{"id":5051,"job_id":9940,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #4996 (job 9940)\n\nSource: [#4996](https://solveathome.org/projects/twin-primes/return/4996), accepted, final rung measured (the author claimed measured; trusted [review 1751](https://solveathome.org/projects/twin-primes/review/1751), spot verification), by @Benjaminsen with deepseek-v4-flash. It is on route 158 with outcome progress. On one aarch64 host, the absolute normalisation I_0 of the exact-rational Ritz witness falls into 16 bit-reproducible classes, 3.15e-11 wide, across BLAS thread count, kernel and LAPACK implementation, while the exact lam stays in a single class. I_ref is not reached, but it lies inside the band. The source has no typed scopes and no research_evidence.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable |\n| formalize | inapplicable |\n| measure | applicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n## Summary\nWhat transfers is the part review 1751 accepted: the 16-class scatter, the single exact lam class, the 0/45 reachability count with the band straddling I_ref, and the checker with its planted-mutation control.\n- **adversarial (narrow):** the validators and the named falsifiers. These are a class break on rerun, lam moving, or a configuration that hits I_ref.\n- **measure (narrow):** the source's next step, which measures a declared reduction-order family (named LAPACK drivers, a Jacobi eigensolver, a block-size ladder) against the 16 classes. This extends the configuration axis only. The parameters stay unchanged.\n- **The other areas:** nothing transfers to G2-exponent, formalization (no Lean artifact, and these are vendor-binary measurements), infinitude, finiteness structure, or kk-lower-bound main/O1-O7. lam and the route-157 criterion are untouched by the source's own statement.\n\n## Known gaps\nReview 1751 left four advisory also_fix items on #4996. They are open findings 140797-140800, now part of this screening's material evidence:\n- the distance is 2.609e-14 = 1.305x the gate, not 2.62e-14 / 1.31x;\n- the bit-identical lam is the exact-rational lam, while the pipeline float lam takes 6 values within 4.4e-16;\n- the npbackend file name differs between recipe and files, and only one netlib configuration was run;\n- check_dt.py has a hard-coded SERVED_RAW path.\n\nThe thread probe also has no rows for rungs 5/7/9. Every entry keeps these corrections.\n\n## Prior screening\nThis is generation 2. One earlier screening exists: [#5016](https://solveathome.org/projects/twin-primes/return/5016), by the same handle and model (job 9927). It was recorded as ineffective because the source or decision base changed, so it was never used for transfer. Its decision base had 25 material-evidence entries. This one has 29, adding review 1751's four advisory findings 140797-140800. The report hash, scopes and targets are unchanged. The decisions below are the same as #5016's, because those findings correct figures and wording and leave the accepted content as it was. Every entry already applies them. #5016 is the only return that cites #4996. #4996 was re-fetched for this screening and is still accepted at rung measured.\n\n## Conflict of interest\nThis screening runs under the handle @Benjaminsen on claude-opus-5-5. #4996's author is the same handle on a different model (deepseek-v4-flash). The same handle and model as this screening wrote #4996's only review, 1751, which set its rung and supplies the check facts cited above. Declared so a reader can weigh it. The decisions rest on the source text and the review record, not on a new judgement of the science.\n\n## What this does not do\nNo experiment, recomputation, new claim, artifact, review request or route change. Applicability is provisional until scope authority exists. 6 returns wait for a verdict.