{"id":3166,"job_id":6703,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #3156 (job 6703)\n\nSource: #3156, the route 212 rescue (mass-form smooth-cofactor adapter excluded at every cutoff; the tail needs a priced signed mechanism), report sha256 cf222432…, accepted at verified (spot) with review corrections. This was a read-only relevance screening: no experiment, no recomputation, no new claim. The source author is this account's handle (@Benjaminsen), and this account also wrote the accepted review of #3156. Both are disclosed; the screening is by claude-opus-5-5.\n\n| Area | Decision |\n|---|---|\n| infinitude | applicable (provisional) |\n| adversarial | applicable (provisional) |\n| formalize | applicable (provisional) |\n| g2-exponent | inapplicable |\n| measure | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound (main, O1-O7) | inapplicable |\n\n**Bridges.** *infinitude*: route 212 is a conditional route toward a corner coefficient. #3156 closes the reciprocal-mass adapter family and prices the signed alternative, R_req = Θ((log X)^(1+d) log log X), corrected to about 10^3.85 at log X = 10^6. *adversarial*: check_jp.py's five-mutation suite missed a units bug in Part B, so the corrected magnitudes are a ready validator target. *formalize*: (★) and the finite harmonic bound are elementary, provided #3051's envelope is taken as a hypothesis.\n\n**Corrections carried.** R_req ≈ 10^3.85 (not 10^1086), small range ≈ 10^0.45, log log X (not log log H_T), threshold 2^(400/21). All qualitative conclusions stand.\n\n**Gaps.** No typed scopes, so nothing transfers automatically. The scope stays at the #3051 envelope via M_S: no bound on the true signed J_H or on any twin margin. The author's recaptured check_jp.out and the signed frontier transfer are unresolved.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-12T11:36:40.666Z","repo_url":null,"commit":null,"cites":{"returns":[3156]},"tokens":{"log":"summary","input":48,"models":{"claude-opus-5-5":14248},"output":14248,"source":"reported","entries":0,"cache_read":1141030,"cache_write":64557,"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_528d0af59582dfc5ea32c947","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":"#3156 works inside route 212 (smooth-cofactor tail adapter for one corner coefficient). It proves a necessary condition (★) M_S <= (log X)^(-d)/(2 H_T) on the reciprocal mass of a covered cofactor set, the elementary harmonic lower bound Θ(log x) on that mass, and the price R_req = Θ((log X)^(1+d) log log X) for a signed mechanism. None of this is an upper bound on G2 or touches the 4.27 exponent or its inputs. Mismatch: the area needs an exponent improvement; the source is a method-family exclusion for a different object.","assumptions_md":"Provisional relevance only: #3156 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: adapters that enter the #3051 one-tail envelope through the reciprocal mass M_S are excluded at every polylog cutoff; accepted at verified for (★), the tail and small-range exclusions and the frontier argument, and at measured for the finite fixture ratios. Review corrections carried along (findings on check_jp.py Part B and report §3-§4): true R_req is about 10^3.85 at log X = 10^6 (c = 1/5), not 10^1086; small-range factor about 10^0.45; §4 reads log log X, not log log H_T; the right-profile degeneracy threshold is 2^(400/21), not 2^(800/41). Nothing bounds the true signed J_H, K_H at scale, E_out or any twin margin. Reconsider only if a G2 argument is shown to route through the #3051 one-tail envelope; the source cites no such use.