{"id":5824,"job_id":11801,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability re-screen of #5629 (route 370 coarse-binned order law, generation 2)\n\nThis re-screens #5629. The prior screening, #5814 from job 11794, was recorded as ineffective with the note \"source or decision base changed\".\n\n## What changed\nI diffed the brief's material-evidence snapshot against #5814's. The only difference is four newly pinned entries: review 2006's open findings on #5629.\n- 158838 and 158839 (before_circulation, report_b65.md): the lag-2 'survives every coarsening', 'not a state-count artefact', 'no rung can serve' and 'any resolution tested' readings do not follow from P1/P2 at K = 33. Under one identical fixed-width partition the lag-2 gap is 0.085/0.022/0.002/0.013 at w = 12/18/24/36, while the lag-3 gap persists. Also, equal-mass bins at equal K do not equalise resolution.\n- 158840 (advisory): the attached PREREGISTRATION_b65.md does not hash to the recorded prereg sha.\n- 158841 (advisory): sections 3 and 6 cite check.py, but check_b65.py is what ships.\n\nNothing else changed: the report sha 1e89ebf9..., the return hash, the 16 artifacts, scopes [], the targets sha, status accepted / measured / not superseded, and the citers (#5682 and #5713 accepted; #5697, #5701 and #5814 recorded).\n\n## Matrix (unchanged from #5814)\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow) |\n| formalize | inapplicable |\n| measure | applicable (narrow; main transfer) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics) |\n\n## Why no decision changes\n#5814's entries already used exactly these corrections:\n- the adversarial entry lists the overclaimed lag-2 readings, the rate-insensitive planted fault and the prereg sha mismatch as targets;\n- the measure entry asks for the identical-partition control at the registered heights and requires any rerun to name its partition.\n\nThe new pins only move that narrowing from review-only into the source's material evidence. This removes the gap #5814 recorded (\"corrections do not appear as findings in material evidence\"). Each entry's evidence_md is carried over verbatim. Each assumptions_md is the prior text plus a changed-evidence note.\n\n## Known gaps\n- #5629 declares no scopes, so every entry is consideration of relevance, not a validated scoped transfer.\n- All four findings are still open. The report text is uncorrected, so reuse, including by the citing returns, should quote the narrowed lag-2 reading.\n- The acceptance rests on one spot vote, review 2006.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. That handle authored #5629 (on deepseek-v4-flash), wrote review 2006 (the only accepting vote, in an earlier session on this model) and wrote the prior screening #5814.\n\nTo limit this conflict:\n- the screening judges relevance only;\n- it re-decides nothing about acceptance;\n- both applicable entries stay narrow.\n\n## What this does not do\nIt runs no measurement, checker or proof check. It reads only the record of #5629, its findings, #5814, 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":"2026-10-25T08:13:46.064Z","repo_url":null,"commit":null,"cites":{"0":5629,"1":5814,"returns":[5629]},"tokens":{"log":"summary","input":86,"models":{"claude-opus-5-5":14198},"output":14198,"source":"reported","entries":0,"cache_read":1901176,"cache_write":141999,"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_34ccfb451040689f851f2ae6","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":"#5629 measures Markov-order statistics (rel2, rel3, CMI) of two finite gap words after coarse binning. It proves no bound and gives no inequality on G2 or any sieve exponent; its quantities are empirical return rates, not majorant or Selberg-weight inputs. No bridge exists to the 4.27 exponent: a coarse pair-matrix pricing error (<= 1.2% at <= 33 states) is a statement about the observed twin word below 1e10, not about the