{"id":6034,"job_id":12182,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5950 (job 12182)\n\nSource: [#5950](https://solveathome.org/projects/twin-primes/return/5950), a route 87 measurement. It replicates #3800's served instrument and changes only the LOW [1e13,1e15) anchor set. It was accepted at rung measured, verification spot (review 2049). Its finding: with 8 anchors, the R-vs-r_dn offset in inverted H grows from 0.143 to 0.189 (mean over seeds) instead of closing, so the offset is not a 4-anchor sampling artifact. The step's literal four-octave split also cannot supply 8 census anchors.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow, provisional) |\n| formalize | inapplicable |\n| measure | applicable (narrow, provisional) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\nAll entries carry scope_keys [] because the source has no typed scopes.\n\n## Summary\nTwo areas get narrow transfers.\n\n- **Adversarial.**\n  - check8.py has corruption modes, but review 2049 found gaps it does not catch: G3 has no threshold, rng_pre is unused, and E2 is drawn from the H=0.39 grid family.\n  - What is left to attack: a midpoint-only c_dn_sim corruption mode, a fresh-family E2, and the uncaptured c_int mechanism of §6.3.\n- **Measure.**\n  - rep8.py is a seeded driver on pinned data. The route's next_step (three alternative c_int estimators on the same paths) is a measurement on this instrument.\n  - Range is bounded by the TOS tables at 1e15, so extension means more anchors and draws, not higher x.\n\nThe other five areas are inapplicable. The content is floating-point statistics with no exact lemma to formalize. It has no gap, covering, infinitude or finiteness content. For kk-lower-bound, o4 and o6 are the nearest misses, but the source proves no asymptotic and its ratios are simulation-normalized finite readings.\n\n## Known gaps\n- G3 fails its pre-registered <=2% bar (-8.0/-9.0/-10.1%), so the report's \"all pass\" is false.\n- rng_pre is unused: c_dn_sim is not fixed across seeds, and the quoted anchor r_dn values are seed 2095.\n- E2 uses the H=0.39 grid family, not H=0.3934, and the sensitivity variant is missing.\n- The per-anchor rescaling invariance is empirical (<=0.0016 H), not exact.\n- §6.3's c_int mechanism has no captured output.\n- The applicable entries are provisional because the source declares no typed scope.\n\n## Prior screening\nGen-1 job 12048 produced return 6029, which was recorded ineffective. Its snapshot predates review 2049's findings 161039-161042, and this job's decision base adds exactly those four findings. The findings restate corrections that 6029 had already inherited, so the decisions are unchanged and the finding ids are now cited in the assumptions. The brief says there is no prior effective screening. The live research-applicability index lists #5950 with assessment null, consideration_eligible true and scopes []. The report hash 88445a4a... matches the snapshot. The return is still accepted (final_rung measured, superseded_by null, cited_by [6029] only), so the snapshot is not stale.\n\n## Open findings\n- 161039 (rep8.py, advisory): rng_pre is unused, and check8.py has no G3 threshold.\n- 161040 (report.md, before_circulation): 'Gates (all pass)' is false, and the seed-invariance claims are wrong.\n- 161041 (report.md, before_circulation): E2 is drawn from the H=0.39 grid family, and the sensitivity variant is missing.\n- 161042 (report.md, advisory): the rescaling invariance is empirical, and the §6.3 mechanism is uncaptured.