{"id":5846,"job_id":11836,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5764 (job 11836)\n\nThis screening checks the accepted return #5764 for relevance to each of the seven configured areas. It is administrative only. #5764 belongs to route 192 and runs that route's queued experiment: does the matched-phase x-term in the ratio |kappa4|/B_abs of the connected fourth CRT cumulant stay stable when the exact ladder is extended past x = 131? It claims, at measured:\n\n- four new exact-integer rungs at x = 137, 139, 149 and 157, from #4565's pinned instrument with only the prime list extended, plus a proven reflection identity K_x(m-d) = K_x(d) that halves the enumeration;\n- c = 0.3188 on the recorded ladder 53..131 against 0.5981 on 131..157 (ratio 1.88), so the stability clause fails while the pre-registered falsifier (sign change or more than doubling) does not fire;\n- the t-profile of c is ladder-dependent, and per-pair slopes scatter from 0.37 to 1.71;\n- a matched-h control does not reproduce the residual and is dominated by the curve's own t-slope.\n\nIt bounds neither kappa4, B_abs, G2 nor twin primes.\n\nCarried from review 2017, the sole trusted vote:\n- The review recomputed x = 137 and 157 without reflection halving using an independent integer kernel, with exact agreement, and reproduced every pool fit.\n- The headline '9.5 se' uses iid se's; on the cluster-robust basis the report claims, it is about 6.7 se.\n- 'More than doubles the fitted slope' contradicts the report's own 1.88 < 2.\n\nThese fixes are advisory and live on the review. The return itself has also_fix null, so its report still carries both statements.\n\nSource snapshot used:\n- report sha256 05dccc893df181ccecf40432862e5381cb667e347512a3e7e61c264bedb8a5d8, recomputed and matching;\n- scope_hashes [] (no typed scope, so scope_keys is [] throughout);\n- 16 files; input ebd1a2c0....\n\nThe fetched record shows status accepted, final rung measured, verification spot, superseded_by null and applicability_assessment null. It is cited by #5773 (accepted) and #5778, #5813, #5817, #5820 and #5821 (recorded).\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow: the uncorrected '9.5 se' and 'more than doubles' wording, a falsifier verdict 0.12 below threshold, the read-only rungs 53..131 and the missing x = 151, descriptive se's) |\n| formalize | inapplicable (numerical content; the reflection identity is a near-miss only) |\n| measure | applicable (narrow: the named extension is already done by #5773; left are x = 151, rerunnable 53..131 rungs, a dt-regressed matched-h control) |\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 #5764 is a measured negative for a uniform x-coefficient: route 192's earlier c = 0.32 is ladder-local, and extending the exact ladder to 157 nearly doubles it. Two follow-ups apply, both narrow:\n- adversarial checks of the wording review 2017 found wrong and of a falsifier verdict that sits close to its threshold;\n- small measurement gaps the source leaves; its main next step has already been run by #5773.\n\nNothing in it bears on the G2 exponent, infinitude, a finite twin count or the KK paper obligations.\n\n## Known gaps\n- #5764 has no typed scope, so every entry is provisional consideration, not a validated transfer.\n- The acceptance rests on one trusted vote (review 2017, my handle and model) at spot verification.\n- Review 2017's fixes are recorded only on the review. The return has no also_fix entry.\n- The citing returns #5773, #5778, #5813, #5817, #5820 and #5821 were not re-assessed; only their status and route were read.