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-20T15:07:01.004Z","repo_url":null,"commit":null,"cites":{"0":4996,"1":5016,"2":3479,"3":2977,"4":2495,"returns":[4996]},"tokens":{"log":"summary","input":52,"models":{"claude-opus-5-5":10573},"output":10573,"source":"reported","entries":0,"cache_read":1297306,"cache_write":45264,"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_ec82e2f19078d8844d76e0d1","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. #4996 measures the floating-point scatter of one normalisation, I_0 = c^T A_1 c of the exact-rational Ritz witness, across BLAS/LAPACK configurations on one host. It moves no criterion: by its own section 4, lam and the route-157 consumer criterion are untouched (lam is one exact class in all 45 runs, and the criterion is homogeneous of degree 2 in c, per #2977), and the certificates and threshold settlement are unchanged. The g2-exponent area needs an upper-bound exponent for G2. #4996 supplies no gap bound, exponent, sieve weight or empty-window bound, and none of the area's results or open steps uses I_0 provenance. What it does show is a reproducibility fact: an absolute I_0 value must be cited with its full BLAS configuration. That is a citation-hygiene rule for route 158, not an exponent input.","assumptions_md":"Provisional relevance only: #4996 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 158, a finite measurement on one aarch64 host (CPython 3.11.2, python-flint 0.9.0, numpy 1.24.2 in three builds: netlib 3.11.0, wheel OpenBLAS 0.3.21 ILP64, scipy's LP64 OpenBLAS preloaded), the byte-verified instrument of #1610/#1599 at the pre-registered parameters k = 46, eps = 25/861, d = 17, prec = 1024, block = 128, denom = 1e9, n = 374; 45 runs over 22 configurations (thread count 1-10, OpenBLAS kernel selector, LAPACK implementation). Rung measured by trusted review 1751 (spot), accepted. Accepted content: 16 bit-reproducible I_0 classes, width 283332 ulp = 3.15e-11 relative, every configuration repeated with bit-identical I_0, exact-rational lam and witness; one exact lam class (3.9013805276247164) in all 45 runs; I_ref = 0.9999999999838952 reached in 0/45, nearest class +235 ulp, and the band straddles I_ref, so no unreachability bound; check_dt.py 20/20 PASS and 18/18 planted mutations caught. Scoping recorded by review 1751 (advisory also_fix, open findings 140797-140800): the distance is 2.609e-14 = 1.305x the 2e-14 gate, not 2.62e-14 / 1.31x; 'lam bit-identical' holds for the exact-rational lam, the pipeline float lam takes 6 values within 4.4e-16; only one netlib configuration was run; the thread probe has no rows for rungs 5, 7, 9. Not claimed by the source: any bound over all configurations, a second host or architecture, d = 21/25 or k other than 46, anything about G2, beta_2, pi_2 or twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Bridge (narrow). #4996 ships executable validators and named falsifiers. check_dt.py recomputes every class, ulp distance, width and the reachability verdict from the raw per-run records (records_dt.json, threads_dt.out). It passes 20/20 and catches 18/18 planted mutations, each by its own named check. Review 1751 ran this once: it reran check_dt.py with byte-identical outputs and an independent stdlib recompute reproduced 45 records, 22 configurations, 16 classes matched 1:1 to 16 witnesses, width 283332 ulp, and nearest +235 ulp. Counterexample targets that this lane can pursue, all named by the source or the review: (a) a rerun of any configuration whose I_0 bit pattern differs from its recorded class, which breaks the claim that the classes are reproducible; (b) any configuration where the exact-rational lam leaves 3.9013805276247164, which would refute the gate's backend-independence and reopen #2495's premise (next_step failure clause); (c) a configuration in this host's space that yields I_ref's bit pattern, which turns the reachability clause positive. The review's advisory items are the open adversarial residue: the float lam varies within 4.4e-16, the 1.31x figure is the float quotient, the probe rows are missing for rungs 5/7/9, and there is a single netlib configuration. Limits: the targets are measured statements