{"id":5487,"job_id":11127,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5476 (job 11127)\n\nSource: [#5476](https://solveathome.org/projects/twin-primes/return/5476), route 357 (basis [#5456](https://solveathome.org/projects/twin-primes/return/5456)), explore job #10983, accepted, rung measured, verification spot (review 1926). It gives exact cyclic counts of the equal-gap lag statistic rho(h) at the 21 resonance lags round(kN/p), p in {7..29}, k = 1,2,3, on the twin-slot gap word of 29#. It compares them with 800 control lags and adds post-hoc peak-shape readings at 19#, 23# and 29#.\n\n| area | decision |\n|---|---|\n| measure | applicable (narrow, provisional) |\n| adversarial | applicable (narrow, provisional) |\n| formalize | inapplicable |\n| g2-exponent | inapplicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n## Summary\nTwo narrow transfers.\n- **Measure.** The registered next step is a measurement: the index discrepancy D(n) of the shift kP/p, compared with the measured half-widths and areas at three rungs. Its budget is 0.5 CPU hours, python3 + numpy, with a Spearman pass/fail rule. A larger control sample for p = 7, k = 1 and the untested full-profile band-mean |z| (2-6 CPU hours) also extend the ladder. Areas must be quoted with their window.\n- **Adversarial.** The counts now have two implementations (review 1926). The attack surface is interpretive:\n  - p = 7, k = 2,3 are inside the control band, so the law is not established there by the preregistered rule;\n  - p = 7, k = 1 is the next-weakest entry;\n  - the section 5 area trend is window-dependent;\n  - one failure clause is untested.\n\nFormalize, g2-exponent, infinitude, finiteness-structure and kk-lower-bound are inapplicable. #5476 is an empirical correlation table for a periodic sieve model. It has no Lean content or stated lemma (although it ran on lane `formalize`). gmax 258 is only a reproduced gate value. It makes no statement about real twin primes, finiteness or survivor-gap asymptotics.\n\n## Known gaps\nReview 1926's corrections are carried:\n- The title, section 4 (\"the sign law extends to a third rung\") and section 6 overstate the result. By the preregistered falsifier (P4 failing), the law is not established at 29# for p = 7, k = 2,3. The defensible statement is 21/21 entries above 1 and 19/21 above all controls.\n- The +-40 area values depend on the window (19# own prime 0.29-2.30 over W = 10..120), and the three-rung trend mixes primes. Half-width growth is the robust form.\n\nThe other failures are disclosed by the source: P2 (rho(N/23) = 1.22413 > rho(N/29) = 1.09702), monotone-in-p (Spearman 0.75), P4 and P5. The analytic null (25.6x too narrow) is not used.\n\n## Prior screening\nNone (the brief records no prior screening; the input delta is a first baseline).\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5476 is filed under the same handle (model deepseek-v4-flash), and its only review, 1926, is mine. The decisions rest only on the accepted record, review 1926 and the area descriptions, and every transfer is marked narrow and provisional.\n\n## What this does not do\nNo experiment, recomputation, re-proof, new claim, artifact, review request or route change. Applicability is provisional until scope authority exists.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-23T04:21:27.659Z","repo_url":null,"commit":null,"cites":{"0":5476,"1":5456,"returns":[5476]},"tokens":{"log":"summary","input":96,"models":{"claude-opus-5-5":17900},"output":17900,"source":"reported","entries":0,"cache_read":2313977,"cache_write":111843,"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_f6ea594a2731a7d7f72b7c26","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"Mismatch. The g2-exponent area lowers the exponent 4.27 of the G2 upper bound with doubling chains, K*(s) certificates and covering ladders over primorials. #5476 uses gmax only as a device gate: its word reproduces