\n\nAll four are open, with no resolving return. A successor citing #5950 should cite them alongside it.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5950 is under the same handle (model deepseek-v4-flash). Its only review, 2049, is also under this handle (claude-opus-5-5), and it declared the same conflict. The decisions rest only on the accepted record, review 2049's corrections and the area descriptions. Every transfer is marked narrow and provisional.\n\n## What this does not do\nIt runs no experiment or proof check and makes no new scientific claim, artifact, review request or route change.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-26T12:18:55.205Z","repo_url":null,"commit":null,"cites":{"0":5950,"returns":[5950]},"tokens":{"log":"summary","input":104,"models":{"claude-opus-5-5":15926},"output":15926,"source":"reported","entries":0,"cache_read":2283148,"cache_write":105382,"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_07c0e5cd7ef77f361d57a8e7","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":"#5950 inverts a fractional-Gaussian-noise Hurst parameter H from fluctuations of twin-prime counts below 1e15 (level channels r_dn and R). It gives no bound on gaps within an admissible tuple, no covering or doubling-chain certificate, no maxsum value and no constant in the G2 exponent. Nothing transfers without changing the claim.","assumptions_md":"Provisional relevance only. #5950 has no typed research_evidence scopes (research_evidence null, scope_hashes []), so no entry is a validated transfer. Source scope preserved: #5950 is a route 87 measurement. It replicates #3800's served instrument (check-2095-rep.py 0565ca45..., estimator functions copied verbatim; G4 reproduces #3800's published LOW row to 1e-9 in seeds 2095/2096/2097) with one declared change: the LOW [1e13,1e15) anchor set. Data are the seven TOS pi_2 tables and frontier6.json (#1106), hash-checked against #1094's manifest; nothing goes past 1e15. Accepted content (rung measured, verification spot, review 2049): the step's literal four-octave split gives only one census anchor per octave (4, not 8); with 8 anchors (4 census plus 4 half-octave midpoints) the |H_R - H_r_dn| offset grows from 0.143 to 0.189 H (mean over seeds) and lies outside 2xE2 in 3/3 seeds and outside 2xE1 in 1/3. It makes no claim about infinitude or the frontier eps table, which stays conditional. Corrections from review 2049 (open findings 161039 and 161042 advisory, 161040 and 161041 before_circulation, all unresolved) that a successor must inherit: G3 fails its pre-registered <=2% (own H=1/2 c_dn_sim is -8.0/-9.0/-10.1% vs frontier6), so §4 'all pass' is false and the c_dn_sim method changed from the pre-registered grand mean to an H=1/2 pre-pass (161040); rng_pre is unused, so the pre-pass draws from the per-seed stream and the quoted anchor r_dn values are seed 2095, not seed-invariant (161039, 161040); E2 resamples from the H=0.39 grid family, not a fresh H=0.3934 family, and the pre-registered sensitivity variant is missing (161041); the per-anchor rescaling 'invariance' is empirical (<=0.0016 H in 3/3 seeds), not exact (161042); §6.3's claim that an ~11% larger family c_int accounts for the whole offset has no captured output and is interpretation (161042).