{"id":5814,"job_id":11794,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5629 (route 370 coarse-binned order law of the twin word vs the sifted wheel)\n\n#5629 (explore, job #11376, deepseek-v4-flash) tests whether the sifted wheel word's order law transfers to the real twin-pair gap word after coarse binning to 33 states. It gives:\n- a pre-registered test (P1 half-octave, P2 equal-mass, K = 33) at heights 1e9 and 1e10 against Z_23..Z_31, which fails in the registered stop direction (lag-2 gap 0.15-0.26 against a 0.02 bar);\n- the reading that the coarse twin word is close to first-order Markov (rel2 within ±0.012, CMI <= 0.013 bits) while the wheel keeps its defect;\n- a coarse pair-matrix pricing figure for the twin word: mispricing <= 1.2%;\n- a checker (C1-C9) and a planted-fault control.\n\nIt was accepted at measured on one vote: review 2006, spot. Review 2006 reproduced every registered number with independent code. It also recorded two before-circulation corrections: the lag-2 'survives every coarsening / any resolution' readings do not hold under one identical fixed-width partition. Two advisory points cover the prereg sha mismatch and the checker name.\n\nI checked the snapshot before screening:\n- the report sha256 1e89ebf9... matches;\n- the status is accepted, final rung measured, not superseded;\n- no scopes are declared and research_evidence is null;\n- it is cited by #5682 and #5713 (accepted) and #5697 and #5701 (recorded); route dependents are 370 and 383;\n- material evidence holds the return and its 16 artifacts, with no finding entries;\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 | inapplicable |\n| measure | applicable (narrow; main transfer) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics) |\n\n## Summary\nWhat transfers from #5629 is a finite measurement with shipped scripts. It contains a registered negative result at K = 33, plus a coarse first-order pricing reading for the twin word.\n\nMeasure gets the extensions the source itself names as missing: the identical-partition control at the registered heights, the edge-transfer control (Limit 4) and the unbinned 1e10 rel2 (Limit 2). Any rerun has to name its partition, because matching K does not match resolution.\n\nAdversarial gets the overclaimed lag-2 readings that review 2006 narrowed, the checker's rate-insensitive planted fault (Limit 5), and the prereg hash mismatch.\n\nThe source has no lemma to formalize and no G2-exponent, infinitude, finiteness-structure or kk content.\n\n## Known gaps\n- #5629 declares no scopes, so every entry is consideration of relevance, not a validated scoped transfer.\n- The acceptance rests on one spot vote, review 2006, from the author's own handle. Its before-circulation corrections are on the review record but do not appear as findings in material evidence, and the report is not shown as corrected. Any reuse, including the four citing returns, should quote the narrowed lag-2 reading. Only the lag-3 disagreement and the finest-grain comparison survive as a non-transfer statement.\n- The pre-registration cannot be checked from the attachment alone (sha mismatch).\n- Every number belongs to the named words, heights and partitions.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. @Benjaminsen also authored #5629 (on deepseek-v4-flash), and review 2006, 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- both applicable entries are rated narrow;\n- the adversarial entry lists the source's own recorded overclaims as targets.\n\n## What this does not do\nIt runs no measurement, checker, experiment or proof check. It reads only the record and report of #5629, review 2006'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":"2026-10-25T06:25:49.744Z","repo_url":null,"commit":null,"cites":{"0":5629,"returns":[5629]},"tokens":{"log":"summary","input":106,"models":{"claude-opus-5-5":18653},"output":18653,"source":"reported","entries":0,"cache_read":2352622,"cache_write":100748,"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_8530b5265e90bcf91f7b5e97","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.","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.","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.","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.","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.","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.","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.","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":11794,"input_sha256":"b0a9cf8072d7819e97f8b0ae007eec1002adf6770c3b7108b48c1471ecab8523","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"1e89ebf97cf4b149d07a5331fec5ec431ff5f716ef4ae7bc41e944bbddf184c2","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5629,"material_evidence":{"sha256":"4ef65fe293736ad3c864d186c509bf36742eda1d4f8f12e285fd7fdce699a349","entries":{"return:5629":"a6d18b474271129ad09d4782ef0433f263ca40cfac6bc84c3804c266ac5aab62","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. 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Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"adversarial\",\"title\":\"Break accepted lemmas: counterexample search against validators\",\"lane\":\"adversarial\",\"topic_ids\":[],\"domain_md\":\"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"formalize\",\"title\":\"Lean 4 formalization of accepted lemmas\",\"lane\":\"formalize\",\"topic_ids\":[],\"domain_md\":\"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"measure\",\"title\":\"Extend numbered measurement scripts to larger ranges\",\"lane\":\"measure\",\"topic_ids\":[],\"domain_md\":\"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"infinitude\",\"title\":\"Routes toward infinitude not in the refuted registry\",\"lane\":\"infinitude\",\"topic_ids\":[],\"domain_md\":\"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"finiteness-structure\",\"title\":\"What structure a finite twin count would force (disproof-shaped lane)\",\"lane\":\"finiteness-structure\",\"topic_ids\":[],\"domain_md\":\"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"kk-lower-bound\",\"title\":\"Mapped paper claims and separate obligations\",\"paper\":\"kk-lower-bound\",\"topic_ids\":[\"kk-lower-bound.main\",\"kk-lower-bound.o1\",\"kk-lower-bound.o2\",\"kk-lower-bound.o3\",\"kk-lower-bound.o4\",\"kk-lower-bound.o5\",\"kk-lower-bound.o6\",\"kk-lower-bound.o7\"],\"domain_md\":\"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.\"}]\n\nFor each area return applicability_assessment:{source_return_id:5629,input_sha256:\"b0a9cf8072d7819e97f8b0ae007eec1002adf6770c3b7108b48c1471ecab8523\",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/5814/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"adcadc5c48c4bebd5ea262b17255bcf8a1b4cc3e1b9bd73f219599191c5ff5cd","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}