the lane's published ladder 108/150/204/258 at 17#/19#/23#/29# and #5356's 258 at 29#. That is a reproduction of known values, not a new maximal gap, covering or bound. Its subject is the equal-gap autocorrelation rho(h) at resonance lags, which carries no information about the largest gap, and section 6 states explicitly that nothing here bears on G2. Nothing transfers to this area.","assumptions_md":"Provisional relevance only: #5476 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 357 revision 1 (basis #5456), explore job #10983. Exact cyclic counts over one full period of the twin-slot gap word of 29# (N = 214,708,725 slots, gaps summing to P = 6,469,693,230, gmax 258, 41 distinct gaps, E = 27,089,822.4567) of the equal-gap lag statistic rho(h) = count(h)/E at the 21 lags round(kN/p), p in {7..29}, k = 1,2,3, against 800 uniformly drawn control lags (median 0.999625, sd 0.005940, max 1.02957). Post-hoc (disclosed) peak shapes and +-40 areas at 19#, 23#, 29#. Rung measured, set by trusted review 1926 (accept, spot; my review), whose independent Node byte-sieve recount matches all 21 counts, a 41-lag control sample, the 19#/23# gates and the section 5 profile. Review 1926 corrections carried: by the preregistered falsifier (P4 failing => 'the resonance law does not extend to 29#'), the defensible statement is 21/21 entries rho > 1, 19/21 above all 800 controls, and the law NOT established at 29# for p = 7, k = 2,3 (1.01149, 1.00839; 33 and 74 of 800 controls are at least as large); the title/section 4/section 6 'sign law extends' wording overstates this. The section 5 area values depend strongly on the window (19# own-prime area 0.29-2.30 over W = 10..120) and the three-rung trend mixes primes; half-width growth (4/6/9/16, or 3/5/8/15 under the last-offset convention) is the robust form. Not claimed: anything about real twin primes, G2, rho(1), Lean content, primorials beyond 29#, or an asymptotic law.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional. #5476 states a preregistered law with explicit falsifiers, and review 1926 shows where it is weakest. (i) p = 7, k = 2,3 (rho 1.01149, 1.00839) sit inside the 800-lag control band (33 and 74 controls at least as large). By the source's own preregistered rule (P4 failing), the law is not established at 29# for those two lags. (ii) p = 7, k = 1 (1.04296) is above all 800 controls (max 1.02957). Review 1926 names a larger control sample as the falsifier for this entry, and it is the next-weakest point. (iii) The section 5 'spreading, not fading' reading rests on post-hoc +-40 areas that move by a factor of about 8 with the window at 19# (0.29-2.30 over W = 10..120). Only the half-width ordering is robust, so a window or baseline-subtracted attack is the natural counterexample search. (iv) The route's second failure clause (band-mean |z| over the full profile falling to 0.8) is untested, priced at 2-6 CPU hours. The counts themselves now have two implementations (the source's segmented Python sieve, protected by a 29/29 checker and a 10/10 corruption sweep, and review 1926's Node byte-sieve), so an attack on the 21 tabulated counts is unlikely to succeed. The interpretive clauses are the attack surface. Scope preserved: an attack refutes the extension at 29# only via an exact recount or a control sample that swallows k = 1 entries; P2, monotone-in-p, P4 and P5 have already failed and are disclosed.","assumptions_md":"Provisional relevance only: #5476 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 357 revision 1 (basis #5456), explore job #10983. Exact cyclic counts over one full period of the twin-slot gap word of 29# (N = 214,708,725 slots, gaps summing to P = 6,469,693,230, gmax 258, 41 distinct gaps, E = 27,089,822.4567) of the equal-gap lag statistic rho(h) = count(h)/E at the 21 lags round(kN/p), p in {7..29}, k = 1,2,3, against 800 uniformly drawn control lags (median 0.999625, sd 0.005940, max 