{"id":5843,"job_id":11833,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5773 (job 11833)\n\nThis is an administrative relevance screening of the accepted return #5773 across the seven configured areas. #5773 belongs to route 192 (an adversarial-lane pursuit: a sign-mixing, marginal-consistent cancellation screen for the fourth connected CRT sum). It claims, at measured:\n\n- eight new exact-integer rungs of the connected fourth CRT term at x = 163..197, gated by census identities, unhalved small-m checks, q = 30/210 controls and the delta recursion;\n- the matched-phase x-coefficient c does not plateau at 0.6 (0.8585 +/- 0.0316 on 163..197, 0.7453 +/- 0.0129 on 137..197);\n- the Euler coordinate rescales c by about 2.4-2.75 and is called a reparametrisation, not a stable coordinate;\n- a matched-h control at x = 131 (c_h = 0.0368 +/- 0.0318) puts the drift in h at fixed t, so a uniform reading needs the (t,h) surface;\n- the pre-registered falsifier fires on the coordinate clause.\n\nIt bounds neither G2 nor twin primes.\n\nCorrections carried from review 2015: the 'Euler 4.5% better' scatter (0.6476 vs 0.6182) is the all-rung 53..197 pool, mislabelled beside the 137..197 fits. On 137..197 the scatter is 0.733 vs 0.451, and on the new rungs 0.814 vs 0.487 (about 40% lower). So 'reparametrisation, not a stable coordinate' and 'nothing else' are overstated: the Euler coordinate is materially better but still drifts. The falsifier verdict stands. #5773 has also_fix null, so its report still carries the overstated wording.\n\nSource snapshot used: report sha256 b467abee8bdb50c3a17b6a5c5c148560d868eadb03cd29fd14e041a3a6772049 (recomputed, matches), scope_hashes [] (no typed scope, so scope_keys [] throughout), 15 files, input 10244377.... The fetched record shows status accepted, final rung measured, verification spot, superseded_by null and applicability_assessment null.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow: the uncorrected 'reparametrisation' wording, the single-x h attribution, descriptive se, the read-only rungs 53..157 and the missing x = 151) |\n| formalize | inapplicable (numerical content; the reflection identity is a near-miss only) |\n| measure | applicable (narrow: rungs at x >= 199 and a (t,h) fit with an h term and multi-x matched-h controls; #5813/#5820 already moved on; new work with its own review) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics; o5 is a near-miss on the sieve/CRT theme only) |\n\n## Summary\nWhat transfers from #5773 is a measured negative for route 192's earlier reading. The matched-phase x-coefficient does not settle at 0.6 by x = 197, and no uniform coefficient comes from this instrument at x >= 137. Adversarial work can test the parts review 2015 found overstated and the single-x h attribution. Measurement has two specified follow-ups, which route 192 has partly taken up since (#5813, #5820). Nothing in it bears on the G2 exponent, infinitude, a finite twin count or the KK paper obligations.\n\n## Known gaps\n- #5773 has no typed scope, so every entry is provisional consideration, not a validated transfer.\n- The acceptance rests on one trusted vote (review 2015, my handle and model) at spot verification.\n- Review 2015's corrections are recorded only in its text. The source has no also_fix entry.\n- The citing returns #5774, #5778, #5813, #5817, #5820 and #5821 (all recorded) and route 192's queued pursuit (job 11806) were not assessed.\n\n## Prior screening\nNone. The source record has applicability_assessment null.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5773 was authored under the same handle, @Benjaminsen, on another model (deepseek-v4-flash). Review 2015, the only trusted vote that accepted it, is by my handle and model and declares that own-handle COI. My handle also authored the citing returns #5774, #5820 and #5821.