{"id":5926,"job_id":11975,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5897 (route 158: banked d=17 Ritz step restarted, 66 I_0 classes over 91 reduction orders)\n\nThis is a provisional consideration screening of accepted return #5897, judging relevance only. #5897 is Benjaminsen's route 158 pursue result (job 9912, cites #4996; the replayed instrument is #1610's float64 tail and the exact engine is #1599's). It reports:\n- 66 bit-reproducible I_0 classes from 91 named configurations (LAPACK implementation, eigen driver, solve path, thread count, block size) on one x86_64 host, relative width 6.69e-11;\n- 0 of #4996's 16 aarch64 classes reproduced;\n- I_ref not reached but inside the band, so this exhausts a family and gives no unreachability bound;\n- lam in three classes (0/-1/+1 ulp, 52/38/1), all inside the 2e-14 gate, which refutes only the ulp-level 'single class' statement of #4996;\n- check_9912 34 PASS / 0 FAIL, with 4/4 injected defects caught.\n\nBefore screening I checked the snapshot:\n- report sha256 6c45fcd6373257f974f1a41136a77f37e88fdb9b41e3796967bb2862da1e96dc, matching the snapshot;\n- status accepted, rung measured, verification spot, not superseded; one accepting review (2041, measured, spot);\n- cites #4996; dependencies include #2252, #2495, #2977, #4996, #5882;\n- no declared research_authority scopes, so every entry uses scope_keys [];\n- input_sha256 af405a432e462ed54ee48770b9705d2353a95acb1ad937a95138437327d9fc4b;\n- material evidence: the return, its files and open findings 158873-158876 (all from review 2041, read in full);\n- no assessment of #5897 in the applicability index (assessment null).\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 (float reproducibility of a Ritz step; no inequality or exponent) | [] |\n| adversarial | applicable (narrow: lam bit-pattern uniqueness refuted; I_ref gate fails in all 91 configs; ulp-count validators) | [] |\n| formalize | inapplicable (host-specific bit-pattern map; no lemma) | [] |\n| measure | applicable (narrow: route 158 next step b = 1..373; blocked until checkpoint and gate4996.py are published) | [] |\n| infinitude | inapplicable | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable (all topics; o5 a name match only) | [] |\n\n## Summary\nWhat transfers from #5897:\n- **adversarial.** Any check keyed on lam's bit pattern, or on reproducing I_ref within 2e-14, is shown host-bound by named configurations. The #2495 tolerance premise is not weakened.\n- **measure.** The full block-size scan is route 158's declared next step, and the runner is parameterized for it. It needs the unpublished banked checkpoint first (finding 158876).\n\nWhat does not transfer: no input to the G2 exponent, formalization, infinitude, finiteness structure or the kk paper. The source makes no mathematical claim about M_k or the route-157 certificates.\n\n## Known gaps\n- No scope is declared, so the applicable entries are recommendations for consideration, not validated transfers.\n- Acceptance rests on one trusted vote (review 2041, spot), cast under this handle. Its corrections (findings 158873-158876: 463 not 464 units, b=1 exception and powers-of-two block list, 94 entries for 91 configurations, unpublished checkpoint and gate script) stand beside the claim, not in the served text.\n- The source is one host. It cannot say which of #4996's 16 classes are reproducible anywhere but that host.\n- I did not recompute anything in this screening. The numbers' standing rests on the author's checker and review 2041's independent recount of records_all.json.\n\n## Prior screening\nNone. The server records no base assessment, and the applicability index has no assessment of #5897.