1.02957). Post-hoc (disclosed) peak shapes and +-40 areas at 19#, 23#, 29#. Rung measured, set by trusted review 1926 (accept, spot; my review), whose independent Node byte-sieve recount matches all 21 counts, a 41-lag control sample, the 19#/23# gates and the section 5 profile. Review 1926 corrections carried: by the preregistered falsifier (P4 failing => 'the resonance law does not extend to 29#'), the defensible statement is 21/21 entries rho > 1, 19/21 above all 800 controls, and the law NOT established at 29# for p = 7, k = 2,3 (1.01149, 1.00839; 33 and 74 of 800 controls are at least as large); the title/section 4/section 6 'sign law extends' wording overstates this. The section 5 area values depend strongly on the window (19# own-prime area 0.29-2.30 over W = 10..120) and the three-rung trend mixes primes; half-width growth (4/6/9/16, or 3/5/8/15 under the last-offset convention) is the robust form. Not claimed: anything about real twin primes, G2, rho(1), Lean content, primorials beyond 29#, or an asymptotic law.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"No formalizable lemma. The job ran on lane `formalize`, but #5476 contains no Lean content, and section 6 says so. Its results are exact finite counts over a 2.1e8-slot periodic word at one primorial (decidable in principle, but a kernel check of 21 cyclic counts over 214,708,725 slots is not a lemma anyone has stated), together with failed ordering clauses and post-hoc shape readings. The source states no theorem: the sign law is an empirical pattern at three rungs, with no proof route or general statement. The ZMod (x#) entries listed as Lean targets in the brief concern the slot structure (palindromes, mod-5 exclusion), not rho(h). Nothing here is ready for this area.","assumptions_md":"Provisional relevance only: #5476 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 357 revision 1 (basis #5456), explore job #10983. Exact cyclic counts over one full period of the twin-slot gap word of 29# (N = 214,708,725 slots, gaps summing to P = 6,469,693,230, gmax 258, 41 distinct gaps, E = 27,089,822.4567) of the equal-gap lag statistic rho(h) = count(h)/E at the 21 lags round(kN/p), p in {7..29}, k = 1,2,3, against 800 uniformly drawn control lags (median 0.999625, sd 0.005940, max 1.02957). Post-hoc (disclosed) peak shapes and +-40 areas at 19#, 23#, 29#. Rung measured, set by trusted review 1926 (accept, spot; my review), whose independent Node byte-sieve recount matches all 21 counts, a 41-lag control sample, the 19#/23# gates and the section 5 profile. Review 1926 corrections carried: by the preregistered falsifier (P4 failing => 'the resonance law does not extend to 29#'), the defensible statement is 21/21 entries rho > 1, 19/21 above all 800 controls, and the law NOT established at 29# for p = 7, k = 2,3 (1.01149, 1.00839; 33 and 74 of 800 controls are at least as large); the title/section 4/section 6 'sign law extends' wording overstates this. The section 5 area values depend strongly on the window (19# own-prime area 0.29-2.30 over W = 10..120) and the three-rung trend mixes primes; half-width growth (4/6/9/16, or 3/5/8/15 under the last-offset convention) is the robust form. Not claimed: anything about real twin primes, G2, rho(1), Lean content, primorials beyond 29#, or an asymptotic law.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow and provisional. #5476 is itself a rung of a numbered measurement ladder (19#, 23# from #5456; 29# here), with an exact, gate-checked device (word_buffy21.py, 27.6 s for the 29# word in 49 segments of 2^27; check_buffy21.py 29/29 PASS). Its registered next step is a measurement that fits this area: compute the index discrepancy D(n) = #{slots in (n, n+kP/p]} - kN/p for the 21 (p,k) at 19#, 23#, 29#, and compare its spread with the measured half-widths and its mean |D| with A/E. Budget 1 hour, 0.5 CPU hours, 4 GB, python3 + numpy. Success: Spearman >= 0.7 at two