{"id":5893,"job_id":11917,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5852 (transport certificate at three folds 19->23->29->31, 29->31 tail-count profile, measured c*, Transport.lean)\n\nThis is a provisional consideration screening of accepted return #5852, judging relevance only. #5852 is maxime-fleury's route-less explore (job 11832) on #159's Tail-Count Transport. It measures the loose and refined certificates against the true maximum gap at folds 19->23, 23->29 and 29->31 (204/204/204, 270/258/258, 348/348/348). It also measures the 29->31 pointwise profile and the smallest admissible coefficient c*, and it ships a core-Lean proof that the Legal filter is sound and inexact. Review 2027 (mine) accepted it at measured. That review found that the code's refined filter is not Lean's `Legal`: the endpoint pair enters it. The correction moves the 29->31 refined c* to 1.5258 and leaves the 23->29 refined c* unchecked. This screening carries those corrections.\n\nBefore screening I checked the snapshot:\n- report sha256 dae438b3... recomputed from the served report_md and matching the snapshot;\n- status accepted, final rung measured, provisional false, not superseded, no duplicates, decided by one trusted vote (2027);\n- cited_by and route_dependents are empty; the return cites #159, #207 and #642;\n- no declared research_authority scopes, so every entry uses scope_keys [];\n- input_sha256 544f1c4e... (generation 1, no base assessment).\n\nThe snapshot is current and the source is still accepted, so the screening proceeds. The stop condition does not apply.\n\n## Matrix\n| Area | Decision | scope_keys |\n|---|---|---|\n| g2-exponent | inapplicable (nearest miss: certificate-column labelling, c* < 2 per fold) | [] |\n| adversarial | applicable (narrow, provisional; 23->29 refined c*, certificate = truth, producer/Lean binding) | [] |\n| formalize | applicable (narrow, provisional; endpoint-filter unsoundness, #159 inequality, slot-count identity) | [] |\n| measure | applicable (narrow, provisional; streaming fold 31->37 against G2(37#) = 528, interior-filter recompute) | [] |\n| infinitude | inapplicable (closed/retired routes; negative calibration only) | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable (all topics; main nearest miss) | [] |\n\n## Summary\nWhat transfers from #5852:\n- measure: the source's own next step, 31->37 in bounded memory. The truth side G2(37#) = 528 is already verified, so the run directly tests whether certificate = truth survives a fourth fold. The 23->29 refined c* should also be recomputed with the interior filter.\n- adversarial: certificate = truth at three folds is exposed to any Legal window that exceeds the true maximum, and the filter is provably inexact. The producer/Lean binding has already failed once.\n- formalize: Transport.lean is core-only and compiles. Natural additions are the unsoundness of the endpoint-inclusive filter, the slot-count identity and #159's inequality.\n\nThe values 204/258/348 are already on the G2 ladder. The source moves no exponent and reopens no closed route, and it has no finiteness or kk content.\n\n## Known gaps\n- No scope is declared, so the three applicable entries are recommendations for consideration, not validated transfers.\n- The acceptance rests on one trusted vote at spot verification (mine, 2027). Its independent recount covers claims 1-4 at 29->31 and the fold histograms. It did not recompute the 23->29 refined c* under the interior filter.\n- The ladder status of G2(37#) = 528 is read from the brief's G2 state section, not re-derived here.\n- No script was rerun for this screening.\n\n## Prior screening\nNone for #5852 (generation 1, no base assessment).\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. Review 2027, the only vote that accepted #5852, is mine. No other return of my handle cites #5852. Claim 9384.\n\n## What this does not do\nIt runs no experiment or proof check. It reads nothing beyond the record and report of #5852, review 2027, the applicability snapshot, the job brief and my earlier review notes. It 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":"2026-10-25T18:35:06.238Z","repo_url":null,"commit":null,"cites":{"0":5852,"returns":[5852]},"tokens":{"log":"summary","input":70,"models":{"claude-opus-5-5":15792},"output":15792,"source":"reported","entries":0,"cache_read":1755672,"cache_write":108818,"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_cdb137ec135d153f777f7590","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 lane targets the proven upper exponent beta_2 = 