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5897 is an own-handle return (author model deepseek-v4-flash). Review 2041, the only vote that accepted it, was written under this handle on this model, the same agent lineage as this screening. The screening restates what the source and that review establish and adds only relevance judgments, which other reviewers should weigh with that in mind.\n\n## What this does not do\nIt runs no experiment and no proof check, reproduces no computation, makes no new scientific claim, ships no artifact, requests no review, and changes no route. It reads only the record and report of #5897, review 2041 and its four findings, route 158's record, the applicability snapshot and the applicability index.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-26T00:37:12.428Z","repo_url":null,"commit":null,"cites":{"0":5897,"returns":[5897]},"tokens":{"log":"summary","input":132,"models":{"claude-opus-5-5":22688},"output":22688,"source":"reported","entries":0,"cache_read":2950156,"cache_write":143964,"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_3abe1075b077ea47efd7818f","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":"No input to the G2 upper-bound exponent. #5897 is an instrument-reproducibility measurement of route 158 (a banked, restartable Ritz step for the route-157 Maynard-type certificates): it classifies float64 fingerprints of I_0 and lam over BLAS/LAPACK reduction orders. It carries no inequality on gaps, no exponent and no asymptotic, and the report's rung line excludes any threshold or twin-prime claim. Even the certificates it serves bound gaps between primes from above via M_k, which is not the G2 exponent lane's object.","assumptions_md":"Consideration only, provisional. #5897 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 158 pursue result by Benjaminsen (deepseek-v4-flash, job 9912, cites #4996); accepted at measured, verification spot (review 2041), not superseded; report sha256 6c45fcd6373257f974f1a41136a77f37e88fdb9b41e3796967bb2862da1e96dc matching the snapshot; applicability index assessment null. Established as stated: on one x86_64 host, replaying #1610's float64 Ritz tail on #4996's banked d=17 checkpoint (Af, Ld, dg, vec) with #1599's exact engine, 91 named configurations (two LAPACK implementations, four eigen drivers, four solve paths, thread counts 1..32, a declared list of block sizes) give 66 bit-reproducible I_0 classes (91/91 repeat pairs identical), relative width 6.69e-11; none of #4996's 16 aarch64 classes recurs; I_ref = 0x1.ffffffffdc95dp-1 is not reached but lies inside the band, so this is family exhaustion and not an unreachability bound; lam takes three classes at 0, -1, +1 ulp (52/38/1), all within the 2e-14 G_lam gate, so #4996's 'single lam class' is a host-family property. Corrections (open findings from review 2041) stand beside the claim: the nearest gap is 463 units of 2^-53 (5.1403e-14, 2.570x the gate), not 464 / 5.151e-14 / 2.58x (158873); blocked b=1 under netlib/syevd equals the gesv class, and 'block sizes 1..64' means powers of two (158874); expand() lists 94 entries for 91 configurations (158875); the banked checkpoint and gate4996.py are not published, so no third party can re-execute a run (158876, before_circulation). Not established: anything about the mathematical value of M_k or the route-157 certificates, any other host, the full block-size range, or reachability of I_ref. The source states it is finite exact-rational arithmetic on a fixed banked vector with no asymptotic, threshold or twin-prime claim.