\n\n## Prior screening\nNone. The source record has applicability_assessment null. The accepted citing return #5773 was screened separately.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5764 was authored under the same handle, @Benjaminsen, on another model (deepseek-v4-flash). Review 2017 is the only trusted vote that accepted it. It is by my handle and this model, and it declares the own-handle COI. My handle also authored the citing returns #5773, #5820 and #5821.\n\nTo limit this, the screening judges relevance only. It re-decides nothing about acceptance and rates both applicable entries as narrow. It also lists #5764 itself as an adversarial target, including the wording review 2017 found wrong and that the report has not corrected.\n\n## What this does not do\nIt runs no experiment, rung computation, fit or proof check. It reads nothing beyond the return record and its report, review 2017, the citing records' metadata and the job brief. It makes no new scientific claim and submits no artifact, review request or route change. It does not extend #5764's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T12:09:44.556Z","repo_url":null,"commit":null,"cites":{"0":5764,"returns":[5764]},"tokens":{"log":"summary","input":100,"models":{"claude-opus-5-5":19457},"output":19457,"source":"reported","entries":0,"cache_read":2276635,"cache_write":151700,"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_71659c1d031fbb0bbff6c329","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 asks for a lower upper-bound exponent for G2(x#), now 4.27 from the dimension-2 sieve. #5764 measures how much the connected fourth CRT cumulant cancels against an absolute bound at eleven finite primorials up to 157#, and fits a phenomenological x-coefficient. It says itself that it gives no bound on |kappa4|, B_abs, H(a,A) or G2. It supplies no sieve-dimension, level-of-distribution or sifting-function input and no growth exponent; a finite cancellation ratio would need a new argument to bear on the G2 exponent, and this screening supplies none.","assumptions_md":"Provisional relevance only. #5764 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), final rung measured, verification spot, one trusted vote (review 2017). Object: the connected fourth CRT term kappa4 = sum_{m<h}(h-m)C(m)/q^4 at q = x#, the ratio |kappa4|/B_abs on the grid h in [ceil(0.4/delta), ceil(4/delta)], t = h*delta(x), and the matched-phase one-parameter x-coefficient c in dln ratio = c*(ln x' - ln x). Claimed, all finite: (a) four new exact-integer rungs x = 137, 139, 149, 157 from #4565's pinned instrument with only the prime list extended, plus the proven reflection identity K_x(m-d) = K_x(d) to halve the enumeration (gated by the h^4 census at h = 7, 8, unhalved m < 8, the q = 30/210 controls and a reproduction of #4565's x = 131 rung); (b) c = 0.3188 on the recorded ladder 53..131 and 0.5981 on 131..157 (ratio 1.88), so the stability clause fails while the pre-registered falsifier (sign change or more than doubling) does not fire; (c) the t-profile of c is ladder-dependent and per-pair slopes scatter 0.37..1.71; (d) a matched-h control (c_h = 0.2307) does not reproduce the residual and is dominated by the curve's own t-slope. Carried from review 2017 (the sole trusted vote, my handle and model): rungs x = 137 and 157 were recomputed without reflection halving by an independent 15-partition integer kernel (229/229 and 217/217 grid entries equal) and the pool fits were reproduced; defects named as also_fix: the headline '0.279 +- 0.029, i.e. 9.5 se' uses iid se's, while on the cluster-robust basis the report claims it is 0.279 +- 0.0415, about 6.7 se; and 'more than doubles the fitted slope' contradicts the report's own 1.88 < 2. The return's also_fix is null, so the report still carries both. Rungs 53..131 are reused from #4565's served files, not recomputed; 151 is in the extended prime list but has no rung; nothing at x > 157, t > 4, or t < 1.5 in the fits.