{"id":6029,"job_id":12048,"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 12048)\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\nNone for #5950. The brief says so, and 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 []), so the snapshot is not stale.\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":"2026-10-26T11:56:51.359Z","repo_url":null,"commit":null,"cites":{"0":5950,"returns":[5950]},"tokens":{"log":"summary","input":102,"models":{"claude-opus-5-5":18104},"output":18104,"source":"reported","entries":0,"cache_read":2277579,"cache_write":137306,"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_d0407067592a5fcbfaf8167d","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 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; 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; E2 resamples from the H=0.39 grid family, not a fresh H=0.3934 family, and the pre-registered sensitivity variant is missing; the per-anchor rescaling 'invariance' is empirical (<=0.0016 H in 3/3 seeds), not exact; §6.3's claim that an ~11% larger family c_int accounts for the whole offset has no captured output and is interpretation.","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 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; 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; E2 resamples from the H=0.39 grid family, not a fresh H=0.3934 family, and the pre-registered sensitivity variant is missing; the per-anchor rescaling 'invariance' is empirical (<=0.0016 H in 3/3 seeds), not exact; §6.3's claim that an ~11% larger family c_int accounts for the whole offset has no captured output and is interpretation.","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 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; 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; E2 resamples from the H=0.39 grid family, not a fresh H=0.3934 family, and the pre-registered sensitivity variant is missing; the per-anchor rescaling 'invariance' is empirical (<=0.0016 H in 3/3 seeds), not exact; §6.3's claim that an ~11% larger family c_int accounts for the whole offset has no captured output and is interpretation.","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 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; 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; E2 resamples from the H=0.39 grid family, not a fresh H=0.3934 family, and the pre-registered sensitivity variant is missing; the per-anchor rescaling 'invariance' is empirical (<=0.0016 H in 3/3 seeds), not exact; §6.3's claim that an ~11% larger family c_int accounts for the whole offset has no captured output and is interpretation.","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 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; 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; E2 resamples from the H=0.39 grid family, not a fresh H=0.3934 family, and the pre-registered sensitivity variant is missing; the per-anchor rescaling 'invariance' is empirical (<=0.0016 H in 3/3 seeds), not exact; §6.3's claim that an ~11% larger family c_int accounts for the whole offset has no captured output and is interpretation.","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 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; 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; E2 resamples from the H=0.39 grid family, not a fresh H=0.3934 family, and the pre-registered sensitivity variant is missing; the per-anchor rescaling 'invariance' is empirical (<=0.0016 H in 3/3 seeds), not exact; §6.3's claim that an ~11% larger family c_int accounts for the whole offset has no captured output and is interpretation.","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 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; 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; E2 resamples from the H=0.39 grid family, not a fresh H=0.3934 family, and the pre-registered sensitivity variant is missing; the per-anchor rescaling 'invariance' is empirical (<=0.0016 H in 3/3 seeds), not exact; §6.3's claim that an ~11% larger family c_int accounts for the whole offset has no captured output and is interpretation.","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":false,"check_job_id":12048,"input_sha256":"b596b2702de6ad1d5aac60f5fcd90ae79803d958232ad0e737ea22b50f3cca7d","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"88445a4a890c28146120a2cd6b993d3c56ee4e4373071a121ef7c6cea3cc6629","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5950,"material_evidence":{"sha256":"9889b7b607b4098c3b6e3d2db295d836edc2a78c7f3ba05bc979d61b73d1357f","entries":{"return:5950":"73bad38fae38ee715bcc2fb3bc5e75a62a62af6ac67eb4b5df5e82dc7a34aab3","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. 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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:5950,input_sha256:\"b596b2702de6ad1d5aac60f5fcd90ae79803d958232ad0e737ea22b50f3cca7d\",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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