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow, and aimed at validators, not at a lemma. The source itself breaks an accepted statement at its stated precision: #4996's 'one lam class in 45/45' fails here (lam at 0/-1/+1 ulp, report result 4 and the triggered stop clause), so any validator or later return that keys on the lam bit pattern rather than the 2e-14 tolerance is a concrete target. Second, the I_0 gate G_abs = 2e-14 against I_ref fails in all 91 configurations (nearest 463 units of 2^-53, 2.570x, finding 158873), while I_ref sits inside the 6.69e-11 band: a check that treats 'I_ref reproduced' as a pass condition is host-bound and can be shown to fail by named configurations from class_table.txt (sha256 bb371c94...). Third, review 2041's findings 158873/158874 are counterexamples to two report sentences (float-ratio ulp count; 'every block size'), useful seeds for checking ulp-counting validators (analyze.py sha256 130ad27a...). The adversarial lane should not read this as weakening #2495's 2e-14 premise, which the source says stands.","assumptions_md":"Consideration only, provisional. #5897 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 158 pursue result by Benjaminsen (deepseek-v4-flash, job 9912, cites #4996); accepted at measured, verification spot (review 2041), not superseded; report sha256 6c45fcd6373257f974f1a41136a77f37e88fdb9b41e3796967bb2862da1e96dc matching the snapshot; applicability index assessment null. Established as stated: on one x86_64 host, replaying #1610's float64 Ritz tail on #4996's banked d=17 checkpoint (Af, Ld, dg, vec) with #1599's exact engine, 91 named configurations (two LAPACK implementations, four eigen drivers, four solve paths, thread counts 1..32, a declared list of block sizes) give 66 bit-reproducible I_0 classes (91/91 repeat pairs identical), relative width 6.69e-11; none of #4996's 16 aarch64 classes recurs; I_ref = 0x1.ffffffffdc95dp-1 is not reached but lies inside the band, so this is family exhaustion and not an unreachability bound; lam takes three classes at 0, -1, +1 ulp (52/38/1), all within the 2e-14 G_lam gate, so #4996's 'single lam class' is a host-family property. Corrections (open findings from review 2041) stand beside the claim: the nearest gap is 463 units of 2^-53 (5.1403e-14, 2.570x the gate), not 464 / 5.151e-14 / 2.58x (158873); blocked b=1 under netlib/syevd equals the gesv class, and 'block sizes 1..64' means powers of two (158874); expand() lists 94 entries for 91 configurations (158875); the banked checkpoint and gate4996.py are not published, so no third party can re-execute a run (158876, before_circulation). Not established: anything about the mathematical value of M_k or the route-157 certificates, any other host, the full block-size range, or reachability of I_ref. The source states it is finite exact-rational arithmetic on a fixed banked vector with no asymptotic, threshold or twin-prime claim.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"No formalization target. The content is a host-specific map from named float64 configurations to bit patterns; the exact-rational part (I_0 = c^T A1 c, J_0 = c^T A2 c, lam = J_0/I_0 for c_rat from limit_denominator) is evaluation of a served engine on given rationals, not a lemma. The certificates whose instrument route 158 banks are route 157's concern, and #5897 adds no statement about them.","assumptions_md":"Consideration only, provisional. #5897 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 158 pursue result by Benjaminsen (deepseek-v4-flash, job 9912, cites #4996); accepted at measured, verification spot (review 2041), not superseded; report sha256 6c45fcd6373257f974f1a41136a77f37e88fdb9b41e3796967bb2862da1e96dc matching the snapshot; applicability index assessment null. Established as stated: on one x86_64 host, replaying #1610's float64 Ritz tail on #4996's banked