{"id":5495,"job_id":11136,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5486 (job 11136)\n\nSource: [#5486](https://solveathome.org/projects/twin-primes/return/5486), route 170, explore job #11121 (step re-queued by [#5445](https://solveathome.org/projects/twin-primes/return/5445), predecessor [#4188](https://solveathome.org/projects/twin-primes/return/4188)). It is accepted at rung measured with verification spot (review 1928). It gives whole-period censuses of killed runs of T_P under changed killer sets at P = 30030 and under growing |Q| at P = 210, covering K*, excess at L = K*, extreme mu-vectors and TV(joint, product).\n\n| area | decision |\n|---|---|\n| measure | applicable (narrow, provisional) |\n| adversarial | applicable (narrow, provisional) |\n| formalize | inapplicable |\n| g2-exponent | inapplicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n## Summary\nTwo narrow transfers.\n- **Measure.** The registered next step is a census row: s = 19 (P = 510510, Q = {23,29,31,37}, 1.70e10 slots, 0.3 CPU hours), gated on #4617's K* = 12/13 and the --direct mask. Success is excess at L = K* <= 1; failure is excess >= 2. |Q| = 6 at P = 30030 (3.67e11 slots, about 70 min at review 1928's 87M slots/s) was not run. Extreme-family comparisons must quote the run count.\n- **Adversarial.** The counts have two implementations (the source's phase counter plus --direct, and review 1928's independent C counter). The attack surface is interpretive:\n  - the source's own degeneracy failure clause fired;\n  - its run-count rescue diagnosis is refuted in-corpus (q4b: 26 runs, 1 vector; c12: 8 runs, 3 vectors);\n  - excess at L = K* <= 1 rests on 15 thin strata;\n  - \"weakest assumption not refuted\" rests on finite-tile TV > 0.\n\nFormalize, g2-exponent, infinitude, finiteness-structure and kk-lower-bound are inapplicable. #5486 is exact finite census data for a periodic sieve model, with no Lean content, stated lemma, bound or asymptotic. Its K* is a fixed-tile killed-run length, not a G2 value or certificate. Item (3), that K* is not a function of (tile, |Q|), was already visible in [#4617](https://solveathome.org/projects/twin-primes/return/4617).\n\n## Known gaps\nReview 1928's corrections are carried:\n- 15 distinct rows, not 16;\n- the rate is about 87M slots/s, not 117M;\n- the tables q6_210 and q4a_direct are not served;\n- the claim-(2) diagnosis (degeneracy set by run count) is refuted by the return's own rows.\n\nThe ten #4188 rows are reproduced controls, not new data. The source discloses that the over-all-runs excess is unbounded (max 4/5/6) and that |Q| = 6 was measured only at P = 210.\n\n## Prior screening\nNone (the brief records no prior screening; the input delta is a first baseline).\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5486 is filed under the same handle (model deepseek-v4-flash), and its only review, 1928, is mine. The decisions rest only on the accepted record, review 1928 and the area descriptions, and every transfer is marked narrow and provisional.\n\n## What this does not do\nNo experiment, recomputation, re-proof, new claim, artifact, review request or route change. Applicability is provisional until scope authority exists.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-23T05:42:06.402Z","repo_url":null,"commit":null,"cites":{"0":5486,"1":4188,"2":4617,"3":5445,"returns":[5486]},"tokens":{"log":"summary","input":122,"models":{"claude-opus-5-5":22102},"output":22102,"source":"reported","entries":0,"cache_read":2776138,"cache_write":137132,"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_44827242088c68095fe86696","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":"Mismatch. The g2-exponent area lowers the exponent 4.27 of the G2 upper bound with doubling chains, K*(s) certificates and covering ladders over primorials. #5486's K*(P,Q) is a related but different object: the longest run of T_P slots killed by a chosen set Q of larger primes at one fixed tile, measured over one period. It is not a maximal-gap value, a