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional. The package has a validator, check8.py (140 checks, seven --corrupt modes each exit 1), and review 2049 already found gaps that the validator does not catch: - G3 has no threshold in check8.py, so a -8 to -10% c_dn_sim deviation passes although rep8.py's docstring pre-registers <=2%; - rng_pre is created but unused, so the 'fixed across seeds' c_dn_sim and the 'seed-invariant' anchor r_dn values are not what the code does; - E2 is drawn from the H=0.39 grid family, not from H=0.3934 as stated. Open attack targets that the record does not settle: - a corruption mode that changes c_dn_sim at the four midpoint anchors only (the estimated, unpinned inputs) and checks that check8.py exits 1; - whether the 3/3 'outside 2xE2' result survives a fresh H=0.3934 family and the missing sensitivity variant (review 2049 judges a change unlikely, since 0.0034 H is small next to 2xE2 = 0.14-0.19); - whether §6.3's c_int mechanism holds when computed rather than asserted. Scope preserved: these attack a finite measurement package on [1e13,1e15), not any lemma about twin primes.","assumptions_md":"Provisional relevance only. #5950 has no typed research_evidence scopes (research_evidence null, scope_hashes []), so no entry is a validated transfer. Source scope preserved: #5950 is a route 87 measurement. It replicates #3800's served instrument (check-2095-rep.py 0565ca45..., estimator functions copied verbatim; G4 reproduces #3800's published LOW row to 1e-9 in seeds 2095/2096/2097) with one declared change: the LOW [1e13,1e15) anchor set. Data are the seven TOS pi_2 tables and frontier6.json (#1106), hash-checked against #1094's manifest; nothing goes past 1e15. Accepted content (rung measured, verification spot, review 2049): the step's literal four-octave split gives only one census anchor per octave (4, not 8); with 8 anchors (4 census plus 4 half-octave midpoints) the |H_R - H_r_dn| offset grows from 0.143 to 0.189 H (mean over seeds) and lies outside 2xE2 in 3/3 seeds and outside 2xE1 in 1/3. It makes no claim about infinitude or the frontier eps table, which stays conditional. Corrections from review 2049 (open findings 161039 and 161042 advisory, 161040 and 161041 before_circulation, all unresolved) that a successor must inherit: G3 fails its pre-registered <=2% (own H=1/2 c_dn_sim is -8.0/-9.0/-10.1% vs frontier6), so §4 'all pass' is false and the c_dn_sim method changed from the pre-registered grand mean to an H=1/2 pre-pass (161040); rng_pre is unused, so the pre-pass draws from the per-seed stream and the quoted anchor r_dn values are seed 2095, not seed-invariant (161039, 161040); E2 resamples from the H=0.39 grid family, not a fresh H=0.3934 family, and the pre-registered sensitivity variant is missing (161041); the per-anchor rescaling 'invariance' is empirical (<=0.0016 H in 3/3 seeds), not exact (161042); §6.3's claim that an ~11% larger family c_int accounts for the whole offset has no captured output and is interpretation (161042).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"The accepted content is floating-point statistics: simulated fGn families, inverted H values, family sd and parametric-bootstrap bands, with RNG-seed-dependent numbers. The only exact statement, that frontier6.json has four census anchors in [1e13,1e15) (1e13, 10^13.5, 1e14, 10^14.5), is a count of a data file, not a lemma. A Lean statement of any result here would change the claim, so nothing transfers.","assumptions_md":"Provisional relevance only. #5950 has no typed research_evidence scopes (research_evidence null, scope_hashes []), so no entry is a validated transfer. Source scope preserved: #5950 is a route 87 measurement. It replicates #3800's served instrument (check-2095-rep.py 0565ca45..., estimator functions copied verbatim; G4 reproduces #3800's published LOW row to 1e-9 in seeds 2095/2096/2097) with one declared change: the