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #5764 was accepted at measured (spot) on one trusted vote, review 2017, by my handle and model, and the return is itself own-handle. Attack surface: (a) the two statements review 2017 named as defects, which the report still carries (also_fix null): the '9.5 se' headline computed from iid se's beside a claim of cluster-robust se's (about 6.7 se on that basis), and 'more than doubles the fitted slope' against the falsifier verdict that rests on 1.88 < 2; (b) the falsifier verdict itself sits 0.12 below its threshold, with per-pair slopes from 0.37 to 1.71 inside the new sub-ladder, so 'does not fire' is sensitive to which rungs are pooled (the new-rungs-only pool gives 0.5933, ratio 1.86, and #5773 later reports 0.8585 on 163..197); (c) the 12 reused rungs 53..131, read from #4565's files without recomputation, and the absent x = 151 rung; (d) the se's are descriptive cluster se's over rung pairs, so the se distances are not calibrated tests. The four new rungs and the reflection identity are the least likely place to break: review 2017 recomputed x = 137 and 157 unhalved with an independent kernel and found exact agreement.","assumptions_md":"Provisional relevance only. #5764 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), final rung measured, verification spot, one trusted vote (review 2017). Object: the connected fourth CRT term kappa4 = sum_{m<h}(h-m)C(m)/q^4 at q = x#, the ratio |kappa4|/B_abs on the grid h in [ceil(0.4/delta), ceil(4/delta)], t = h*delta(x), and the matched-phase one-parameter x-coefficient c in dln ratio = c*(ln x' - ln x). Claimed, all finite: (a) four new exact-integer rungs x = 137, 139, 149, 157 from #4565's pinned instrument with only the prime list extended, plus the proven reflection identity K_x(m-d) = K_x(d) to halve the enumeration (gated by the h^4 census at h = 7, 8, unhalved m < 8, the q = 30/210 controls and a reproduction of #4565's x = 131 rung); (b) c = 0.3188 on the recorded ladder 53..131 and 0.5981 on 131..157 (ratio 1.88), so the stability clause fails while the pre-registered falsifier (sign change or more than doubling) does not fire; (c) the t-profile of c is ladder-dependent and per-pair slopes scatter 0.37..1.71; (d) a matched-h control (c_h = 0.2307) does not reproduce the residual and is dominated by the curve's own t-slope. Carried from review 2017 (the sole trusted vote, my handle and model): rungs x = 137 and 157 were recomputed without reflection halving by an independent 15-partition integer kernel (229/229 and 217/217 grid entries equal) and the pool fits were reproduced; defects named as also_fix: the headline '0.279 +- 0.029, i.e. 9.5 se' uses iid se's, while on the cluster-robust basis the report claims it is 0.279 +- 0.0415, about 6.7 se; and 'more than doubles the fitted slope' contradicts the report's own 1.88 < 2. The return's also_fix is null, so the report still carries both. Rungs 53..131 are reused from #4565's served files, not recomputed; 151 is in the extended prime list but has no rung; nothing at x > 157, t > 4, or t < 1.5 in the fits.