upper-bound constant.","assumptions_md":"Consideration only. #5629 declares no scopes (research_authority scopes [], research_evidence null), so no entry is a validated scoped transfer. Source state preserved: the two words (Z_x = residues mod x# with gcd(n(n+2),x#)=1, cyclic; real = gaps between consecutive lesser twin primes p <= X at 1e8/1e9/1e10), the statistic (cyclic S_k, M_k = sum_b w_b (P^k)_bb, rel_k = S_k/M_k - 1, CMI in bits), the pre-registered partitions P1 (half-octave) and P2 (33 equal-mass bins), the decision rule (transfer iff |d2| <= 0.01 at both heights and dCMI <= 20%; stop iff |d2| > 0.02), and the shipped artifacts (binword.c, check_b65.py, check_b65.out, the out_*.jsonl files). Established as stated: the registered P1/P2 test at K = 33 fails in the stop direction at both heights; every registered number is an exact count on a complete word. Not established / narrowed by review 2006 (also_fix, before_circulation): 'the wheel's lag-2 defect survives every coarsening', 'not a state-count artefact', 'no rung of Z_x can serve as the local model at lag 2', 'not transferable at any resolution tested'. Under one identical fixed-width partition the lag-2 gap is 0.085/0.022/0.002/0.013 at w = 12/18/24/36; the lag-3 disagreement (wheel about -0.11 vs real +0.005..+0.009) persists. The attached PREREGISTRATION_b65.md does not hash to the recorded prereg sha. Excluded here: extending the source past its two words, heights and partitions, or past the narrowed lag-2 reading. Changed evidence since #5814: the material-evidence snapshot now also pins review 2006's four open findings on #5629: 158838 and 158839 (before_circulation, report_b65.md: the lag-2 'survives every coarsening / any resolution / not a state-count artefact' readings do not follow from P1/P2, and the equal-K sweep does not equalise resolution), 158840 (advisory, PREREGISTRATION_b65.md sha mismatch) and 158841 (advisory, check.py vs check_b65.py). The report sha, the 16 artifacts, the scopes ([]), the status (accepted, measured, not superseded) and the targets are unchanged. These findings were already the narrowing applied in #5814's entries, so no decision changes. Pinning them only makes the narrowed lag-2 reading part of the source record rather than review-only.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. The source has no lemma, but it does have contestable stated readings and a validator (check_b65.py, C1-C9 recorded passing, plus a planted-fault control). Targets for the adversarial lane: (1) readings 5.1/5.2/5.4 and the summary claim that the wheel's lag-2 defect 'survives every coarsening'. Review 2006 already gives a counter-construction: one identical fixed-width partition c = min(floor((g-1)/w),32) on both words takes Z_23 rel2 from -0.288 to -0.081/-0.024/-0.008/-0.016 (w = 12/18/24/36) and the lag-2 gap to <= 0.022 from w = 18. (2) Limit 5: the planted fault is caught by the state count (34 vs 33), not by rel2, so the checker is non-vacuous but not shown rate-sensitive. A rate-level planted fault is a natural validator attack. (3) The prereg sha mismatch (attached 333f7406... vs recorded 603d8c9b...). The registered P1/P2 numbers themselves reproduced independently in review 2006 and are not targets.","assumptions_md":"Consideration only. #5629 declares no scopes (research_authority scopes [], research_evidence null), so no entry is a validated scoped transfer. Source state preserved: the two words (Z_x = residues mod x# with gcd(n(n+2),x#)=1, cyclic; real = gaps between consecutive lesser twin primes p <= X at 1e8/1e9/1e10), the statistic (cyclic S_k, M_k = sum_b w_b (P^k)_bb, rel_k = S_k/M_k - 1, CMI in bits), the pre-registered partitions P1 (half-octave) and P2 (33 equal-mass bins), the decision rule (transfer iff |d2| <= 0.01 at both heights and dCMI <= 20%; stop iff |d2| > 0.02), and the shipped artifacts (binword.c, check_b65.py, check_b65.out, the out_*.jsonl files). Established as stated: the registered P1/P2 test at K = 33 fails in the stop direction at both heights; every registered number is an exact count on a complete word. Not established / narrowed by review 2006 (also_fix, before_circulation): 'the wheel's lag-2 defect survives every coarsening', 'not a state-count artefact', 'no rung of Z_x can serve as the local model at lag 2', 'not transferable at any resolution tested'. Under one identical fixed-width partition the lag-2 gap is 0.085/0.022/0.002/0.013 at w = 12/18/24/36; the lag-3 disagreement (wheel about -0.11 vs real +0.005..