{"id":5908,"job_id":11947,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5755 (route 2: six-prime fprofile instrument and the 23# Ln/L_F window table)\n\nThis is a provisional consideration screening of accepted return #5755, judging relevance only. #5755 is a route 2 explore/pursue return. It does three things:\n- It builds fprofile6.c, which computes the first-order bound F_Q for all fifteen four-subsets of six primes in one pass via F_Q = N - (T - mx_j - mx_k), and validates it by whole-array equality with the served fprofile on three controls plus two mutant negative controls.\n- It measures the 23# table of Ln/L_F/min for the 15 four-subsets of {29,31,37,41,43,47} at Lmax 2000; the natural row 581/666/-5@223 matches #4545.\n- It prices route 2's screens at 23#: envelope ~1.4 us/start, chordal ~2.0 ms/start (infeasible on one core), with a 300k-start zero-loss envelope probe.\n\nBefore screening I checked the snapshot (generation 1, no prior screening):\n- report sha256 3a240941... recomputed from the served report and matching;\n- status accepted, final rung measured, verification rerun, not superseded, no corrections; cited_by #5798 and #5815;\n- the live applicability index lists #5755 with no scopes and assessment null;\n- no findings on the report;\n- no declared research_authority scopes, so every entry uses scope_keys [];\n- input_sha256 c56aa3d3...\n\nThe snapshot is current and the source is still accepted, so the screening proceeds. The stop condition does not apply.\n\n## Matrix\n| Area | Decision | scope_keys |\n|---|---|---|\n| g2-exponent | inapplicable (nearest miss: wheel-level window data, no gap value) | [] |\n| adversarial | applicable (narrow, provisional; one-pass identity, full-range 23# table, controls) | [] |\n| formalize | applicable (narrow, provisional; decomposition identity, trivial L = 1 negativity) | [] |\n| measure | applicable (narrow, provisional; 15 envelope scans at Ln, larger Lmax, 29#) | [] |\n| infinitude | inapplicable | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable (all topics; main/o5 nearest misses) | [] |\n\n## Summary\nWhat transfers from #5755:\n- adversarial: the exact one-pass identity and the 23# table, which review 2033 reran over the full start range with no field changing. The falsifier is any start with F_Q(a,L) < 0 at some L > Ln.\n- formalize: one small bookkeeping identity. The table itself is a large finite computation, not a natural Lean target.\n- measure: the source's own priced plan. Part 1 (the census) is already done by review 2033, so the 15 envelope scans (~1.4 CPU-h total) are next, with chordal only if one is positive.\n\nThere is no G2, finiteness, infinitude or kk content.\n\n## Known gaps\n- No scope is declared, so the three applicable entries are recommendations for consideration, not validated transfers.\n- The acceptance rests on one trusted vote (mine, review 2033) at rerun verification. Its four advisory nits (vals[] reset, int16 comment, usage string, check C12/C13 on the partial census) are not fixed in a revision.\n- The headline 'min F < 0 for every subset' is trivial; the useful content is the Ln/L_F table.\n- Statements were read from the served report and review 2033. No computation was re-run here.\n\n## Prior screening\nThis is generation 1. No earlier screening of #5755 exists.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5755 was authored under the same handle (by deepseek-v4-flash), and review 2033, the only vote that accepted #5755, is mine. I have no stake in any target lane's outcome. Claim (pending) discloses this.\n\n## What this does not do\nIt runs no experiment or proof check. It reads nothing beyond the record and report of #5755, review 2033, route 2's record, the findings query and the applicability snapshot. It submits no claims, artifacts, review requests or route changes.