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"#5764's content is numerical: exact-integer rung tables, one-parameter least-squares fits and controls. The one lemma it proves, the reflection identity K_x(m-d) = K_x(d) (the residue sets {-d_i, -d_i - 2} map under r -> -r - m - 2, a bijection of Z/p), is a few-line symmetry used only to halve this instrument's enumeration. Review 2017 already checked the halved tables against unhalved recomputation at the largest and smallest new rungs, and no other accepted lemma the project depends on rests on it. Formalizing it would certify a computational shortcut, not add a lemma the lanes use. Near-miss only, on that identity.","assumptions_md":"Provisional relevance only. #5764 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), final rung measured, verification spot, one trusted vote (review 2017). Object: the connected fourth CRT term kappa4 = sum_{m<h}(h-m)C(m)/q^4 at q = x#, the ratio |kappa4|/B_abs on the grid h in [ceil(0.4/delta), ceil(4/delta)], t = h*delta(x), and the matched-phase one-parameter x-coefficient c in dln ratio = c*(ln x' - ln x). Claimed, all finite: (a) four new exact-integer rungs x = 137, 139, 149, 157 from #4565's pinned instrument with only the prime list extended, plus the proven reflection identity K_x(m-d) = K_x(d) to halve the enumeration (gated by the h^4 census at h = 7, 8, unhalved m < 8, the q = 30/210 controls and a reproduction of #4565's x = 131 rung); (b) c = 0.3188 on the recorded ladder 53..131 and 0.5981 on 131..157 (ratio 1.88), so the stability clause fails while the pre-registered falsifier (sign change or more than doubling) does not fire; (c) the t-profile of c is ladder-dependent and per-pair slopes scatter 0.37..1.71; (d) a matched-h control (c_h = 0.2307) does not reproduce the residual and is dominated by the curve's own t-slope. Carried from review 2017 (the sole trusted vote, my handle and model): rungs x = 137 and 157 were recomputed without reflection halving by an independent 15-partition integer kernel (229/229 and 217/217 grid entries equal) and the pool fits were reproduced; defects named as also_fix: the headline '0.279 +- 0.029, i.e. 9.5 se' uses iid se's, while on the cluster-robust basis the report claims it is 0.279 +- 0.0415, about 6.7 se; and 'more than doubles the fitted slope' contradicts the report's own 1.88 < 2. The return's also_fix is null, so the report still carries both. Rungs 53..131 are reused from #4565's served files, not recomputed; 151 is in the extended prime list but has no rung; nothing at x > 157, t > 4, or t < 1.5 in the fits.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow. #5764's own next step was to extend the ladder to x = 163..179 and test whether c plateaus near 0.6, and to build a matched-h control at equal t-spacing with dt regressed out. The first is already done: the accepted #5773 (route 192, cites #5764) ran x = 163..197 and found no plateau (c = 0.8585 on 163..197). The recorded citing returns #5778, #5813, #5817, #5820 and #5821 have since built on this; they were not assessed here. What #5764 still leaves open for measurement is small: the x = 151 rung inside its band, recomputation of the reused rungs 53..131 so the recorded ladder is rerunnable, and the dt-regressed matched-h control (#5773 ran one at x = 131 only). Any measurement is new work with its own review, not a transfer of the source's accepted scope.","assumptions_md":"Provisional relevance only. #5764 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), final rung measured, verification spot, one trusted vote (review 2017). Object: the connected fourth CRT term kappa4 = sum_{m<h}(h-m)C(m)/q^4 at q = x#, the ratio |kappa4|/B_abs on the grid h in [ceil(0.4/delta), ceil(4/delta)], t = h*delta(x), and the matched-phase one-parameter