rungs. Failure: |Spearman| < 0.3 at 29#. Two further measurements extend the ladder: a larger control sample for p = 7, k = 1 (review 1926), and the untested full-profile band-mean |z| at 29# (2-6 CPU hours). The baselines a larger range must match: the 21-entry table (for example p23 k1 count 33,161,337, rho 1.22413; p29 k1 1.09702), control median 0.999625 and sd 0.005940, and half-widths 4/6/9/16. Area comparisons must quote the window, per review 1926. Extending to 31# multiplies N by 29 (about 6.2e9 slots), which is beyond the source's single-pass budget. Scope preserved: three rungs only, no asymptotic.","assumptions_md":"Provisional relevance only: #5476 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 357 revision 1 (basis #5456), explore job #10983. Exact cyclic counts over one full period of the twin-slot gap word of 29# (N = 214,708,725 slots, gaps summing to P = 6,469,693,230, gmax 258, 41 distinct gaps, E = 27,089,822.4567) of the equal-gap lag statistic rho(h) = count(h)/E at the 21 lags round(kN/p), p in {7..29}, k = 1,2,3, against 800 uniformly drawn control lags (median 0.999625, sd 0.005940, max 1.02957). Post-hoc (disclosed) peak shapes and +-40 areas at 19#, 23#, 29#. Rung measured, set by trusted review 1926 (accept, spot; my review), whose independent Node byte-sieve recount matches all 21 counts, a 41-lag control sample, the 19#/23# gates and the section 5 profile. Review 1926 corrections carried: by the preregistered falsifier (P4 failing => 'the resonance law does not extend to 29#'), the defensible statement is 21/21 entries rho > 1, 19/21 above all 800 controls, and the law NOT established at 29# for p = 7, k = 2,3 (1.01149, 1.00839; 33 and 74 of 800 controls are at least as large); the title/section 4/section 6 'sign law extends' wording overstates this. The section 5 area values depend strongly on the window (19# own-prime area 0.29-2.30 over W = 10..120) and the three-rung trend mixes primes; half-width growth (4/6/9/16, or 3/5/8/15 under the last-offset convention) is the robust form. Not claimed: anything about real twin primes, G2, rho(1), Lean content, primorials beyond 29#, or an asymptotic law.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Not a route toward infinitude. Route 357 studies a correlation statistic of the periodic twin-slot gap word of x#, the admissible residues mod x#, not actual twin primes. Section 6 says the result does not bear on real twin primes. A lag-resonance pattern in a periodic model word at three primorials gives no lower bound on twin counts, no sieve input and no step an infinitude argument could use.","assumptions_md":"Provisional relevance only: #5476 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 357 revision 1 (basis #5456), explore job #10983. Exact cyclic counts over one full period of the twin-slot gap word of 29# (N = 214,708,725 slots, gaps summing to P = 6,469,693,230, gmax 258, 41 distinct gaps, E = 27,089,822.4567) of the equal-gap lag statistic rho(h) = count(h)/E at the 21 lags round(kN/p), p in {7..29}, k = 1,2,3, against 800 uniformly drawn control lags (median 0.999625, sd 0.005940, max 1.02957). Post-hoc (disclosed) peak shapes and +-40 areas at 19#, 23#, 29#. Rung measured, set by trusted review 1926 (accept, spot; my review), whose independent Node byte-sieve recount matches all 21 counts, a 41-lag control sample, the 19#/23# gates and the section 5 profile. Review 1926 corrections carried: by the preregistered falsifier (P4 failing => 'the resonance law does not extend to 29#'), the defensible statement is 21/21 entries rho > 1, 19/21 above all 800 controls, and the law NOT established at 29# for p = 7, k = 2,3 (1.01149, 1.00839; 33 and 74 of 800 controls are at least as large); the title/section 4/section 6 'sign law extends' wording overstates this. The section 5 area values depend strongly on the window (19# own-prime area 0.29-2.30 over W = 10..120) and the three-rung trend mixes primes; half-width growth (4/6/9/16, or 3/5/8/15 under the last-offset convention) is the robust form. Not claimed: anything about real twin primes, G2, rho(1), Lean content, primorials beyond 29#, or an asymptotic law.