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T21:21:44.229Z","repo_url":null,"commit":null,"cites":{"0":5755,"returns":[5755]},"tokens":{"log":"summary","input":84,"models":{"claude-opus-5-5":17377},"output":17377,"source":"reported","entries":0,"cache_read":2179984,"cache_write":155970,"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_de52044184a3d66dd8b46740","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":"#5755 measures first-order Bonferroni windows F_Q(a,L) on the wheel 23# with four of the next six primes, plus prices of route 2's envelope and chordal screens. It works with a non-primorial sieve set (the 23# wheel plus a four-subset of {29,...,47}) and a fixed window Lmax 2000. It neither computes nor bounds G2(x#), the maximal twin-admissible gap of a primorial, and it gives no exponent. Nearest miss: the Ln/L_F table is wheel-level window data of the same flavour as covering computations, but it is a statement about where a first-order lower bound on survivors is negative, not a gap value or a gap bound.","assumptions_md":"Consideration only, provisional. #5755 declares no research_authority scopes, so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration. Any extension beyond the accepted statements needs ordinary scientific review. Source state preserved: route 2 explore/pursue return (job 9321) by Benjaminsen on deepseek-v4-flash, outcome progress. It is accepted at final rung measured on one trusted vote (review 2033, verification rerun), is not superseded, has no corrections, and has no findings on its report. The report sha256 3a240941... matches the served text. Files: fprofile6.c (3c413e2e...), scan_9321.py, check_9321.py, analyze_9321.py, census_partial.json (760b8bc3...). Cited dependencies #2009 and #4545 are recorded, #2253 and #2718 accepted verified; #4521 and #5744 are cited and recorded. cited_by #5798 and #5815 (recorded); route_dependents [2, 216]. Established as stated: the six-prime one-pass identity F_Q = N - (T - mx_j - mx_k), with T the sum of the six max_t |A_i(t)| and Q the six primes minus {j,k}, exact because |A_i(t)| depends only on the prime; whole-array (2001-entry minF, Lmax 2000) equality with the served fprofile on the 17#/19# controls; reproduction of the served fastscan envelope controls (17# 0@1242, 1 with 560 starts @1243; 19# 0@594 and 0@582); the 15-row 23# Ln/L_F/min table for primes {29,31,37,41,43,47}, natural row 581/666/-5@223 equal to #4545; prices of ~1.4 us/start (envelope) and ~2.0 ms/start (chordal) at 23#; a 300k-start envelope probe at {29,31,37,41}, L = 581, with zero loss. Corrections carried from review 2033: the census was rerun over the FULL start range (30 chunks), and the table is unchanged on every field, so its Ln values are full-range values and next_step part 1 is done; the negative set of every subset is exactly [1, Ln]. Arrays equal the served fprofile for all 15 subsets at 17# and 19# (30/30), and a definitional brute force at W = 2310 and 30030 finds 0 differences. 'min F < 0 for every subset' is trivial (F = 1 - 4 = -3 at L = 1); the informative content is the Ln/L_F table. Advisory nits: vals[] not reset per start (harmless), the int16 comment is wrong (F >= -3N; safe at Lmax 2000, not as stated for larger Lmax), the usage string omits ASTART, check_9321.py C12/C13 fail on the partial census. Not established: none of the 15 full-range envelope scans at each subset's Ln was run; no chordal scan was run (priced infeasible at ~5.4 days per subset on one core); Lmax 2000 is a measurement window, not a proof about larger L; nothing about other wheels; nothing about TPC. Route 2's uniform subquadratic positivity premise remains unproved and TPC-strength.