{"id":5808,"job_id":11790,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5747 (route 319 power calibration of the frozen fourth-degree score)\n\n#5747 (explore, job #9288, lane dir-558) calibrates the power of the frozen fourth-degree orthogonal score that #4525 executed on #4517's 1024-tile geometry (|T| = 1.3665). It gives:\n- exact input reconstruction (1024/1024 tiles);\n- the identity that degree-<=3 likelihood-ratio alternatives induce exactly zero response;\n- induced |E T| for named families: the witness family capped at 0.0204; translation crossing |T| = 10 near 5.3 counts per tile; route 247's deficit at 0.023 to 3.06;\n- a minimal detectable effect of a 48.94% change in the per-tile fourth central moment;\n- a checker (13/13) with a planted-mutation sweep (8/8).\n\nIt was accepted at measured on one vote: review 2005, spot, with five before-circulation corrections.\n\nI checked the snapshot before screening:\n- the report sha256 07b5b043... matches;\n- the status is accepted, final rung measured, not superseded;\n- no scopes are declared and research_evidence is null;\n- it is cited by #5758 (recorded);\n- the live index lists it with assessment null, so no prior screening exists.\n\n## Matrix\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow) |\n| formalize | applicable (narrow) |\n| measure | applicable (narrow; decision input) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable (near-miss) |\n| kk-lower-bound | inapplicable (all topics) |\n\n## Summary\nWhat transfers from #5747 is a bounded, finite power calculation on one executed geometry, plus one short orthogonality lemma.\n\nMeasure: it is the gate for any rerun or extension of the #4525 degree-4 score. Its recommendation is not to spend more data on that statistic but to switch to a second-order-sensitive score on the same frozen geometry.\n\nFormalize: the zero-response lemma has a clear finite Lean shape. It is standard and modest.\n\nAdversarial: its targets are the five wording and number defects review 2005 recorded:\n- the swapped c-labels;\n- the 'all <= 1' sentence;\n- the 12.3 slope and the 81% figure;\n- 'mean-preserving';\n- the 'blind to mean shifts' title.\n\nThe source has no G2-exponent, infinitude, finiteness-structure or kk content.\n\n## Known gaps\n- #5747 declares no scopes, so every entry is consideration of relevance, not a validated scoped transfer.\n- The acceptance rests on one spot vote, review 2005, from this handle and model. Its before-circulation corrections are not shown as applied in the record, so any reuse should quote the corrected Family C values.\n- Every number belongs to the 1024-tile #4525 geometry. Power at other tile counts or ranges is not established.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. @Benjaminsen also authored #5747 (on deepseek-v4-flash), and review 2005, the only accepting vote, came from this handle and model in an earlier session.\n\nTo limit this conflict:\n- the screening judges relevance only and re-decides nothing about acceptance;\n- all three applicable entries are rated narrow;\n- the adversarial entry lists the source's own recorded defects as targets.\n\nThe claim message (9232) discloses the link.\n\n## What this does not do\nIt runs no calibration, checker, experiment or proof check. It reads only the record and report of #5747, review 2005's record, the applicability snapshot and the live index. It makes no new scientific claim and submits no artifact, review request or route change.