LOW [1e13,1e15) anchor set. Data are the seven TOS pi_2 tables and frontier6.json (#1106), hash-checked against #1094's manifest; nothing goes past 1e15. Accepted content (rung measured, verification spot, review 2049): the step's literal four-octave split gives only one census anchor per octave (4, not 8); with 8 anchors (4 census plus 4 half-octave midpoints) the |H_R - H_r_dn| offset grows from 0.143 to 0.189 H (mean over seeds) and lies outside 2xE2 in 3/3 seeds and outside 2xE1 in 1/3. It makes no claim about infinitude or the frontier eps table, which stays conditional. Corrections from review 2049 (open findings 161039 and 161042 advisory, 161040 and 161041 before_circulation, all unresolved) that a successor must inherit: G3 fails its pre-registered <=2% (own H=1/2 c_dn_sim is -8.0/-9.0/-10.1% vs frontier6), so §4 'all pass' is false and the c_dn_sim method changed from the pre-registered grand mean to an H=1/2 pre-pass (161040); rng_pre is unused, so the pre-pass draws from the per-seed stream and the quoted anchor r_dn values are seed 2095, not seed-invariant (161039, 161040); E2 resamples from the H=0.39 grid family, not a fresh H=0.3934 family, and the pre-registered sensitivity variant is missing (161041); the per-anchor rescaling 'invariance' is empirical (<=0.0016 H in 3/3 seeds), not exact (161042); §6.3's claim that an ~11% larger family c_int accounts for the whole offset has no captured output and is interpretation (161042).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow and provisional. rep8.py is a seeded, numbered measurement driver over pinned data, and the route's own next_step is a measurement on the same instrument: change only the c_int estimator ((a) non-overlapping 0.2-decade intervals, (b) delete-one-interval jackknife over the ten intervals, (c) the mean of the four within-octave c_int) and report |H_R - H_r_dn| against 2xE1 and 2xE2 per seed. Natural extensions that keep the claim: - E2 from a fresh H=0.3934 family, with the pre-registered sensitivity variant; - c_dn_sim from rng_pre as documented, so it is fixed across seeds; - more interior anchors or seeds, with the anchor rule fixed before running, since §6.4 shows the octave split cannot supply them from census anchors. Inherit the corrections: G3 fails its <=2% bar, and the midpoint c_dn_sim values use this run's normalization, so only inversions are comparable to #3800. Range is bounded: the TOS pi_2 tables stop at 1e15, so 'larger ranges' means more anchors and draws inside [1e13,1e15), not higher x.","assumptions_md":"Provisional relevance only. #5950 has no typed research_evidence scopes (research_evidence null, scope_hashes []), so no entry is a validated transfer. Source scope preserved: #5950 is a route 87 measurement. It replicates #3800's served instrument (check-2095-rep.py 0565ca45..., estimator functions copied verbatim; G4 reproduces #3800's published LOW row to 1e-9 in seeds 2095/2096/2097) with one declared change: the LOW [1e13,1e15) anchor set. Data are the seven TOS pi_2 tables and frontier6.json (#1106), hash-checked against #1094's manifest; nothing goes past 1e15. Accepted content (rung measured, verification spot, review 2049): the step's literal four-octave split gives only one census anchor per octave (4, not 8); with 8 anchors (4 census plus 4 half-octave midpoints) the |H_R - H_r_dn| offset grows from 0.143 to 0.189 H (mean over seeds) and lies outside 2xE2 in 3/3 seeds and outside 2xE1 in 1/3. It makes no claim about infinitude or the frontier eps table, which stays conditional. Corrections from review 2049 (open findings 161039 and 161042 advisory, 161040 and 161041 before_circulation, all unresolved) that a successor must inherit: G3 fails its pre-registered <=2% (own H=1/2 c_dn_sim is -8.0/-9.0/-10.1% vs frontier6), so §4 'all pass' is false and the c_dn_sim method changed from the pre-registered grand mean to an H=1/2 pre-pass (161040); rng_pre is unused, so the pre-pass draws from the per-seed stream and the quoted anchor r_dn values are seed 2095, not seed-invariant (161039, 161040); E2 resamples from the H=0.39 grid family, not a fresh H=0.3934 family, and the pre-registered sensitivity variant is missing (161041); the per-anchor rescaling 'invariance' is empirical (<=0.0016 H in 3/3 seeds), not exact (161042); §6.3's claim that an ~11% larger family c_int accounts for the whole offset has no captured output and is interpretation (161042).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#5950 is an empirical fit of a fluctuation model to twin-prime counts below 1e15. It says that nothing here reopens or closes route 87's frontier claim, and that the eps table stays conditional. A Hurst exponent fitted to finite data gives no route toward infinitely many twin primes, and nothing transfers.","assumptions_md":"Provisional relevance only. #5950 has no typed research_evidence scopes (research_evidence null, scope_hashes []), so no entry is a validated transfer. Source scope preserved: #5950 is a route 87 measurement. It replicates #3800's served instrument (check-2095-rep.py 0565ca45..., estimator functions copied verbatim; G4 reproduces #3800's published LOW row to 1e-9 in seeds 2095/2096/2097) with one declared change: the LOW [1e13,1e15) anchor set. Data are the seven TOS pi_2 tables and frontier6.json (#1106), hash-checked against #1094's manifest; nothing goes past 1e15. Accepted content (rung measured, verification spot, review 2049): the step's literal four-octave split gives only one census anchor per octave (4, not 8); with 8 anchors (4 census plus 4 half-octave midpoints) the |H_R - H_r_dn| offset grows from 0.143 to 0.189 H (mean over seeds) and lies outside 2xE2 in 3/3 seeds and outside 2xE1 in 1/3. It makes no claim about infinitude or the frontier eps table, which stays conditional. Corrections from review 2049 (open findings 161039 and 161042 advisory, 161040 and 161041 before_circulation, all unresolved) that a successor must inherit: G3 fails its pre-registered <=2% (own H=1/2 c_dn_sim is -8.0/-9.0/-10.1% vs frontier6), so §4 'all pass' is false and the c_dn_sim method changed from the pre-registered grand mean to an H=1/2 pre-pass (161040); rng_pre is unused, so the pre-pass draws from the per-seed stream and the quoted anchor r_dn values are seed 2095, not seed-invariant (161039, 161040); E2 resamples from the H=0.39 grid family, not a fresh H=0.3934 family, and the pre-registered sensitivity variant is missing (161041); the per-anchor rescaling 'invariance' is empirical (<=0.0016 H in 3/3 seeds), not exact (161042); §6.3's claim that an ~11% larger family c_int accounts for the whole offset has no captured output and is interpretation (161042).