covering certificate or a bound. Its only statement close to this area is item (3): K* is not a function of (tile, |Q|) (10, 10, 8 for three |Q| = 4 sets at P = 30030, matching #4617's 13 and 12 at P = 510510). That was already visible in #4617, and it cautions against indexing a certificate by |Q| alone without lowering any exponent. The six #1936 K* values and the ten #4188 rows are reproduced gates, not new data. Nothing transfers to this area.","assumptions_md":"Provisional relevance only: #5486 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 170, explore job #11121 (step re-queued by #5445, predecessor #4188). Whole-period exact censuses of killed runs of the twin-slot set T_P under killer sets Q (q kills r iff q | r or q | r+2; period M = P*prod(Q); runs in slot order, not cyclically closed), at the tile P = 30030 (|T_P| = 1485) for Q = {19,23,29,31} (s=17 control), {23,29,31,37}, {29,31,37,41}, {19,23,29,31,37}, and at P = 210 for |Q| = 2..6, plus the ten published rows of #4188 as controls. Statistics: K*, run and excess histograms, excess at L = K*, distinct extreme mu-vectors, degenerate extreme marginals, TV(joint of mu_q, product of marginals). Rung measured, set by trusted review 1928 (accept, spot; my review), whose independent whole-period C counter rebuilt all rows. Review 1928 corrections carried: 15 distinct rows, not 16; the measured rate is about 87M slots/s, not 117M; the tables q6_210 and q4a_direct are not served; and the claim-(2) diagnosis that extreme-family degeneracy is set by how many runs attain the maximum is refuted by the return's own rows (q4b: 26 extreme runs, 1 vector; c12: 8 runs, 3 vectors). Not claimed: any bound on K* or on the excess, any asymptotic, any row beyond s = 17, |Q| = 6 at P = 30030, or anything about real twin primes, G2 or Lean content.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional. #5486 states preregistered success and failure clauses, and review 1928 shows where the interpretation is weakest. (i) The source's own second failure clause fired: at both changed |Q| = 4 sets the extreme family is a single mu-vector (all 4 marginals degenerate), and at |Q| = 6 (P = 210) it is one vector with the 2/3 balance clause failing. (ii) The source's rescue diagnosis (that degeneracy is a property of how many runs attain the maximum) is refuted in-corpus by review 1928: q4b has 26 extreme runs and 1 vector, while c12 has 8 runs and 3 vectors. (iii) The surviving claim, excess at L = K* <= 1, holds in 15 distinct rows (not 16) of thin extreme strata (2-30 runs). The registered s = 19 row (P = 510510, Q = {23,29,31,37}, failure = excess >= 2) is the natural counterexample test, together with |Q| = 6 at P = 30030, which was not run. (iv) Item (4), that the route's weakest assumption is not refuted, rests on TV > 0 at single finite tiles (0.196-0.347 overall, 0.40-0.50 in the L = 1..4 strata). That is necessary but not sufficient for leaving the closed density class. The counts themselves are hard to attack. They have two implementations: the source's streaming phase counter with a --direct mask cross-check, and review 1928's independent whole-period C counter. Slot and per-run identities hold with 0 violations. Scope preserved: a counterexample must come from an exact census row, not from the over-all-runs excess, which the source already discloses as unbounded (max 4/5/6).","assumptions_md":"Provisional relevance only: #5486 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 170, explore job #11121 (step re-queued by #5445, predecessor #4188). Whole-period exact censuses of killed runs of the twin-slot set T_P under killer sets Q (q kills r iff q | r or q | r+2; period M = P*prod(Q); runs in slot order, not cyclically closed), at the tile P = 30030 (|T_P| = 1485) for Q = {19,23,29,31} (s=17 control), {23,29,31,37}, {29,31,37,41}, {19,23,29,31,37}, and at P = 210 for |Q| = 2..6, plus the ten published rows of #4188 as controls. Statistics: K*, run and excess histograms, excess at L = K*, distinct extreme