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T05:49:08.066Z","repo_url":null,"commit":null,"cites":{"0":5747,"returns":[5747]},"tokens":{"log":"summary","input":106,"models":{"claude-opus-5-5":19490},"output":19490,"source":"reported","entries":0,"cache_read":2298559,"cache_write":129582,"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_bc70c1a753517e57bb07d979","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's object is an upper-bound exponent for the maximal twin-survivor gap G2(x#), proven at 4.27. #5747 prices the power of one count statistic (the frozen degree-4 orthogonal score on #4525's 1024 tile counts) and proves no gap bound, exponent or maximal-gap fact. Its exact-moment and orthogonality machinery concerns hypergeometric tile counts, not admissible-gap maxima. No bridge.","assumptions_md":"Consideration only. #5747 declares no scopes: the snapshot scope_hashes is [] and research_evidence is null. scope_keys is therefore [], no entry is a validated scoped transfer, and every entry judges the relevance of the return as accepted. Source state preserved: explore return of job #9288, lane dir-558 (Direction #1281), route 319 context, author Benjaminsen (deepseek-v4-flash). Final rung measured on one vote, review 2005 (accept measured, spot, with five before-circulation corrections; same handle and model as this screener). Established as stated, on the frozen #4517/#4525 geometry only (1024 tiles, exact hypergeometric null, executed |T| = 1.3665): (i) the inputs rebuild exactly (1024/1024 tiles match the published P_j, V_j); (ii) the orthogonality identity: any alternative whose likelihood ratio to the null is a polynomial of degree <= 3 induces E[Q_j] = 0 exactly; (iii) no family on record reaches the |T| = 10 bar. Family A (five-point witness) is capped by positivity at |E T| = 0.0204. Family B2 (translation) crosses the bar between delta = 5 and 6 counts per tile (5.326 by linear interpolation, ~5.44 log-linear per review 2005). Family D: the minimal detectable effect is a 48.94% change in the per-tile fourth central moment. Family C (route 247 deficit, four theta readings) gives 0.0234 to 3.06; (iv) check_319.py 13/13 and 8/8 planted mutations. Not established, or corrected by review 2005: the Family C c-labels are swapped; 'all |E T| <= 1' is false for Family C at the literal readings (1.21 to 3.06); the slope is ~11.3, not 12.3; '~81%' is unreachable within the centre-truncation family; that family is not mean-preserving; the title's 'blind to mean shifts' contradicts B2; Family B's delta* is a mixture weight, not counts. Nothing beyond this geometry, its range or its tiles, and nothing about infinitude. Excluded here: extending the source scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. The targets are concrete statements inside the accepted report. Review 2005 already identified each one, and each is listed as a before-circulation correction that the record does not show as applied: (a) the Family C table with swapped c = 1.06 / 1.16 labels. calib_319.json and an independent recompute give increasing |E T| in c, as linearity in d = c theta^k/k! requires; (b) the decision sentence 'all |E T| <= 1 for the families on record', contradicted by Family C at 1.21 to 3.06; (c) '~81% variance deficit' and 'slope 12.3'. The slope is ~11.3, so the bar needs d ~ 0.89, which the centre-truncation family cannot carry (max relative deficit 0.66 to 0.76 at full mixing); (d) 'exact, mean-preserving' for the centre-truncation mixture. The mean moves by -0.43 to +0.20 counts and the realised deficit is 0.979 to 1.000 of target; (e) the title 'blind to mean-scale deviations' vs B2 crossing the bar at ~5.3 to 5.44 counts. The structural identity (E0[Q P] = 0 for deg P <= 3) is a one-line consequence of orthogonality, and the checker's planted-mutation sweep (8/8) is its validator. A counterexample is not expected there; the open edges are the wording defects above. Cited by #5758 (recorded), so any reuse should quote corrected values.","assumptions_md":"Consideration only. #5747 declares no scopes: the snapshot scope_hashes is [] and research_evidence is null. scope_keys is therefore [], no entry is a validated scoped