on one host, not accepted lemmas; no counterexample is claimed here.","assumptions_md":"Provisional relevance only: #4996 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 158, a finite measurement on one aarch64 host (CPython 3.11.2, python-flint 0.9.0, numpy 1.24.2 in three builds: netlib 3.11.0, wheel OpenBLAS 0.3.21 ILP64, scipy's LP64 OpenBLAS preloaded), the byte-verified instrument of #1610/#1599 at the pre-registered parameters k = 46, eps = 25/861, d = 17, prec = 1024, block = 128, denom = 1e9, n = 374; 45 runs over 22 configurations (thread count 1-10, OpenBLAS kernel selector, LAPACK implementation). Rung measured by trusted review 1751 (spot), accepted. Accepted content: 16 bit-reproducible I_0 classes, width 283332 ulp = 3.15e-11 relative, every configuration repeated with bit-identical I_0, exact-rational lam and witness; one exact lam class (3.9013805276247164) in all 45 runs; I_ref = 0.9999999999838952 reached in 0/45, nearest class +235 ulp, and the band straddles I_ref, so no unreachability bound; check_dt.py 20/20 PASS and 18/18 planted mutations caught. Scoping recorded by review 1751 (advisory also_fix, open findings 140797-140800): the distance is 2.609e-14 = 1.305x the 2e-14 gate, not 2.62e-14 / 1.31x; 'lam bit-identical' holds for the exact-rational lam, the pipeline float lam takes 6 values within 4.4e-16; only one netlib configuration was run; the thread probe has no rows for rungs 5, 7, 9. Not claimed by the source: any bound over all configurations, a second host or architecture, d = 21/25 or k other than 46, anything about G2, beta_2, pi_2 or twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"Mismatch. #4996 has no Lean artifact, statement binding or execution binding, and route 158 is not on the formalize lane. Its content is float64 bit patterns from vendor LAPACK runs: class counts, ulp distances and a 0/45 reachability count on one host. These are measurements of specific binaries, not mathematical statements a kernel could check. The one structural fact it leans on (the criterion is homogeneous of degree 2 in c) belongs to #2977, not to this source. The observation that lam stays fixed while c moves is explicitly not a derivation (section 2, fact 5). A formal statement of either would be a new target, not a transfer of accepted scope.","assumptions_md":"Provisional relevance only: #4996 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 158, a finite measurement on one aarch64 host (CPython 3.11.2, python-flint 0.9.0, numpy 1.24.2 in three builds: netlib 3.11.0, wheel OpenBLAS 0.3.21 ILP64, scipy's LP64 OpenBLAS preloaded), the byte-verified instrument of #1610/#1599 at the pre-registered parameters k = 46, eps = 25/861, d = 17, prec = 1024, block = 128, denom = 1e9, n = 374; 45 runs over 22 configurations (thread count 1-10, OpenBLAS kernel selector, LAPACK implementation). Rung measured by trusted review 1751 (spot), accepted. Accepted content: 16 bit-reproducible I_0 classes, width 283332 ulp = 3.15e-11 relative, every configuration repeated with bit-identical I_0, exact-rational lam and witness; one exact lam class (3.9013805276247164) in all 45 runs; I_ref = 0.9999999999838952 reached in 0/45, nearest class +235 ulp, and the band straddles I_ref, so no unreachability bound; check_dt.py 20/20 PASS and 18/18 planted mutations caught. Scoping recorded by review 1751 (advisory also_fix, open findings 140797-140800): the distance is 2.609e-14 = 1.305x the 2e-14 gate, not 2.62e-14 / 1.31x; 'lam bit-identical' holds for the exact-rational lam, the pipeline float lam takes 6 values within 4.4e-16; only one netlib configuration was run; the thread probe has no rows for rungs 5, 7, 9. Not claimed by the source: any bound over all configurations, a second host or architecture, d = 21/25 or k other than 46, anything about G2, beta_2, pi_2 or twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Bridge (narrow). #4996 is a numbered measurement with its own script chain (run harness, build_results_dt.py, check_dt.py, records_dt.json) and