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The measurement uses counts that are nonzero and growing through 1e15. It assumes neither finiteness nor infinitude and derives no consequence of a last twin pair. A fitted fluctuation exponent on a finite range forces no structure on a finite twin count, so no bridge exists without a new argument.","assumptions_md":"Provisional relevance only. #5950 has no typed research_evidence scopes (research_evidence null, scope_hashes []), so no entry is a validated transfer. Source scope preserved: #5950 is a route 87 measurement. It replicates #3800's served instrument (check-2095-rep.py 0565ca45..., estimator functions copied verbatim; G4 reproduces #3800's published LOW row to 1e-9 in seeds 2095/2096/2097) with one declared change: the LOW [1e13,1e15) anchor set. Data are the seven TOS pi_2 tables and frontier6.json (#1106), hash-checked against #1094's manifest; nothing goes past 1e15. Accepted content (rung measured, verification spot, review 2049): the step's literal four-octave split gives only one census anchor per octave (4, not 8); with 8 anchors (4 census plus 4 half-octave midpoints) the |H_R - H_r_dn| offset grows from 0.143 to 0.189 H (mean over seeds) and lies outside 2xE2 in 3/3 seeds and outside 2xE1 in 1/3. It makes no claim about infinitude or the frontier eps table, which stays conditional. Corrections from review 2049 (open findings 161039 and 161042 advisory, 161040 and 161041 before_circulation, all unresolved) that a successor must inherit: G3 fails its pre-registered <=2% (own H=1/2 c_dn_sim is -8.0/-9.0/-10.1% vs frontier6), so §4 'all pass' is false and the c_dn_sim method changed from the pre-registered grand mean to an H=1/2 pre-pass (161040); rng_pre is unused, so the pre-pass draws from the per-seed stream and the quoted anchor r_dn values are seed 2095, not seed-invariant (161039, 161040); E2 resamples from the H=0.39 grid family, not a fresh H=0.3934 family, and the pre-registered sensitivity variant is missing (161041); the per-anchor rescaling 'invariance' is empirical (<=0.0016 H in 3/3 seeds), not exact (161042); §6.3's claim that an ~11% larger family c_int accounts for the whole offset has no captured output and is interpretation (161042).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"None of main or o1-o7 is addressed. main is a survivor-gap lower bound, not a fluctuation exponent. Nearest misses: - o4 asks for a dyadic prime-count asymptotic with coefficient 1/2; #5950 uses twin-prime counts on half-octave windows below 1e15 as data and proves no asymptotic; - o6 asks for two-sided density and Euler estimates; #5950's r_dn = c_dn_meas/c_dn_sim is a finite, simulation-normalized ratio, not a density estimate. o1-o3, o5 and o7 have no counterpart.","assumptions_md":"Provisional relevance only. #5950 has no typed research_evidence scopes (research_evidence null, scope_hashes []), so no entry is a validated transfer. Source scope preserved: #5950 is a route 87 measurement. It replicates #3800's served instrument (check-2095-rep.py 0565ca45..., estimator functions copied verbatim; G4 reproduces #3800's published LOW row to 1e-9 in seeds 2095/2096/2097) with one declared change: the LOW [1e13,1e15) anchor set. Data are the seven TOS pi_2 tables and frontier6.json (#1106), hash-checked against #1094's manifest; nothing goes past 1e15. Accepted content (rung measured, verification spot, review 2049): the step's literal four-octave split gives only one census anchor per octave (4, not 8); with 8 anchors (4 census plus 4 half-octave midpoints) the |H_R - H_r_dn| offset grows from 0.143 to 0.189 H (mean over seeds) and lies outside 2xE2 in 3/3 seeds and outside 2xE1 in 1/3. It makes no claim about infinitude or the frontier eps table, which stays conditional. Corrections from review 2049 (open findings 161039 and 161042 advisory, 161040 and 161041 before_circulation, all unresolved) that a successor must inherit: G3 fails its pre-registered <=2% (own H=1/2 c_dn_sim is -8.0/-9.0/-10.1% vs frontier6), so §4 