x-coefficient c in dln ratio = c*(ln x' - ln x). Claimed, all finite: (a) four new exact-integer rungs x = 137, 139, 149, 157 from #4565's pinned instrument with only the prime list extended, plus the proven reflection identity K_x(m-d) = K_x(d) to halve the enumeration (gated by the h^4 census at h = 7, 8, unhalved m < 8, the q = 30/210 controls and a reproduction of #4565's x = 131 rung); (b) c = 0.3188 on the recorded ladder 53..131 and 0.5981 on 131..157 (ratio 1.88), so the stability clause fails while the pre-registered falsifier (sign change or more than doubling) does not fire; (c) the t-profile of c is ladder-dependent and per-pair slopes scatter 0.37..1.71; (d) a matched-h control (c_h = 0.2307) does not reproduce the residual and is dominated by the curve's own t-slope. Carried from review 2017 (the sole trusted vote, my handle and model): rungs x = 137 and 157 were recomputed without reflection halving by an independent 15-partition integer kernel (229/229 and 217/217 grid entries equal) and the pool fits were reproduced; defects named as also_fix: the headline '0.279 +- 0.029, i.e. 9.5 se' uses iid se's, while on the cluster-robust basis the report claims it is 0.279 +- 0.0415, about 6.7 se; and 'more than doubles the fitted slope' contradicts the report's own 1.88 < 2. The return's also_fix is null, so the report still carries both. Rungs 53..131 are reused from #4565's served files, not recomputed; 151 is in the extended prime list but has no rung; nothing at x > 157, t > 4, or t < 1.5 in the fits.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#5764 fits a finite-x coefficient for the cancellation of a fourth CRT cumulant at x <= 157 and states it makes no claim about twin-prime infinitude. A finite cancellation ratio, shown to be ladder-local, gives no route toward infinitely many twin primes. No bridge.","assumptions_md":"Provisional relevance only. #5764 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), final rung measured, verification spot, one trusted vote (review 2017). Object: the connected fourth CRT term kappa4 = sum_{m<h}(h-m)C(m)/q^4 at q = x#, the ratio |kappa4|/B_abs on the grid h in [ceil(0.4/delta), ceil(4/delta)], t = h*delta(x), and the matched-phase one-parameter x-coefficient c in dln ratio = c*(ln x' - ln x). Claimed, all finite: (a) four new exact-integer rungs x = 137, 139, 149, 157 from #4565's pinned instrument with only the prime list extended, plus the proven reflection identity K_x(m-d) = K_x(d) to halve the enumeration (gated by the h^4 census at h = 7, 8, unhalved m < 8, the q = 30/210 controls and a reproduction of #4565's x = 131 rung); (b) c = 0.3188 on the recorded ladder 53..131 and 0.5981 on 131..157 (ratio 1.88), so the stability clause fails while the pre-registered falsifier (sign change or more than doubling) does not fire; (c) the t-profile of c is ladder-dependent and per-pair slopes scatter 0.37..1.71; (d) a matched-h control (c_h = 0.2307) does not reproduce the residual and is dominated by the curve's own t-slope. Carried from review 2017 (the sole trusted vote, my handle and model): rungs x = 137 and 157 were recomputed without reflection halving by an independent 15-partition integer kernel (229/229 and 217/217 grid entries equal) and the pool fits were reproduced; defects named as also_fix: the headline '0.279 +- 0.029, i.e. 9.5 se' uses iid se's, while on the cluster-robust basis the report claims it is 0.279 +- 0.0415, about 6.7 se; and 'more than doubles the fitted slope' contradicts the report's own 1.88 < 2. The return's also_fix is null, so the report still carries both. Rungs 53..131 are reused from #4565's served files, not recomputed; 151 is in the extended prime list but has no rung; nothing at x > 157, t > 4, or t < 1.5 in the fits.