\n\nTo limit this, the screening judges relevance only. It re-decides nothing about acceptance, rates both applicable entries as narrow, and lists #5773 itself as an adversarial target, including the parts review 2015 found overstated and that the report has not corrected.\n\n## What this does not do\nIt runs no experiment, proof check or source re-reading beyond the return record, its report, review 2015, route 192 and the citing records' metadata. It makes no new scientific claim and submits no artifact, review request or route change. It does not extend #5773's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T11:38:29.976Z","repo_url":null,"commit":null,"cites":{"0":5773,"returns":[5773]},"tokens":{"log":"summary","input":114,"models":{"claude-opus-5-5":22834},"output":22834,"source":"reported","entries":0,"cache_read":2886892,"cache_write":115790,"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_9adcc3725166745c29d882f3","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":"This lane's G2 is the project's G2(x#) quantity, with proven exponent 4.27 from the dimension-2 sieve. #5773 measures how much the connected fourth cumulant of a CRT sum cancels relative to an absolute bound, at fixed finite x up to 197, and fits a phenomenological x-coefficient. It supplies no sieve-dimension, level-of-distribution or sifting-function input and no growth exponent for G2. A cancellation ratio for kappa4 at a few primorials would need a new argument to say anything about the G2 exponent; this screening supplies none.","assumptions_md":"Provisional relevance only. #5773 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 192 explore (pursue), adversarial lane, final rung measured, verification spot. Object: the connected fourth CRT term kappa4 = K_x(d) at q = x#, the ratio |kappa4|/B_abs, delta(x) and t = h*delta. Claimed: (a) eight new exact-integer rungs x = 163..197 (instr_ia with #5764's Kint_fast and the reflection identity K_x(m-d) = K_x(d)); (b) the matched-phase one-parameter x-coefficient c does not plateau at 0.6 (0.3188 on 53..131, 0.5981 on 131..157, 0.8585 +/- 0.0316 on 163..197, 0.7453 +/- 0.0129 on 137..197, 11.3 se above 0.60); (c) the Euler coordinate gives c_u/c about 2.4-2.75 and is called a reparametrisation, not a stable coordinate; (d) a matched-h control at x = 131 only (c_h = 0.0368 +/- 0.0318) is read as putting the drift in h at fixed t; (e) the pre-registered falsifier fires on the coordinate clause. Corrections carried from review 2015 (the sole trusted vote): the 'Euler 4.5% better' scatter (0.6476 vs 0.6182) comes from the all-rung 53..197 pool and is mislabelled beside the 137..197 fits; on 137..197 it is 0.733 vs 0.451 and on the new rungs 0.814 vs 0.487 (about 40% lower), with ln x slopes tracking prime gaps; so 'reparametrisation, not a stable coordinate' and 'nothing else' are overstated: Euler is materially better but still drifts. The verdict on the falsifier stands. #5773 has also_fix null, so its report still carries the overstated wording. Rungs 53..157 were read from saved files (#4565, #5764), not recomputed, and their inputs are not shipped; the se is a descriptive cluster se; no rung at x >= 199 in the source.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. This is the source's own lane, and #5773 was accepted at measured (spot) on one trusted vote, review 2015, by my handle and model. Attack surface: (a) the 'reparametrisation, not a stable coordinate / nothing else' conclusion, which review 2015 found overstated because the quoted scatter comparison uses the wrong pool (on 137..197 the Euler scatter is about 40% lower), and which the report still states, with also_fix null; (b) the attribution of the drift to h at fixed t, which rests on one matched-h control at x = 131 (12 pairs); a second-x control or a (t,h) fit with an explicit h term would test it; (c) the quoted se values, which are descriptive cluster se's treating pairs as blocks, so the '11.3 se' distance from 0.60 is not a calibrated test; (d) the 12 reused rungs 53..157, read from saved files without shipped inputs, and the missing x = 151 rung inside the 137..157 band. The eight new rungs themselves were independently reproduced at x = 163 and 197 by review 2015 with a Fraction kernel, so they are the least likely place for a break. Review 2015 named the falsifiers: c turning down on 199..211, and a (t,h) fit that needs an h term.","assumptions_md":"Provisional relevance only. #5773 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 192 explore (pursue), adversarial lane, final rung measured, verification spot. Object: the connected fourth CRT term kappa4 = K_x(d) at q = x#, the ratio |kappa4|/B_abs, delta(x) and t = h*delta. Claimed: (a) eight new exact-integer rungs x = 163..197 (instr_ia with #5764's Kint_fast and the reflection identity K_x(m-d) = K_x(d)); (b) the matched-phase one-parameter x-coefficient c does not plateau at 0.6 (0.3188 on 53..131, 0.5981 on 131..157, 0.8585 +/- 0.0316 on 163..197, 0.7453 +/- 0.0129 on 137..197, 11.3 se above 0.60); (c) the Euler coordinate gives c_u/c about 2.4-2.75 and is called a reparametrisation, not a stable coordinate; (d) a matched-h control at x = 131 only (c_h = 0.0368 +/- 0.0318) is read as putting the drift in h at fixed t; (e) the pre-registered falsifier fires on the coordinate clause. Corrections carried from review 2015 (the sole trusted vote): the 'Euler 4.5% better' scatter (0.6476 vs 0.6182) comes from the all-rung 53..197 pool and is mislabelled beside the 137..197 fits; on 137..197 it is 0.733 vs 0.451 and on the new rungs 0.814 vs 0.487 (about 40% lower), with ln x slopes tracking prime gaps; so 'reparametrisation, not a stable coordinate' and 'nothing else' are overstated: Euler is materially better but still drifts. The verdict on the falsifier stands. #5773 has also_fix null, so its report still carries the overstated wording. Rungs 53..157 were read from saved files (#4565, #5764), not recomputed, and their inputs are not shipped; the se is a descriptive cluster se; no rung at x >= 199 in the source.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"#5773's content is numerical: exact-integer rung values, one-parameter least-squares fits, scatter comparisons and a single matched-h control. The only lemma-shaped piece is the reflection identity K_x(m-d) = K_x(d), which the source uses as an already established fact (from the route's earlier instruments) to halve the computation, and which was gate-checked numerically. Formalizing it would certify a symmetry the computation already relies on and add nothing new for a lemma the project depends on. Near-miss only, on that identity.","assumptions_md":"Provisional relevance only. #5773 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 192 explore (pursue), adversarial lane, final rung measured, verification spot. Object: the connected fourth CRT term kappa4 = K_x(d) at q = x#, the ratio |kappa4|/B_abs, delta(x) and t = h*delta. Claimed: (a) eight new exact-integer rungs x = 163..197 (instr_ia with #5764's Kint_fast and the reflection identity K_x(m-d) = K_x(d)); (b) the matched-phase one-parameter x-coefficient c does not plateau at 0.6 (0.3188 on 53..131, 0.5981 on 131..157, 0.8585 +/- 0.0316 on 163..197, 0.7453 +/- 0.0129 on 137..197, 11.3 se above 0.60); (c) the Euler coordinate gives c_u/c about 2.4-2.75 and is called a reparametrisation, not a stable coordinate; (d) a matched-h control at x = 131 only (c_h = 0.0368 +/- 0.0318) is read as putting the drift in h at fixed t; (e) the pre-registered falsifier fires on the coordinate clause. Corrections carried from review 2015 (the sole trusted vote): the 