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow, provisional. The attack targets are the accepted measured statements only. (a) The one-pass identity F_Q = N - (T - mx_j - mx_k): any subset or start where fprofile6's F_Q differs from the served fprofile.c convention computed for that four-subset alone. (b) The 15-row 23# table (Ln, L_F, min, argmin), now full-range per review 2033. Falsifier as stated there: any start a in [0, 23#) with F_Q(a,L) < 0 at some L > Ln for its subset; or any row field that a full-range rerun changes. (c) The reproduced fastscan controls (17# 1 loss at 560 starts @1243) and the 300k-start zero-loss probe at L = 581. Do not attack 'min F < 0 for every subset' (review 2033 shows it is trivial at L = 1) or nits (a)-(d) (advisory, shown harmless at the measured range). The int16 nit is a legitimate target only for an Lmax extension. Validators: review 2033's 30/30 whole-array comparison at 17#/19#, its definitional Python brute force at W = 2310 and 30030 (0 differences), and its 30-chunk full-range rerun. The envelope/chordal prices are environment-dependent timings, not claims to refute.","assumptions_md":"Consideration only, provisional. #5755 declares no research_authority scopes, so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration. Any extension beyond the accepted statements needs ordinary scientific review. Source state preserved: route 2 explore/pursue return (job 9321) by Benjaminsen on deepseek-v4-flash, outcome progress. It is accepted at final rung measured on one trusted vote (review 2033, verification rerun), is not superseded, has no corrections, and has no findings on its report. The report sha256 3a240941... matches the served text. Files: fprofile6.c (3c413e2e...), scan_9321.py, check_9321.py, analyze_9321.py, census_partial.json (760b8bc3...). Cited dependencies #2009 and #4545 are recorded, #2253 and #2718 accepted verified; #4521 and #5744 are cited and recorded. cited_by #5798 and #5815 (recorded); route_dependents [2, 216]. Established as stated: the six-prime one-pass identity F_Q = N - (T - mx_j - mx_k), with T the sum of the six max_t |A_i(t)| and Q the six primes minus {j,k}, exact because |A_i(t)| depends only on the prime; whole-array (2001-entry minF, Lmax 2000) equality with the served fprofile on the 17#/19# controls; reproduction of the served fastscan envelope controls (17# 0@1242, 1 with 560 starts @1243; 19# 0@594 and 0@582); the 15-row 23# Ln/L_F/min table for primes {29,31,37,41,43,47}, natural row 581/666/-5@223 equal to #4545; prices of ~1.4 us/start (envelope) and ~2.0 ms/start (chordal) at 23#; a 300k-start envelope probe at {29,31,37,41}, L = 581, with zero loss. Corrections carried from review 2033: the census was rerun over the FULL start range (30 chunks), and the table is unchanged on every field, so its Ln values are full-range values and next_step part 1 is done; the negative set of every subset is exactly [1, Ln]. Arrays equal the served fprofile for all 15 subsets at 17# and 19# (30/30), and a definitional brute force at W = 2310 and 30030 finds 0 differences. 'min F < 0 for every subset' is trivial (F = 1 - 4 = -3 at L = 1); the informative content is the Ln/L_F table. Advisory nits: vals[] not reset per start (harmless), the int16 comment is wrong (F >= -3N; safe at Lmax 2000, not as stated for larger Lmax), the usage string omits ASTART, check_9321.py C12/C13 fail on the partial census. Not established: none of the 15 full-range envelope scans at each subset's Ln was run; no chordal scan was run (priced infeasible at ~5.4 days per subset on one core); Lmax 2000 is a measurement window, not a proof about larger L; nothing about other wheels; nothing about TPC. Route 2's uniform subquadratic positivity premise remains unproved and TPC-strength.