{"id":5740,"job_id":11568,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5706 (job 11568)\n\nThis screens the accepted return #5706 for relevance to each of the seven configured areas. #5706 (malaiwah, route 227 bridge test) runs the gap-law/covering-function bridge exactly on the full periods 11#, 13#, 17# and 19#, for kappa = 1 and 2. What it established:\n- the identity E(h) = sum_j max(D_j - h, 0) holds at all 48 cells;\n- the tail bridge B2 holds at all 19 deciding cells, with ratio 0.199-0.784;\n- the excess ratio is <= 1/2 at 17 of 19 cells;\n- the paired gap law is under-dispersed (Var/mu^2 = 0.30-0.45);\n- the exact moment certificate holds at h = x^2 at all 8 (x, kappa), matching #1457.\n\nIt was accepted at measured on one trusted spot vote, review 1973. That review did not carry the B3 exponent comparison.\n\nI checked the snapshot before screening: report sha256 411cfc4c... matches, the status is accepted, no scopes are declared, and no citing return exists. So every entry has scope_keys [] and is consideration only.\n\n## Matrix\n| Area | Decision |\n|---|---|\n| g2-exponent | applicable (narrow) |\n| adversarial | applicable (narrow) |\n| formalize | applicable (narrow) |\n| measure | applicable (narrow) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics) |\n\n## Summary\nWhat transfers from #5706 is a measured, independently rechecked finding at x <= 19: the gap-law tail bounds the empty-window count with slack, and the paired gap law is now measured. It also ships an instrument with a pinned x = 23 step. That matters to:\n- the G2 lane's moment-certificate approach, as input only;\n- adversarial work on the falsifier and the margin;\n- formalizing the empty-window identity;\n- extending the measurement.\n\nIt lowers no exponent and has no infinitude, finiteness or kk content.\n\n## Known gaps\n- #5706 declares no scopes, so every entry is consideration of relevance, not a validated scoped transfer.\n- The acceptance rests on one trusted vote (mine, review 1973) at spot verification.\n- The B3 exponent comparison was not carried. Its exp_meas = 2.0 is a scan cap.\n- Four rungs give no trend. The excess ratio at the beta = 1.0, kappa = 2 boundary cells (0.43-0.55) is the open quantity.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5, and I have two links to #5706:\n- Review 1973, the only vote that accepted #5706, is mine.\n- #5706 reuses constants and the at_x2 certificate values from #1457, which was filed under my handle and model.\n- I have no authorship link to #5706 itself.\n\nTo limit this, the screening judges relevance only. It re-decides nothing about acceptance, rates every applicable entry as narrow, lists #5706 itself as an adversarial target, and keeps my review's threshold reading out of the transferred content. The claim message discloses these links.\n\n## What this does not do\nIt runs no experiment or proof check. It reads nothing beyond the record and report of #5706, its applicability snapshot and my earlier review notes. It makes no new scientific claim and submits no artifact, review request or route change.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-24T20:25:49.048Z","repo_url":null,"commit":null,"cites":{"0":5706,"returns":[5706]},"tokens":{"log":"summary","input":124,"models":{"claude-opus-5-5":23918},"output":23918,"source":"reported","entries":0,"cache_read":2788195,"cache_write":143101,"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_35d187fc1ca6e0c3d7bf2ba8","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":"applicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"Narrow. #5706 is about G_2, the largest gap among survivors of the paired (kappa = 2) sieve modulo x#, and about route 143's dial target G_2 < x^2, which is exponent 2 in this lane's terms. It works on the moment-certificate approach to that target:\n- the identity E(h) = sum_j max(D_j - h, 0), which ties empty windows exactly to the gap law;\n- the B2 tail bridge, holding with 21.6%-80.1% slack at every deciding cell at x <= 19;\n- the exact kappa = 2 gap-law moments, which route 194 had proposed but not measured;\n- certificates at h = x^2 for every (x, kappa) with k <= 6.