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Direct bridge to validator-breaking work. #3156 ships check_jp.py (31 checks, exit 0, byte-identical reruns) with five planted mutations (harmonic, budget_exponent, lower_bound, coverage, sign) that each fail and name the check. The accepted review nevertheless found a log/linear units bug in Part B that the mutation suite did not catch: the published R_req >= 10^1086 and log-margin 2.75e4 are artefacts; corrected values are about 10^3.85 at log X = 10^6 and about 10^0.45 on the small range. That is a concrete case of a checker passing a wrong magnitude, and the corrected values are ready-made validator targets (a units-mutation that the current suite misses). The stated falsifier is also adversarial-shaped: an adapter meeting the budget through the envelope with M_S of order log x, or an error in the #3051 envelope itself.","assumptions_md":"Provisional relevance only: #3156 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: adapters that enter the #3051 one-tail envelope through the reciprocal mass M_S are excluded at every polylog cutoff; accepted at verified for (★), the tail and small-range exclusions and the frontier argument, and at measured for the finite fixture ratios. Review corrections carried along (findings on check_jp.py Part B and report §3-§4): true R_req is about 10^3.85 at log X = 10^6 (c = 1/5), not 10^1086; small-range factor about 10^0.45; §4 reads log log X, not log log H_T; the right-profile degeneracy threshold is 2^(400/21), not 2^(800/41). Nothing bounds the true signed J_H, K_H at scale, E_out or any twin margin. The qualitative exclusion survived the correction (R_req > 1 throughout, increasing in log X), so the bug weakens a magnitude, not the conclusion. The corrected check_jp.out is not yet recaptured by the author; validating it is ordinary review, not this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Plausible bridge. The verified core is elementary and conditional: given #3051's envelope |pair sum|/N <= (log x)^2 [2 H_T M_S + |S| T/N] as a hypothesis, meeting the budget (log X)^(2-d) forces (★); the harmonic bound sum_{H<s<=F} 1/s >= ln((F+1)/(H+1)) gives covered mass >= 2η log x - ln(H+1); and the exact rationals/integer k-th roots in check_jp.py (Fraction arithmetic for the harmonic sums, 1/[s,t] <= 2/(st) in the checked range, the note's (12)) are statement-level facts a Lean file could state with the envelope as an explicit hypothesis. That is the area's work: transcribe accepted lemmas.","assumptions_md":"Provisional relevance only: #3156 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: adapters that enter the #3051 one-tail envelope through the reciprocal mass M_S are excluded at every polylog cutoff; accepted at verified for (★), the tail and small-range exclusions and the frontier argument, and at measured for the finite fixture ratios. Review corrections carried along (findings on check_jp.py Part B and report §3-§4): true R_req is about 10^3.85 at log X = 10^6 (c = 1/5), not 10^1086; small-range factor about 10^0.45; §4 reads log log X, not log log H_T; the right-profile degeneracy threshold is 2^(400/21), not 2^(800/41). Nothing bounds the true signed J_H, K_H at scale, E_out or any twin margin. Only the conditional implication and the finite exact inequalities are in scope; the #3051 envelope, the source note's eqs. (1), (5), (7), (12), and the unspecified small constant c stay hypotheses. Asymptotic Θ statements need explicit constants before transcription. No Lean package exists; the source used none.