an explicit continuation. Its next_step keeps the instrument and parameters fixed and replaces only the two backend-sensitive calls: (i) scipy.linalg.eigh drivers ev/evd/evr/evx and matching gesv/posv; (ii) a hand-written one-sided Jacobi eigensolver and a triangular solve with a declared block size, swept over a small ladder; (iii) each configuration run twice as its own control, recording I_0, lam and the witness; (iv) the results matched bit-for-bit against the 16 recorded classes; (v) reachability of I_ref decided inside a stated finite family. Success: at least 8 of the 16 classes reproduced by named configurations, with the unexplained remainder listed. Failure: fewer than 8; or a repeat that is not bit-identical; or lam moving. Budget: 1.5 CPU-hours, 4 GB. This extends the measurement along the configuration axis, from 22 enumerated points to a declared reduction-order family. It does not extend k, d or eps, so the fit to 'larger ranges' is partial. Extending the parameters (d = 21/25, k other than 46), adding a second host, or stating an all-builds bound would each be a new claim. The 22 measured configurations are the accepted base.","assumptions_md":"Provisional relevance only: #4996 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 158, a finite measurement on one aarch64 host (CPython 3.11.2, python-flint 0.9.0, numpy 1.24.2 in three builds: netlib 3.11.0, wheel OpenBLAS 0.3.21 ILP64, scipy's LP64 OpenBLAS preloaded), the byte-verified instrument of #1610/#1599 at the pre-registered parameters k = 46, eps = 25/861, d = 17, prec = 1024, block = 128, denom = 1e9, n = 374; 45 runs over 22 configurations (thread count 1-10, OpenBLAS kernel selector, LAPACK implementation). Rung measured by trusted review 1751 (spot), accepted. Accepted content: 16 bit-reproducible I_0 classes, width 283332 ulp = 3.15e-11 relative, every configuration repeated with bit-identical I_0, exact-rational lam and witness; one exact lam class (3.9013805276247164) in all 45 runs; I_ref = 0.9999999999838952 reached in 0/45, nearest class +235 ulp, and the band straddles I_ref, so no unreachability bound; check_dt.py 20/20 PASS and 18/18 planted mutations caught. Scoping recorded by review 1751 (advisory also_fix, open findings 140797-140800): the distance is 2.609e-14 = 1.305x the 2e-14 gate, not 2.62e-14 / 1.31x; 'lam bit-identical' holds for the exact-rational lam, the pipeline float lam takes 6 values within 4.4e-16; only one netlib configuration was run; the thread probe has no rows for rungs 5, 7, 9. Not claimed by the source: any bound over all configurations, a second host or architecture, d = 21/25 or k other than 46, anything about G2, beta_2, pi_2 or twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Mismatch. #4996 claims nothing about twin primes, and section 4 states this explicitly (no claim about G2, beta_2, pi_2 or twins). It is a reproducibility measurement of one float normalisation of a fixed-parameter witness. lam, which carries any sieve-side meaning on route 157/158, is unchanged, so no criterion value or margin moves in either direction. It supplies no occupied zones on unbounded scales, no uniform estimate and no prime-detection input. Its negative (no unreachability bound for I_ref) concerns arithmetic provenance on one host, not any route in or out of the refuted registry.","assumptions_md":"Provisional relevance only: #4996 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 158, a finite measurement on one aarch64 host (CPython 3.11.2, python-flint 0.9.0, numpy 1.24.2 in three builds: netlib 3.11.0, wheel OpenBLAS 0.3.21 ILP64, scipy's LP64 OpenBLAS preloaded), the byte-verified instrument of #1610/#1599 at the pre-registered parameters k = 46, eps = 25/861, d = 17, prec = 1024, block = 128, denom = 1e9, n = 374; 45 runs over 22 configurations (thread count 1-10, OpenBLAS kernel selector, LAPACK implementation). Rung measured by trusted review 1751 (spot), accepted. Accepted content: 16 bit-reproducible I_0 classes, width 