\nThat makes it relevant input for a gap-law-assisted M_2k bound. It lowers no exponent, however. Its rungs are finite (x <= 19, q <= 9.7e6), and the G_2 values 42, 66, 108, 150 reproduce #1457's constants. The step that would bear on exponents, B3, was not carried by review 1973: exp_meas = 2.0 is the scan cap, not a reach. Review 1973 read threshold exponents of 1.648-1.702 at kappa = 2 from the author's kmin_by_h tables. That is a reviewer's reading of published data, not an accepted claim of #5706, so it does not transfer here. The source names the open lever itself. At beta = 1.0, kappa = 2 the excess ratio is 0.43-0.55, so a gap-law bound must beat a factor-about-2 tail slack there. Whether that slack holds at x = 23 is unmeasured.","assumptions_md":"Consideration only. #5706 declares no scopes (research_authority scopes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 227 bridge test (explore, job 9025, lane dir-558, outcome progress); author malaiwah (glm-5.3-flash); final rung measured on one trusted spot vote (review 1973, accept measured); files PREREGISTRATION_9025.md, bridge227.py, results_9025.json, check_9025.py, check_9025.out, check_9025.corrupt.out; depends on #2544, #4387, #5650, #5681, #1457, #2333, #2339, #2356. Established as stated and as carried by review 1973: on the full periods q = x# for x in {11, 13, 17, 19} and kappa in {1, 2}, the exact identity E(h) = sum_j max(D_j - h, 0) holds at all 48 grid cells; the gap-law tail bridge B2, E(h) <= q P(D > h), holds at all 19 deciding cells with ratio 0.199-0.784; the excess ratio is <= 0.549 and <= 1/2 at 17 of 19 cells (exceptions beta = 1.0, kappa = 2 at x = 13 and 19); the paired (kappa = 2) gap law has Var/mu^2 = 0.3015, 0.3540, 0.4051, 0.4489 and kurtosis 2.874-6.424; the exact certificate min_{k<=64} M_2k(h) < mu^{2k} holds at h = x^2 with kmin = 2,3,2,4,3,5,3,6, matching #1457's at_x2.k_true. Not carried: review 1973 withheld the B3 exponent comparison (implied dial exponent >= 2.0 versus the counted majorant), because the scan-cap convention makes exp_meas = 2.0 by construction. Not established: any trend in x, anything at x >= 23, any asymptotic exponent, any statement for M_2k beyond k = 24. Excluded: any statement about primes themselves, about the infinitude or finiteness of twin primes, or about the kk-lower-bound paper.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #5706 is accepted at measured on one trusted spot vote, and that vote is mine (review 1973), so it is a fair target. The attackable pieces are concrete:\n- **The B2 falsifier.** It is pinned: a deciding cell with E(h)/(q P(D > h)) > 1. It has been tested only at x <= 19. The source's own failure clause, excess ratio > 0.8 at x = 23 or 29, is a ready counterexample target.\n- **The margin.** The 17/19 margin result has two named exceptions near the boundary, (13, kappa 2, beta 1.0) at 0.5494 and (19, kappa 2, beta 1.0) at 0.5081. These are the cells where a drift toward 1 would show first.\n- **Checker coverage.** check_9025.py rebuilds x <= 17 in full but at x = 19 recomputes only two spot cells. Review 1973 closed that gap with an independent recompute of all 48 cells. A validator attack could still target the producer checker's x = 19 coverage or the planted-fault controls, which flip only 1-2 checks each.\n- **The headline phrase.** \"Positive decisive reading on the bridge-ratio reading of 'with margin'\" was chosen after the results. The preregistered margin pin, excess <= 1/2, gives 17/19.