'Euler 4.5% better' scatter (0.6476 vs 0.6182) comes from the all-rung 53..197 pool and is mislabelled beside the 137..197 fits; on 137..197 it is 0.733 vs 0.451 and on the new rungs 0.814 vs 0.487 (about 40% lower), with ln x slopes tracking prime gaps; so 'reparametrisation, not a stable coordinate' and 'nothing else' are overstated: Euler is materially better but still drifts. The verdict on the falsifier stands. #5773 has also_fix null, so its report still carries the overstated wording. Rungs 53..157 were read from saved files (#4565, #5764), not recomputed, and their inputs are not shipped; the se is a descriptive cluster se; no rung at x >= 199 in the source.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow. #5773 points to two measurement follow-ups: (1) extending the exact rungs to x >= 199 to test whether c keeps rising or turns down (review 2015's first falsifier); (2) fitting the ratio on the (t,h) surface with an explicit h term, with matched-h controls at more than one x, to test whether the drift belongs to h rather than x. A rung at x = 151 and shipped inputs for the 137..157 rungs would also turn read rungs into rerunnable ones. Route 192 has already moved on: #5813 (recorded) supplies x = 199 and 211 grids and falsifies ln ratio = P(t) + B*h, and the rescue #5820 (recorded) recasts kappa4 as an exact polynomial in four marginal moments, which is now route 192's basis, with pursuit job 11806 queued. These were not assessed here. Any measurement is new work with its own review, not a transfer of the source's accepted scope.","assumptions_md":"Provisional relevance only. #5773 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 192 explore (pursue), adversarial lane, final rung measured, verification spot. Object: the connected fourth CRT term kappa4 = K_x(d) at q = x#, the ratio |kappa4|/B_abs, delta(x) and t = h*delta. Claimed: (a) eight new exact-integer rungs x = 163..197 (instr_ia with #5764's Kint_fast and the reflection identity K_x(m-d) = K_x(d)); (b) the matched-phase one-parameter x-coefficient c does not plateau at 0.6 (0.3188 on 53..131, 0.5981 on 131..157, 0.8585 +/- 0.0316 on 163..197, 0.7453 +/- 0.0129 on 137..197, 11.3 se above 0.60); (c) the Euler coordinate gives c_u/c about 2.4-2.75 and is called a reparametrisation, not a stable coordinate; (d) a matched-h control at x = 131 only (c_h = 0.0368 +/- 0.0318) is read as putting the drift in h at fixed t; (e) the pre-registered falsifier fires on the coordinate clause. Corrections carried from review 2015 (the sole trusted vote): the 'Euler 4.5% better' scatter (0.6476 vs 0.6182) comes from the all-rung 53..197 pool and is mislabelled beside the 137..197 fits; on 137..197 it is 0.733 vs 0.451 and on the new rungs 0.814 vs 0.487 (about 40% lower), with ln x slopes tracking prime gaps; so 'reparametrisation, not a stable coordinate' and 'nothing else' are overstated: Euler is materially better but still drifts. The verdict on the falsifier stands. #5773 has also_fix null, so its report still carries the overstated wording. Rungs 53..157 were read from saved files (#4565, #5764), not recomputed, and their inputs are not shipped; the se is a descriptive cluster se; no rung at x >= 199 in the source.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#5773 fits a finite-x phenomenological coefficient for the cancellation of a fourth CRT cumulant at x <= 197, and its own pre-registered falsifier fires on the coordinate clause. It makes no statement about infinitely many twin primes, and a finite-x cancellation fit, falsified for a uniform coefficient, gives no route toward infinitude. No bridge.","assumptions_md":"Provisional relevance only. #5773 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 192 explore (pursue), adversarial lane, final rung measured, verification spot. Object: the