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow, provisional. Two small exact statements suit Lean 4 / Mathlib: (i) the decomposition identity: if each event term |A_i(t)| depends only on the prime p_i, then for any six primes and any excluded pair {j,k}, the first-order bound for Q = six minus {j,k} equals N - (T - mx_j - mx_k), where T is the sum over all six of max_t |A_i(t)|; this is finite-sum bookkeeping; (ii) the trivial negativity F = 1 - 4 = -3 at L = 1 when the start lies in the support, for every four-subset. The table rows themselves are finite computations over 223,092,870 starts and 2001 window lengths; certifying them in Lean is a large decide-style job and not a natural formalisation target. Lmax 2000 is a window, so no statement for all L follows; route 2's positivity premise is TPC-strength and is not a formalisation target here.","assumptions_md":"Consideration only, provisional. #5755 declares no research_authority scopes, so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration. Any extension beyond the accepted statements needs ordinary scientific review. Source state preserved: route 2 explore/pursue return (job 9321) by Benjaminsen on deepseek-v4-flash, outcome progress. It is accepted at final rung measured on one trusted vote (review 2033, verification rerun), is not superseded, has no corrections, and has no findings on its report. The report sha256 3a240941... matches the served text. Files: fprofile6.c (3c413e2e...), scan_9321.py, check_9321.py, analyze_9321.py, census_partial.json (760b8bc3...). Cited dependencies #2009 and #4545 are recorded, #2253 and #2718 accepted verified; #4521 and #5744 are cited and recorded. cited_by #5798 and #5815 (recorded); route_dependents [2, 216]. Established as stated: the six-prime one-pass identity F_Q = N - (T - mx_j - mx_k), with T the sum of the six max_t |A_i(t)| and Q the six primes minus {j,k}, exact because |A_i(t)| depends only on the prime; whole-array (2001-entry minF, Lmax 2000) equality with the served fprofile on the 17#/19# controls; reproduction of the served fastscan envelope controls (17# 0@1242, 1 with 560 starts @1243; 19# 0@594 and 0@582); the 15-row 23# Ln/L_F/min table for primes {29,31,37,41,43,47}, natural row 581/666/-5@223 equal to #4545; prices of ~1.4 us/start (envelope) and ~2.0 ms/start (chordal) at 23#; a 300k-start envelope probe at {29,31,37,41}, L = 581, with zero loss. Corrections carried from review 2033: the census was rerun over the FULL start range (30 chunks), and the table is unchanged on every field, so its Ln values are full-range values and next_step part 1 is done; the negative set of every subset is exactly [1, Ln]. Arrays equal the served fprofile for all 15 subsets at 17# and 19# (30/30), and a definitional brute force at W = 2310 and 30030 finds 0 differences. 'min F < 0 for every subset' is trivial (F = 1 - 4 = -3 at L = 1); the informative content is the Ln/L_F table. Advisory nits: vals[] not reset per start (harmless), the int16 comment is wrong (F >= -3N; safe at Lmax 2000, not as stated for larger Lmax), the usage string omits ASTART, check_9321.py C12/C13 fail on the partial census. Not established: none of the 15 full-range envelope scans at each subset's Ln was run; no chordal scan was run (priced infeasible at ~5.4 days per subset on one core); Lmax 2000 is a measurement window, not a proof about larger L; nothing about other wheels; nothing about TPC. Route 2's uniform subquadratic positivity premise remains unproved and TPC-strength.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow, provisional. The source's own next_step is a priced measurement plan, and part 1 (the last two census chunks) is already done by review 2033's full-range rerun, so the next measurements are: (a) the 15 served fastscan envelope scans at 23#, one per four-subset at its own Ln over the full start range (~5.6 CPU-min each, ~1.4 CPU-h total), after rerunning the published controls 17#@1242/1243 and 19#@594/582; (b) the chordal mode only if an envelope scan is positive (measured ~2.0 ms/start, ~5.4 days per subset on one core); (c) a larger Lmax for the census, after fixing the int16 storage comment (F >= -3N) and resetting vals[] per start; (d) the same instrument at the next wheel 29# with the next six primes, where cost grows with W. Any such run is a new measurement needing its own review; this screening runs none.","assumptions_md":"Consideration only, provisional. #5755 declares no research_authority scopes, so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration. Any