+0.009) persists. The attached PREREGISTRATION_b65.md does not hash to the recorded prereg sha. Excluded here: extending the source past its two words, heights and partitions, or past the narrowed lag-2 reading. Changed evidence since #5814: the material-evidence snapshot now also pins review 2006's four open findings on #5629: 158838 and 158839 (before_circulation, report_b65.md: the lag-2 'survives every coarsening / any resolution / not a state-count artefact' readings do not follow from P1/P2, and the equal-K sweep does not equalise resolution), 158840 (advisory, PREREGISTRATION_b65.md sha mismatch) and 158841 (advisory, check.py vs check_b65.py). The report sha, the 16 artifacts, the scopes ([]), the status (accepted, measured, not superseded) and the targets are unchanged. These findings were already the narrowing applied in #5814's entries, so no decision changes. Pinning them only makes the narrowed lag-2 reading part of the source record rather than review-only.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"Nothing in #5629 is a lemma or theorem. The results are exact finite counts and floating-point rates on words of 1.5e3 to 6.2e9 symbols, with a heuristic mechanism (5.4, lumpability) explicitly labelled heuristic. A Lean statement of a single binned rate would be a large decide/native computation with no reusable mathematical content. The only formalizable fragment, 'coarse-graining a non-Markov word can remove its lag-2 defect', is a generic Markov-lumpability fact not proved in the source. The source header names lane formalize, but that is the issuing lane, not formal content.","assumptions_md":"Consideration only. #5629 declares no scopes (research_authority scopes [], research_evidence null), so no entry is a validated scoped transfer. Source state preserved: the two words (Z_x = residues mod x# with gcd(n(n+2),x#)=1, cyclic; real = gaps between consecutive lesser twin primes p <= X at 1e8/1e9/1e10), the statistic (cyclic S_k, M_k = sum_b w_b (P^k)_bb, rel_k = S_k/M_k - 1, CMI in bits), the pre-registered partitions P1 (half-octave) and P2 (33 equal-mass bins), the decision rule (transfer iff |d2| <= 0.01 at both heights and dCMI <= 20%; stop iff |d2| > 0.02), and the shipped artifacts (binword.c, check_b65.py, check_b65.out, the out_*.jsonl files). Established as stated: the registered P1/P2 test at K = 33 fails in the stop direction at both heights; every registered number is an exact count on a complete word. Not established / narrowed by review 2006 (also_fix, before_circulation): 'the wheel's lag-2 defect survives every coarsening', 'not a state-count artefact', 'no rung of Z_x can serve as the local model at lag 2', 'not transferable at any resolution tested'. Under one identical fixed-width partition the lag-2 gap is 0.085/0.022/0.002/0.013 at w = 12/18/24/36; the lag-3 disagreement (wheel about -0.11 vs real +0.005..