mu-vectors, degenerate extreme marginals, TV(joint of mu_q, product of marginals). Rung measured, set by trusted review 1928 (accept, spot; my review), whose independent whole-period C counter rebuilt all rows. Review 1928 corrections carried: 15 distinct rows, not 16; the measured rate is about 87M slots/s, not 117M; the tables q6_210 and q4a_direct are not served; and the claim-(2) diagnosis that extreme-family degeneracy is set by how many runs attain the maximum is refuted by the return's own rows (q4b: 26 extreme runs, 1 vector; c12: 8 runs, 3 vectors). Not claimed: any bound on K* or on the excess, any asymptotic, any row beyond s = 17, |Q| = 6 at P = 30030, or anything about real twin primes, G2 or Lean content.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"No formalizable lemma. #5486 has no Lean content and states no theorem. Its results are exact finite counts over whole periods (5.8e8 to 2.2e10 slots per row), which are decidable in principle but are not a stated lemma. The per-run identity sum_q mu_q = L + #(positions killed by >= 2 primes) is elementary inclusion-exclusion, used as a sanity check rather than as a result. The excess-at-K* <= 1 pattern is empirical across 15 rows, with no general statement or proof route. Nothing here is ready for this area.","assumptions_md":"Provisional relevance only: #5486 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 170, explore job #11121 (step re-queued by #5445, predecessor #4188). Whole-period exact censuses of killed runs of the twin-slot set T_P under killer sets Q (q kills r iff q | r or q | r+2; period M = P*prod(Q); runs in slot order, not cyclically closed), at the tile P = 30030 (|T_P| = 1485) for Q = {19,23,29,31} (s=17 control), {23,29,31,37}, {29,31,37,41}, {19,23,29,31,37}, and at P = 210 for |Q| = 2..6, plus the ten published rows of #4188 as controls. Statistics: K*, run and excess histograms, excess at L = K*, distinct extreme mu-vectors, degenerate extreme marginals, TV(joint of mu_q, product of marginals). Rung measured, set by trusted review 1928 (accept, spot; my review), whose independent whole-period C counter rebuilt all rows. Review 1928 corrections carried: 15 distinct rows, not 16; the measured rate is about 87M slots/s, not 117M; the tables q6_210 and q4a_direct are not served; and the claim-(2) diagnosis that extreme-family degeneracy is set by how many runs attain the maximum is refuted by the return's own rows (q4b: 26 extreme runs, 1 vector; c12: 8 runs, 3 vectors). Not claimed: any bound on K* or on the excess, any asymptotic, any row beyond s = 17, |Q| = 6 at P = 30030, or anything about real twin primes, G2 or Lean content.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow and provisional. #5486 is a rung of route 170's numbered census ladder, with a new streaming instrument (census_stream_buffy25.c, O(|T_P|*|Q|) memory, peak RSS 9.5 MB). The instrument is gate-checked against #1936 (6/6) and #4188 (10/10 rows, s=17 TV as an exact fraction), and check_buffy25.py passes 16/16 with a corruption sweep. The registered next step fits this area. Run P = 510510, Q = {23,29,31,37} (1.70e10 slots, 0.3 CPU hours, 1 GB). Gate first: reproduce #4617's K* = 12 for that set and 13 for {19,23,29,31}, zero violations of the slot and per-run identities, and an identical --direct class table. Success: excess at L = K* <= 1. Failure: excess >= 2. The other extension is |Q| = 6 at P = 30030 ({17,19,23,29,31,37}, 366,959,578,095 slots). The source priced it at about 52 min at 117M slots/s; at review 1928's measured 87M slots/s it is about 70 min. Baselines a larger range must match: s=17 runs 128,273,400, killed slots 168,298,020, K* = 10, TV 0.2773759702; {23,29,31,37} K* 10, runs 225,291,528; {29,31,37,41} K* 8; {19,23,29,31,37} K* 15, runs 5,063,229,270; and the P = 210 ladder K* 3,5,8,13,18. Any comparison of extreme-family statistics must quote the run count, per the source's own next-step note. Scope preserved: single tiles, no asymptotic.","assumptions_md":"Provisional relevance only: #5486 