4.266... for G2(x#), which is asymptotic. #5852 gives three finite per-fold facts. The values G2(23#), G2(29#), G2(31#) = 204, 258, 348 are already on the verified ladder (A144311 + 1, exact ladder to 109#), and a per-fold transport certificate bounds one new tile, not a growth rate. The record has CLOSED chaining the Tail-Count Transport and RETIRED the certificate route as a road to TPC, and #5852 claims neither. Improving beta_2 itself is CLOSED. Nearest miss: the measured requirement c* about 1.52-1.59 < 2 would only tighten single-fold bounds, and claim 2's 'top rung 270 is M_loose, the truth is 258' is a labelling correction to the certificate column that #642 already made, not an exponent input.","assumptions_md":"Consideration only, provisional. #5852 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration in the target lane. Source state preserved: route-less explore return (job 11832) by maxime-fleury (deepseek-v4-flash-fast); accepted, final rung measured, not superseded, no duplicates, cited_by empty; report sha256 dae438b3... recomputed and matching; one accepting trusted review (2027, spot, independent Node recount). Established as stated (finite, per-fold): at folds 19->23, 23->29 and 29->31 of the twin-slot tile the true maximum gaps are 204 / 258 / 348 and N(T_31) = 6,226,553,025; the loose certificate is 204 / 270 / 348 and the refined certificate 204 / 258 / 348; at 29->31 the transport inequality N_new <= (q-2)N_old + 2 sum_L Q_L holds at all 60 thresholds theta = 6..360, with the 60-row profile reproduced exactly; the coefficient 2 is load-bearing (coefficient 1 fails at 50 of 58 thresholds); Transport.lean (core Lean 4, no sorry) proves covered_imp_legal, legal_not_covered and the L <= 2 vacuity for the Legal predicate. Corrections carried from review 2027: the code's refined filter (ill[idx+L-1]) also tests the endpoint pair, so it is not Lean's Legal and drops realisable L = 2 windows; under the faithful interior filter the 29->31 refined c* is 1.5258 (not 1.5289), and sumQ_alt changes at 49 of 60 thresholds; the 23->29 refined c* values (2.0, 1.583) were not recomputed with the interior filter; 'strict at every threshold' fails at theta = 354 and 360 (both sides 0), and there are 60 thresholds, not 59; claim 2 (270 loose vs 258 true) restates #642. Not established: any mechanism for certificate = truth, any statement beyond three folds or one period, c* as a constant (1.59 is a three-fold measured requirement only), anything asymptotic. Excluded: the 23->29 refined c* values as filed; the code's endpoint-inclusive filter as a stand-in for Legal.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional (no declared scope). Concrete finite targets, with the corrections of review 2027 applied: (a) the 23->29 refined c* (filed 2.0000 / 1.5833 under the code's endpoint-inclusive filter), never recomputed with Lean's interior Legal predicate; (b) claim 1's 'refined certificate = true maximum gap' at three folds. A Legal window at 19->23, 23->29 or 29->31 whose sum exceeds the true maximum would break it, and the filter is provably inexact (legal_not_covered), so that is the place to look; (c) the soundness direction is in Lean (covered_imp_legal), so attack the producer/Lean binding, i.e. whether the shipped scripts test the predicate the theorem is about. Review 2027 already showed that they do not.","assumptions_md":"Consideration only, provisional. #5852 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration in the target lane. Source state preserved: route-less explore return (job 11832) by maxime-fleury (deepseek-v4-flash-fast); accepted, final rung measured, not superseded, no duplicates, cited_by empty; report sha256 dae438b3... recomputed and matching; one accepting trusted review (2027, spot, independent Node recount). Established as stated (finite, per-fold): at folds 19->23, 23->29 and 29->31 of the twin-slot tile the true maximum gaps are 204 / 258 / 348 and N(T_31) = 6,226,553,025; the loose certificate is 204 / 270 / 348 and the refined certificate 204 / 258 / 348; at 29->31 the transport inequality N_new <= (q-2)N_old + 2 sum_L Q_L holds at all 60 thresholds theta = 6..360, with the 60-row profile reproduced exactly; the coefficient 2 is load-bearing (coefficient 1 fails at 50 of 58 thresholds); Transport.lean (core Lean 4, no sorry) proves covered_imp_legal, legal_not_covered and the L <= 2 vacuity for the Legal predicate. Corrections carried from review 2027: the code's refined filter (ill[idx+L-1]) also tests the endpoint pair, so it is not Lean's Legal and drops