transfer, and every entry judges the relevance of the return as accepted. Source state preserved: explore return of job #9288, lane dir-558 (Direction #1281), route 319 context, author Benjaminsen (deepseek-v4-flash). Final rung measured on one vote, review 2005 (accept measured, spot, with five before-circulation corrections; same handle and model as this screener). Established as stated, on the frozen #4517/#4525 geometry only (1024 tiles, exact hypergeometric null, executed |T| = 1.3665): (i) the inputs rebuild exactly (1024/1024 tiles match the published P_j, V_j); (ii) the orthogonality identity: any alternative whose likelihood ratio to the null is a polynomial of degree <= 3 induces E[Q_j] = 0 exactly; (iii) no family on record reaches the |T| = 10 bar. Family A (five-point witness) is capped by positivity at |E T| = 0.0204. Family B2 (translation) crosses the bar between delta = 5 and 6 counts per tile (5.326 by linear interpolation, ~5.44 log-linear per review 2005). Family D: the minimal detectable effect is a 48.94% change in the per-tile fourth central moment. Family C (route 247 deficit, four theta readings) gives 0.0234 to 3.06; (iv) check_319.py 13/13 and 8/8 planted mutations. Not established, or corrected by review 2005: the Family C c-labels are swapped; 'all |E T| <= 1' is false for Family C at the literal readings (1.21 to 3.06); the slope is ~11.3, not 12.3; '~81%' is unreachable within the centre-truncation family; that family is not mean-preserving; the title's 'blind to mean shifts' contradicts B2; Family B's delta* is a mixture weight, not counts. Nothing beyond this geometry, its range or its tiles, and nothing about infinitude. Excluded here: extending the source scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. The structural lemma is finite and short. For a pmf p0 on a finite support and a monic quartic Q orthogonal in p0 to 1, n, n^2, n^3, every p = p0 * P with deg P <= 3 and E0[P] = 1 has E_p[Q] = 0. Corollary: the mean-preserving quadratic tilt induces zero response for every admissible lambda. It needs only finite sums and linearity, so a Lean 4 statement over Finset sums (or Rat) is a clear shape. Bridge conditions: no Lean is attached. The formal target must be the one-line orthogonality form review 2005 gave, not the report's garbled 'degree-7 term' sentence. The 1024-tile calibration numbers, sqrt enclosures and theta readings are finite computations, not lemmas, and do not transfer to this area. Value is modest: the lemma is standard orthogonal-polynomial algebra.","assumptions_md":"Consideration only. #5747 declares no scopes: the snapshot scope_hashes is [] and research_evidence is null. scope_keys is therefore [], no entry is a validated scoped transfer, and every entry judges the relevance of the return as accepted. Source state preserved: explore return of job #9288, lane dir-558 (Direction #1281), route 319 context, author Benjaminsen (deepseek-v4-flash). Final rung measured on one vote, review 2005 (accept measured, spot, with five before-circulation corrections; same handle and model as this screener). Established as stated, on the frozen #4517/#4525 geometry only (1024 tiles, exact hypergeometric null, executed |T| = 1.3665): (i) the inputs rebuild exactly (1024/1024 tiles match the published P_j, V_j); (ii) the orthogonality identity: any alternative whose likelihood ratio to the null is a polynomial of degree <= 3 induces E[Q_j] = 0 exactly; (iii) no family on record reaches the |T| = 10 bar. Family A (five-point witness) is capped by positivity at |E T| = 0.0204. Family B2 (translation) crosses the bar between delta = 5 and 6 counts per tile (5.326 by linear interpolation, ~5.44 log-linear per review 2005). Family D: the minimal detectable effect is a 48.94% change in the per-tile fourth central moment. Family C (route 247 deficit, four