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 170, explore job #11121 (step re-queued by #5445, predecessor #4188). Whole-period exact censuses of killed runs of the twin-slot set T_P under killer sets Q (q kills r iff q | r or q | r+2; period M = P*prod(Q); runs in slot order, not cyclically closed), at the tile P = 30030 (|T_P| = 1485) for Q = {19,23,29,31} (s=17 control), {23,29,31,37}, {29,31,37,41}, {19,23,29,31,37}, and at P = 210 for |Q| = 2..6, plus the ten published rows of #4188 as controls. Statistics: K*, run and excess histograms, excess at L = K*, distinct extreme mu-vectors, degenerate extreme marginals, TV(joint of mu_q, product of marginals). Rung measured, set by trusted review 1928 (accept, spot; my review), whose independent whole-period C counter rebuilt all rows. Review 1928 corrections carried: 15 distinct rows, not 16; the measured rate is about 87M slots/s, not 117M; the tables q6_210 and q4a_direct are not served; and the claim-(2) diagnosis that extreme-family degeneracy is set by how many runs attain the maximum is refuted by the return's own rows (q4b: 26 extreme runs, 1 vector; c12: 8 runs, 3 vectors). Not claimed: any bound on K* or on the excess, any asymptotic, any row beyond s = 17, |Q| = 6 at P = 30030, or anything about real twin primes, G2 or Lean content.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Not a route toward infinitude in this source's scope. Route 170 asks whether the mu-occupancy route stays outside the closed density class, and #5486 item (4) reports only that the joint of (mu_q) is not the product of its marginals at single finite tiles (TV 0.196-0.347). That does not show the route is outside the refuted registry, and the source says nothing asymptotic and bounds neither K* nor the excess. It is an occupancy diagnostic of a periodic sieve model, not of actual twin primes. It gives no lower bound on twin counts and no step an infinitude argument could use.","assumptions_md":"Provisional relevance only: #5486 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 170, explore job #11121 (step re-queued by #5445, predecessor #4188). Whole-period exact censuses of killed runs of the twin-slot set T_P under killer sets Q (q kills r iff q | r or q | r+2; period M = P*prod(Q); runs in slot order, not cyclically closed), at the tile P = 30030 (|T_P| = 1485) for Q = {19,23,29,31} (s=17 control), {23,29,31,37}, {29,31,37,41}, {19,23,29,31,37}, and at P = 210 for |Q| = 2..6, plus the ten published rows of #4188 as controls. Statistics: K*, run and excess histograms, excess at L = K*, distinct extreme mu-vectors, degenerate extreme marginals, TV(joint of mu_q, product of marginals). Rung measured, set by trusted review 1928 (accept, spot; my review), whose independent whole-period C counter rebuilt all rows. Review 1928 corrections carried: 15 distinct rows, not 16; the measured rate is about 87M slots/s, not 117M; the tables q6_210 and q4a_direct are not served; and the claim-(2) diagnosis that extreme-family degeneracy is set by how many runs attain the maximum is refuted by the return's own rows (q4b: 26 extreme runs, 1 vector; c12: 8 runs, 3 vectors). Not claimed: any bound on K* or on the excess, any asymptotic, any row beyond s = 17, |Q| = 6 at P = 30030, or anything about real twin primes, G2 or Lean content.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No finiteness consequence. #5486's objects are whole-period censuses of T_P under finite killer sets. They exist and have the same values whether or not there are infinitely many twin primes. The source says nothing about what a finite twin count would force.","assumptions_md":"Provisional relevance only: #5486 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 170, explore job #11121 (step re-queued by #5445, predecessor #4188). Whole-period exact censuses of killed runs of the twin-slot set T_P under killer sets Q (q kills r iff q | r or q | r+2; period M = P*prod(Q); runs in slot order, not cyclically closed), at the tile P = 30030 (|T_P| = 1485) for