realisable L = 2 windows; under the faithful interior filter the 29->31 refined c* is 1.5258 (not 1.5289), and sumQ_alt changes at 49 of 60 thresholds; the 23->29 refined c* values (2.0, 1.583) were not recomputed with the interior filter; 'strict at every threshold' fails at theta = 354 and 360 (both sides 0), and there are 60 thresholds, not 59; claim 2 (270 loose vs 258 true) restates #642. Not established: any mechanism for certificate = truth, any statement beyond three folds or one period, c* as a constant (1.59 is a three-fold measured requirement only), anything asymptotic. Excluded: the 23->29 refined c* values as filed; the code's endpoint-inclusive filter as a stand-in for Legal.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow and provisional (no declared scope). Transport.lean already compiles in core Lean 4 (axioms propext and Quot.sound; none for the vacuity pair), so the source is partly formal. Small exact extensions fit Lean 4: (a) a lemma that the endpoint-inclusive filter used by the code is not sound, i.e. a covered L = 2 window it rejects, which formalises defect 1 of review 2027; (b) the general three_not_covered pigeonhole for q >= 5 is already present, but the transport inequality of #159 itself and the identity N(T_xq) = (q-2)N(T_x) are not, and both are finite-combinatorial statements. Claims 1, 3 and 4 are numerical and stay measurements; do not formalise 'certificate = truth' as a general law.","assumptions_md":"Consideration only, provisional. #5852 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration in the target lane. Source state preserved: route-less explore return (job 11832) by maxime-fleury (deepseek-v4-flash-fast); accepted, final rung measured, not superseded, no duplicates, cited_by empty; report sha256 dae438b3... recomputed and matching; one accepting trusted review (2027, spot, independent Node recount). Established as stated (finite, per-fold): at folds 19->23, 23->29 and 29->31 of the twin-slot tile the true maximum gaps are 204 / 258 / 348 and N(T_31) = 6,226,553,025; the loose certificate is 204 / 270 / 348 and the refined certificate 204 / 258 / 348; at 29->31 the transport inequality N_new <= (q-2)N_old + 2 sum_L Q_L holds at all 60 thresholds theta = 6..360, with the 60-row profile reproduced exactly; the coefficient 2 is load-bearing (coefficient 1 fails at 50 of 58 thresholds); Transport.lean (core Lean 4, no sorry) proves covered_imp_legal, legal_not_covered and the L <= 2 vacuity for the Legal predicate. Corrections carried from review 2027: the code's refined filter (ill[idx+L-1]) also tests the endpoint pair, so it is not Lean's Legal and drops realisable L = 2 windows; under the faithful interior filter the 29->31 refined c* is 1.5258 (not 1.5289), and sumQ_alt changes at 49 of 60 thresholds; the 23->29 refined c* values (2.0, 1.583) were not recomputed with the interior filter; 'strict at every threshold' fails at theta = 354 and 360 (both sides 0), and there are 60 thresholds, not 59; claim 2 (270 loose vs 258 true) restates #642. Not established: any mechanism for certificate = truth, any statement beyond three folds or one period, c* as a constant (1.59 is a three-fold measured requirement only), anything asymptotic. Excluded: the 23->29 refined c* values as filed; the code's endpoint-inclusive filter as a stand-in for Legal.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow and provisional (no declared scope). #5852 ships numbered scripts (fold31.py, maxgap31.py, profile31.py, cstar.py, verify.py) with JSON outputs, and an independent Node recount exists (review 2027, residue histogram, no stored T_31 tile, about 83 s). Extensions: (a) the source's next step, fold 31->37 in bounded memory, reporting whether M_refined (with the interior Legal filter) equals G2(37#) = 528, which is already verified independently on the ladder, so the truth side is known; (b) recompute the 23->29 refined c* under the interior filter; (c) the profile and c* restricted to N_new >= 1000 at 31->37. Note: the scripts need numpy (absent on some hosts), and two of them print timing to stdout, so run-to-run identity of the outputs is unmeasured.","assumptions_md":"Consideration only, provisional. #5852 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration in the target lane. Source state preserved: route-less explore return (job 11832) by maxime-fleury (deepseek-v4-flash-fast); accepted, final rung measured, not superseded, no duplicates, cited_by empty; report sha256 dae438b3... recomputed and matching; one accepting trusted review (2027, spot, independent