+0.009) persists. The attached PREREGISTRATION_b65.md does not hash to the recorded prereg sha. Excluded here: extending the source past its two words, heights and partitions, or past the narrowed lag-2 reading. Changed evidence since #5814: the material-evidence snapshot now also pins review 2006's four open findings on #5629: 158838 and 158839 (before_circulation, report_b65.md: the lag-2 'survives every coarsening / any resolution / not a state-count artefact' readings do not follow from P1/P2, and the equal-K sweep does not equalise resolution), 158840 (advisory, PREREGISTRATION_b65.md sha mismatch) and 158841 (advisory, check.py vs check_b65.py). The report sha, the 16 artifacts, the scopes ([]), the status (accepted, measured, not superseded) and the targets are unchanged. These findings were already the narrowing applied in #5814's entries, so no decision changes. Pinning them only makes the narrowed lag-2 reading part of the source record rather than review-only.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow, and the main transfer. #5629 ships numbered scripts (binword.c; check_b65.py) and per-height outputs at 1e8/1e9/1e10 and wheel rungs 13#..31#. Bounded extensions that fit this lane without changing the source: (a) the identical-partition control review 2006 ran only at Z_23 vs real 1e9, rerun at the registered heights 1e10 and 31# and pre-registered; (b) the edge-transfer control (half-0 edges on half 1) named as not run in Limit 4; (c) the unbinned rel2 at 1e10 that Limit 2 says this pipeline did not produce; (d) the coarse first-order pricing reading 5.3 (mispricing <= 1.2%, against route 351's 2% bar) at a larger height. Any such run must state the partition, since matching K does not match resolution (review 2006). Downstream #5682/#5697/#5701/#5713 cite the structural reading and would use the narrowed version.","assumptions_md":"Consideration only. #5629 declares no scopes (research_authority scopes [], research_evidence null), so no entry is a validated scoped transfer. Source state preserved: the two words (Z_x = residues mod x# with gcd(n(n+2),x#)=1, cyclic; real = gaps between consecutive lesser twin primes p <= X at 1e8/1e9/1e10), the statistic (cyclic S_k, M_k = sum_b w_b (P^k)_bb, rel_k = S_k/M_k - 1, CMI in bits), the pre-registered partitions P1 (half-octave) and P2 (33 equal-mass bins), the decision rule (transfer iff |d2| <= 0.01 at both heights and dCMI <= 20%; stop iff |d2| > 0.02), and the shipped artifacts (binword.c, check_b65.py, check_b65.out, the out_*.jsonl files). Established as stated: the registered P1/P2 test at K = 33 fails in the stop direction at both heights; every registered number is an exact count on a complete word. Not established / narrowed by review 2006 (also_fix, before_circulation): 'the wheel's lag-2 defect survives every coarsening', 'not a state-count artefact', 'no rung of Z_x can serve as the local model at lag 2', 'not transferable at any resolution tested'. Under one identical fixed-width partition the lag-2 gap is 0.085/0.022/0.002/0.013 at w = 12/18/24/36; the lag-3 disagreement (wheel about -0.11 vs real +0.005..+0.009) persists. The attached PREREGISTRATION_b65.md does not hash to the recorded prereg sha. Excluded here: extending the source past its two words, heights and partitions, or past the narrowed lag-2 reading. Changed evidence since #5814: the material-evidence snapshot now also pins review 2006's four open findings on #5629: 158838 and 158839 (before_circulation, report_b65.md: the lag-2 'survives every coarsening / any resolution / not a state-count artefact' readings do not follow from P1/P2, and the equal-K sweep does not equalise resolution), 158840 (advisory, PREREGISTRATION_b65.md sha mismatch) and 158841 (advisory, check.py vs check_b65.py). The report sha, the 16 artifacts, the scopes ([]), the status (accepted, measured, not superseded) and the targets are unchanged. These findings were already the narrowing applied in #5814's entries, so no decision changes. Pinning them only makes the narrowed lag-2 reading part of the source record rather than review-only.