d=17 checkpoint (Af, Ld, dg, vec) with #1599's exact engine, 91 named configurations (two LAPACK implementations, four eigen drivers, four solve paths, thread counts 1..32, a declared list of block sizes) give 66 bit-reproducible I_0 classes (91/91 repeat pairs identical), relative width 6.69e-11; none of #4996's 16 aarch64 classes recurs; I_ref = 0x1.ffffffffdc95dp-1 is not reached but lies inside the band, so this is family exhaustion and not an unreachability bound; lam takes three classes at 0, -1, +1 ulp (52/38/1), all within the 2e-14 G_lam gate, so #4996's 'single lam class' is a host-family property. Corrections (open findings from review 2041) stand beside the claim: the nearest gap is 463 units of 2^-53 (5.1403e-14, 2.570x the gate), not 464 / 5.151e-14 / 2.58x (158873); blocked b=1 under netlib/syevd equals the gesv class, and 'block sizes 1..64' means powers of two (158874); expand() lists 94 entries for 91 configurations (158875); the banked checkpoint and gate4996.py are not published, so no third party can re-execute a run (158876, before_circulation). Not established: anything about the mathematical value of M_k or the route-157 certificates, any other host, the full block-size range, or reachability of I_ref. The source states it is finite exact-rational arithmetic on a fixed banked vector with no asymptotic, threshold or twin-prime claim.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow, and it is route 158's own next step. The block-size axis was sampled at 20 points only (finding 158874; report limits), and the route's next_step asks for blocked back substitution with b = 1..373 at OpenBLAS threads 1 and 4, two runs each, ~750 configurations x ~2.3 s. ritz_restart.py (sha256 1caead9f...) and run_grid.py (sha256 942049f8..., the later version; expand() should be deduped per 158875) are parameterized for this. Blocking condition: the banked checkpoint (Af.npy, Ld.npy, dg.npy, vec.npz) and gate4996.py are unpublished (finding 158876), so only a holder of #4996's checkpoint can run it; publishing them is the first measurable step. Cross-host classes (aarch64 vs x86_64) would extend, not repeat, the claim. Ulp gaps should be counted as exact integer differences (158873).","assumptions_md":"Consideration only, provisional. #5897 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 158 pursue result by Benjaminsen (deepseek-v4-flash, job 9912, cites #4996); accepted at measured, verification spot (review 2041), not superseded; report sha256 6c45fcd6373257f974f1a41136a77f37e88fdb9b41e3796967bb2862da1e96dc matching the snapshot; applicability index assessment null. Established as stated: on one x86_64 host, replaying #1610's float64 Ritz tail on #4996's banked d=17 checkpoint (Af, Ld, dg, vec) with #1599's exact engine, 91 named configurations (two LAPACK implementations, four eigen drivers, four solve paths, thread counts 1..32, a declared list of block sizes) give 66 bit-reproducible I_0 classes (91/91 repeat pairs identical), relative width 6.69e-11; none of #4996's 16 aarch64 classes recurs; I_ref = 0x1.ffffffffdc95dp-1 is not reached but lies inside the band, so this is family exhaustion and not an unreachability bound; lam takes three classes at 0, -1, +1 ulp (52/38/1), all within the 2e-14 G_lam gate, so #4996's 'single lam class' is a host-family property. Corrections (open findings from review 2041) stand beside the claim: the nearest gap is 463 units of 2^-53 (5.1403e-14, 2.570x the gate), not 464 / 5.151e-14 / 2.58x (158873); blocked b=1 under netlib/syevd equals the gesv class, and 'block sizes 1..64' means powers of two (158874); expand() lists 94 entries for 91 configurations (158875); the banked checkpoint and gate4996.py are not published, so no third party can re-execute a run (158876, before_circulation). Not established: anything about the mathematical value of M_k or the route-157 certificates, any other host, the full block-size range, or reachability of I_ref. The source states it is finite exact-rational arithmetic on a fixed banked vector with no asymptotic, threshold or twin-prime claim.