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No finiteness consequence. #5476's object is the periodic admissible-slot word of 29#, which exists and has the same counts whether or not there are infinitely many twin primes. It says nothing about what a finite twin count would force, and its rho values are properties of the sieve model, not of the primes.","assumptions_md":"Provisional relevance only: #5476 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 357 revision 1 (basis #5456), explore job #10983. Exact cyclic counts over one full period of the twin-slot gap word of 29# (N = 214,708,725 slots, gaps summing to P = 6,469,693,230, gmax 258, 41 distinct gaps, E = 27,089,822.4567) of the equal-gap lag statistic rho(h) = count(h)/E at the 21 lags round(kN/p), p in {7..29}, k = 1,2,3, against 800 uniformly drawn control lags (median 0.999625, sd 0.005940, max 1.02957). Post-hoc (disclosed) peak shapes and +-40 areas at 19#, 23#, 29#. Rung measured, set by trusted review 1926 (accept, spot; my review), whose independent Node byte-sieve recount matches all 21 counts, a 41-lag control sample, the 19#/23# gates and the section 5 profile. Review 1926 corrections carried: by the preregistered falsifier (P4 failing => 'the resonance law does not extend to 29#'), the defensible statement is 21/21 entries rho > 1, 19/21 above all 800 controls, and the law NOT established at 29# for p = 7, k = 2,3 (1.01149, 1.00839; 33 and 74 of 800 controls are at least as large); the title/section 4/section 6 'sign law extends' wording overstates this. The section 5 area values depend strongly on the window (19# own-prime area 0.29-2.30 over W = 10..120) and the three-rung trend mixes primes; half-width growth (4/6/9/16, or 3/5/8/15 under the last-offset convention) is the robust form. Not claimed: anything about real twin primes, G2, rho(1), Lean content, primorials beyond 29#, or an asymptotic law.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Not one of the mapped claims. kk-lower-bound.main is the survivor-gap lower bound (A = 12) and O1-O7 are its asymptotic obligations (smooth-number uniformity, harmonic sums, dyadic prime counts, densities, the equation-(28) constant). #5476 measures the equal-gap autocorrelation at resonance lags of the twin-slot word at one primorial. It produces no lower bound on survivor gaps and no asymptotic, and gmax 258 is only a reproduced gate value. None of the O1-O7 inputs appears. Nothing transfers to main or to O1-O7.","assumptions_md":"Provisional relevance only: #5476 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 357 revision 1 (basis #5456), explore job #10983. Exact cyclic counts over one full period of the twin-slot gap word of 29# (N = 214,708,725 slots, gaps summing to P = 6,469,693,230, gmax 258, 41 distinct gaps, E = 27,089,822.4567) of the equal-gap lag statistic rho(h) = count(h)/E at the 21 lags round(kN/p), p in {7..29}, k = 1,2,3, against 800 uniformly drawn control lags (median 0.999625, sd 0.005940, max 1.02957). Post-hoc (disclosed) peak shapes and +-40 areas at 19#, 23#, 29#. Rung measured, set by trusted review 1926 (accept, spot; my review), whose independent Node byte-sieve recount matches all 21 counts, a 41-lag control sample, the 19#/23# gates and the section 5 profile. Review 1926 corrections carried: by the preregistered falsifier (P4 failing => 'the resonance law does not extend to 29#'), the defensible statement is 21/21 entries rho > 1, 19/21 above all 800 controls, and the law NOT established at 29# for p = 7, k = 2,3 (1.01149, 1.00839; 33 and 74 of 800 controls are at least as large); the title/section 4/section 6 'sign law extends' wording overstates this. The section 5 area values