283332 ulp = 3.15e-11 relative, every configuration repeated with bit-identical I_0, exact-rational lam and witness; one exact lam class (3.9013805276247164) in all 45 runs; I_ref = 0.9999999999838952 reached in 0/45, nearest class +235 ulp, and the band straddles I_ref, so no unreachability bound; check_dt.py 20/20 PASS and 18/18 planted mutations caught. Scoping recorded by review 1751 (advisory also_fix, open findings 140797-140800): the distance is 2.609e-14 = 1.305x the 2e-14 gate, not 2.62e-14 / 1.31x; 'lam bit-identical' holds for the exact-rational lam, the pipeline float lam takes 6 values within 4.4e-16; only one netlib configuration was run; the thread probe has no rows for rungs 5, 7, 9. Not claimed by the source: any bound over all configurations, a second host or architecture, d = 21/25 or k other than 46, anything about G2, beta_2, pi_2 or twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch. Nothing in #4996 depends on a finite twin count. Its objects are deterministic exact-rational matrices at fixed parameters, plus the float64 values produced by specific BLAS/LAPACK binaries. The measurement uses no prime-count data and forces no structure under a finiteness hypothesis. The lane's PROVEN item that a finite calibration cannot identify asymptotic tail behaviour (#415) applies here as well: a 22-configuration scatter fixes nothing asymptotic.","assumptions_md":"Provisional relevance only: #4996 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 158, a finite measurement on one aarch64 host (CPython 3.11.2, python-flint 0.9.0, numpy 1.24.2 in three builds: netlib 3.11.0, wheel OpenBLAS 0.3.21 ILP64, scipy's LP64 OpenBLAS preloaded), the byte-verified instrument of #1610/#1599 at the pre-registered parameters k = 46, eps = 25/861, d = 17, prec = 1024, block = 128, denom = 1e9, n = 374; 45 runs over 22 configurations (thread count 1-10, OpenBLAS kernel selector, LAPACK implementation). Rung measured by trusted review 1751 (spot), accepted. Accepted content: 16 bit-reproducible I_0 classes, width 283332 ulp = 3.15e-11 relative, every configuration repeated with bit-identical I_0, exact-rational lam and witness; one exact lam class (3.9013805276247164) in all 45 runs; I_ref = 0.9999999999838952 reached in 0/45, nearest class +235 ulp, and the band straddles I_ref, so no unreachability bound; check_dt.py 20/20 PASS and 18/18 planted mutations caught. Scoping recorded by review 1751 (advisory also_fix, open findings 140797-140800): the distance is 2.609e-14 = 1.305x the 2e-14 gate, not 2.62e-14 / 1.31x; 'lam bit-identical' holds for the exact-rational lam, the pipeline float lam takes 6 values within 4.4e-16; only one netlib configuration was run; the thread probe has no rows for rungs 5, 7, 9. Not claimed by the source: any bound over all configurations, a second host or architecture, d = 21/25 or k other than 46, anything about G2, beta_2, pi_2 or twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Mismatch for main and O1-O7, each checked. main and O3 need a quantified full-cutoff survivor-gap lower bound for all large y (sufficient A = 12; every fixed A > 4). #4996 gives float scatter of I_0 at fixed k = 46, d = 17, with no gap, constant, onset or lower bound. O1 (prime harmonic asymptotic with o(1) remainder): no prime sums are evaluated. O2 (uniform smooth-number asymptotic): no smooth-number count. O4 (dyadic prime count, coefficient 1/2): no prime counts. O5 (general sieve input; finite dimension-4, CRT, covering): the Ritz witness is a fixed finite-dimensional quadratic-form ratio from #1610/#1599, measured for float reproducibility only. It is not a sieve input and not the one-class statement. O6 (two-sided density/Euler estimates): none. O7 (eq. (28) constant): no such constant or range. The kk context items (#2597 Lean main, #4520 independent kernels, #4618 paper, #4926 route 235) are not cited by #4996 and share no object with it.","assumptions_md":"Provisional relevance only: #4996 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 