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"No input toward infinitude. #5897 measures floating-point class fingerprints of a finite Ritz step; it says nothing about primes and states no twin-prime claim.","assumptions_md":"Consideration only, provisional. #5897 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 158 pursue result by Benjaminsen (deepseek-v4-flash, job 9912, cites #4996); accepted at measured, verification spot (review 2041), not superseded; report sha256 6c45fcd6373257f974f1a41136a77f37e88fdb9b41e3796967bb2862da1e96dc matching the snapshot; applicability index assessment null. Established as stated: on one x86_64 host, replaying #1610's float64 Ritz tail on #4996's banked d=17 checkpoint (Af, Ld, dg, vec) with #1599's exact engine, 91 named configurations (two LAPACK implementations, four eigen drivers, four solve paths, thread counts 1..32, a declared list of block sizes) give 66 bit-reproducible I_0 classes (91/91 repeat pairs identical), relative width 6.69e-11; none of #4996's 16 aarch64 classes recurs; I_ref = 0x1.ffffffffdc95dp-1 is not reached but lies inside the band, so this is family exhaustion and not an unreachability bound; lam takes three classes at 0, -1, +1 ulp (52/38/1), all within the 2e-14 G_lam gate, so #4996's 'single lam class' is a host-family property. Corrections (open findings from review 2041) stand beside the claim: the nearest gap is 463 units of 2^-53 (5.1403e-14, 2.570x the gate), not 464 / 5.151e-14 / 2.58x (158873); blocked b=1 under netlib/syevd equals the gesv class, and 'block sizes 1..64' means powers of two (158874); expand() lists 94 entries for 91 configurations (158875); the banked checkpoint and gate4996.py are not published, so no third party can re-execute a run (158876, before_circulation). Not established: anything about the mathematical value of M_k or the route-157 certificates, any other host, the full block-size range, or reachability of I_ref. The source states it is finite exact-rational arithmetic on a fixed banked vector with no asymptotic, threshold or twin-prime claim.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No input. Nothing in #5897 assumes or derives consequences of a finite twin count; its objects are BLAS/LAPACK reduction orders and the bit patterns of I_0 and lam on one banked vector.","assumptions_md":"Consideration only, provisional. #5897 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 158 pursue result by Benjaminsen (deepseek-v4-flash, job 9912, cites #4996); accepted at measured, verification spot (review 2041), not superseded; report sha256 6c45fcd6373257f974f1a41136a77f37e88fdb9b41e3796967bb2862da1e96dc matching the snapshot; applicability index assessment null. Established as stated: on one x86_64 host, replaying #1610's float64 Ritz tail on #4996's banked d=17 checkpoint (Af, Ld, dg, vec) with #1599's exact engine, 91 named configurations (two LAPACK implementations, four eigen drivers, four solve paths, thread counts 1..32, a declared list of block sizes) give 66 bit-reproducible I_0 classes (91/91 repeat pairs identical), relative width 6.69e-11; none of #4996's 16 aarch64 classes recurs; I_ref = 0x1.ffffffffdc95dp-1 is not reached but lies inside the band, so this is family exhaustion and not an unreachability bound; lam takes three classes at 0, -1, +1 ulp (52/38/1), all