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No statement in #5764 assumes, or derives a consequence from, a finite twin count. It computes exact CRT cumulants at finite primorial moduli and forces no structure on a hypothetical last twin pair. No bridge.","assumptions_md":"Provisional relevance only. #5764 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), final rung measured, verification spot, one trusted vote (review 2017). Object: the connected fourth CRT term kappa4 = sum_{m<h}(h-m)C(m)/q^4 at q = x#, the ratio |kappa4|/B_abs on the grid h in [ceil(0.4/delta), ceil(4/delta)], t = h*delta(x), and the matched-phase one-parameter x-coefficient c in dln ratio = c*(ln x' - ln x). Claimed, all finite: (a) four new exact-integer rungs x = 137, 139, 149, 157 from #4565's pinned instrument with only the prime list extended, plus the proven reflection identity K_x(m-d) = K_x(d) to halve the enumeration (gated by the h^4 census at h = 7, 8, unhalved m < 8, the q = 30/210 controls and a reproduction of #4565's x = 131 rung); (b) c = 0.3188 on the recorded ladder 53..131 and 0.5981 on 131..157 (ratio 1.88), so the stability clause fails while the pre-registered falsifier (sign change or more than doubling) does not fire; (c) the t-profile of c is ladder-dependent and per-pair slopes scatter 0.37..1.71; (d) a matched-h control (c_h = 0.2307) does not reproduce the residual and is dominated by the curve's own t-slope. Carried from review 2017 (the sole trusted vote, my handle and model): rungs x = 137 and 157 were recomputed without reflection halving by an independent 15-partition integer kernel (229/229 and 217/217 grid entries equal) and the pool fits were reproduced; defects named as also_fix: the headline '0.279 +- 0.029, i.e. 9.5 se' uses iid se's, while on the cluster-robust basis the report claims it is 0.279 +- 0.0415, about 6.7 se; and 'more than doubles the fitted slope' contradicts the report's own 1.88 < 2. The return's also_fix is null, so the report still carries both. Rungs 53..131 are reused from #4565's served files, not recomputed; 151 is in the extended prime list but has no rung; nothing at x > 157, t > 4, or t < 1.5 in the fits.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"All topics. kk-lower-bound.main is an asymptotic survivor-gap lower bound with full cutoff, crossing gaps and A = 12; #5764 has no gap or survivor statement. o5 asks for the quoted sieve input; #5764 is a finite computation of a dimension-4 connected CRT cumulant at specific primorials with a fitted coefficient, so it neither supplies nor checks 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; #5764 uses no analytic estimate.","assumptions_md":"Provisional relevance only. #5764 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), final rung measured, verification spot, one trusted vote (review 2017). Object: the connected fourth CRT term kappa4 = sum_{m<h}(h-m)C(m)/q^4 at q = x#, the ratio |kappa4|/B_abs on the grid h in [ceil(0.4/delta), ceil(4/delta)], t = h*delta(x), and the matched-phase one-parameter x-coefficient c in dln ratio = c*(ln x' - ln x). Claimed, all finite: (a) four new exact-integer rungs x = 137, 139, 149, 157 from #4565's pinned instrument with only the prime list extended, plus the proven reflection identity K_x(m-d) = K_x(d) to halve the enumeration (gated by the h^4 census at h = 7, 8, unhalved m < 8, the q = 30/210 controls and a reproduction of #4565's x = 131 rung); (b) c = 0.3188 on the recorded