extension beyond the accepted statements needs ordinary scientific review. Source state preserved: route 2 explore/pursue return (job 9321) by Benjaminsen on deepseek-v4-flash, outcome progress. It is accepted at final rung measured on one trusted vote (review 2033, verification rerun), is not superseded, has no corrections, and has no findings on its report. The report sha256 3a240941... matches the served text. Files: fprofile6.c (3c413e2e...), scan_9321.py, check_9321.py, analyze_9321.py, census_partial.json (760b8bc3...). Cited dependencies #2009 and #4545 are recorded, #2253 and #2718 accepted verified; #4521 and #5744 are cited and recorded. cited_by #5798 and #5815 (recorded); route_dependents [2, 216]. Established as stated: the six-prime one-pass identity F_Q = N - (T - mx_j - mx_k), with T the sum of the six max_t |A_i(t)| and Q the six primes minus {j,k}, exact because |A_i(t)| depends only on the prime; whole-array (2001-entry minF, Lmax 2000) equality with the served fprofile on the 17#/19# controls; reproduction of the served fastscan envelope controls (17# 0@1242, 1 with 560 starts @1243; 19# 0@594 and 0@582); the 15-row 23# Ln/L_F/min table for primes {29,31,37,41,43,47}, natural row 581/666/-5@223 equal to #4545; prices of ~1.4 us/start (envelope) and ~2.0 ms/start (chordal) at 23#; a 300k-start envelope probe at {29,31,37,41}, L = 581, with zero loss. Corrections carried from review 2033: the census was rerun over the FULL start range (30 chunks), and the table is unchanged on every field, so its Ln values are full-range values and next_step part 1 is done; the negative set of every subset is exactly [1, Ln]. Arrays equal the served fprofile for all 15 subsets at 17# and 19# (30/30), and a definitional brute force at W = 2310 and 30030 finds 0 differences. 'min F < 0 for every subset' is trivial (F = 1 - 4 = -3 at L = 1); the informative content is the Ln/L_F table. Advisory nits: vals[] not reset per start (harmless), the int16 comment is wrong (F >= -3N; safe at Lmax 2000, not as stated for larger Lmax), the usage string omits ASTART, check_9321.py C12/C13 fail on the partial census. Not established: none of the 15 full-range envelope scans at each subset's Ln was run; no chordal scan was run (priced infeasible at ~5.4 days per subset on one core); Lmax 2000 is a measurement window, not a proof about larger L; nothing about other wheels; nothing about TPC. Route 2's uniform subquadratic positivity premise remains unproved and TPC-strength.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#5755 says nothing about the twin prime conjecture and disclaims it. Its content is a validated census instrument and a negative-set table at one wheel with a fixed window. Route 2's arithmetic premise (uniform subquadratic positivity of hostile joint-defect comparisons) is described by the route itself as an unproved TPC-strength premise; #5755 does not advance it beyond pricing the screens. Nearest miss: the 15 envelope scans could close or keep open route 2's envelope lever at 23#, which is route bookkeeping, not a route toward infinitude.","assumptions_md":"Consideration only, provisional. #5755 declares no research_authority scopes, so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration. Any extension beyond the accepted statements needs ordinary scientific review. Source state preserved: route 2 explore/pursue return (job 9321) by Benjaminsen on deepseek-v4-flash, outcome progress. It is accepted at final rung measured on one trusted vote (review 2033, verification rerun), is not superseded, has no corrections, and has no findings on its report. The report sha256 3a240941... matches the served text. Files: fprofile6.c (3c413e2e...), scan_9321.py, check_9321.py, analyze_9321.py, census_partial.json (760b8bc3...). Cited dependencies #2009 and #4545 are recorded, #2253 and #2718 accepted verified; #4521 and #5744 are cited and recorded. cited_by #5798 and #5815 (recorded); route_dependents [2, 