within the 2e-14 G_lam gate, so #4996's 'single lam class' is a host-family property. Corrections (open findings from review 2041) stand beside the claim: the nearest gap is 463 units of 2^-53 (5.1403e-14, 2.570x the gate), not 464 / 5.151e-14 / 2.58x (158873); blocked b=1 under netlib/syevd equals the gesv class, and 'block sizes 1..64' means powers of two (158874); expand() lists 94 entries for 91 configurations (158875); the banked checkpoint and gate4996.py are not published, so no third party can re-execute a run (158876, before_circulation). Not established: anything about the mathematical value of M_k or the route-157 certificates, any other host, the full block-size range, or reachability of I_ref. The source states it is finite exact-rational arithmetic on a fixed banked vector with no asymptotic, threshold or twin-prime claim.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Inapplicable on all topics. main (survivor-gap lower bound, full cutoff, crossing gaps, A = 12) needs a gap lower bound with logarithmic quantifiers; #5897 has no gap statement. o1, o2, o4 (prime harmonic, uniform smooth-number and dyadic prime-count asymptotics), o6 (two-sided density and Euler estimates) and o7 (the exact constant in eq. (28)) are untouched. o3 has no A. o5 is the nearest name match only: a sieve-weight Ritz computation is sieve-adjacent, but #5897 states nothing about the quoted general sieve input or the one-class statement; it fingerprints float64 reproducibility of a fixed vector.","assumptions_md":"Consideration only, provisional. #5897 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target area. Source state preserved: route 158 pursue result by Benjaminsen (deepseek-v4-flash, job 9912, cites #4996); accepted at measured, verification spot (review 2041), not superseded; report sha256 6c45fcd6373257f974f1a41136a77f37e88fdb9b41e3796967bb2862da1e96dc matching the snapshot; applicability index assessment null. Established as stated: on one x86_64 host, replaying #1610's float64 Ritz tail on #4996's banked d=17 checkpoint (Af, Ld, dg, vec) with #1599's exact engine, 91 named configurations (two LAPACK implementations, four eigen drivers, four solve paths, thread counts 1..32, a declared list of block sizes) give 66 bit-reproducible I_0 classes (91/91 repeat pairs identical), relative width 6.69e-11; none of #4996's 16 aarch64 classes recurs; I_ref = 0x1.ffffffffdc95dp-1 is not reached but lies inside the band, so this is family exhaustion and not an unreachability bound; lam takes three classes at 0, -1, +1 ulp (52/38/1), all within the 2e-14 G_lam gate, so #4996's 'single lam class' is a host-family property. Corrections (open findings from review 2041) stand beside the claim: the nearest gap is 463 units of 2^-53 (5.1403e-14, 2.570x the gate), not 464 / 5.151e-14 / 2.58x (158873); blocked b=1 under netlib/syevd equals the gesv class, and 'block sizes 1..64' means powers of two (158874); expand() lists 94 entries for 91 configurations (158875); the banked checkpoint and gate4996.py are not published, so no third party can re-execute a run (158876, before_circulation). Not established: anything about the mathematical value of M_k or the route-157 certificates, any other host, the full block-size range, or reachability of I_ref. The source states it is finite exact-rational arithmetic on a fixed banked vector with no asymptotic, threshold or twin-prime