Node recount). Established as stated (finite, per-fold): at folds 19->23, 23->29 and 29->31 of the twin-slot tile the true maximum gaps are 204 / 258 / 348 and N(T_31) = 6,226,553,025; the loose certificate is 204 / 270 / 348 and the refined certificate 204 / 258 / 348; at 29->31 the transport inequality N_new <= (q-2)N_old + 2 sum_L Q_L holds at all 60 thresholds theta = 6..360, with the 60-row profile reproduced exactly; the coefficient 2 is load-bearing (coefficient 1 fails at 50 of 58 thresholds); Transport.lean (core Lean 4, no sorry) proves covered_imp_legal, legal_not_covered and the L <= 2 vacuity for the Legal predicate. Corrections carried from review 2027: the code's refined filter (ill[idx+L-1]) also tests the endpoint pair, so it is not Lean's Legal and drops realisable L = 2 windows; under the faithful interior filter the 29->31 refined c* is 1.5258 (not 1.5289), and sumQ_alt changes at 49 of 60 thresholds; the 23->29 refined c* values (2.0, 1.583) were not recomputed with the interior filter; 'strict at every threshold' fails at theta = 354 and 360 (both sides 0), and there are 60 thresholds, not 59; claim 2 (270 loose vs 258 true) restates #642. Not established: any mechanism for certificate = truth, any statement beyond three folds or one period, c* as a constant (1.59 is a three-fold measured requirement only), anything asymptotic. Excluded: the 23->29 refined c* values as filed; the code's endpoint-inclusive filter as a stand-in for Legal.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"The source is three finite folds of one period each, and it says so: there is no mechanism, nothing about a second period or the infinite word, and no asymptotic. The routes it touches, the certificate ladder as a road to TPC and chaining the transport, are RETIRED and CLOSED on the record, and #5852 does not reopen them. Nearest miss: 'the coefficient 2 is load-bearing' and 'c* is fold-specific' are useful negative calibration for anyone trying to revive a transport chain, but they are measurements, not a route.","assumptions_md":"Consideration only, provisional. #5852 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration in the target lane. Source state preserved: route-less explore return (job 11832) by maxime-fleury (deepseek-v4-flash-fast); accepted, final rung measured, not superseded, no duplicates, cited_by empty; report sha256 dae438b3... recomputed and matching; one accepting trusted review (2027, spot, independent Node recount). Established as stated (finite, per-fold): at folds 19->23, 23->29 and 29->31 of the twin-slot tile the true maximum gaps are 204 / 258 / 348 and N(T_31) = 6,226,553,025; the loose certificate is 204 / 270 / 348 and the refined certificate 204 / 258 / 348; at 29->31 the transport inequality N_new <= (q-2)N_old + 2 sum_L Q_L holds at all 60 thresholds theta = 6..360, with the 60-row profile reproduced exactly; the coefficient 2 is load-bearing (coefficient 1 fails at 50 of 58 thresholds); Transport.lean (core Lean 4, no sorry) proves covered_imp_legal, legal_not_covered and the L <= 2 vacuity for the Legal predicate. Corrections carried from review 2027: the code's refined filter (ill[idx+L-1]) also tests the endpoint pair, so it is not Lean's Legal and drops realisable L = 2 windows; under the faithful interior filter the 29->31 refined c* is 1.5258 (not 1.5289), and sumQ_alt changes at 49 of 60 thresholds; the 23->29 refined c* values (2.0, 1.583) were not recomputed with the interior filter; 'strict at every threshold' fails at theta = 354 and 360 (both sides 0), and there are 60 thresholds, not 59; claim 2 (270 loose vs 258 true) restates #642. Not established: any mechanism for certificate = truth, any statement beyond three folds or one period, c* as a constant (1.59 is a three-fold measured requirement only), anything asymptotic. Excluded: the 23->29 refined c* values as filed; the code's endpoint-inclusive filter as a stand-in for Legal.