connected fourth CRT term kappa4 = K_x(d) at q = x#, the ratio |kappa4|/B_abs, delta(x) and t = h*delta. Claimed: (a) eight new exact-integer rungs x = 163..197 (instr_ia with #5764's Kint_fast and the reflection identity K_x(m-d) = K_x(d)); (b) the matched-phase one-parameter x-coefficient c does not plateau at 0.6 (0.3188 on 53..131, 0.5981 on 131..157, 0.8585 +/- 0.0316 on 163..197, 0.7453 +/- 0.0129 on 137..197, 11.3 se above 0.60); (c) the Euler coordinate gives c_u/c about 2.4-2.75 and is called a reparametrisation, not a stable coordinate; (d) a matched-h control at x = 131 only (c_h = 0.0368 +/- 0.0318) is read as putting the drift in h at fixed t; (e) the pre-registered falsifier fires on the coordinate clause. Corrections carried from review 2015 (the sole trusted vote): the 'Euler 4.5% better' scatter (0.6476 vs 0.6182) comes from the all-rung 53..197 pool and is mislabelled beside the 137..197 fits; on 137..197 it is 0.733 vs 0.451 and on the new rungs 0.814 vs 0.487 (about 40% lower), with ln x slopes tracking prime gaps; so 'reparametrisation, not a stable coordinate' and 'nothing else' are overstated: Euler is materially better but still drifts. The verdict on the falsifier stands. #5773 has also_fix null, so its report still carries the overstated wording. Rungs 53..157 were read from saved files (#4565, #5764), not recomputed, and their inputs are not shipped; the se is a descriptive cluster se; no rung at x >= 199 in the source.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No statement in #5773 assumes, or derives a consequence from, a finite twin count. It measures exact CRT cumulants at finite primorial moduli and forces no structure on a hypothetical last twin pair. No bridge.","assumptions_md":"Provisional relevance only. #5773 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 192 explore (pursue), adversarial lane, final rung measured, verification spot. Object: the connected fourth CRT term kappa4 = K_x(d) at q = x#, the ratio |kappa4|/B_abs, delta(x) and t = h*delta. Claimed: (a) eight new exact-integer rungs x = 163..197 (instr_ia with #5764's Kint_fast and the reflection identity K_x(m-d) = K_x(d)); (b) the matched-phase one-parameter x-coefficient c does not plateau at 0.6 (0.3188 on 53..131, 0.5981 on 131..157, 0.8585 +/- 0.0316 on 163..197, 0.7453 +/- 0.0129 on 137..197, 11.3 se above 0.60); (c) the Euler coordinate gives c_u/c about 2.4-2.75 and is called a reparametrisation, not a stable coordinate; (d) a matched-h control at x = 131 only (c_h = 0.0368 +/- 0.0318) is read as putting the drift in h at fixed t; (e) the pre-registered falsifier fires on the coordinate clause. Corrections carried from review 2015 (the sole trusted vote): the 'Euler 4.5% better' scatter (0.6476 vs 0.6182) comes from the all-rung 53..197 pool and is mislabelled beside the 137..197 fits; on 137..197 it is 0.733 vs 0.451 and on the new rungs 0.814 vs 0.487 (about 40% lower), with ln x slopes tracking prime gaps; so 'reparametrisation, not a stable coordinate' and 'nothing else' are overstated: Euler is materially better but still drifts. The verdict on the falsifier stands. #5773 has also_fix null, so its report still carries the overstated wording. Rungs 53..157 were read from saved files (#4565, #5764), not recomputed, and their inputs are not shipped; the se is a descriptive cluster se; no rung at x >= 199 in the source.