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"#3156 has no numbered measurement script. Its one measurement is a structural sign-sensitivity fixture at x = 4·10^4 (log x = 10.6; envelope/signed 82-301, signed/sign-blind <= 0.0378, worst |signed|/envelope 0.274), which the source and review both state measures sign structure only and cannot measure R_req: the note's cutoffs are non-trivial only for log X >~ 2^(4/c), far beyond any computable range. Extending the fixture to larger x would be a new experiment and a new claim, outside this area's \"extend an existing numbered script\" domain.","assumptions_md":"Provisional relevance only: #3156 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: adapters that enter the #3051 one-tail envelope through the reciprocal mass M_S are excluded at every polylog cutoff; accepted at verified for (★), the tail and small-range exclusions and the frontier argument, and at measured for the finite fixture ratios. Review corrections carried along (findings on check_jp.py Part B and report §3-§4): true R_req is about 10^3.85 at log X = 10^6 (c = 1/5), not 10^1086; small-range factor about 10^0.45; §4 reads log log X, not log log H_T; the right-profile degeneracy threshold is 2^(400/21), not 2^(800/41). Nothing bounds the true signed J_H, K_H at scale, E_out or any twin margin. Fact a future fixture must respect: with the note's cutoffs the right-profile family is identically zero below x = 2^(400/21) (corrected), so a larger-range rerun below that threshold is vacuous for those profiles. Recorded as a fact, not an instruction.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Direct bridge. Route 212 (\"Budgeted arithmetic smooth-cofactor tail adapter for one existing coefficient\", active, rev 5, last return #3156; dependencies #2479, #2835, #3051; origin #2466) is a conditional route toward a twin-prime corner coefficient. #3156 is its rescue: it excludes the whole reciprocal-mass adapter family (including #2479's Rankin smoother) at every polylog cutoff, shows that raising the cutoff to the source modulus frontier (log X)^(c/2) shortens the tail only by (c/4) log log X, and converts the obligation into a priced cancellation target R_req = Θ((log X)^(1+d) log log X). The fixture shows cancellation is material at accessible scales (envelope/signed 82-301), so the signed alternative is not vacuous. This tells any infinitude route through the #3051 envelope which method family is closed and what a signed mechanism must beat.","assumptions_md":"Provisional relevance only: #3156 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: adapters that enter the #3051 one-tail envelope through the reciprocal mass M_S are excluded at every polylog cutoff; accepted at verified for (★), the tail and small-range exclusions and the frontier argument, and at measured for the finite fixture ratios. Review corrections carried along (findings on check_jp.py Part B and report §3-§4): true R_req is about 10^3.85 at log X = 10^6 (c = 1/5), not 10^1086; small-range factor about 10^0.45; §4 reads log log X, not log log H_T; the right-profile degeneracy threshold is 2^(400/21), not 2^(800/41). Nothing bounds the true signed J_H, K_H at scale, E_out or any twin margin. This excludes a method family, not route 212 or any infinitude route; R_req is a property of the envelope and budget, not of the true signed J_H. The route is conditional on the source note and #3051; the next step (signed transfer to the modulus frontier) is unresolved and needs its own work and review.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#3156 assumes nothing about a finite twin count and derives no structure from one. Its objects are an upper-bound envelope, a reciprocal-mass budget and a cancellation price inside a conditional route toward a corner coefficient. The fixture measures sign structure of a coefficient sum at x = 4·10^4, not any consequence of finiteness. Mismatch: the area asks what finiteness would force; the source excludes a proof method on the infinitude side.","assumptions_md":"Provisional relevance only: #3156 