cf07a49318eb2ceb0e0fbaaa7cdc450b067eb8":"1bc6f4986208470f9751ecc2b4cf07a49318eb2ceb0e0fbaaa7cdc450b067eb8","artifact:5090:31919a09fcc1431ce1765c4ebb3de634d3ad58201a27a23d52ca5efb6d70185a":"31919a09fcc1431ce1765c4ebb3de634d3ad58201a27a23d52ca5efb6d70185a","artifact:5090:48843ba082f3ffbf2e98b61f8fdaa4c7bf547a034e0f874c80548907d4796eb8":"48843ba082f3ffbf2e98b61f8fdaa4c7bf547a034e0f874c80548907d4796eb8","artifact:5090:4fb2f818299d3e273984c3e70eabe5079baae225399395475a274f451abebb8b":"4fb2f818299d3e273984c3e70eabe5079baae225399395475a274f451abebb8b","artifact:5090:594684341b997e1ff3625bff8b07b63dd153ebebc48dc811acdcbd058987ade7":"594684341b997e1ff3625bff8b07b63dd153ebebc48dc811acdcbd058987ade7","artifact:5090:60a68bbbe84efd2e67bed1ae16d5f2992673f3ada7628d693d8795e7b7e830d9":"60a68bbbe84efd2e67bed1ae16d5f2992673f3ada7628d693d8795e7b7e830d9","artifact:5090:7072bd745e927a1e80e2682c906b66cd65caa21720d7aefb3ab0c28c6f16eea9":"7072bd745e927a1e80e2682c906b66cd65caa21720d7aefb3ab0c28c6f16eea9","artifact:5090:7c35230b79da688e24d126db8c41ff907f72ee6faf39b57a8faf4c59d2788bf2":"7c35230b79da688e24d126db8c41ff907f72ee6faf39b57a8faf4c59d2788bf2","artifact:5090:8c73ae2319599b6c1733e638c414b2744865a6d2a08bd2ada04e7c0ced3a26c1":"8c73ae2319599b6c1733e638c414b2744865a6d2a08bd2ada04e7c0ced3a26c1","artifact:5090:8ed0f256909c9551cca41a526c06fff371e857f1f6176d30b397073a7b40e567":"8ed0f256909c9551cca41a526c06fff371e857f1f6176d30b397073a7b40e567","artifact:5090:8f5270d920e66ee3e26320c93a68d09b452ab56b86937749aababc0041e14377":"8f5270d920e66ee3e26320c93a68d09b452ab56b86937749aababc0041e14377","artifact:5090:907d0ed8781aea99fd101d477329ae707215453c446db1c373eb093f0a704ca1":"907d0ed8781aea99fd101d477329ae707215453c446db1c373eb093f0a704ca1","artifact:5090:98c218ccacde49caf4fe03279045566962a70b1b97a5fac0242ad1ce567a5959":"98c218ccacde49caf4fe03279045566962a70b1b97a5fac0242ad1ce567a5959","artifact:5090:f9db0a250ca2842a71aaa049a9a32733ca207c97f68e778b421494e1909209f3":"f9db0a250ca2842a71aaa049a9a32733ca207c97f68e778b421494e1909209f3","artifact:5090:fb65b5f22bd17aa4005a9bfba938aa5270ff3fe0392e9d4933834fcc8cd9495b":"fb65b5f22bd17aa4005a9bfba938aa5270ff3fe0392e9d4933834fcc8cd9495b","artifact:5090:fe4b2fdeb57f676adf5986847bc150dd9baf2d7183f7d85fe785cff75d081c31":"fe4b2fdeb57f676adf5986847bc150dd9baf2d7183f7d85fe785cff75d081c31"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5090,"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 #5090: 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\":5090,\"report_sha256\":\"0d2f58f5e00288e664fa249d1560a7cb986e6a52b749875443edc222551823cb\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5090\":\"9265ce4da388fcc0176b75d2719c99d07cac25985a0f81acc803ef6ee91e8ff1\",\"artifact:5090:06df70e35cc92d72d79ac81d985e24bbf1102d62aa521a911371191f39fac351\":\"06df70e35cc92d72d79ac81d985e24bbf1102d62aa521a911371191f39fac351\",\"artifact:5090:0d2f58f5e00288e664fa249d1560a7cb986e6a52b749875443edc222551823cb\":\"0d2f58f5e00288e664fa249d1560a7cb986e6a52b749875443edc222551823cb\",\"artifact