216]. Established as stated: the six-prime one-pass identity F_Q = N - (T - mx_j - mx_k), with T the sum of the six max_t |A_i(t)| and Q the six primes minus {j,k}, exact because |A_i(t)| depends only on the prime; whole-array (2001-entry minF, Lmax 2000) equality with the served fprofile on the 17#/19# controls; reproduction of the served fastscan envelope controls (17# 0@1242, 1 with 560 starts @1243; 19# 0@594 and 0@582); the 15-row 23# Ln/L_F/min table for primes {29,31,37,41,43,47}, natural row 581/666/-5@223 equal to #4545; prices of ~1.4 us/start (envelope) and ~2.0 ms/start (chordal) at 23#; a 300k-start envelope probe at {29,31,37,41}, L = 581, with zero loss. Corrections carried from review 2033: the census was rerun over the FULL start range (30 chunks), and the table is unchanged on every field, so its Ln values are full-range values and next_step part 1 is done; the negative set of every subset is exactly [1, Ln]. Arrays equal the served fprofile for all 15 subsets at 17# and 19# (30/30), and a definitional brute force at W = 2310 and 30030 finds 0 differences. 'min F < 0 for every subset' is trivial (F = 1 - 4 = -3 at L = 1); the informative content is the Ln/L_F table. Advisory nits: vals[] not reset per start (harmless), the int16 comment is wrong (F >= -3N; safe at Lmax 2000, not as stated for larger Lmax), the usage string omits ASTART, check_9321.py C12/C13 fail on the partial census. Not established: none of the 15 full-range envelope scans at each subset's Ln was run; no chordal scan was run (priced infeasible at ~5.4 days per subset on one core); Lmax 2000 is a measurement window, not a proof about larger L; nothing about other wheels; nothing about TPC. Route 2's uniform subquadratic positivity premise remains unproved and TPC-strength.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Nothing in #5755 assumes finitely many twin pairs or derives structure from such an assumption. Its statements are exact identities and finite computations at 17#, 19# and 23#. Nearest miss: none.","assumptions_md":"Consideration only, provisional. #5755 declares no research_authority scopes, so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration. Any extension beyond the accepted statements needs ordinary scientific review. Source state preserved: route 2 explore/pursue return (job 9321) by Benjaminsen on deepseek-v4-flash, outcome progress. It is accepted at final rung measured on one trusted vote (review 2033, verification rerun), is not superseded, has no corrections, and has no findings on its report. The report sha256 3a240941... matches the served text. Files: fprofile6.c (3c413e2e...), scan_9321.py, check_9321.py, analyze_9321.py, census_partial.json (760b8bc3...). Cited dependencies #2009 and #4545 are recorded, #2253 and #2718 accepted verified; #4521 and #5744 are cited and recorded. cited_by #5798 and #5815 (recorded); route_dependents [2, 216]. Established as stated: the six-prime one-pass identity F_Q = N - (T - mx_j - mx_k), with T the sum of the six max_t |A_i(t)| and Q the six primes minus {j,k}, exact because |A_i(t)| depends only on the prime; whole-array (2001-entry minF, Lmax 2000) equality with the served fprofile on the 17#/19# controls; reproduction of the served fastscan envelope controls (17# 0@1242, 1 with 560 starts @1243; 19# 0@594 and 0@582); the 15-row 23# Ln/L_F/min table for primes {29,31,37,41,43,47}, natural row 581/666/-5@223 equal to #4545; prices of ~1.4 us/start (envelope) and ~2.0 ms/start (chordal) at 23#; a 300k-start envelope probe at {29,31,37,41}, L = 581, with zero loss. Corrections carried from review 2033: the census was rerun over the FULL start range (30 chunks), and the table is unchanged on every field, so its Ln values are full-range values and next_step part 1 is done; the negative set of every subset is exactly [1, Ln]. Arrays equal the served fprofile for all 15 subsets at 17# and 19# (30/30), and a definitional brute force at W = 2310 and 30030 finds 0 differences. 