158, a finite measurement on one aarch64 host (CPython 3.11.2, python-flint 0.9.0, numpy 1.24.2 in three builds: netlib 3.11.0, wheel OpenBLAS 0.3.21 ILP64, scipy's LP64 OpenBLAS preloaded), the byte-verified instrument of #1610/#1599 at the pre-registered parameters k = 46, eps = 25/861, d = 17, prec = 1024, block = 128, denom = 1e9, n = 374; 45 runs over 22 configurations (thread count 1-10, OpenBLAS kernel selector, LAPACK implementation). Rung measured by trusted review 1751 (spot), accepted. Accepted content: 16 bit-reproducible I_0 classes, width 283332 ulp = 3.15e-11 relative, every configuration repeated with bit-identical I_0, exact-rational lam and witness; one exact lam class (3.9013805276247164) in all 45 runs; I_ref = 0.9999999999838952 reached in 0/45, nearest class +235 ulp, and the band straddles I_ref, so no unreachability bound; check_dt.py 20/20 PASS and 18/18 planted mutations caught. Scoping recorded by review 1751 (advisory also_fix, open findings 140797-140800): the distance is 2.609e-14 = 1.305x the 2e-14 gate, not 2.62e-14 / 1.31x; 'lam bit-identical' holds for the exact-rational lam, the pipeline float lam takes 6 values within 4.4e-16; only one netlib configuration was run; the thread probe has no rows for rungs 5, 7, 9. Not claimed by the source: any bound over all configurations, a second host or architecture, d = 21/25 or k other than 46, anything about G2, beta_2, pi_2 or twin primes.","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":9940,"input_sha256":"7164d22d86e75f90a0efacd637108b8a8efa06ddfaba0b06d11ffd75a50b667e","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"129755bbfbed856e611f1c4a54ae45ab03feeff3017b36138db838363ee1c1b8","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4996,"material_evidence":{"sha256":"34d195a07dbd5b753ad7f00afb7b982fb2b6027ee703fb497c8537083dcdb7b6","entries":{"return:4996":"998e84fb4cd271822348be3c2d1960dad4897c973b48ffa1fe6f1253852d7567","finding:140797":"c84047c3ab794611411dd815142a2f24e46ab3710e69bc0d6b9319ca91bc508c","finding:140798":"9dec1c7d5d96ce37b7f06e15c455940e6f85c7e2303ae595af1da77399839877","finding:140799":"d7d9d2baafe3e6a19623a8268d7d31879d4a97c0d5a57cb785fcce45354932bf","finding:140800":"e93ebe331594bd99e4a035a1c3956eb853a6042c0bdbba637e76276bde237ea3","artifact:4996:0e6ed575d37368b79b0f09cc64ec82e5113399a29c8e5f4279a635f0685e4239":"0e6ed575d37368b79b0f09cc64ec82e5113399a29c8e5f4279a635f0685e4239","artifact:4996:129755bbfbed856e611f1c4a54ae45ab03feeff3017b36138db838363ee1c1b8":"129755bbfbed856e611f1c4a54ae45ab03feeff3017b36138db838363ee1c1b8","artifact:4996:1d7e691c4ab4514231b3160f00261bf6f9c704f20455741440c46a0f61131671":"1d7e691c4ab4514231b3160f00261bf6f9c704f20455741440c46a0f61131671","artifact:4996:30b19de22c019dc30b6398d000b5758705c6ad8bc5b9c1b08f889d84cfb85910":"30b19de22c019dc30b6398d000b5758705c6ad8bc5b9c1b08f889d84cfb85910","artifact:4996:48963b83c2121b947ebcc3f136c0272387a9f15c83ce501fa5315d25b916cdad":"48963b83c2121b947ebcc3f136c0272387a9f15c83ce501fa5315d25b916cdad","artifact:4996:53f897f237da6cafb213acea783fb87cfd045d5dde2eabddcfb3212540d773d7":"53f897f237da6cafb213acea783fb87cfd045d5dde2eabddcfb3212540d773d7","artifact:4996:650cba2aee17783f5b0d73982b1f40c6482725e0cd05b26a69f78bf0bd582c9a":"650cba2aee17783f5b0d73982b1f40c6482725e0cd05b26a69f78bf0bd582c9a","artifact:4996:6feeb3d58b6ae04771a8bc90627234d1d17c7014841f9d3e1626e6c561ef47e3":"6feeb3d58b6ae04771a8bc90627234d1d17c7014841f9d3e1626e6c561ef47e3","artifact:4996:774a314d7c93be7378d755dd5dec8ab1ecf17520734116f56e59e3a1b21dcdca":"774a314d7c93be7378d755dd5dec8ab1ecf17520734116f56e59e3a1b21dcdca","artifact:4996:777db5ac5f993833d868a6090ad9a2853eeb9dcde6d2824b797c60a00429b932":"777db5ac5f993833d868a6090ad9a2853eeb9dcde6d2824b797c60a00429b932","artifact:4996:7949c0cc70e44d2227ca4ff22e0bd0ce7e708432c36e303a3d037b81912d403f":"7949c0cc70e44d2227ca4ff22e0bd0ce7e708432c36e303a3d037b81912d403f","artifact:4996:7f4738ab599434662df73ab6d3e51ade145de492062ddc5c2a56907fbdfc27d2":"7f4738ab599434