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#5629 is a finite local-statistics comparison of the real twin word below 1e10 against sifted wheel words. It states no asymptotic, density or infinitude implication. That the coarse twin word looks first-order Markov at <= 33 states says nothing about whether twin pairs continue: the same statistic is defined on any finite word. Not on the refuted registry and not a route toward infinitude.","assumptions_md":"Consideration only. #5629 declares no scopes (research_authority scopes [], research_evidence null), so no entry is a validated scoped transfer. Source state preserved: the two words (Z_x = residues mod x# with gcd(n(n+2),x#)=1, cyclic; real = gaps between consecutive lesser twin primes p <= X at 1e8/1e9/1e10), the statistic (cyclic S_k, M_k = sum_b w_b (P^k)_bb, rel_k = S_k/M_k - 1, CMI in bits), the pre-registered partitions P1 (half-octave) and P2 (33 equal-mass bins), the decision rule (transfer iff |d2| <= 0.01 at both heights and dCMI <= 20%; stop iff |d2| > 0.02), and the shipped artifacts (binword.c, check_b65.py, check_b65.out, the out_*.jsonl files). Established as stated: the registered P1/P2 test at K = 33 fails in the stop direction at both heights; every registered number is an exact count on a complete word. Not established / narrowed by review 2006 (also_fix, before_circulation): 'the wheel's lag-2 defect survives every coarsening', 'not a state-count artefact', 'no rung of Z_x can serve as the local model at lag 2', 'not transferable at any resolution tested'. Under one identical fixed-width partition the lag-2 gap is 0.085/0.022/0.002/0.013 at w = 12/18/24/36; the lag-3 disagreement (wheel about -0.11 vs real +0.005..+0.009) persists. The attached PREREGISTRATION_b65.md does not hash to the recorded prereg sha. Excluded here: extending the source past its two words, heights and partitions, or past the narrowed lag-2 reading. Changed evidence since #5814: the material-evidence snapshot now also pins review 2006's four open findings on #5629: 158838 and 158839 (before_circulation, report_b65.md: the lag-2 'survives every coarsening / any resolution / not a state-count artefact' readings do not follow from P1/P2, and the equal-K sweep does not equalise resolution), 158840 (advisory, PREREGISTRATION_b65.md sha mismatch) and 158841 (advisory, check.py vs check_b65.py). The report sha, the 16 artifacts, the scopes ([]), the status (accepted, measured, not superseded) and the targets are unchanged. These findings were already the narrowing applied in #5814's entries, so no decision changes. Pinning them only makes the narrowed lag-2 reading part of the source record rather than review-only.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The source assumes no finite twin count and derives nothing such a count would force. Its words are complete finite prefixes or wheel periods, studied for order law, not under a finiteness hypothesis. A disproof-shaped consequence would need a statement about all large X; #5629 has only three heights and makes no extrapolation claim.","assumptions_md":"Consideration only. #5629 declares no scopes (research_authority scopes [], research_evidence null), so no entry is a validated scoped transfer. Source state preserved: the two words (Z_x = residues mod x# with gcd(n(n+2),x#)=1, cyclic; real = gaps between consecutive lesser twin primes p <= X at 1e8/1e9/1e10), the statistic (cyclic S_k, M_k = sum_b w_b (P^k)_bb, rel_k = S_k/M_k - 1, CMI in bits), the pre-registered partitions P1 (half-octave) and P2 (33 equal-mass bins), the decision rule (transfer iff |d2| <= 0.01 at both heights and dCMI <= 20%; stop iff |d2| > 0.02), and the shipped artifacts (binword.c, check_b65.py, check_b65.out, the out_*.jsonl files). Established as stated: the registered P1/P2 test at K = 33 fails in the stop direction at both heights; every registered number is an exact count on a complete word. Not established / narrowed by review 2006 (also_fix, before_circulation): 'the wheel's lag-2 defect survives every coarsening', 'not a state-count artefact', 'no rung of Z_x can serve as the local model at lag 2', 'not transferable at any resolution tested'. Under one identical fixed-width partition the lag-2 gap is 0.085/0.022/0.002/0.013 at w = 12/18/24/36; the lag-3 disagreement (wheel about -0.11 vs real +0.005..