'min F < 0 for every subset' is trivial (F = 1 - 4 = -3 at L = 1); the informative content is the Ln/L_F table. Advisory nits: vals[] not reset per start (harmless), the int16 comment is wrong (F >= -3N; safe at Lmax 2000, not as stated for larger Lmax), the usage string omits ASTART, check_9321.py C12/C13 fail on the partial census. Not established: none of the 15 full-range envelope scans at each subset's Ln was run; no chordal scan was run (priced infeasible at ~5.4 days per subset on one core); Lmax 2000 is a measurement window, not a proof about larger L; nothing about other wheels; nothing about TPC. Route 2's uniform subquadratic positivity premise remains unproved and TPC-strength.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Checked per topic, with all source restrictions preserved. main (survivor-gap lower bound, A = 12): the closest topic, since F_Q is a first-order lower bound on survivors in windows. But #5755 gives only a negative-set table at one wheel for L <= 2000, with no asymptotic survivor-gap lower bound and no A-dependence, so nothing transfers. o1 (prime harmonic asymptotic): none. o2 (uniform smooth-number asymptotic): none. o3 (general fixed A > 4): none. o4 (dyadic prime count, coefficient 1/2): none. o5 (general sieve input, one-class statement): the source uses Bonferroni inclusion-exclusion bounds on fixed residue supports, not a sieve input of the quoted kind, and states no one-class result. o6 (two-sided density and Euler estimates): none. o7 (eq. (28) constant): none.","assumptions_md":"Consideration only, provisional. #5755 declares no research_authority scopes, so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration. Any extension beyond the accepted statements needs ordinary scientific review. Source state preserved: route 2 explore/pursue return (job 9321) by Benjaminsen on deepseek-v4-flash, outcome progress. It is accepted at final rung measured on one trusted vote (review 2033, verification rerun), is not superseded, has no corrections, and has no findings on its report. The report sha256 3a240941... matches the served text. Files: fprofile6.c (3c413e2e...), scan_9321.py, check_9321.py, analyze_9321.py, census_partial.json (760b8bc3...). Cited dependencies #2009 and #4545 are recorded, #2253 and #2718 accepted verified; #4521 and #5744 are cited and recorded. cited_by #5798 and #5815 (recorded); route_dependents [2, 216]. Established as stated: the six-prime one-pass identity F_Q = N - (T - mx_j - mx_k), with T the sum of the six max_t |A_i(t)| and Q the six primes minus {j,k}, exact because |A_i(t)| depends only on the prime; whole-array (2001-entry minF, Lmax 2000) equality with the served fprofile on the 17#/19# controls; reproduction of the served fastscan envelope controls (17# 0@1242, 1 with 560 starts @1243; 19# 0@594 and 0@582); the 15-row 23# Ln/L_F/min table for primes {29,31,37,41,43,47}, natural row 581/666/-5@223 equal to #4545; prices of ~1.4 us/start (envelope) and ~2.0 ms/start (chordal) at 23#; a 300k-start envelope probe at {29,31,37,41}, L = 581, with zero loss. Corrections carried from review 2033: the census was rerun over the FULL start range (30 chunks), and the table is unchanged on every field, so its Ln values are full-range values and next_step part 1 is done; the negative set of every subset is exactly [1, Ln]. Arrays equal the served fprofile for all 15 subsets at 17# and 19# (30/30), and a definitional brute force at W = 2310 and 30030 finds 0 differences. 