claim.","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":11975,"input_sha256":"af405a432e462ed54ee48770b9705d2353a95acb1ad937a95138437327d9fc4b","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"6c45fcd6373257f974f1a41136a77f37e88fdb9b41e3796967bb2862da1e96dc","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5897,"material_evidence":{"sha256":"648b1e0ef8cc1e3d53941d2dc03563cfc901366c5d859dec8f9ac693623a91ba","entries":{"return:5897":"80d9580d8e61f37317d812630c292d5bd6425aa73dfa1bb8fe82854f352deb80","finding:158873":"ad48d0360413584cbaa8d1ad9c7ec6a823a49f69e8301f3b2e2e54d22887e8fa","finding:158874":"b54f708a7ede96dd8efdce9255e302d47706f7e95d157d49936741b9fd997d51","finding:158875":"357faf06496505226689a3a4811ddb61c465a22660099a52e4753b3ce9c9da0d","finding:158876":"76767846a3232712f8d8f67b20ac4cf0ff0fc9234af574c22d2bc36469f97ea4","artifact:5897:081d0ea87c26bddfb792be485a38f07513b50e9ae89a11aea0fc8aeadc34cc7a":"081d0ea87c26bddfb792be485a38f07513b50e9ae89a11aea0fc8aeadc34cc7a","artifact:5897:0ad32e25276d2ae403be353569ebad10cb54df13c64675961caa6e23e58144e1":"0ad32e25276d2ae403be353569ebad10cb54df13c64675961caa6e23e58144e1","artifact:5897:130ad27a18b39400dfe8d1792864523017892730edda37cafe6cdd41e0bd294d":"130ad27a18b39400dfe8d1792864523017892730edda37cafe6cdd41e0bd294d","artifact:5897:1caead9f80664d4cc05934fe42adb10cef5a2bad2d23a03478ed7bdca808341e":"1caead9f80664d4cc05934fe42adb10cef5a2bad2d23a03478ed7bdca808341e","artifact:5897:219ceea0a2e931e85961e27028e477c1a673cbdfff8390a52d092fee13a40325":"219ceea0a2e931e85961e27028e477c1a673cbdfff8390a52d092fee13a40325","artifact:5897:39e7acc97a9d273ab92f1bb4e05daa88a7ac84df41a38549a1ce916e1351d94e":"39e7acc97a9d273ab92f1bb4e05daa88a7ac84df41a38549a1ce916e1351d94e","artifact:5897:69d9111a0f62e086dde7b74ae299bcc2f41a4e7ff0d630aedb853da052448897":"69d9111a0f62e086dde7b74ae299bcc2f41a4e7ff0d630aedb853da052448897","artifact:5897:6c45fcd6373257f974f1a41136a77f37e88fdb9b41e3796967bb2862da1e96dc":"6c45fcd6373257f974f1a41136a77f37e88fdb9b41e3796967bb2862da1e96dc","artifact:5897:8b5fb5a02adcda0abc1b5d7675386ffeda09a65fa32d37af77660e05047e1d5d":"8b5fb5a02adcda0abc1b5d7675386ffeda09a65fa32d37af77660e05047e1d5d","artifact:5897:942049f83f5997b42e474816a3b50b753bb6763ae0a5cf06c1426200806657ce":"942049f83f5997b42e474816a3b50b753bb6763ae0a5cf06c1426200806657ce","artifact:5897:9aaf4f956727403d8beccf103cb70f72d084c8aaa69b8d6e9c941f3509e8822a":"9aaf4f956727403d8beccf103cb70f72d084c8aaa69b8d6e9c941f3509e8822a","artifact:5897:9c5515ff27e72cad5fb44425027b270dc0262b08150d7fe11526756a718a66bb":"9c5515ff27e72cad5fb44425027b270dc0262b08150d7fe11526756a718a66bb","artifact:5897:9cf97b83c628888ccb9e85d7b4d67390f73510b41d283ab28d6ab57a351499b0":"9cf97b83c628888ccb9e85d7b4d67390f73510b41d283ab28d6ab57a351499b0","artifact:5897:9f5a5b1951d663520e490c74b547830a2388c31139c5ecb22d80f426a4821905":"9f5a5b1951d663520e490c74b547830a2388c31139c5ecb22d80f426a4821905","artifact:5897:b14d360fd680bc5ce174d70bfea7c2d989c99241722fb01008969b5c54b8a86d":"b14d360fd680bc5ce174d70bfea7c2d989c99241722fb01008969b5c54b8a86d","artifact:5897:b8277cccbe81d8236906b4bcd615ca2926a9ed9d1ee1b6c1363bb347dc98dbc9":"b8277cccbe81d8236906b4bcd615ca2926a9ed9d1ee1b6c1363bb347dc98dbc9","artifact:5897:bb371c94028fd04e17832d4fa933b8535ee6a3f1e78a5786ee340df9810017f3":"bb371c94028fd04e17832d4fa933b8535ee6a3f1e78a5786ee340df9810017f3","artifact:5897:bcb66b8e50b74e53db06bb421b2d4ae65e2c31b74f7401185aad8a56e7975f78":"bcb66b8e50b74e53db06bb421b2d4ae65e2c31b74f7401185aad8a56e7975f78","artifact:5897:c12afe2c49b73ddc4a272e8582d49dc1aa6377964bb9fa2efc79e3360e21fbf3":"c12afe2c49b73ddc4a272e8582d49dc1aa6377964bb9fa2efc79e3360e21fbf3"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5897,"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 #5897: 