{"id":5811,"job_id":11793,"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 matches;\n- the status is accepted, final rung measured, not superseded;\n- no scopes are declared and research_evidence is null;\n- it is cited by #5758 (recorded);\n- material evidence now includes review 2005's five open findings #158833-#158837. The earlier screening (job 11790, return 5808) was recorded ineffective because these findings joined the snapshot after that job was issued; this screening cites them and uses the current input hash;\n- the live index lists it with assessment null, so no screening is recorded yet.\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 corrections (findings #158833-#158837, all open) 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\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 and findings, 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":"2026-10-25T06:08:24.763Z","repo_url":null,"commit":null,"cites":{"0":5747,"returns":[5747]},"tokens":{"log":"summary","input":92,"models":{"claude-opus-5-5":13587},"output":13587,"source":"reported","entries":0,"cache_read":1859677,"cache_write":87970,"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_a11aa468bdecba3e6693cc0a","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 (open findings #158833-#158837, now in material evidence): 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 recorded as an open finding that the record does not show as applied (#158833-#158836 before_circulation, #158837 advisory): (a) [#158833] 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) [#158834] the decision sentence 'all |E T| <= 1 for the families on record', contradicted by Family C at 1.21 to 3.06; (c) [#158835] '~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) [#158836] '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) [#158837, advisory] 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 (open findings #158833-#158837, now in material evidence): 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 (open findings #158833-#158837, now in material evidence): 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 (open findings #158833-#158837, now in material evidence): 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 (open findings #158833-#158837, now in material evidence): 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 (open findings #158833-#158837, now in material evidence): 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 (open findings #158833-#158837, now in material evidence): 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":true,"check_job_id":11793,"input_sha256":"198fa39da0b30f553f6eb281a0a8c53459e6a65d91d235b6507fb9ecb68ad1e0","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"07b5b0433f7f2b440d5c0c1f0bc9ceb8cc7c851370c21cf027737683dff40429","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5747,"material_evidence":{"sha256":"2949fc7ad15aa29bf99e52e0fabf458bdc5236165401afdb3ddd9665c4fdcda1","entries":{"return:5747":"1bd1d980eefb69ee301263b71d4f9d3b4709931c4e535c7344fe64c8518de037","finding:158833":"1ede165da4b0614989af8f8aab24e63abdd8e94efc1d7be2ebcaad9e42e5efb3","finding:158834":"6107300e151d289c46f3521314b71d400e9547694264d7703e8711e99239abc9","finding:158835":"7ea183e557b2876a2e0a01ac6661d9d5689b42d68e6df442f24309b8fb37b865","finding:158836":"4d97e89a185097702dc9977a585de1e9936b2b1c3642b0bd8e42b318fe5a24ac","finding:158837":"e780ddff7e247cfc4f56e1405a5db5afab41ed775d90fa48df847d36434becc2","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\",\"finding:158833\":\"1ede165da4b0614989af8f8aab24e63abdd8e94efc1d7be2ebcaad9e42e5efb3\",\"finding:158834\":\"6107300e151d289c46f3521314b71d400e9547694264d7703e8711e99239abc9\",\"finding:158835\":\"7ea183e557b2876a2e0a01ac6661d9d5689b42d68e6df442f24309b8fb37b865\",\"finding:158836\":\"4d97e89a185097702dc9977a585de1e9936b2b1c3642b0bd8e42b318fe5a24ac\",\"finding:158837\":\"e780ddff7e247cfc4f56e1405a5db5afab41ed775d90fa48df847d36434becc2\",\"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\":\"2949fc7ad15aa29bf99e52e0fabf458bdc5236165401afdb3ddd9665c4fdcda1\"},\"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:\"198fa39da0b30f553f6eb281a0a8c53459e6a65d91d235b6507fb9ecb68ad1e0\",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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