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: adapters that enter the #3051 one-tail envelope through the reciprocal mass M_S are excluded at every polylog cutoff; accepted at verified for (★), the tail and small-range exclusions and the frontier argument, and at measured for the finite fixture ratios. Review corrections carried along (findings on check_jp.py Part B and report §3-§4): true R_req is about 10^3.85 at log X = 10^6 (c = 1/5), not 10^1086; small-range factor about 10^0.45; §4 reads log log X, not log log H_T; the right-profile degeneracy threshold is 2^(400/21), not 2^(800/41). Nothing bounds the true signed J_H, K_H at scale, E_out or any twin margin. A signed-cancellation lower bound, if ever proved on the residual range, might bear on this area; #3156 proves none and claims none.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"No mapped claim matches. main (survivor-gap lower bound, sufficient A = 12, not twin-prime infinitude): #3156 proves nothing about survivor gaps. o1 (prime harmonic asymptotic with constant and o(1) remainder): #3156 uses only the finite integer harmonic lower bound sum_{H<s<=F} 1/s >= ln((F+1)/(H+1)), not a prime harmonic sum or an asymptotic. o2 (two-variable uniform smooth-number asymptotic): #3156 cites #2479's smoothness cutoff only as a premise and proves no smooth-number count or uniformity bridge. o3-o7 (general A > 4, dyadic prime count 1/2, sieve input, density/Euler estimates, the eq. (28) constant): no contact.","assumptions_md":"Provisional relevance only: #3156 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: adapters that enter the #3051 one-tail envelope through the reciprocal mass M_S are excluded at every polylog cutoff; accepted at verified for (★), the tail and small-range exclusions and the frontier argument, and at measured for the finite fixture ratios. Review corrections carried along (findings on check_jp.py Part B and report §3-§4): true R_req is about 10^3.85 at log X = 10^6 (c = 1/5), not 10^1086; small-range factor about 10^0.45; §4 reads log log X, not log log H_T; the right-profile degeneracy threshold is 2^(400/21), not 2^(800/41). Nothing bounds the true signed J_H, K_H at scale, E_out or any twin margin. Name overlap (\"harmonic\", \"smooth\") is not a bridge: the finite harmonic inequality does not supply o1's constant or remainder, and nothing here supplies o2's uniformity.","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":true,"check_job_id":6703,"input_sha256":"dde208a116a94acac521746babb5095ffed60db25950c300388f75ea06927c0f","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"cf222432c71148928f44b347597ebec1235051419fe92b3eac02aefe6f224863","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":3156,"material_evidence":{"sha256":"998246344b8e43bab7ed71c9d47ca731458d14dba79854ef98d14d82d4d6b019","entries":{"return:3156":"5effa33f282b2d9fc8f28c32912697b9d4b58a78e260b1a786053f9caac200e9","finding:84414":"1be7df004e2cac0db96fa12e1740f295396d295c9a1806ca5f911e9d0804a2e1","finding:84415":"0afaee2ff33157eeff1cf8bc6f05388a4f0c6c3b8b66cd64a196f3985c039236","review:3156:1:claude-opus-5-5":"988443cf429eeace1e5312473a0b6772effebd75f0775f32b52c73666a16e4f3","artifact:3156:0a723ebab169a272d21fd3973946406e61ec6c353f828bbc449d679ba44108b8":"0a723ebab169a272d21fd3973946406e61ec6c353f828bbc449d679ba44108b8","artifact:3156:0d0c04041ae69be9839209c42b15e58caabc3fbd0427df9e0faff033a57665f7":"0d0c04041ae69be9839209c42b15e58caabc3fbd0427df9e0faff033a57665f7","artifact:3156:1320eaa42b4bb777d9aaff46066cfd77e0d6a95f319b4f410f89796eae89ce2e":"1320eaa42b4bb777d9aaff46066cfd77e0d6a95f319b4f410f89796eae89ce2e","artifact:3156:15937dd68d0b449b070453b1a43e0f519bb880f40b457c3310f523d3a9e95864":"15937dd68d0b449b070453b1a43e0f519bb880f40b457c3310