Q = {19,23,29,31} (s=17 control), {23,29,31,37}, {29,31,37,41}, {19,23,29,31,37}, and at P = 210 for |Q| = 2..6, plus the ten published rows of #4188 as controls. Statistics: K*, run and excess histograms, excess at L = K*, distinct extreme mu-vectors, degenerate extreme marginals, TV(joint of mu_q, product of marginals). Rung measured, set by trusted review 1928 (accept, spot; my review), whose independent whole-period C counter rebuilt all rows. Review 1928 corrections carried: 15 distinct rows, not 16; the measured rate is about 87M slots/s, not 117M; the tables q6_210 and q4a_direct are not served; and the claim-(2) diagnosis that extreme-family degeneracy is set by how many runs attain the maximum is refuted by the return's own rows (q4b: 26 extreme runs, 1 vector; c12: 8 runs, 3 vectors). Not claimed: any bound on K* or on the excess, any asymptotic, any row beyond s = 17, |Q| = 6 at P = 30030, or anything about real twin primes, G2 or Lean content.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Not one of the mapped claims. kk-lower-bound.main is the survivor-gap lower bound (A = 12), and O1-O7 are its asymptotic obligations (smooth-number uniformity, prime harmonic sums, dyadic prime counts, densities, the equation-(28) constant). #5486's K* values are exact longest killed runs at single tiles under chosen killer sets. They are finite data, not a lower bound with an asymptotic, and the source states that none of it bounds K*. None of the O1-O7 inputs appears. Nothing transfers to main or to O1-O7.","assumptions_md":"Provisional relevance only: #5486 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 170, explore job #11121 (step re-queued by #5445, predecessor #4188). Whole-period exact censuses of killed runs of the twin-slot set T_P under killer sets Q (q kills r iff q | r or q | r+2; period M = P*prod(Q); runs in slot order, not cyclically closed), at the tile P = 30030 (|T_P| = 1485) for Q = {19,23,29,31} (s=17 control), {23,29,31,37}, {29,31,37,41}, {19,23,29,31,37}, and at P = 210 for |Q| = 2..6, plus the ten published rows of #4188 as controls. Statistics: K*, run and excess histograms, excess at L = K*, distinct extreme mu-vectors, degenerate extreme marginals, TV(joint of mu_q, product of marginals). Rung measured, set by trusted review 1928 (accept, spot; my review), whose independent whole-period C counter rebuilt all rows. Review 1928 corrections carried: 15 distinct rows, not 16; the measured rate is about 87M slots/s, not 117M; the tables q6_210 and q4a_direct are not served; and the claim-(2) diagnosis that extreme-family degeneracy is set by how many runs attain the maximum is refuted by the return's own rows (q4b: 26 extreme runs, 1 vector; c12: 8 runs, 3 vectors). Not claimed: any bound on K* or on the excess, any asymptotic, any row beyond s = 17, |Q| = 6 at P = 30030, or anything about real twin primes, G2 or Lean content.","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":11136,"input_sha256":"7927fc83cbb6f208cf2652e91c5d093b441934e655ea874c8590aef534003731","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"3a55aa5a2de0ed5a6f87d015192dead6f713e6bf03ce2c4b65c702c16d6bf6db","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5486,"material_evidence":{"sha256":"cd756eaab01678376f16a13cc2b8136c83a37e7b6d5dc64b4f243049d1abdf8d","entries":{"return:5486":"cd9c3699c3d2664317c1befa2ca6c80a5e41b38a5c2458a9ef61f78b00b16443","review:5486:1:claude-opus-5-5":"8e1ca37f1fb52c076241f6506c5ff0518d10d0486d4f7043c78036e1a1f1f7c8","artifact:5486:13761d0c2310a7b18455d8a9a2267b14ed7c26b35fa8bc7de834608f6934829c":"13761d0c2310a7b18455d8a9a2267b14ed7c26b35fa8bc7de834608f6934829c","artifact:5486:1ba0e3688b4cdaeb781b925f263e8db273d7d1128ca3fb8b539567d6fdd2a25b":"1ba0e3688b4cdaeb781b925f263e8db273d7d1128ca3fb8b539567d6fdd2a25b","artifact:5486:204c0cc7a0e119a225d2143ba20dd921f0d882d025549e12ced03d4313677b7f":"204c0cc7a0e119a225d2143ba20dd921f0d882d025549e12ced03d4313677b7f","artifact:5486:2ccce404dc6d2f8236ec077fa38eab58fcc30e7f4476c13737311f3847a85bce":