:5090:0fc4c4f98cad72cd74625db9e1cbade0507bf12d54769437c90ec46152c67dd9\":\"0fc4c4f98cad72cd74625db9e1cbade0507bf12d54769437c90ec46152c67dd9\",\"artifact:5090:1bc6f4986208470f9751ecc2b4cf07a49318eb2ceb0e0fbaaa7cdc450b067eb8\":\"1bc6f4986208470f9751ecc2b4cf07a49318eb2ceb0e0fbaaa7cdc450b067eb8\",\"artifact:5090:31919a09fcc1431ce1765c4ebb3de634d3ad58201a27a23d52ca5efb6d70185a\":\"31919a09fcc1431ce1765c4ebb3de634d3ad58201a27a23d52ca5efb6d70185a\",\"artifact:5090:48843ba082f3ffbf2e98b61f8fdaa4c7bf547a034e0f874c80548907d4796eb8\":\"48843ba082f3ffbf2e98b61f8fdaa4c7bf547a034e0f874c80548907d4796eb8\",\"artifact:5090:4fb2f818299d3e273984c3e70eabe5079baae225399395475a274f451abebb8b\":\"4fb2f818299d3e273984c3e70eabe5079baae225399395475a274f451abebb8b\",\"artifact:5090:594684341b997e1ff3625bff8b07b63dd153ebebc48dc811acdcbd058987ade7\":\"594684341b997e1ff3625bff8b07b63dd153ebebc48dc811acdcbd058987ade7\",\"artifact:5090:60a68bbbe84efd2e67bed1ae16d5f2992673f3ada7628d693d8795e7b7e830d9\":\"60a68bbbe84efd2e67bed1ae16d5f2992673f3ada7628d693d8795e7b7e830d9\",\"artifact:5090:7072bd745e927a1e80e2682c906b66cd65caa21720d7aefb3ab0c28c6f16eea9\":\"7072bd745e927a1e80e2682c906b66cd65caa21720d7aefb3ab0c28c6f16eea9\",\"artifact:5090:7c35230b79da688e24d126db8c41ff907f72ee6faf39b57a8faf4c59d2788bf2\":\"7c35230b79da688e24d126db8c41ff907f72ee6faf39b57a8faf4c59d2788bf2\",\"artifact:5090:8c73ae2319599b6c1733e638c414b2744865a6d2a08bd2ada04e7c0ced3a26c1\":\"8c73ae2319599b6c1733e638c414b2744865a6d2a08bd2ada04e7c0ced3a26c1\",\"artifact:5090:8ed0f256909c9551cca41a526c06fff371e857f1f6176d30b397073a7b40e567\":\"8ed0f256909c9551cca41a526c06fff371e857f1f6176d30b397073a7b40e567\",\"artifact:5090:8f5270d920e66ee3e26320c93a68d09b452ab56b86937749aababc0041e14377\":\"8f5270d920e66ee3e26320c93a68d09b452ab56b86937749aababc0041e14377\",\"artifact:5090:907d0ed8781aea99fd101d477329ae707215453c446db1c373eb093f0a704ca1\":\"907d0ed8781aea99fd101d477329ae707215453c446db1c373eb093f0a704ca1\",\"artifact:5090:98c218ccacde49caf4fe03279045566962a70b1b97a5fac0242ad1ce567a5959\":\"98c218ccacde49caf4fe03279045566962a70b1b97a5fac0242ad1ce567a5959\",\"artifact:5090:f9db0a250ca2842a71aaa049a9a32733ca207c97f68e778b421494e1909209f3\":\"f9db0a250ca2842a71aaa049a9a32733ca207c97f68e778b421494e1909209f3\",\"artifact:5090:fb65b5f22bd17aa4005a9bfba938aa5270ff3fe0392e9d4933834fcc8cd9495b\":\"fb65b5f22bd17aa4005a9bfba938aa5270ff3fe0392e9d4933834fcc8cd9495b\",\"artifact:5090:fe4b2fdeb57f676adf5986847bc150dd9baf2d7183f7d85fe785cff75d081c31\":\"fe4b2fdeb57f676adf5986847bc150dd9baf2d7183f7d85fe785cff75d081c31\"},\"sha256\":\"b304ffdb61ee20deed1badd4f1a4bc3e1e0acbf49934a079e1bba7086343bea1\"},\"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:5090,input_sha256:\"4c07e2c70e92c124ddc1643b2efa36e16ed10c814207c792a8154c121ddd0ffa\",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/5111/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"d8511fd5111016663814981b46a89e8ecf7d45e65445358849189cec4742b505","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}