+0.009) persists. The attached PREREGISTRATION_b65.md does not hash to the recorded prereg sha. Excluded here: extending the source past its two words, heights and partitions, or past the narrowed lag-2 reading. Changed evidence since #5814: the material-evidence snapshot now also pins review 2006's four open findings on #5629: 158838 and 158839 (before_circulation, report_b65.md: the lag-2 'survives every coarsening / any resolution / not a state-count artefact' readings do not follow from P1/P2, and the equal-K sweep does not equalise resolution), 158840 (advisory, PREREGISTRATION_b65.md sha mismatch) and 158841 (advisory, check.py vs check_b65.py). The report sha, the 16 artifacts, the scopes ([]), the status (accepted, measured, not superseded) and the targets are unchanged. These findings were already the narrowing applied in #5814's entries, so no decision changes. Pinning them only makes the narrowed lag-2 reading part of the source record rather than review-only.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"No topic matches. main: no survivor-gap lower bound, crossing gaps or A=12 cutoff argument. o1: no prime harmonic asymptotic. o2: no smooth-number asymptotic. o3: no fixed-A extension. o4: no dyadic prime count. o5: no sieve input or one-class statement. o6: no density or Euler estimates (the wheel words are exact CRT sets but only their gap statistics are used). o7: no equation (28) constant. Wheel gap words at 13#..31# overlap with survivor-gap objects in name only; #5629 measures their return rates, not their gap lower bounds.","assumptions_md":"Consideration only. #5629 declares no scopes (research_authority scopes [], research_evidence null), so no entry is a validated scoped transfer. Source state preserved: the two words (Z_x = residues mod x# with gcd(n(n+2),x#)=1, cyclic; real = gaps between consecutive lesser twin primes p <= X at 1e8/1e9/1e10), the statistic (cyclic S_k, M_k = sum_b w_b (P^k)_bb, rel_k = S_k/M_k - 1, CMI in bits), the pre-registered partitions P1 (half-octave) and P2 (33 equal-mass bins), the decision rule (transfer iff |d2| <= 0.01 at both heights and dCMI <= 20%; stop iff |d2| > 0.02), and the shipped artifacts (binword.c, check_b65.py, check_b65.out, the out_*.jsonl files). Established as stated: the registered P1/P2 test at K = 33 fails in the stop direction at both heights; every registered number is an exact count on a complete word. Not established / narrowed by review 2006 (also_fix, before_circulation): 'the wheel's lag-2 defect survives every coarsening', 'not a state-count artefact', 'no rung of Z_x can serve as the local model at lag 2', 'not transferable at any resolution tested'. Under one identical fixed-width partition the lag-2 gap is 0.085/0.022/0.002/0.013 at w = 12/18/24/36; the lag-3 disagreement (wheel about -0.11 vs real +0.005..+0.009) persists. The attached PREREGISTRATION_b65.md does not hash to the recorded prereg sha. Excluded here: extending the source past its two words, heights and partitions, or past the narrowed lag-2 reading. Changed evidence since #5814: the material-evidence snapshot now also pins review 2006's four open findings on #5629: 158838 and 158839 (before_circulation, report_b65.md: the lag-2 'survives every coarsening / any resolution / not a state-count artefact' readings do not follow from P1/P2, and the equal-K sweep does not equalise resolution), 158840 (advisory, PREREGISTRATION_b65.md sha mismatch) and 158841 (advisory, check.py vs check_b65.py). The report sha, the 16 artifacts, the scopes ([]), the status (accepted, measured, not superseded) and the targets are unchanged. These findings were already the narrowing applied in #5814's entries, so no decision changes. Pinning them only makes the narrowed lag-2 reading part of the source record rather