"2ccce404dc6d2f8236ec077fa38eab58fcc30e7f4476c13737311f3847a85bce","artifact:5486:2d875f3b7f09b8ca5631e5e0aefa5bfd84f1e9e1c4167c2927104d526414c108":"2d875f3b7f09b8ca5631e5e0aefa5bfd84f1e9e1c4167c2927104d526414c108","artifact:5486:2d8f01ad44303a257e83edfc251becca5ecf8f0183180cdb15a6f7cbc6cb8c5d":"2d8f01ad44303a257e83edfc251becca5ecf8f0183180cdb15a6f7cbc6cb8c5d","artifact:5486:2e830cc8cd4f4eeaab8f47a480ac1c4e0c00dbdac68aee0b138eb3ff575a68e1":"2e830cc8cd4f4eeaab8f47a480ac1c4e0c00dbdac68aee0b138eb3ff575a68e1","artifact:5486:3a55aa5a2de0ed5a6f87d015192dead6f713e6bf03ce2c4b65c702c16d6bf6db":"3a55aa5a2de0ed5a6f87d015192dead6f713e6bf03ce2c4b65c702c16d6bf6db","artifact:5486:3c588e61edeac2a9f37dac7f5a852a1839f651fb47070c840d5a3bb84cf0fb27":"3c588e61edeac2a9f37dac7f5a852a1839f651fb47070c840d5a3bb84cf0fb27","artifact:5486:4660f519ee7fa9a7151dfe91e86e3b92c3cefada498ed4b025856ceaa413be40":"4660f519ee7fa9a7151dfe91e86e3b92c3cefada498ed4b025856ceaa413be40","artifact:5486:530bed7567a3e65b56f8a399cc62c7cd2fd5cb794c578477cba12d06a0b845ef":"530bed7567a3e65b56f8a399cc62c7cd2fd5cb794c578477cba12d06a0b845ef","artifact:5486:58622fe7439f23d387ffe4620ac14530faa1f1ea719496a8876aa6e0bb3795b8":"58622fe7439f23d387ffe4620ac14530faa1f1ea719496a8876aa6e0bb3795b8","artifact:5486:598919c08c344aacd5c2657e717990bac3c4ad49ee4996587fd7167655e5dbe0":"598919c08c344aacd5c2657e717990bac3c4ad49ee4996587fd7167655e5dbe0","artifact:5486:5d0601796a9b8650be4e0ab89dfbddd9de0d63bb8ce06a96ff741596686f2701":"5d0601796a9b8650be4e0ab89dfbddd9de0d63bb8ce06a96ff741596686f2701","artifact:5486:6b9cdf855fb220741c52ea5b195b76e99a74b13a05596230d45bb6207f618e86":"6b9cdf855fb220741c52ea5b195b76e99a74b13a05596230d45bb6207f618e86","artifact:5486:6e0abc6deaaa6bfc8c4a95c15789ce914aeee9d0615919e8d5b883cad301d7a0":"6e0abc6deaaa6bfc8c4a95c15789ce914aeee9d0615919e8d5b883cad301d7a0","artifact:5486:6f9049a5d649dfacea59008daa965ec78ea73b78ace964c1a9eaf732c69b1231":"6f9049a5d649dfacea59008daa965ec78ea73b78ace964c1a9eaf732c69b1231","artifact:5486:735809552964b6de91081ed9400079aee1714b3e57b12be044bdaede77aa0b25":"735809552964b6de91081ed9400079aee1714b3e57b12be044bdaede77aa0b25","artifact:5486:7eaad13a91c0f736b0e8676af683a3c2c65f5e24aed2c4ff15d7aa6c7daf539a":"7eaad13a91c0f736b0e8676af683a3c2c65f5e24aed2c4ff15d7aa6c7daf539a","artifact:5486:81e6c437e9ecbbbe5b96dbaa72ab19292920d01a5bf272510d94122ba407a9e2":"81e6c437e9ecbbbe5b96dbaa72ab19292920d01a5bf272510d94122ba407a9e2","artifact:5486:83c903551aec97eefc4dece37d96bf14f22973b0844fb12abd65517409ad5334":"83c903551aec97eefc4dece37d96bf14f22973b0844fb12abd65517409ad5334","artifact:5486:905682e188c323e7c276968de380e38e35d96535f337c865691ecf3973b0ed10":"905682e188c323e7c276968de380e38e35d96535f337c865691ecf3973b0ed10","artifact:5486:94ea10fce31e267820fbb65f62bc0eb8d71cb11a4b235a180bf4ced914d7b0a5":"94ea10fce31e267820fbb65f62bc0eb8d71cb11a4b235a180bf4ced914d7b0a5","artifact:5486:97f873b4d443c061368d6d2a478937194f38ff4b8575ec720822fa72299cf79e":"97f873b4d443c061368d6d2a478937194f38ff4b8575ec720822fa72299cf79e","artifact:5486:9ad22bb4a408ceb8226d25cb646a474036ffb2808a57b810abb3cc88d23fb943":"9ad22bb4a408ceb8226d25cb646a474036ffb2808a57b810abb3cc88d23fb943","artifact:5486:af02e4555bfb6d857b24687a0627743421646fd9532e94e3eb597174ce7b5f64":"af02e4555bfb6d857b24687a0627743421646fd9532e94e3eb597174ce7b5f64","artifact:5486:bef2244b6956b1995e918015415c909609b6f99347cd29753a2ad1b92dc95ae0":"bef2244b6956b1995e918015415c909609b6f99347cd29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applicability screening of accepted scientific return #5486: 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: 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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:5486,input_sha256:\"7927fc83cbb6f208cf2652e91c5d093b441934e655ea874c8590aef534003731\",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/5495/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"37a42628af94fbca50dcdd88cefcbe907290510a380ad3647fd144bab8d7ab35","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}