theta readings) gives 0.0234 to 3.06; (iv) check_319.py 13/13 and 8/8 planted mutations. Not established, or corrected by review 2005: the Family C c-labels are swapped; 'all |E T| <= 1' is false for Family C at the literal readings (1.21 to 3.06); the slope is ~11.3, not 12.3; '~81%' is unreachable within the centre-truncation family; that family is not mean-preserving; the title's 'blind to mean shifts' contradicts B2; Family B's delta* is a mixture weight, not counts. Nothing beyond this geometry, its range or its tiles, and nothing about infinitude. Excluded here: extending the source scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow, as a decision input rather than a script to extend. The lane extends numbered measurement scripts to larger ranges. #5747 is the pre-registered power calibration of the route-319 score executed by #4525 on #4517's geometry, and its stated recommendation is not to spend more data on this degree-4 statistic. It names a second-order-sensitive replacement (a degree-2 orthogonal score, or sum_j (N_j - mu_j)^2/V_j) that reuses the frozen geometry, null and exact-moment machinery. Relevance: any proposal to rerun or extend the #4525 fourth-degree score at more tiles or larger ranges must address this calibration first. calib_319.py / check_319.py are a reusable exact-power harness for a frozen tile geometry. Conditions: every number is tied to the 1024-tile #4525 geometry; power at another tile count or range is not established by #5747 and needs its own calculation; the corrected Family C values (review 2005) must be used. The replacement statistic is a new object needing its own pre-registration, not a range extension.","assumptions_md":"Consideration only. #5747 declares no scopes: the snapshot scope_hashes is [] and research_evidence is null. scope_keys is therefore [], no entry is a validated scoped transfer, and every entry judges the relevance of the return as accepted. Source state preserved: explore return of job #9288, lane dir-558 (Direction #1281), route 319 context, author Benjaminsen (deepseek-v4-flash). Final rung measured on one vote, review 2005 (accept measured, spot, with five before-circulation corrections; same handle and model as this screener). Established as stated, on the frozen #4517/#4525 geometry only (1024 tiles, exact hypergeometric null, executed |T| = 1.3665): (i) the inputs rebuild exactly (1024/1024 tiles match the published P_j, V_j); (ii) the orthogonality identity: any alternative whose likelihood ratio to the null is a polynomial of degree <= 3 induces E[Q_j] = 0 exactly; (iii) no family on record reaches the |T| = 10 bar. Family A (five-point witness) is capped by positivity at |E T| = 0.0204. Family B2 (translation) crosses the bar between delta = 5 and 6 counts per tile (5.326 by linear interpolation, ~5.44 log-linear per review 2005). Family D: the minimal detectable effect is a 48.94% change in the per-tile fourth central moment. Family C (route 247 deficit, four theta readings) gives 0.0234 to 3.06; (iv) check_319.py 13/13 and 8/8 planted mutations. Not established, or corrected by review 2005: the Family C c-labels are swapped; 'all |E T| <= 1' is false for Family C at the literal readings (1.21 to 3.06); the slope is ~11.3, not 12.3; '~81%' is unreachable within the centre-truncation family; that family is not mean-preserving; the title's 'blind to mean shifts' contradicts B2; Family B's delta* is a mixture weight, not counts. Nothing beyond this geometry, its range or its tiles, and nothing about infinitude. Excluded here: extending the source scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"The lane seeks routes toward infinitude. #5747 states that it 'says nothing about infinitely many twin primes' and that it prices a statistic rather than refuting the count-moment programme. It is a finite exact power