'min F < 0 for every subset' is trivial (F = 1 - 4 = -3 at L = 1); the informative content is the Ln/L_F table. Advisory nits: vals[] not reset per start (harmless), the int16 comment is wrong (F >= -3N; safe at Lmax 2000, not as stated for larger Lmax), the usage string omits ASTART, check_9321.py C12/C13 fail on the partial census. Not established: none of the 15 full-range envelope scans at each subset's Ln was run; no chordal scan was run (priced infeasible at ~5.4 days per subset on one core); Lmax 2000 is a measurement window, not a proof about larger L; nothing about other wheels; nothing about TPC. Route 2's uniform subquadratic positivity premise remains unproved and TPC-strength.","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":11947,"input_sha256":"c56aa3d38647f0379fb74ee9de388ce647e5bbe37d1958697a3fd251d99ad62d","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"3a240941392cfe854081ffebacd181495e8e916620a4a04f6d6271911909a063","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5755,"material_evidence":{"sha256":"1e8b9d9c13f503c4b649b42a52a015a39c8c58595c0503a7438b4f968579b868","entries":{"return:5755":"0f52b90baeeb089aa1c3fba9fddcfaf44bbc6c09dbf728f7afd21e03a1d498d3","artifact:5755:0031ba4365d3a8c3c0a9e06833fa2c3b8db6f7ec30c86bf4971347471262bf36":"0031ba4365d3a8c3c0a9e06833fa2c3b8db6f7ec30c86bf4971347471262bf36","artifact:5755:3c413e2e9d75c75c05fd35db82b237acc3e9fbe2af7c6f262956f974d64a30d6":"3c413e2e9d75c75c05fd35db82b237acc3e9fbe2af7c6f262956f974d64a30d6","artifact:5755:676f02a187c625bc38e5c2071de8d413f2055f053c9f9efd7dd5b0cf56a46a82":"676f02a187c625bc38e5c2071de8d413f2055f053c9f9efd7dd5b0cf56a46a82","artifact:5755:760b8bc3bce97eb1a22ed7133e8af2178d8323c2b34db7498fcff2e0cde89e47":"760b8bc3bce97eb1a22ed7133e8af2178d8323c2b34db7498fcff2e0cde89e47","artifact:5755:85bcfd7d26aa807549c24dcce928d1753dee1454b2e6d0efa0d881b89b78e60a":"85bcfd7d26aa807549c24dcce928d1753dee1454b2e6d0efa0d881b89b78e60a","artifact:5755:dcebd4f32d7db58afceb0b06c765e9b2c1480fd26ff36e72c2840b30e3b3e2db":"dcebd4f32d7db58afceb0b06c765e9b2c1480fd26ff36e72c2840b30e3b3e2db","artifact:5755:dde567ddd8a4ce2eff389779efc51ac2fc32e0d34fe9e0b3ce766f4251f08236":"dde567ddd8a4ce2eff389779efc51ac2fc32e0d34fe9e0b3ce766f4251f08236","artifact:5755:f37262ef7754f88f45eb1a19d15e613287577cf7938c18aed2785eef15fa00a0":"f37262ef7754f88f45eb1a19d15e613287577cf7938c18aed2785eef15fa00a0"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5755,"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 #5755: 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\":5755,\"report_sha256\":\"3a240941392cfe854081ffebacd181495e8e916620a4a04f6d6271911909a063\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5755\":\"0f52b90baeeb089aa1c3fba9fddcfaf44bbc6c09dbf728f7afd21e03a1d498d3\",\"artifact:5755:0031ba4365d3a8c3c0a9e06833fa2c3b8db6f7ec30c86bf4971347471262bf36\":\"0031ba4365d3a8c3c0a9e06833fa2c3b8db6f7ec30c86bf4971347471262bf36\",\"artifact:5755:3c413e2e9d75c75c05fd35db82b237acc3e9fbe2af7c6f262956f974d64a30d6\":\"3c413e2e9d75c75c05fd35db82b237acc3e9fbe2af7c6f262956f974d64a30d6\",\"artifact:5755:676f02a187c625bc38e5c2071de8d413f2055f053c9f9efd7dd5b0cf56a46a82\":\"676f02a187c625bc38e5c2071de8d413f2055f053c9f9efd7dd5b0cf56a46a82\",\"artifact:5755:760b8bc3bce97eb1a22ed7133e8af2178d8323c2b34db7498fcff2e0cde89e47\":\"760b8bc3bce97eb1a22ed7133e8af2178d8323c2b34db7498fcff2e0cde89e47\",\"artifact:5755:85bcfd7d26aa807549c24dcce928d1753dee1454b2e6d0efa0d881b89b78e60a\":\"85bcfd7d26aa807549c24dcce928d1753dee1454b2e6d0efa0d881b89b78e60a\",\"artifact:5755:dcebd4f32d7db58afceb0b06c765e9b2c1480fd26ff36e72c2840b30e3b3e2db\":\"dcebd4f32d7db58afceb0b06c765e9b2c1480fd26ff36e72c2840b30e3b3e2db\",\"artifact:5755:dde567ddd8a4ce2eff389779efc51ac2fc32e0d34fe9e0b3ce766f4251f08236\":\"dde567ddd8a4ce2eff389779efc51ac2fc32e0d34fe9e0b3ce766f4251f08236\",\"artifact:5755:f37262ef7754f88f45eb1a19d15e613287577cf7938c18aed2785eef15fa00a0\":\"f37262ef7754f88f45eb1a19d15e613287577cf7938c18aed2785eef15fa00a0\"},\"sha256\":\"1e8b9d9c13f503c4b649b42a52a015a39c8c58595c0503a7438b4f968579b868\"},\"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:5755,input_sha256:\"c56aa3d38647f0379fb74ee9de388ce647e5bbe37d1958697a3fd251d99ad62d\",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/5908/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"6d9cad01eb3ebea8adb253e9a48f7c217b51b93070f23c87656fc7786a000cb5","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}