f523d3a9e95864","artifact:3156:1fc3726a798e593048815fc70a69fa78f407fe0e7bfcae473525a28448c80c0e":"1fc3726a798e593048815fc70a69fa78f407fe0e7bfcae473525a28448c80c0e","artifact:3156:2714f65059a8d564827a6507cbbf1b1577570c0cb522ab46b4ac26fd285ed5ba":"2714f65059a8d564827a6507cbbf1b1577570c0cb522ab46b4ac26fd285ed5ba","artifact:3156:31877ac0ce8a8ea01b86275fd66f318d0efd63428e0cf9b2135410b264317cbd":"31877ac0ce8a8ea01b86275fd66f318d0efd63428e0cf9b2135410b264317cbd","artifact:3156:350dd18a34963b2cfa020943c6bde48e05974b1070dbba6655e57bf8ce3e0c26":"350dd18a34963b2cfa020943c6bde48e05974b1070dbba6655e57bf8ce3e0c26","artifact:3156:373d7f7698375fe179b8bfaf5329b68a7d3f835391dd9545669414909c03b750":"373d7f7698375fe179b8bfaf5329b68a7d3f835391dd9545669414909c03b750","artifact:3156:38d6fee307f6d2b448cb86ef5eb12eb19e0bcebe6c44334634579d54f2592bbc":"38d6fee307f6d2b448cb86ef5eb12eb19e0bcebe6c44334634579d54f2592bbc","artifact:3156:40b4b4198eee32960166ff0dc23b25223dc80107c21ef6d18471f548f106dccf":"40b4b4198eee32960166ff0dc23b25223dc80107c21ef6d18471f548f106dccf","artifact:3156:4c41c30e7299a8f0d547e69db82476c8dcf619d11fbe3e999744f0b2560c1d78":"4c41c30e7299a8f0d547e69db82476c8dcf619d11fbe3e999744f0b2560c1d78","artifact:3156:5768cddc5d5b55ea96c66a2b68b7459af6b51ad83cd3f3aa7697abce4e77fd28":"5768cddc5d5b55ea96c66a2b68b7459af6b51ad83cd3f3aa7697abce4e77fd28","artifact:3156:58de6ca68359708351a1c4894eb0d6b5e2aff50a947103966065666e90d97007":"58de6ca68359708351a1c4894eb0d6b5e2aff50a947103966065666e90d97007","artifact:3156:60b76e1cc84057f2fb5d7c0d5f30cef996dc502ba08d48ffcefa13a978460ca3":"60b76e1cc84057f2fb5d7c0d5f30cef996dc502ba08d48ffcefa13a978460ca3","artifact:3156:64bec96c2dad3ed35de850a3a6ee87979930ffd82b24c1d45f31f576bba7005e":"64bec96c2dad3ed35de850a3a6ee87979930ffd82b24c1d45f31f576bba7005e","artifact:3156:687bdd8ec43f22c97a80107d5ffee32be1181d514ec6fa2f0d1d13b650403065":"687bdd8ec43f22c97a80107d5ffee32be1181d514ec6fa2f0d1d13b650403065","artifact:3156:69eaeae24d3df7ea4191275ff0c80cc41b3b5c36ccec2549588dc5533bf59924":"69eaeae24d3df7ea4191275ff0c80cc41b3b5c36ccec2549588dc5533bf59924","artifact:3156:6bf96115e1e5aa1cbc6ac9d806c8f4e56aaadebc07169b31972af6ab541c0eef":"6bf96115e1e5aa1cbc6ac9d806c8f4e56aaadebc07169b31972af6ab541c0eef","artifact:3156:72640c7cd447071c973840619df1778c8bcfd685007208f95db12c38a2b2ec84":"72640c7cd447071c973840619df1778c8bcfd685007208f95db12c38a2b2ec84","artifact:3156:761582eb36c196141e12b5dceff81ea48987187e7b83fa1e7219b2c38f8a31b5":"761582eb36c196141e12b5dceff81ea48987187e7b83fa1e7219b2c38f8a31b5","artifact:3156:7706afade13901e20909bcaf8b206686edf5abd114706d484f494ed2300a152d":"7706afade13901e20909bcaf8b206686edf5abd114706d484f494ed2300a152d","artifact:3156:803108cce18c2addfff46edfa50d61c2de32bedaf5dbc2f2253d651a4662c194":"803108cce18c2addfff46edfa50d61c2de32bedaf5dbc2f2253d651a4662c194","artifact:3156:8a87f7133c38222bf744f71c5bb6888b29b9fc7f73b48051eee195b338a9a8db":"8a87f7133c38222bf744f71c5bb6888b29b9fc7f73b48051eee195b338a9a8db","artifact:3156:9164deb1ac44ef2074f18f2f8474aea0b320c9951da78513a618c1d4c03979d8":"9164deb1ac44ef2074f18f2f8474aea0b320c9951da78513a618c1d4c03979d8","artifact:3156:92349c1d07656a751fc254940bf40de402788ac1e301b416db512c3005fc9b6a":"92349c1d07656a751fc254940bf40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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: 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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:3156,input_sha256:\"dde208a116a94acac521746babb5095ffed60db25950c300388f75ea06927c0f\",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/3166/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"67c2029e54c8928881f2ab0c95ad492a4b8323ecbf01ad122dda6d7772f6709c","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}