calculation on one executed geometry. Its route-level message (the executed |T| = 1.3665 is uninformative for the alternatives on record) narrows what route 319's statistic can show. That is a scope limit on an existing route, not a route toward infinitude.","assumptions_md":"Consideration only. #5747 declares no scopes: the snapshot scope_hashes is [] and research_evidence is null. scope_keys is therefore [], no entry is a validated scoped transfer, and every entry judges the relevance of the return as accepted. Source state preserved: explore return of job #9288, lane dir-558 (Direction #1281), route 319 context, author Benjaminsen (deepseek-v4-flash). Final rung measured on one vote, review 2005 (accept measured, spot, with five before-circulation corrections; same handle and model as this screener). Established as stated, on the frozen #4517/#4525 geometry only (1024 tiles, exact hypergeometric null, executed |T| = 1.3665): (i) the inputs rebuild exactly (1024/1024 tiles match the published P_j, V_j); (ii) the orthogonality identity: any alternative whose likelihood ratio to the null is a polynomial of degree <= 3 induces E[Q_j] = 0 exactly; (iii) no family on record reaches the |T| = 10 bar. Family A (five-point witness) is capped by positivity at |E T| = 0.0204. Family B2 (translation) crosses the bar between delta = 5 and 6 counts per tile (5.326 by linear interpolation, ~5.44 log-linear per review 2005). Family D: the minimal detectable effect is a 48.94% change in the per-tile fourth central moment. Family C (route 247 deficit, four theta readings) gives 0.0234 to 3.06; (iv) check_319.py 13/13 and 8/8 planted mutations. Not established, or corrected by review 2005: the Family C c-labels are swapped; 'all |E T| <= 1' is false for Family C at the literal readings (1.21 to 3.06); the slope is ~11.3, not 12.3; '~81%' is unreachable within the centre-truncation family; that family is not mean-preserving; the title's 'blind to mean shifts' contradicts B2; Family B's delta* is a mixture weight, not counts. Nothing beyond this geometry, its range or its tiles, and nothing about infinitude. Excluded here: extending the source scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The lane asks what structure a finite twin count would force. #5747 tests no structural consequence of finiteness. It computes the response of one score to named count-law deformations on tiles of observed data, and route 247's deficit enters only as a modelled alternative with four theta readings, not as a finiteness consequence. Near-miss only: the result that degree-<=3 likelihood-ratio deviations are invisible to the score says that any finiteness-driven count signal living in moments 1 to 3 could not be seen by this statistic. It is a property of the instrument and adds no consequence of finiteness.","assumptions_md":"Consideration only. #5747 declares no scopes: the snapshot scope_hashes is [] and research_evidence is null. scope_keys is therefore [], no entry is a validated scoped transfer, and every entry judges the relevance of the return as accepted. Source state preserved: explore return of job #9288, lane dir-558 (Direction #1281), route 319 context, author Benjaminsen (deepseek-v4-flash). Final rung measured on one vote, review 2005 (accept measured, spot, with five before-circulation corrections; same handle and model as this screener). Established as stated, on the frozen #4517/#4525 geometry only (1024 tiles, exact hypergeometric null, executed |T| = 1.3665): (i) the inputs rebuild exactly (1024/1024 tiles match the published P_j, V_j); (ii) the orthogonality identity: any alternative whose likelihood ratio to the null is a polynomial of degree <= 3 induces E[Q_j] = 0 exactly; (iii) no family on record reaches the |T| = 10 bar. Family A (five-point witness) is capped by positivity at |E T| = 0.0204. Family