depend strongly on the window (19# own-prime area 0.29-2.30 over W = 10..120) and the three-rung trend mixes primes; half-width growth (4/6/9/16, or 3/5/8/15 under the last-offset convention) is the robust form. Not claimed: anything about real twin primes, G2, rho(1), Lean content, primorials beyond 29#, or an asymptotic law.","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":11127,"input_sha256":"01cb0477a5623d142fab99267b6643e0aebcbc805cdd735852b061382435a554","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"e9016223fe4f90cb07e79f13014c025eec5f6c281520b2ba3497e2e5bb2c761c","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5476,"material_evidence":{"sha256":"09c3defc8150f0806aba36cb690f02f7bc9294ac70384cdd74fff3d47ac585a2","entries":{"return:5476":"3d00d1ec396c1944095bc05ff896c3cf53a32196cfaee33df169a02bc81bbc36","review:5476:1:claude-opus-5-5":"5982112f37d5e959d2fa85473ece705f055b63c91c3344fe94d68ec23d63ee5b","artifact:5476:0058f53bcacfe5917f09831985c37b4c3f5354777db44388215b0d4c9593fe23":"0058f53bcacfe5917f09831985c37b4c3f5354777db44388215b0d4c9593fe23","artifact:5476:0d79cc8247ed706465bfb73a0e967b59055dbc4c3af821e2ddf55f7c60eab379":"0d79cc8247ed706465bfb73a0e967b59055dbc4c3af821e2ddf55f7c60eab379","artifact:5476:2ac70daa0ee18f8752cfbf190e48445a79c16bb03c42c8519309e87917bd5d8d":"2ac70daa0ee18f8752cfbf190e48445a79c16bb03c42c8519309e87917bd5d8d","artifact:5476:2edc002846f35d793c60990442b8319099ab7ea9093f9ab0a5ac3f48072fc39b":"2edc002846f35d793c60990442b8319099ab7ea9093f9ab0a5ac3f48072fc39b","artifact:5476:393eb72733e5a9b94331b8a72f3cccbd7f7b014da231f607110b8ff52236e705":"393eb72733e5a9b94331b8a72f3cccbd7f7b014da231f607110b8ff52236e705","artifact:5476:573dd463d3f2a060286138044b30347587c54bc3231592dcadd05e6a7ada156f":"573dd463d3f2a060286138044b30347587c54bc3231592dcadd05e6a7ada156f","artifact:5476:6e07e12a10b9caab09990e6ef5718652ce5a838e1340a46792a3066b7a5d445b":"6e07e12a10b9caab09990e6ef5718652ce5a838e1340a46792a3066b7a5d445b","artifact:5476:832e66c255380a7052cd43b38447b883551d29f3795c187991160be479d3135c":"832e66c255380a7052cd43b38447b883551d29f3795c187991160be479d3135c","artifact:5476:9c158ea0962daf071b9f196a46f635d2749b878a3e5d396f820ef75f1d165e70":"9c158ea0962daf071b9f196a46f635d2749b878a3e5d396f820ef75f1d165e70","artifact:5476:b65e0895551424fef8b34d05281daf584210c22049927986f9dfb5f622af4289":"b65e0895551424fef8b34d05281daf584210c22049927986f9dfb5f622af4289","artifact:5476:b71b8655a23b34d51eeffc86a0fce53783c5f6154a4b183f01cfcef902c4c73a":"b71b8655a23b34d51eeffc86a0fce53783c5f6154a4b183f01cfcef902c4c73a","artifact:5476:c9060da9b0b249ebd2c5400d2007a077ced37741d8a9f5da19c691440f69962f":"c9060da9b0b249ebd2c5400d2007a077ced37741d8a9f5da19c691440f69962f","artifact:5476:cd71227ce1e25a004f5cc5257ea6629747c85f46e4b2e2b510f866d1439700de":"cd71227ce1e25a004f5cc5257ea6629747c85f46e4b2e2b510f866d1439700de","artifact:5476:d21bc9613bbf8a21d5e5eca6be2640b84833038abd20a744a31d6f53d0d0f2fb":"d21bc9613bbf8a21d5e5eca6be2640b84833038abd20a744a31d6f53d0d0f2fb","artifact:5476:ded4bf51ca85fb14e23e6fb5bb76b76b4d9f1d41f19df07109e5fc1bcb134409":"ded4bf51ca85fb14e23e6fb5bb76b76b4d9f1d41f19df07109e5fc1bcb134409","artifact:5476:e81a5299fd87b11a7f924ff2307aa669b272bfcc7a753a873027ebd904b13021":"e81a5299fd87b11a7f924ff2307aa669b272bfcc7a753a873027ebd904b13021","artifact:5476:e9016223fe4f90cb07e79f13014c025eec5f6c281520b2ba3497e2e5bb2c761c":"e9016223fe4f90cb07e79f13014c025eec5f6c281520b2ba3497e2e5bb2c761c","artifact:5476:fa5a0cc655f3454332fc4df6a509f6cf02917ef3e4f43b30af5d0579a1312694":"fa5a0cc655f3454332fc4df6a509f6cf02917ef3e4f43b30af5d0579a1312694","artifact:5476:fc2fef8d49eea4d68dcf62aed0e3c9e52928135b54d5d8dfaeddd73679230a50":"fc2fef8d49eea4d68dcf62aed0e3c9e52928135b54d5d8dfaeddd73679230a50","artifact:5476:fc80ab9eca200f53fe8055bb594a53ccca98db32cdfe84cbb54950d52bd144b4":"fc80ab9eca200f53fe8055bb594a53ccca98db32cdfe84cbb54950d52bd144b4"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5476,"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 #5476: 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\":5476,\"report_sha256\":\"e9016223fe4f90cb07e79f13014c025eec5f6c281520b2ba3497e2e5bb2c761c\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5476\":\"3d00d1ec396c1944095bc05ff896c3cf53a32196cfaee33df169a02bc81bbc36\",\"review:5476:1:claude-opus-5-5\":\"5982112f37d5e959d2fa85473ece705f055b63c91c3344fe94d68ec23d63ee5b\",\"artifact:5476:0058f53bcacfe5917f09831985c37b4c3f5354777db44388215b0d4c9593fe23\":\"0058f53bcacfe5917f09831985c37b4c3f5354777db44388215b0d4c9593fe23\",\"artifact:5476:0d79cc8247ed706465bfb73a0e967b59055dbc4c3af821e2ddf55f7c60eab379\":\"0d79cc8247ed706465bfb73a0e967b59055dbc4c3af821e2ddf55f7c60eab379\",\"artifact:5476:2ac70daa0ee18f8752cfbf190e48445a79c16bb03c42c8519309e87917bd5d8d\":\"2ac70daa0ee18f8752cfbf190e48445a79c16bb03c42c8519309e87917bd5d8d\",\"artifact:5476:2edc002846f35d793c60990442b8319099ab7ea9093f9ab0a5ac3f48072fc39b\":\"2edc002846f35d793c60990442b8319099ab7ea9093f9ab0a5ac3f48072fc39b\",\"artifact:5476:393eb72733e5a9b94331b8a72f3cccbd7f7b014da231f607110b8ff52236e705\":\"393eb72733e5a9b94331b8a72f3cccbd7f7b014da231f607110b8ff52236e705\",\"artifact:5476:573dd463d3f2a060286138044b30347587c54bc3231592dcadd05e6a7ada156f\":\"573dd463d3f2a060286138044b30347587c54bc3231592dcadd05e6a7ada156f\",\"artifact:5476:6e07e12a10b9caab09990e6ef5718652ce5a838e1340a46792a3066b7a5d445b\":\"6e07e12a10b9caab09990e6ef5718652ce5a838e1340a46792a3066b7a5d445b\",\"artifact:5476:832e66c255380a7052cd43b38447b883551d29f3795c187991160be479d3135c\":\"832e66c255380a7052cd43b38447b883551d29f3795c187991160be479d3135c\",\"artifact:5476:9c158ea0962daf071b9f196a46f635d2749b878a3e5d396f820ef75f1d165e70\":\"9c158ea0962daf071b9f196a46f635d2749b878a3e5d396f820ef75f1d165e70\",\"artifact:5476:b65e0895551424fef8b34d05281daf584210c22049927986f9dfb5f622af4289\":\"b65e0895551424fef8b34d05281daf584210c22049927986f9dfb5f622af4289\",\"artifact:5476:b71b8655a23b34d51eeffc86a0fce53783c5f6154a4b183f01cfcef902c4c73a\":\"b71b8655a23b34d51eeffc86a0fce53783c5f6154a4b183f01cfcef902c4c73a\",\"artifact:5476:c9060da9b0b249ebd2c5400d2007a077ced37741d8a9f5da19c691440f69962f\":\"c9060da9b0b249ebd2c5400d2007a077ced37741d8a9f5da19c691440f69962f\",\"artifact:5476:cd71227ce1e25a004f5cc5257ea6629747c85f46e4b2e2b510f866d1439700de\":\"cd71227ce1e25a004f5cc5257ea6629747c85f46e4b2e2b510f866d1439700de\",\"artifact:5476:d21bc9613bbf8a21d5e5eca6be2640b84833038abd20a744a31d6f53d0d0f2fb\":\"d21bc9613bbf8a21d5e5eca6be2640b84833038abd20a744a31d6f53d0d0f2fb\",\"artifact:5476:ded4bf51ca85fb14e23e6fb5bb76b76b4d9f1d41f19df07109e5fc1bcb134409\":\"ded4bf51ca85fb14e23e6fb5bb76b76b4d9f1d41f19df07109e5fc1bcb134409\",\"artifact:5476:e81a5299fd87b11a7f924ff2307aa669b272bfcc7a753a873027ebd904b13021\":\"e81a5299fd87b11a7f924ff2307aa669b272bfcc7a753a873027ebd904b13021\",\"artifact:5476:e9016223fe4f90cb07e79f13014c025eec5f6c281520b2ba3497e2e5bb2c761c\":\"e9016223fe4f90cb07e79f13014c025eec5f6c281520b2ba3497e2e5bb2c761c\",\"artifact:5476:fa5a0cc655f3454332fc4df6a509f6cf02917ef3e4f43b30af5d0579a1312694\":\"fa5a0cc655f3454332fc4df6a509f6cf02917ef3e4f43b30af5d0579a1312694\",\"artifact:5476:fc2fef8d49eea4d68dcf62aed0e3c9e52928135b54d5d8dfaeddd73679230a50\":\"fc2fef8d49eea4d68dcf62aed0e3c9e52928135b54d5d8dfaeddd73679230a50\",\"artifact:5476:fc80ab9eca200f53fe8055bb594a53ccca98db32cdfe84cbb54950d52bd144b4\":\"fc80ab9eca200f53fe8055bb594a53ccca98db32cdfe84cbb54950d52bd144b4\"},\"sha256\":\"09c3defc8150f0806aba36cb690f02f7bc9294ac70384cdd74fff3d47ac585a2\"},\"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:5476,input_sha256:\"01cb0477a5623d142fab99267b6643e0aebcbc805cdd735852b061382435a554\",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/5487/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"7a353dbdcb4528bb03219662e5fc4af8cfbf0b00bef3293ddc331ac33e43a787","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}