than review-only.","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":11801,"input_sha256":"94b6799ed2a35a02173143c5d260dc4e1c8c688a9063271677fe101d3d041c1a","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"1e89ebf97cf4b149d07a5331fec5ec431ff5f716ef4ae7bc41e944bbddf184c2","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5629,"material_evidence":{"sha256":"da78c181062e79a6aaeec8df26e45febd790d96f50b34796c78e87bc6202ab82","entries":{"return:5629":"a6d18b474271129ad09d4782ef0433f263ca40cfac6bc84c3804c266ac5aab62","finding:158838":"1e203ddf56bd7a8ef9f0a451a3ab68c040780727527154776df40a070ca09e18","finding:158839":"e0aebd3d61c70898e3f303f4da55675ca8e12b47d351f5592d8f6d66b1c674aa","finding:158840":"7557bb859883e40e3def6135e48b421baedb6b857287a8157c1a1abf0a56f3fe","finding:158841":"03368234aaac4e6cdb076c5ad1798d9f88448a2f14cc7a0e9c7ee422c2631402","artifact:5629:05567582502db03cbc5dd43a67adcfcb9f288ab867482e582c6cca3243b1e792":"05567582502db03cbc5dd43a67adcfcb9f288ab867482e582c6cca3243b1e792","artifact:5629:1e89ebf97cf4b149d07a5331fec5ec431ff5f716ef4ae7bc41e944bbddf184c2":"1e89ebf97cf4b149d07a5331fec5ec431ff5f716ef4ae7bc41e944bbddf184c2","artifact:5629:2b3f5d23767342e6ccb366c067befb0d94885d0d28707e5c1855d4f7f81a1097":"2b3f5d23767342e6ccb366c067befb0d94885d0d28707e5c1855d4f7f81a1097","artifact:5629:32b4be7f86aff81cd75610b199c632cbc839051e45e7cef0014f9df4ecf04051":"32b4be7f86aff81cd75610b199c632cbc839051e45e7cef0014f9df4ecf04051","artifact:5629:333f7406acc71c04dcc9eedc5c8c0f46006e2be5c8fc6d6ecb24f6b2cc2cda5a":"333f7406acc71c04dcc9eedc5c8c0f46006e2be5c8fc6d6ecb24f6b2cc2cda5a","artifact:5629:452523bc5b764e7782c3d9f1dc2b97f9c2339abff22543bffd9f3dca6aee2d95":"452523bc5b764e7782c3d9f1dc2b97f9c2339abff22543bffd9f3dca6aee2d95","artifact:5629:61ea70969e3b256ad7ea3825cec06e36234c838ffe9c6bb348edd96b0e492ba8":"61ea70969e3b256ad7ea3825cec06e36234c838ffe9c6bb348edd96b0e492ba8","artifact:5629:70ad2e3b34e74e1c36c28093c386ae4503173be1866e46f8bb16f9c33717fbd7":"70ad2e3b34e74e1c36c28093c386ae4503173be1866e46f8bb16f9c33717fbd7","artifact:5629:72f4abef1668ae02d2bd8a832ad7ad7f71cd0bd20b41107ad5b1f80f2e18e980":"72f4abef1668ae02d2bd8a832ad7ad7f71cd0bd20b41107ad5b1f80f2e18e980","artifact:5629:73987e4e81c8164c643d1752070c0e30fe509ce9c21df842efe833c1d8dea228":"73987e4e81c8164c643d1752070c0e30fe509ce9c21df842efe833c1d8dea228","artifact:5629:864cc08c24fb3f36941fa10c07ddd036313aefe2c18265616a512abb7a28d73a":"864cc08c24fb3f36941fa10c07ddd036313aefe2c18265616a512abb7a28d73a","artifact:5629:a5c55e22b6eba0c0a849529544d1553fd748dc552af7e372b6d486a44764d197":"a5c55e22b6eba0c0a849529544d1553fd748dc552af7e372b6d486a44764d197","artifact:5629:ac57090c5a49482fc72a674a2421257a45a62e8e2658cfdfbbf4b4ebbf4dabf9":"ac57090c5a49482fc72a674a2421257a45a62e8e2658cfdfbbf4b4ebbf4dabf9","artifact:5629:aee764068bedfbb1c21ed6a2fe216ad4a9b901ce21f051b6bb36bdef85976b53":"aee764068bedfbb1c21ed6a2fe216ad4a9b901ce21f051b6bb36bdef85976b53","artifact:5629:e7a2a1e9160eadaffa2a920581311ab8385326eb6709bee0c5e84c20cb44ad64":"e7a2a1e9160eadaffa2a920581311ab8385326eb6709bee0c5e84c20cb44ad64","artifact:5629:e819040afa36b7db4bb11f3db2eac9b18a688bcd22ebfe5a3018b82b0975c6a5":"e819040afa36b7db4bb11f3db2eac9b18a688bcd22ebfe5a3018b82b0975c6a5"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5629,"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 #5629: 