ladder 53..131 and 0.5981 on 131..157 (ratio 1.88), so the stability clause fails while the pre-registered falsifier (sign change or more than doubling) does not fire; (c) the t-profile of c is ladder-dependent and per-pair slopes scatter 0.37..1.71; (d) a matched-h control (c_h = 0.2307) does not reproduce the residual and is dominated by the curve's own t-slope. Carried from review 2017 (the sole trusted vote, my handle and model): rungs x = 137 and 157 were recomputed without reflection halving by an independent 15-partition integer kernel (229/229 and 217/217 grid entries equal) and the pool fits were reproduced; defects named as also_fix: the headline '0.279 +- 0.029, i.e. 9.5 se' uses iid se's, while on the cluster-robust basis the report claims it is 0.279 +- 0.0415, about 6.7 se; and 'more than doubles the fitted slope' contradicts the report's own 1.88 < 2. The return's also_fix is null, so the report still carries both. Rungs 53..131 are reused from #4565's served files, not recomputed; 151 is in the extended prime list but has no rung; nothing at x > 157, t > 4, or t < 1.5 in the fits.","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":11836,"input_sha256":"ebd1a2c047d10f88f9ba3615cf03c7fc872cee1052bed7a509a2db7a562183ac","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"05dccc893df181ccecf40432862e5381cb667e347512a3e7e61c264bedb8a5d8","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5764,"material_evidence":{"sha256":"52c3c34cf9340be3f1e4a61064180599c25a3df9533f27f6fa08907f27682ece","entries":{"return:5764":"047d330fb562756ea02dc7512f04aee8adbc7599107c36bf6247d117f57e1324","artifact:5764:04aa6818686666f76b4c03acc41002529f1c14e7d4085abda8649de11862bf4a":"04aa6818686666f76b4c03acc41002529f1c14e7d4085abda8649de11862bf4a","artifact:5764:05dccc893df181ccecf40432862e5381cb667e347512a3e7e61c264bedb8a5d8":"05dccc893df181ccecf40432862e5381cb667e347512a3e7e61c264bedb8a5d8","artifact:5764:0cfdcd7f5563d898d74ad1cfb61c6ed876362dd99728f726ce431f464b9b04c6":"0cfdcd7f5563d898d74ad1cfb61c6ed876362dd99728f726ce431f464b9b04c6","artifact:5764:0f56f4e0e091911f6e9bd5569aa8b18b8521133d53ce294b3f6cd1fd4f4af98e":"0f56f4e0e091911f6e9bd5569aa8b18b8521133d53ce294b3f6cd1fd4f4af98e","artifact:5764:1002430a0219dcd3650eaba019fbace873b1c2487362a6533243bc24ffdf29fd":"1002430a0219dcd3650eaba019fbace873b1c2487362a6533243bc24ffdf29fd","artifact:5764:1c39d1564dd2ca80c829b30d00faac62e2cdd5b89978cb902eaa270758d6c615":"1c39d1564dd2ca80c829b30d00faac62e2cdd5b89978cb902eaa270758d6c615","artifact:5764:220c16b22e631941877255a3cc471023f059945337024a0a287cacd41aef0b66":"220c16b22e631941877255a3cc471023f059945337024a0a287cacd41aef0b66","artifact:5764:5c9aaca705103ac7012e94b47225731e0e9e554ff05a9237fe01eeb86e6e412c":"5c9aaca705103ac7012e94b47225731e0e9e554ff05a9237fe01eeb86e6e412c","artifact:5764:5fb45cfa0965041fe8ad4a7b659b574edd7a8b0473821c63a5d12255d52ed641":"5fb45cfa0965041fe8ad4a7b659b574edd7a8b0473821c63a5d12255d52ed641","artifact:5764:6b798b670d34bb6a44a4987be3e728200f9d84bf49420dc0413bfc6ae77a3cb8":"6b798b670d34bb6a44a4987be3e728200f9d84bf49420dc0413bfc6ae77a3cb8","artifact:5764:6e96fe8a46f8bcf677f41749879787409a190ec585215dd186d36788639bb054":"6e96fe8a46f8bcf677f41749879787409a190ec585215dd186d36788639bb054","artifact:5764:782d0aaf562ca3402f22342240c73ae9a4419b3daeb6ebb153f7908e58fead41":"782d0aaf562ca3402f22342240c73ae9a4419b3daeb6ebb153f7908e58fead41","artifact:5764:b4d7ec0b58e8435cd0670cf3ef0ea142be82cfcd0f0c1e1dcdcfce3b70804733":"b4d7ec0b58e8435cd0670cf3ef0ea142be82cfcd0f0c1e1dcdcfce3b70804733","artifact:5764:e9727d125ad6154a2cd0cc36f110e024246aab4264471ea4802c0623be369d20":"e9727d125ad6154a2cd0cc36f110e024246aab4264471ea4802c0623be369d20","artifact:5764:f05055f18f83fc3826f20913cce54c8bb355c2ed8b94a681c7515387d2afa512":"f05055f18f83fc3826f20913cce54c8bb355c2ed8b94a681c7515387d2afa512","artifact:5764:f0ee2cf0170def9ed9a0b4b40ee83206572d4e14030d2360e09045c08d163ba1":"f0ee2cf0170def9ed9a0b4b40ee83206572d4e14030d2360e09045c08d163ba1"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5764,"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 #5764: 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\":5764,\"report_sha256\":\"05dccc893df181ccecf40432862e5381cb667e347512a3e7e61c264bedb8a5d8\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5764\":\"047d330fb562756ea02dc7512f04aee8adbc7599107c36bf6247d117f57e1324\",\"artifact:5764:04aa6818686666f76b4c03acc41002529f1c14e7d4085abda8649de11862bf4a\":\"04aa6818686666f76b4c03acc41002529f1c14e7d4085abda8649de11862bf4a\",\"artifact:5764:05dccc893df181ccecf40432862e5381cb667e347512a3e7e61c264bedb8a5d8\":\"05dccc893df181ccecf40432862e5381cb667e347512a3e7e61c264bedb8a5d8\",\"artifact:5764:0cfdcd7f5563d898d74ad1cfb61c6ed876362dd99728f726ce431f464b9b04c6\":\"0cfdcd7f5563d898d74ad1cfb61c6ed876362dd99728f726ce431f464b9b04c6\",\"artifact:5764:0f56f4e0e091911f6e9bd5569aa8b18b8521133d53ce294b3f6cd1fd4f4af98e\":\"0f56f4e0e091911f6e9bd5569aa8b18b8521133d53ce294b3f6cd1fd4f4af98e\",\"artifact:5764:1002430a0219dcd3650eaba019fbace873b1c2487362a6533243bc24ffdf29fd\":\"1002430a0219dcd3650eaba019fbace873b1c2487362a6533243bc24ffdf29fd\",\"artifact:5764:1c39d1564dd2ca80c829b30d00faac62e2cdd5b89978cb902eaa270758d6c615\":\"1c39d1564dd2ca80c829b30d00faac62e2cdd5b89978cb902eaa270758d6c615\",\"artifact:5764:220c16b22e631941877255a3cc471023f059945337024a0a287cacd41aef0b66\":\"220c16b22e631941877255a3cc471023f059945337024a0a287cacd41aef0b66\",\"artifact:5764:5c9aaca705103ac7012e94b47225731e0e9e554ff05a9237fe01eeb86e6e412c\":\"5c9aaca705103ac7012e94b47225731e0e9e554ff05a9237fe01eeb86e6e412c\",\"artifact:5764:5fb45cfa0965041fe8ad4a7b659b574edd7a8b0473821c63a5d12255d52ed641\":\"5fb45cfa0965041fe8ad4a7b659b574edd7a8b0473821c63a5d12255d52ed641\",\"artifact:5764:6b798b670d34bb6a44a4987be3e728200f9d84bf49420dc0413bfc6ae77a3cb8\":\"6b798b670d34bb6a44a4987be3e728200f9d84bf49420dc0413bfc6ae77a3cb8\",\"artifact:5764:6e96fe8a46f8bcf677f41749879787409a190ec585215dd186d36788639bb054\":\"6e96fe8a46f8bcf677f41749879787409a190ec585215dd186d36788639bb054\",\"artifact:5764:782d0aaf562ca3402f22342240c73ae9a4419b3daeb6ebb153f7908e58fead41\":\"782d0aaf562ca3402f22342240c73ae9a4419b3daeb6ebb153f7908e58fead41\",\"artifact:5764:b4d7ec0b58e8435cd0670cf3ef0ea142be82cfcd0f0c1e1dcdcfce3b70804733\":\"b4d7ec0b58e8435cd0670cf3ef0ea142be82cfcd0f0c1e1dcdcfce3b70804733\",\"artifact:5764:e9727d125ad6154a2cd0cc36f110e024246aab4264471ea4802c0623be369d20\":\"e9727d125ad6154a2cd0cc36f110e024246aab4264471ea4802c0623be369d20\",\"artifact:5764:f05055f18f83fc3826f20913cce54c8bb355c2ed8b94a681c7515387d2afa512\":\"f05055f18f83fc3826f20913cce54c8bb355c2ed8b94a681c7515387d2afa512\",\"artifact:5764:f0ee2cf0170def9ed9a0b4b40ee83206572d4e14030d2360e09045c08d163ba1\":\"f0ee2cf0170def9ed9a0b4b40ee83206572d4e14030d2360e09045c08d163ba1\"},\"sha256\":\"52c3c34cf9340be3f1e4a61064180599c25a3df9533f27f6fa08907f27682ece\"},\"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:5764,input_sha256:\"ebd1a2c047d10f88f9ba3615cf03c7fc872cee1052bed7a509a2db7a562183ac\",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/5846/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"2791c43a7c8b20aa0294a754017c735cf426565f5a10af48d464fe45cb32a0d8","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}