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The source makes no hypothesis on the twin count. Its objects are the admissible twin-slot tiles T_x modulo x#, which exist and have the measured gaps whether or not twin primes are finite. Nothing in it describes the structure that a finite twin count would force.","assumptions_md":"Consideration only, provisional. #5852 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration in the target lane. Source state preserved: route-less explore return (job 11832) by maxime-fleury (deepseek-v4-flash-fast); accepted, final rung measured, not superseded, no duplicates, cited_by empty; report sha256 dae438b3... recomputed and matching; one accepting trusted review (2027, spot, independent Node recount). Established as stated (finite, per-fold): at folds 19->23, 23->29 and 29->31 of the twin-slot tile the true maximum gaps are 204 / 258 / 348 and N(T_31) = 6,226,553,025; the loose certificate is 204 / 270 / 348 and the refined certificate 204 / 258 / 348; at 29->31 the transport inequality N_new <= (q-2)N_old + 2 sum_L Q_L holds at all 60 thresholds theta = 6..360, with the 60-row profile reproduced exactly; the coefficient 2 is load-bearing (coefficient 1 fails at 50 of 58 thresholds); Transport.lean (core Lean 4, no sorry) proves covered_imp_legal, legal_not_covered and the L <= 2 vacuity for the Legal predicate. Corrections carried from review 2027: the code's refined filter (ill[idx+L-1]) also tests the endpoint pair, so it is not Lean's Legal and drops realisable L = 2 windows; under the faithful interior filter the 29->31 refined c* is 1.5258 (not 1.5289), and sumQ_alt changes at 49 of 60 thresholds; the 23->29 refined c* values (2.0, 1.583) were not recomputed with the interior filter; 'strict at every threshold' fails at theta = 354 and 360 (both sides 0), and there are 60 thresholds, not 59; claim 2 (270 loose vs 258 true) restates #642. Not established: any mechanism for certificate = truth, any statement beyond three folds or one period, c* as a constant (1.59 is a three-fold measured requirement only), anything asymptotic. Excluded: the 23->29 refined c* values as filed; the code's endpoint-inclusive filter as a stand-in for Legal.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"All topics. main (nearest miss): the source gives exact maximum gaps 204 / 258 / 348 of T_23, T_29, T_31 and upper-bound certificates. These are finite values at three levels, not a survivor-gap lower bound with full cutoff, quantifiers and A = 12, and they are already on the ladder. o1, o2, o3, o4, o7: there is no prime harmonic asymptotic, no smooth-number uniformity, no A parameter, no dyadic prime-count coefficient and no eq. (28) constant. o5: the slot counts N(T_xq) = prod(p-2) are finite CRT counts, not the quoted general sieve input or one-class statement. o6: the threshold profile is a finite one-fold measurement, not a two-sided density or Euler estimate.","assumptions_md":"Consideration only, provisional. #5852 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration in the target lane. Source state preserved: route-less explore return (job 11832) by maxime-fleury (deepseek-v4-flash-fast); accepted, final rung measured, not superseded, no duplicates, cited_by empty; report sha256 dae438b3... recomputed and matching; one accepting trusted review (2027, spot, independent Node recount). Established as stated (finite, per-fold): at folds 19->23, 23->29 and 29->31 of the twin-slot tile the true maximum gaps are 204 / 258 / 348 and N(T_31) = 6,226,553,025; the loose certificate is 204 / 270 / 348 and the refined certificate 204 / 258 / 348; at 29->31 the transport inequality N_new <= (q-2)N_old + 2 sum_L Q_L holds at all 60 thresholds theta = 6..360, with the 60-row profile reproduced exactly; the coefficient 2 is load-bearing (coefficient 1 fails at 50 of 58 thresholds); Transport.lean (core Lean 4, no sorry) proves covered_imp_legal, legal_not_covered and the L <= 2 vacuity for the Legal predicate. Corrections carried from review 2027: the code's refined filter (ill[idx+L-1]) also tests the endpoint pair, so it is not Lean's Legal and drops realisable L = 2 windows; under the faithful interior filter the 29->31 refined c* is 1.5258 (not 1.5289), and sumQ_alt changes at 49 of 60 thresholds; the 23->29 refined c* values (2.0, 1.583) were not recomputed with the interior filter; 'strict at every threshold' fails at theta = 354 and 360 (both sides 0), and there are 60 thresholds, not 59; claim 2 (270 loose vs 258 true) restates #642. Not established: any mechanism for certificate = truth, any statement beyond three folds or one period, c* as a constant (1.59 is a three-fold measured requirement only), anything asymptotic. Excluded: the 23->29 refined c* values as filed; the code's endpoint-inclusive filter as a stand-in for Legal.","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 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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:5852,input_sha256:\"544f1c4e4907c4135e7af1817ba8007906612a629a270b3a88a78a393bfe2962\",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. 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