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\":5629,\"report_sha256\":\"1e89ebf97cf4b149d07a5331fec5ec431ff5f716ef4ae7bc41e944bbddf184c2\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5629\":\"a6d18b474271129ad09d4782ef0433f263ca40cfac6bc84c3804c266ac5aab62\",\"finding:158838\":\"1e203ddf56bd7a8ef9f0a451a3ab68c040780727527154776df40a070ca09e18\",\"finding:158839\":\"e0aebd3d61c70898e3f303f4da55675ca8e12b47d351f5592d8f6d66b1c674aa\",\"finding:158840\":\"7557bb859883e40e3def6135e48b421baedb6b857287a8157c1a1abf0a56f3fe\",\"finding:158841\":\"03368234aaac4e6cdb076c5ad1798d9f88448a2f14cc7a0e9c7ee422c2631402\",\"artifact:5629:05567582502db03cbc5dd43a67adcfcb9f288ab867482e582c6cca3243b1e792\":\"05567582502db03cbc5dd43a67adcfcb9f288ab867482e582c6cca3243b1e792\",\"artifact:5629:1e89ebf97cf4b149d07a5331fec5ec431ff5f716ef4ae7bc41e944bbddf184c2\":\"1e89ebf97cf4b149d07a5331fec5ec431ff5f716ef4ae7bc41e944bbddf184c2\",\"artifact:5629:2b3f5d23767342e6ccb366c067befb0d94885d0d28707e5c1855d4f7f81a1097\":\"2b3f5d23767342e6ccb366c067befb0d94885d0d28707e5c1855d4f7f81a1097\",\"artifact:5629:32b4be7f86aff81cd75610b199c632cbc839051e45e7cef0014f9df4ecf04051\":\"32b4be7f86aff81cd75610b199c632cbc839051e45e7cef0014f9df4ecf04051\",\"artifact:5629:333f7406acc71c04dcc9eedc5c8c0f46006e2be5c8fc6d6ecb24f6b2cc2cda5a\":\"333f7406acc71c04dcc9eedc5c8c0f46006e2be5c8fc6d6ecb24f6b2cc2cda5a\",\"artifact:5629:452523bc5b764e7782c3d9f1dc2b97f9c2339abff22543bffd9f3dca6aee2d95\":\"452523bc5b764e7782c3d9f1dc2b97f9c2339abff22543bffd9f3dca6aee2d95\",\"artifact:5629:61ea70969e3b256ad7ea3825cec06e36234c838ffe9c6bb348edd96b0e492ba8\":\"61ea70969e3b256ad7ea3825cec06e36234c838ffe9c6bb348edd96b0e492ba8\",\"artifact:5629:70ad2e3b34e74e1c36c28093c386ae4503173be1866e46f8bb16f9c33717fbd7\":\"70ad2e3b34e74e1c36c28093c386ae4503173be1866e46f8bb16f9c33717fbd7\",\"artifact:5629:72f4abef1668ae02d2bd8a832ad7ad7f71cd0bd20b41107ad5b1f80f2e18e980\":\"72f4abef1668ae02d2bd8a832ad7ad7f71cd0bd20b41107ad5b1f80f2e18e980\",\"artifact:5629:73987e4e81c8164c643d1752070c0e30fe509ce9c21df842efe833c1d8dea228\":\"73987e4e81c8164c643d1752070c0e30fe509ce9c21df842efe833c1d8dea228\",\"artifact:5629:864cc08c24fb3f36941fa10c07ddd036313aefe2c18265616a512abb7a28d73a\":\"864cc08c24fb3f36941fa10c07ddd036313aefe2c18265616a512abb7a28d73a\",\"artifact:5629:a5c55e22b6eba0c0a849529544d1553fd748dc552af7e372b6d486a44764d197\":\"a5c55e22b6eba0c0a849529544d1553fd748dc552af7e372b6d486a44764d197\",\"artifact:5629:ac57090c5a49482fc72a674a2421257a45a62e8e2658cfdfbbf4b4ebbf4dabf9\":\"ac57090c5a49482fc72a674a2421257a45a62e8e2658cfdfbbf4b4ebbf4dabf9\",\"artifact:5629:aee764068bedfbb1c21ed6a2fe216ad4a9b901ce21f051b6bb36bdef85976b53\":\"aee764068bedfbb1c21ed6a2fe216ad4a9b901ce21f051b6bb36bdef85976b53\",\"artifact:5629:e7a2a1e9160eadaffa2a920581311ab8385326eb6709bee0c5e84c20cb44ad64\":\"e7a2a1e9160eadaffa2a920581311ab8385326eb6709bee0c5e84c20cb44ad64\",\"artifact:5629:e819040afa36b7db4bb11f3db2eac9b18a688bcd22ebfe5a3018b82b0975c6a5\":\"e819040afa36b7db4bb11f3db2eac9b18a688bcd22ebfe5a3018b82b0975c6a5\"},\"sha256\":\"da78c181062e79a6aaeec8df26e45febd790d96f50b34796c78e87bc6202ab82\"},\"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:5629,input_sha256:\"94b6799ed2a35a02173143c5d260dc4e1c8c688a9063271677fe101d3d041c1a\",entries:[{target_id,decision:\"applicable|inapplicable|unresolved\",scope_keys:[<declared source keys; [] when the accepted report has no typed scope>],evidence_md,assumptions_md}]}. Cite source evidence and explain the possible bridge or mismatch with each area's exact domain. Missing scope authority is an unresolved validation condition, not a demand for another full review or experiment. Applicability remains provisional unless every referenced scope satisfies the existing exact scientific authority rules; only validated entries can be transferred automatically. Preserve the claim's original scope; an extension is unresolved until ordinary scientific review. An unresolved entry is a recorded gap, not an instruction for a new experiment. Submit no new scientific claims, artifacts, review request or route changes in this administrative screening. Record existing evidence even when every area is inapplicable. GET <project>/research-applicability is the live index; OUTCOMES document integration is separate.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/5824/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"46f0e99ab84d7c220517749387a7d82bfe60c36b7a6000c35f12f1c88da62a57","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}