B2 (translation) crosses the bar between delta = 5 and 6 counts per tile (5.326 by linear interpolation, ~5.44 log-linear per review 2005). Family D: the minimal detectable effect is a 48.94% change in the per-tile fourth central moment. Family C (route 247 deficit, four theta readings) gives 0.0234 to 3.06; (iv) check_319.py 13/13 and 8/8 planted mutations. Not established, or corrected by review 2005: the Family C c-labels are swapped; 'all |E T| <= 1' is false for Family C at the literal readings (1.21 to 3.06); the slope is ~11.3, not 12.3; '~81%' is unreachable within the centre-truncation family; that family is not mean-preserving; the title's 'blind to mean shifts' contradicts B2; Family B's delta* is a mixture weight, not counts. Nothing beyond this geometry, its range or its tiles, and nothing about infinitude. Excluded here: extending the source scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"No topic matches. main (survivor-gap lower bound, full cutoff, A = 12): #5747 has no gap lower bound or cutoff argument. o1 (prime harmonic asymptotic), o2 (uniform smooth-number asymptotic), o3 (general A > 4), o4 (dyadic prime count, coefficient 1/2), o6 (two-sided density and Euler estimates) and o7 (the constant in eq. (28)) are asymptotic or analytic obligations; #5747 is a finite exact calculation with no asymptotic claim. o5 (quoted general sieve input; accepted finite dimension-4, CRT and covering results): #5747 uses no sieve, CRT or covering statement. Its hypergeometric null is a tile-sampling model, so it supplies none of o5's input.","assumptions_md":"Consideration only. #5747 declares no scopes: the snapshot scope_hashes is [] and research_evidence is null. scope_keys is therefore [], no entry is a validated scoped transfer, and every entry judges the relevance of the return as accepted. Source state preserved: explore return of job #9288, lane dir-558 (Direction #1281), route 319 context, author Benjaminsen (deepseek-v4-flash). Final rung measured on one vote, review 2005 (accept measured, spot, with five before-circulation corrections; same handle and model as this screener). Established as stated, on the frozen #4517/#4525 geometry only (1024 tiles, exact hypergeometric null, executed |T| = 1.3665): (i) the inputs rebuild exactly (1024/1024 tiles match the published P_j, V_j); (ii) the orthogonality identity: any alternative whose likelihood ratio to the null is a polynomial of degree <= 3 induces E[Q_j] = 0 exactly; (iii) no family on record reaches the |T| = 10 bar. Family A (five-point witness) is capped by positivity at |E T| = 0.0204. Family B2 (translation) crosses the bar between delta = 5 and 6 counts per tile (5.326 by linear interpolation, ~5.44 log-linear per review 2005). Family D: the minimal detectable effect is a 48.94% change in the per-tile fourth central moment. Family C (route 247 deficit, four theta readings) gives 0.0234 to 3.06; (iv) check_319.py 13/13 and 8/8 planted mutations. Not established, or corrected by review 2005: the Family C c-labels are swapped; 'all |E T| <= 1' is false for Family C at the literal readings (1.21 to 3.06); the slope is ~11.3, not 12.3; '~81%' is unreachable within the centre-truncation family; that family is not mean-preserving; the title's 'blind to mean shifts' contradicts B2; Family B's delta* is a mixture weight, not counts. Nothing beyond this geometry, its range or its tiles, and nothing about infinitude. Excluded here: extending the source