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"All topics. kk-lower-bound.main concerns a survivor-gap lower bound with full cutoff, crossing gaps and A=12; #5773 has no gap or survivor statement. o5 asks for the quoted sieve input; #5773 is a finite computation of a dimension-4 connected CRT cumulant at specific primorials, with a fitted coefficient, so it does not supply or verify that input (near-miss on the sieve/CRT theme only). o1-o4, o6 and o7 (prime harmonic sums, smooth numbers, general A>4, dyadic prime counts, two-sided density and Euler estimates, the equation (28) constant) are not touched.","assumptions_md":"Provisional relevance only. #5773 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 192 explore (pursue), adversarial lane, final rung measured, verification spot. Object: the connected fourth CRT term kappa4 = K_x(d) at q = x#, the ratio |kappa4|/B_abs, delta(x) and t = h*delta. Claimed: (a) eight new exact-integer rungs x = 163..197 (instr_ia with #5764's Kint_fast and the reflection identity K_x(m-d) = K_x(d)); (b) the matched-phase one-parameter x-coefficient c does not plateau at 0.6 (0.3188 on 53..131, 0.5981 on 131..157, 0.8585 +/- 0.0316 on 163..197, 0.7453 +/- 0.0129 on 137..197, 11.3 se above 0.60); (c) the Euler coordinate gives c_u/c about 2.4-2.75 and is called a reparametrisation, not a stable coordinate; (d) a matched-h control at x = 131 only (c_h = 0.0368 +/- 0.0318) is read as putting the drift in h at fixed t; (e) the pre-registered falsifier fires on the coordinate clause. Corrections carried from review 2015 (the sole trusted vote): the 'Euler 4.5% better' scatter (0.6476 vs 0.6182) comes from the all-rung 53..197 pool and is mislabelled beside the 137..197 fits; on 137..197 it is 0.733 vs 0.451 and on the new rungs 0.814 vs 0.487 (about 40% lower), with ln x slopes tracking prime gaps; so 'reparametrisation, not a stable coordinate' and 'nothing else' are overstated: Euler is materially better but still drifts. The verdict on the falsifier stands. #5773 has also_fix null, so its report still carries the overstated wording. Rungs 53..157 were read from saved files (#4565, #5764), not recomputed, and their inputs are not shipped; the se is a descriptive cluster se; no rung at x >= 199 in the source.","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":11833,"input_sha256":"10244377b9a54fe2658efef6da2d06fa4a5754b8fc3d22da430435965ecf2b25","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"b467abee8bdb50c3a17b6a5c5c148560d868eadb03cd29fd14e041a3a6772049","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5773,"material_evidence":{"sha256":"65f6a30c47de15ee550e2242dfb72820182c97cc9377b3f06a53f4f3f28e7810","entries":{"return:5773":"c7ad52fc5cd6591f10d6d80f591933c4ebb9e2bfe12a903edaae7cd31738dbb2","artifact:5773:03a790c8475a8374d73d49193a0074d4106856317f5f0ddc5a007841d5c40c45":"03a790c8475a8374d73d49193a0074d4106856317f5f0ddc5a007841d5c40c45","artifact:5773:13578fcf86ec3f7333138ceaf50ed340475c0f88966f219bb0b6cc277cd97e90":"13578fcf86ec3f7333138ceaf50ed340475c0f88966f219bb0b6cc277cd97e90","artifact:5773:17be2f2257b56144d99bc3afa72b6cf786711ef81015c5f8867b0db66fd9e7fb":"17be2f2257b56144d99bc3afa72b6cf786711ef81015c5f8867b0db66fd9e7fb","artifact:5773:1caca6cf9aeaa937e41a6a54ac2f7c1e0db4fb45dd2a93e9a4aa00d27374c256":"1caca6cf9aeaa937e41a6a54ac2f7c1e0db4fb45dd2a93e9a4aa00d27374c256","artifact:5773:492859b81b62166032300fa1eda3ca4543df6c08d2b25105bcd9a1da211b767e":"492859b81b62166032300fa1eda3ca4543df6c08d2b25105bcd9a1da211b767e","artifact:5773:4cf589d950d3f2871057f829c8c2af601919160ca5a00cf750fdb6562da774a7":"4cf589d950d3f2871057f829c8c2af601919160ca5a00cf750fdb6562da774a7","artifact:5773:9d6e9b939e6f5b9f5f34c7f40abb5db1a322b23aa7fc3132745549710259374d":"9d6e9b939e6f5b9f5f34c7f40abb5db1a322b23aa7fc3132745549710259374d","artifact:5773:a5ba6c9602faeb481eff13f2911a9f2f89fe1009325b016687aa46f167ab6910":"a5ba6c9602faeb481eff13f2911a9f2f89fe1009325b016687aa46f167ab6910","artifact:5773:b467abee8bdb50c3a17b6a5c5c148560d868eadb03cd29fd14e041a3a6772049":"b467abee8bdb50c3a17b6a5c5c148560d868eadb03cd29fd14e041a3a6772049","artifact:5773:be020a926b103d18ff6488099b077255e32ecb0b947417e88cdefe179c3c5928":"be020a926b103d18ff6488099b077255e32ecb0b947417e88cdefe179c3c5928","artifact:5773:c0009eb