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\":5897,\"report_sha256\":\"6c45fcd6373257f974f1a41136a77f37e88fdb9b41e3796967bb2862da1e96dc\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5897\":\"80d9580d8e61f37317d812630c292d5bd6425aa73dfa1bb8fe82854f352deb80\",\"finding:158873\":\"ad48d0360413584cbaa8d1ad9c7ec6a823a49f69e8301f3b2e2e54d22887e8fa\",\"finding:158874\":\"b54f708a7ede96dd8efdce9255e302d47706f7e95d157d49936741b9fd997d51\",\"finding:158875\":\"357faf06496505226689a3a4811ddb61c465a22660099a52e4753b3ce9c9da0d\",\"finding:158876\":\"76767846a3232712f8d8f67b20ac4cf0ff0fc9234af574c22d2bc36469f97ea4\",\"artifact:5897:081d0ea87c26bddfb792be485a38f07513b50e9ae89a11aea0fc8aeadc34cc7a\":\"081d0ea87c26bddfb792be485a38f07513b50e9ae89a11aea0fc8aeadc34cc7a\",\"artifact:5897:0ad32e25276d2ae403be353569ebad10cb54df13c64675961caa6e23e58144e1\":\"0ad32e25276d2ae403be353569ebad10cb54df13c64675961caa6e23e58144e1\",\"artifact:5897:130ad27a18b39400dfe8d1792864523017892730edda37cafe6cdd41e0bd294d\":\"130ad27a18b39400dfe8d1792864523017892730edda37cafe6cdd41e0bd294d\",\"artifact:5897:1caead9f80664d4cc05934fe42adb10cef5a2bad2d23a03478ed7bdca808341e\":\"1caead9f80664d4cc05934fe42adb10cef5a2bad2d23a03478ed7bdca808341e\",\"artifact:5897:219ceea0a2e931e85961e27028e477c1a673cbdfff8390a52d092fee13a40325\":\"219ceea0a2e931e85961e27028e477c1a673cbdfff8390a52d092fee13a40325\",\"artifact:5897:39e7acc97a9d273ab92f1bb4e05daa88a7ac84df41a38549a1ce916e1351d94e\":\"39e7acc97a9d273ab92f1bb4e05daa88a7ac84df41a38549a1ce916e1351d94e\",\"artifact:5897:69d9111a0f62e086dde7b74ae299bcc2f41a4e7ff0d630aedb853da052448897\":\"69d9111a0f62e086dde7b74ae299bcc2f41a4e7ff0d630aedb853da052448897\",\"artifact:5897:6c45fcd6373257f974f1a41136a77f37e88fdb9b41e3796967bb2862da1e96dc\":\"6c45fcd6373257f974f1a41136a77f37e88fdb9b41e3796967bb2862da1e96dc\",\"artifact:5897:8b5fb5a02adcda0abc1b5d7675386ffeda09a65fa32d37af77660e05047e1d5d\":\"8b5fb5a02adcda0abc1b5d7675386ffeda09a65fa32d37af77660e05047e1d5d\",\"artifact:5897:942049f83f5997b42e474816a3b50b753bb6763ae0a5cf06c1426200806657ce\":\"942049f83f5997b42e474816a3b50b753bb6763ae0a5cf06c1426200806657ce\",\"artifact:5897:9aaf4f956727403d8beccf103cb70f72d084c8aaa69b8d6e9c941f3509e8822a\":\"9aaf4f956727403d8beccf103cb70f72d084c8aaa69b8d6e9c941f3509e8822a\",\"artifact:5897:9c5515ff27e72cad5fb44425027b270dc0262b08150d7fe11526756a718a66bb\":\"9c5515ff27e72cad5fb44425027b270dc0262b08150d7fe11526756a718a66bb\",\"artifact:5897:9cf97b83c628888ccb9e85d7b4d67390f73510b41d283ab28d6ab57a351499b0\":\"9cf97b83c628888ccb9e85d7b4d67390f73510b41d283ab28d6ab57a351499b0\",\"artifact:5897:9f5a5b1951d663520e490c74b547830a2388c31139c5ecb22d80f426a4821905\":\"9f5a5b1951d663520e490c74b547830a2388c31139c5ecb22d80f426a4821905\",\"artifact:5897:b14d360fd680bc5ce174d70bfea7c2d989c99241722fb01008969b5c54b8a86d\":\"b14d360fd680bc5ce174d70bfea7c2d989c99241722fb01008969b5c54b8a86d\",\"artifact:5897:b8277cccbe81d8236906b4bcd615ca2926a9ed9d1ee1b6c1363bb347dc98dbc9\":\"b8277cccbe81d8236906b4bcd615ca2926a9ed9d1ee1b6c1363bb347dc98dbc9\",\"artifact:5897:bb371c94028fd04e17832d4fa933b8535ee6a3f1e78a5786ee340df9810017f3\":\"bb371c94028fd04e17832d4fa933b8535ee6a3f1e78a5786ee340df9810017f3\",\"artifact:5897:bcb66b8e50b74e53db06bb421b2d4ae65e2c31b74f7401185aad8a56e7975f78\":\"bcb66b8e50b74e53db06bb421b2d4ae65e2c31b74f7401185aad8a56e7975f78\",\"artifact:5897:c12afe2c49b73ddc4a272e8582d49dc1aa6377964bb9fa2efc79e3360e21fbf3\":\"c12afe2c49b73ddc4a272e8582d49dc1aa6377964bb9fa2efc79e3360e21fbf3\"},\"sha256\":\"648b1e0ef8cc1e3d53941d2dc03563cfc901366c5d859dec8f9ac693623a91ba\"},\"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:5897,input_sha256:\"af405a432e462ed54ee48770b9705d2353a95acb1ad937a95138437327d9fc4b\",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/5926/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"7451c6be01c97c9be327aa7a470d964d199fca6e2eaec3f5c1dda98fd2bdbc65","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}