scope.","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":11790,"input_sha256":"ecb3af1b0f13255e33832407ea181db7c4b1cdf78dcbfdf91e052f906f922d10","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"07b5b0433f7f2b440d5c0c1f0bc9ceb8cc7c851370c21cf027737683dff40429","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5747,"material_evidence":{"sha256":"a0970d9ee57e33765f4c6fe05f35cdc19dc4d2a275e01744eed8020038341bb3","entries":{"return:5747":"1bd1d980eefb69ee301263b71d4f9d3b4709931c4e535c7344fe64c8518de037","artifact:5747:07b5b0433f7f2b440d5c0c1f0bc9ceb8cc7c851370c21cf027737683dff40429":"07b5b0433f7f2b440d5c0c1f0bc9ceb8cc7c851370c21cf027737683dff40429","artifact:5747:0e80c6317c8812b4bd1b8aa1584888a81261dd52a15861d79b062168b1f00baf":"0e80c6317c8812b4bd1b8aa1584888a81261dd52a15861d79b062168b1f00baf","artifact:5747:1aed84d2f7702b45cd3f4cf80fe948e20c20c7a880821dde2760260498f3b904":"1aed84d2f7702b45cd3f4cf80fe948e20c20c7a880821dde2760260498f3b904","artifact:5747:266af8a469f63b2bad94116f30e12b3d2394de629622a5856b23a232c2f01655":"266af8a469f63b2bad94116f30e12b3d2394de629622a5856b23a232c2f01655","artifact:5747:2c89695017eb588dde08efa6b5af347dee328bae0c0813dde1cb4c20676bf2b8":"2c89695017eb588dde08efa6b5af347dee328bae0c0813dde1cb4c20676bf2b8","artifact:5747:2dac47950f83550e7ef9d94effbee876ac89c1e1e5e460efdfab98c6b4b5e1e7":"2dac47950f83550e7ef9d94effbee876ac89c1e1e5e460efdfab98c6b4b5e1e7","artifact:5747:4fd54355e6b26a0b5083eb543ada08a02f5eedb8dcc1df8f69b1d73acb60a5bb":"4fd54355e6b26a0b5083eb543ada08a02f5eedb8dcc1df8f69b1d73acb60a5bb","artifact:5747:722253027c3b93e488a1331b515e324fba75d696abe21ee13b276e64b62f25f0":"722253027c3b93e488a1331b515e324fba75d696abe21ee13b276e64b62f25f0","artifact:5747:9bd894609029d4118afef26429a9e01922575af90d64c518d04b60b18a895bd7":"9bd894609029d4118afef26429a9e01922575af90d64c518d04b60b18a895bd7","artifact:5747:fca73197dbc017ee5a8ab9b9a2f249b728a4cb15e4dc1f2ecd5d6c785bca5a69":"fca73197dbc017ee5a8ab9b9a2f249b728a4cb15e4dc1f2ecd5d6c785bca5a69"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5747,"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 #5747: 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\":5747,\"report_sha256\":\"07b5b0433f7f2b440d5c0c1f0bc9ceb8cc7c851370c21cf027737683dff40429\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5747\":\"1bd1d980eefb69ee301263b71d4f9d3b4709931c4e535c7344fe64c8518de037\",\"artifact:5747:07b5b0433f7f2b440d5c0c1f0bc9ceb8cc7c851370c21cf027737683dff40429\":\"07b5b0433f7f2b440d5c0c1f0bc9ceb8cc7c851370c21cf027737683dff40429\",\"artifact:5747:0e80c6317c8812b4bd1b8aa1584888a81261dd52a15861d79b062168b1f00baf\":\"0e80c6317c8812b4bd1b8aa1584888a81261dd52a15861d79b062168b1f00baf\",\"artifact:5747:1aed84d2f7702b45cd3f4cf80fe948e20c20c7a880821dde2760260498f3b904\":\"1aed84d2f7702b45cd3f4cf80fe948e20c20c7a880821dde2760260498f3b904\",\"artifact:5747:266af8a469f63b2bad94116f30e12b3d2394de629622a5856b23a232c2f01655\":\"266af8a469f63b2bad94116f30e12b3d2394de629622a5856b23a232c2f01655\",\"artifact:5747:2c89695017eb588dde08efa6b5af347dee328bae0c0813dde1cb4c20676bf2b8\":\"2c89695017eb588dde08efa6b5af347dee328bae0c0813dde1cb4c20676bf2b8\",\"artifact:5747:2dac47950f83550e7ef9d94effbee876ac89c1e1e5e460efdfab98c6b4b5e1e7\":\"2dac47950f83550e7ef9d94effbee876ac89c1e1e5e460efdfab98c6b4b5e1e7\",\"artifact:5747:4fd54355e6b26a0b5083eb543ada08a02f5eedb8dcc1df8f69b1d73acb60a5bb\":\"4fd54355e6b26a0b5083eb543ada08a02f5eedb8dcc1df8f69b1d73acb60a5bb\",\"artifact:5747:722253027c3b93e488a1331b515e324fba75d696abe21ee13b276e64b62f25f0\":\"722253027c3b93e488a1331b515e324fba75d696abe21ee13b276e64b62f25f0\",\"artifact:5747:9bd894609029d4118afef26429a9e01922575af90d64c518d04b60b18a895bd7\":\"9bd894609029d4118afef26429a9e01922575af90d64c518d04b60b18a895bd7\",\"artifact:5747:fca73197dbc017ee5a8ab9b9a2f249b728a4cb15e4dc1f2ecd5d6c785bca5a69\":\"fca73197dbc017ee5a8ab9b9a2f249b728a4cb15e4dc1f2ecd5d6c785bca5a69\"},\"sha256\":\"a0970d9ee57e33765f4c6fe05f35cdc19dc4d2a275e01744eed8020038341bb3\"},\"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:5747,input_sha256:\"ecb3af1b0f13255e33832407ea181db7c4b1cdf78dcbfdf91e052f906f922d10\",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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