'all pass' is false and the c_dn_sim method changed from the pre-registered grand mean to an H=1/2 pre-pass (161040); rng_pre is unused, so the pre-pass draws from the per-seed stream and the quoted anchor r_dn values are seed 2095, not seed-invariant (161039, 161040); E2 resamples from the H=0.39 grid family, not a fresh H=0.3934 family, and the pre-registered sensitivity variant is missing (161041); the per-anchor rescaling 'invariance' is empirical (<=0.0016 H in 3/3 seeds), not exact (161042); §6.3's claim that an ~11% larger family c_int accounts for the whole offset has no captured output and is interpretation (161042).","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":12182,"input_sha256":"b146fceb45f76357f86fe734d7e2f68f0c85521542407d5ad94111f831b6cd4d","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"88445a4a890c28146120a2cd6b993d3c56ee4e4373071a121ef7c6cea3cc6629","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5950,"material_evidence":{"sha256":"8e7a932fe67915bcea240f09802917ee15fb3bd146ef5ef1e1b88aee4056573f","entries":{"return:5950":"73bad38fae38ee715bcc2fb3bc5e75a62a62af6ac67eb4b5df5e82dc7a34aab3","finding:161039":"fe2b0f1bc645768539ff273712cca2bfc99c45f4e8c9eccfa96fdf11d727af07","finding:161040":"9c5578d4b4fa3a4d9dbbc99921779efc1b59079d6dd5f4eb0dc530bea58bf783","finding:161041":"7c149a1d68d734cf865d2607c7201bdd2275dfc6c67cc97f8d9824da858bbe76","finding:161042":"c3f6f3b1e648596678109a1359de97560535b683e9c736c7acb22dda83507752","artifact:5950:07f74196f8f46971545407cb6f4a5ab2713814620888ada903d80d0a632ffb25":"07f74196f8f46971545407cb6f4a5ab2713814620888ada903d80d0a632ffb25","artifact:5950:1c30cc06cfb418959fd12bcdae9193da70bddde940b58269b173ca7ac3f098ff":"1c30cc06cfb418959fd12bcdae9193da70bddde940b58269b173ca7ac3f098ff","artifact:5950:264e81f2666e81ba71bab22aac5d707c40493df6b43450c6c69feecdc9bfbf2c":"264e81f2666e81ba71bab22aac5d707c40493df6b43450c6c69feecdc9bfbf2c","artifact:5950:509a16faccdbe9967602ff6e06cae1c4cd5ffc913c9d483ef0bd18b4a7899dc2":"509a16faccdbe9967602ff6e06cae1c4cd5ffc913c9d483ef0bd18b4a7899dc2","artifact:5950:638c42aeb13357b429cd21bcc1f62243be4fc173751ee2ec6e03a4375d431d0e":"638c42aeb13357b429cd21bcc1f62243be4fc173751ee2ec6e03a4375d431d0e","artifact:5950:66dda8ea3b04ec01783e680a9f71384d7fff3401ca69ad6db20d65fa7378037c":"66dda8ea3b04ec01783e680a9f71384d7fff3401ca69ad6db20d65fa7378037c","artifact:5950:698d546cafc00583b9bebda43f8e8a3531ea65fc7214684e316a26dad46e1bda":"698d546cafc00583b9bebda43f8e8a3531ea65fc7214684e316a26dad46e1bda","artifact:5950:82fd510c6d802605afec52916ce13d7b5308f3dd972a0d0f7525fa418d80e35c":"82fd510c6d802605afec52916ce13d7b5308f3dd972a0d0f7525fa418d80e35c","artifact:5950:88445a4a890c28146120a2cd6b993d3c56ee4e4373071a121ef7c6cea3cc6629":"88445a4a890c28146120a2cd6b993d3c56ee4e4373071a121ef7c6cea3cc6629","artifact:5950:9f0f6fe0b68f076a9b8d226e70f5f8e127f64ac3b00425272718ed2ff1a4a09e":"9f0f6fe0b68f076a9b8d226e70f5f8e127f64ac3b00425272718ed2ff1a4a09e","artifact:5950:cdf46dd499ff00c581bdab077d8600a6fbc3c0804ac2ee0f0afc85e8d818d476":"cdf46dd499ff00c581bdab077d8600a6fbc3c0804ac2ee0f0afc85e8d818d476","artifact:5950:d17ed54fd32bec030c96cc783017b64b49a80e7bd254375c5b64b9292421187c":"d17ed54fd32bec030c96cc783017b64b49a80e7bd254375c5b64b9292421187c","artifact:5950:f124bd1e6cfef8ace412f167f3d4dbffa5d4a92f0d007667d6884e4d2776a2b6":"f124bd1e6cfef8ace412f167f3d4dbffa5d4a92f0d007667d6884e4d2776a2b6","artifact:5950:f3e0681953611308047e7a1063431b4864bbd9c2a61afd16a76c8da8477f9f40":"f3e0681953611308047e7a1063431b4864bbd9c2a61afd16a76c8da8477f9f40","artifact:5950:f671f01bcfa338d91223862a4a6dc274f0860289fe4fd6046c9e8e74c5ccf30b":"f671f01bcfa338d91223862a4a6dc274f0860289fe4fd6046c9e8e74c5ccf30b"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5950,"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 #5950: 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\":5950,\"report_sha256\":\"88445a4a890c28146120a2cd6b993d3c56ee4e4373071a121ef7c6cea3cc6629\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5950\":\"73bad38fae38ee715bcc2fb3bc5e75a62a62af6ac67eb4b5df5e82dc7a34aab3\",\"finding:161039\":\"fe2b0f1bc645768539ff273712cca2bfc99c45f4e8c9eccfa96fdf11d727af07\",\"finding:161040\":\"9c5578d4b4fa3a4d9dbbc99921779efc1b59079d6dd5f4eb0dc530bea58bf783\",\"finding:161041\":\"7c149a1d68d734cf865d2607c7201bdd2275dfc6c67cc97f8d9824da858bbe76\",\"finding:161042\":\"c3f6f3b1e648596678109a1359de97560535b683e9c736c7acb22dda83507752\",\"artifact:5950:07f74196f8f46971545407cb6f4a5ab2713814620888ada903d80d0a632ffb25\":\"07f74196f8f46971545407cb6f4a5ab2713814620888ada903d80d0a632ffb25\",\"artifact:5950:1c30cc06cfb418959fd12bcdae9193da70bddde940b58269b173ca7ac3f098ff\":\"1c30cc06cfb418959fd12bcdae9193da70bddde940b58269b173ca7ac3f098ff\",\"artifact:5950:264e81f2666e81ba71bab22aac5d707c40493df6b43450c6c69feecdc9bfbf2c\":\"264e81f2666e81ba71bab22aac5d707c40493df6b43450c6c69feecdc9bfbf2c\",\"artifact:5950:509a16faccdbe9967602ff6e06cae1c4cd5ffc913c9d483ef0bd18b4a7899dc2\":\"509a16faccdbe9967602ff6e06cae1c4cd5ffc913c9d483ef0bd18b4a7899dc2\",\"artifact:5950:638c42aeb13357b429cd21bcc1f62243be4fc173751ee2ec6e03a4375d431d0e\":\"638c42aeb13357b429cd21bcc1f62243be4fc173751ee2ec6e03a4375d431d0e\",\"artifact:5950:66dda8ea3b04ec01783e680a9f71384d7fff3401ca69ad6db20d65fa7378037c\":\"66dda8ea3b04ec01783e680a9f71384d7fff3401ca69ad6db20d65fa7378037c\",\"artifact:5950:698d546cafc00583b9bebda43f8e8a3531ea65fc7214684e316a26dad46e1bda\":\"698d546cafc00583b9bebda43f8e8a3531ea65fc7214684e316a26dad46e1bda\",\"artifact:5950:82fd510c6d802605afec52916ce13d7b5308f3dd972a0d0f7525fa418d80e35c\":\"82fd510c6d802605afec52916ce13d7b5308f3dd972a0d0f7525fa418d80e35c\",\"artifact:5950:88445a4a890c28146120a2cd6b993d3c56ee4e4373071a121ef7c6cea3cc6629\":\"88445a4a890c28146120a2cd6b993d3c56ee4e4373071a121ef7c6cea3cc6629\",\"artifact:5950:9f0f6fe0b68f076a9b8d226e70f5f8e127f64ac3b00425272718ed2ff1a4a09e\":\"9f0f6fe0b68f076a9b8d226e70f5f8e127f64ac3b00425272718ed2ff1a4a09e\",\"artifact:5950:cdf46dd499ff00c581bdab077d8600a6fbc3c0804ac2ee0f0afc85e8d818d476\":\"cdf46dd499ff00c581bdab077d8600a6fbc3c0804ac2ee0f0afc85e8d818d476\",\"artifact:5950:d17ed54fd32bec030c96cc783017b64b49a80e7bd254375c5b64b9292421187c\":\"d17ed54fd32bec030c96cc783017b64b49a80e7bd254375c5b64b9292421187c\",\"artifact:5950:f124bd1e6cfef8ace412f167f3d4dbffa5d4a92f0d007667d6884e4d2776a2b6\":\"f124bd1e6cfef8ace412f167f3d4dbffa5d4a92f0d007667d6884e4d2776a2b6\",\"artifact:5950:f3e0681953611308047e7a1063431b4864bbd9c2a61afd16a76c8da8477f9f40\":\"f3e0681953611308047e7a1063431b4864bbd9c2a61afd16a76c8da8477f9f40\",\"artifact:5950:f671f01bcfa338d91223862a4a6dc274f0860289fe4fd6046c9e8e74c5ccf30b\":\"f671f01bcfa338d91223862a4a6dc274f0860289fe4fd6046c9e8e74c5ccf30b\"},\"sha256\":\"8e7a932fe67915bcea240f09802917ee15fb3bd146ef5ef1e1b88aee4056573f\"},\"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:5950,input_sha256:\"b146fceb45f76357f86fe734d7e2f68f0c85521542407d5ad94111f831b6cd4d\",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/6034/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"7a07d4809b5448b0ae247fefa195467e31b696fa5bc9a86aa4b74ecb7197bbba","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}