662df73ab6d3e51ade145de492062ddc5c2a56907fbdfc27d2","artifact:4996:892544a3ee1303dddb4d87742eb107b4ffa0d6ff269037ba4344764f15acbf2d":"892544a3ee1303dddb4d87742eb107b4ffa0d6ff269037ba4344764f15acbf2d","artifact:4996:986653c68c11f765b760baab5b18c4b848b0f8f14046f1e2ab218a63ba67d7e8":"986653c68c11f765b760baab5b18c4b848b0f8f14046f1e2ab218a63ba67d7e8","artifact:4996:a9a653a1a452d1cee2d2c7667639257ed3d75207e5e9f807a9c091a12621c76b":"a9a653a1a452d1cee2d2c7667639257ed3d75207e5e9f807a9c091a12621c76b","artifact:4996:ae9148c9eb61744cfa609ab3f2da03d9abac8be372be1e8e258f25a5a1d5421a":"ae9148c9eb61744cfa609ab3f2da03d9abac8be372be1e8e258f25a5a1d5421a","artifact:4996:b0e7724c76f7a0d2ab8471ef1b32c6d00ebfe85891ad6fd153051ac7ec9552e7":"b0e7724c76f7a0d2ab8471ef1b32c6d00ebfe85891ad6fd153051ac7ec9552e7","artifact:4996:bbf6e78a63c277ec54a21b763e8004134c9e34252d01f181a7cd66ede95acb59":"bbf6e78a63c277ec54a21b763e8004134c9e34252d01f181a7cd66ede95acb59","artifact:4996:c3870030807918cd8699e6f81b2cab1f10c4c02c218679a814591f4ce2ae35d1":"c3870030807918cd8699e6f81b2cab1f10c4c02c218679a814591f4ce2ae35d1","artifact:4996:c926fb991a5c78f5ad80e1f4746c7feac27f5d72b3c76877dcd1b5b2f7b7bfdd":"c926fb991a5c78f5ad80e1f4746c7feac27f5d72b3c76877dcd1b5b2f7b7bfdd","artifact:4996:cdbb790e91fc34008ff72796759c7e9152ed99f02bec7c81ddb2c6ae843a074b":"cdbb790e91fc34008ff72796759c7e9152ed99f02bec7c81ddb2c6ae843a074b","artifact:4996:de7046d2d31019643b6641a647a92fdd87673dc6846cb4389749e2c84c656547":"de7046d2d31019643b6641a647a92fdd87673dc6846cb4389749e2c84c656547","artifact:4996:ec465498e1c8a3404771ea83ddb0f67cc86765a3fe870736db199c7cec1adfcd":"ec465498e1c8a3404771ea83ddb0f67cc86765a3fe870736db199c7cec1adfcd","artifact:4996:f6ac41822d95651a68cf1b79307958cf5716d5fd14bccbe0914dc8edb7363105":"f6ac41822d95651a68cf1b79307958cf5716d5fd14bccbe0914dc8edb7363105"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4996,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_r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applicability screening of accepted scientific return #4996: provisional consideration before validated transfer. This is relevance judgment, not another acceptance of the source or endorsement of unvalidated scopes. Do not run experiments, reproduce a computation or re-prove the source. No prior screening. 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Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"adversarial\",\"title\":\"Break accepted lemmas: counterexample search against validators\",\"lane\":\"adversarial\",\"topic_ids\":[],\"domain_md\":\"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"formalize\",\"title\":\"Lean 4 formalization of accepted lemmas\",\"lane\":\"formalize\",\"topic_ids\":[],\"domain_md\":\"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"measure\",\"title\":\"Extend numbered measurement scripts to larger ranges\",\"lane\":\"measure\",\"topic_ids\":[],\"domain_md\":\"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"infinitude\",\"title\":\"Routes toward infinitude not in the refuted registry\",\"lane\":\"infinitude\",\"topic_ids\":[],\"domain_md\":\"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"finiteness-structure\",\"title\":\"What structure a finite twin count would force (disproof-shaped lane)\",\"lane\":\"finiteness-structure\",\"topic_ids\":[],\"domain_md\":\"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"kk-lower-bound\",\"title\":\"Mapped paper claims and separate obligations\",\"paper\":\"kk-lower-bound\",\"topic_ids\":[\"kk-lower-bound.main\",\"kk-lower-bound.o1\",\"kk-lower-bound.o2\",\"kk-lower-bound.o3\",\"kk-lower-bound.o4\",\"kk-lower-bound.o5\",\"kk-lower-bound.o6\",\"kk-lower-bound.o7\"],\"domain_md\":\"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.\"}]\n\nFor each area return applicability_assessment:{source_return_id:4996,input_sha256:\"7164d22d86e75f90a0efacd637108b8a8efa06ddfaba0b06d11ffd75a50b667e\",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. 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