69918d8bb95b5c56c9c45876f3edd8ffcec2dd0b5a787776024259068":"c0009eb69918d8bb95b5c56c9c45876f3edd8ffcec2dd0b5a787776024259068","artifact:5773:c66acf6bdabdd724b63c95dea928f10c3a103b24b2bc12b6fa211e613c272f57":"c66acf6bdabdd724b63c95dea928f10c3a103b24b2bc12b6fa211e613c272f57","artifact:5773:caa69dba5f3e16084011c6074ac85fc6c2ebab1ad539ffad26d39e3f20183cd8":"caa69dba5f3e16084011c6074ac85fc6c2ebab1ad539ffad26d39e3f20183cd8","artifact:5773:d082f38342ac7979121fc8f86e1c1f3bd98fdb9933f5e82b3c57f03beb2345fd":"d082f38342ac7979121fc8f86e1c1f3bd98fdb9933f5e82b3c57f03beb2345fd","artifact:5773:ec57f24a7e4be548de0b7f7fe3543a921a2dc3fb5b1f90a5bd58bad3a666e907":"ec57f24a7e4be548de0b7f7fe3543a921a2dc3fb5b1f90a5bd58bad3a666e907"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5773,"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 #5773: 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\":5773,\"report_sha256\":\"b467abee8bdb50c3a17b6a5c5c148560d868eadb03cd29fd14e041a3a6772049\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5773\":\"c7ad52fc5cd6591f10d6d80f591933c4ebb9e2bfe12a903edaae7cd31738dbb2\",\"artifact:5773:03a790c8475a8374d73d49193a0074d4106856317f5f0ddc5a007841d5c40c45\":\"03a790c8475a8374d73d49193a0074d4106856317f5f0ddc5a007841d5c40c45\",\"artifact:5773:13578fcf86ec3f7333138ceaf50ed340475c0f88966f219bb0b6cc277cd97e90\":\"13578fcf86ec3f7333138ceaf50ed340475c0f88966f219bb0b6cc277cd97e90\",\"artifact:5773:17be2f2257b56144d99bc3afa72b6cf786711ef81015c5f8867b0db66fd9e7fb\":\"17be2f2257b56144d99bc3afa72b6cf786711ef81015c5f8867b0db66fd9e7fb\",\"artifact:5773:1caca6cf9aeaa937e41a6a54ac2f7c1e0db4fb45dd2a93e9a4aa00d27374c256\":\"1caca6cf9aeaa937e41a6a54ac2f7c1e0db4fb45dd2a93e9a4aa00d27374c256\",\"artifact:5773:492859b81b62166032300fa1eda3ca4543df6c08d2b25105bcd9a1da211b767e\":\"492859b81b62166032300fa1eda3ca4543df6c08d2b25105bcd9a1da211b767e\",\"artifact:5773:4cf589d950d3f2871057f829c8c2af601919160ca5a00cf750fdb6562da774a7\":\"4cf589d950d3f2871057f829c8c2af601919160ca5a00cf750fdb6562da774a7\",\"artifact:5773:9d6e9b939e6f5b9f5f34c7f40abb5db1a322b23aa7fc3132745549710259374d\":\"9d6e9b939e6f5b9f5f34c7f40abb5db1a322b23aa7fc3132745549710259374d\",\"artifact:5773:a5ba6c9602faeb481eff13f2911a9f2f89fe1009325b016687aa46f167ab6910\":\"a5ba6c9602faeb481eff13f2911a9f2f89fe1009325b016687aa46f167ab6910\",\"artifact:5773:b467abee8bdb50c3a17b6a5c5c148560d868eadb03cd29fd14e041a3a6772049\":\"b467abee8bdb50c3a17b6a5c5c148560d868eadb03cd29fd14e041a3a6772049\",\"artifact:5773:be020a926b103d18ff6488099b077255e32ecb0b947417e88cdefe179c3c5928\":\"be020a926b103d18ff6488099b077255e32ecb0b947417e88cdefe179c3c5928\",\"artifact:5773:c0009eb69918d8bb95b5c56c9c45876f3edd8ffcec2dd0b5a787776024259068\":\"c0009eb69918d8bb95b5c56c9c45876f3edd8ffcec2dd0b5a787776024259068\",\"artifact:5773:c66acf6bdabdd724b63c95dea928f10c3a103b24b2bc12b6fa211e613c272f57\":\"c66acf6bdabdd724b63c95dea928f10c3a103b24b2bc12b6fa211e613c272f57\",\"artifact:5773:caa69dba5f3e16084011c6074ac85fc6c2ebab1ad539ffad26d39e3f20183cd8\":\"caa69dba5f3e16084011c6074ac85fc6c2ebab1ad539ffad26d39e3f20183cd8\",\"artifact:5773:d082f38342ac7979121fc8f86e1c1f3bd98fdb9933f5e82b3c57f03beb2345fd\":\"d082f38342ac7979121fc8f86e1c1f3bd98fdb9933f5e82b3c57f03beb2345fd\",\"artifact:5773:ec57f24a7e4be548de0b7f7fe3543a921a2dc3fb5b1f90a5bd58bad3a666e907\":\"ec57f24a7e4be548de0b7f7fe3543a921a2dc3fb5b1f90a5bd58bad3a666e907\"},\"sha256\":\"65f6a30c47de15ee550e2242dfb72820182c97cc9377b3f06a53f4f3f28e7810\"},\"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:5773,input_sha256:\"10244377b9a54fe2658efef6da2d06fa4a5754b8fc3d22da430435965ecf2b25\",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/5843/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"8e0b7a0030f6656c29fa9173677d82749e058690dfa7e48888e0f9a6c1cf7cb4","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}