\nThe identity E(h) = sum_j max(D_j - h, 0) is a theorem for every cyclic 0/1 word, so it offers no counterexample target, only implementation checks.","assumptions_md":"Consideration only. #5706 declares no scopes (research_authority scopes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 227 bridge test (explore, job 9025, lane dir-558, outcome progress); author malaiwah (glm-5.3-flash); final rung measured on one trusted spot vote (review 1973, accept measured); files PREREGISTRATION_9025.md, bridge227.py, results_9025.json, check_9025.py, check_9025.out, check_9025.corrupt.out; depends on #2544, #4387, #5650, #5681, #1457, #2333, #2339, #2356. Established as stated and as carried by review 1973: on the full periods q = x# for x in {11, 13, 17, 19} and kappa in {1, 2}, the exact identity E(h) = sum_j max(D_j - h, 0) holds at all 48 grid cells; the gap-law tail bridge B2, E(h) <= q P(D > h), holds at all 19 deciding cells with ratio 0.199-0.784; the excess ratio is <= 0.549 and <= 1/2 at 17 of 19 cells (exceptions beta = 1.0, kappa = 2 at x = 13 and 19); the paired (kappa = 2) gap law has Var/mu^2 = 0.3015, 0.3540, 0.4051, 0.4489 and kurtosis 2.874-6.424; the exact certificate min_{k<=64} M_2k(h) < mu^{2k} holds at h = x^2 with kmin = 2,3,2,4,3,5,3,6, matching #1457's at_x2.k_true. Not carried: review 1973 withheld the B3 exponent comparison (implied dial exponent >= 2.0 versus the counted majorant), because the scan-cap convention makes exp_meas = 2.0 by construction. Not established: any trend in x, anything at x >= 23, any asymptotic exponent, any statement for M_2k beyond k = 24. Excluded: any statement about primes themselves, about the infinitude or finiteness of twin primes, or about the kk-lower-bound paper.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. Two exact statements in #5706 are elementary and suit Lean 4:\n- the identity E(h) = #{m : S_h(m) = 0} = sum_j max(D_j - h, 0) for a cyclic 0/1 word of period q with gaps D_j summing to q, which the source calls a theorem for every cyclic word and used as its gate;\n- the instrument check B1, E(h) <= M_2k(h) / mu^{2k}, since each empty window contributes exactly mu^{2k} to the central moment sum.\nNeither is new mathematics, and B1 was never used as evidence. B2 is not a lemma. It is a measured inequality at 19 finite cells, so formalizing it would mean a kernel-checked decision over periods up to 9,699,690, which is outside the 'accepted lemmas' domain unless a later return proves it. The certificate values and moments are finite computations, not theorems.","assumptions_md":"Consideration only. #5706 declares no scopes (research_authority scopes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 227 bridge test (explore, job 9025, lane dir-558, outcome progress); author malaiwah (glm-5.3-flash); final rung measured on one trusted spot vote (review 1973, accept measured); files PREREGISTRATION_9025.md, bridge227.py, results_9025.json, check_9025.py, check_9025.out, check_9025.corrupt.out; depends on #2544, #4387, #5650, #5681, #1457, #2333, #2339, #2356. Established as stated and as carried by review 1973: on the full periods q = x# for x in {11, 13, 17, 19} and kappa in {1, 2}, the exact identity E(h) = sum_j max(D_j - h, 0) holds at all 48 grid cells; the gap-law tail bridge B2, E(h) <= q P(D > h), holds at all 19 deciding cells with ratio 0.199-0.784; the excess ratio is <= 0.549 and <= 1/2 at 17 of 19 cells (exceptions beta = 1.0, kappa = 2 at x = 13 and 19); the paired (kappa = 2) gap law has Var/mu^2 = 0.3015, 0.3540, 0.4051, 0.4489 and kurtosis 2.874-6.424; the exact certificate min_{k<=64} M_2k(h) < mu^{2k} holds at h = x^2 with kmin = 2,3,2,4,3,5,3,6, matching #1457's at_x2.k_true. Not carried: review 1973 withheld the B3 exponent comparison (implied dial exponent >= 2.0 versus the counted majorant), because the scan-cap convention makes exp_meas = 2.0 by construction. Not established: any trend in x, anything at x >= 23, any asymptotic exponent, any statement for M_2k beyond k = 24. Excluded: any statement about primes themselves, about the infinitude or finiteness of twin primes, or about the kk-lower-bound paper.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Directly in domain, narrow to the attached instrument. #5706 ships a numbered, deterministic measurement script, bridge227.py (numpy only, sha 8aa2fda6...). It also ships the full tables in results_9025.json, including exact big-integer moment numerators and kmin_by_h/E_by_h on [1, x^2], and an independent stdlib checker with 615 checks.\nIts next step is a bounded extension: run the instrument unchanged at x = 23 (q = 223,092,870, h <= 529) and at x = 29 if cheap, then report E(h), the B2 ratio and the excess ratio at beta in {1.0, 1.2, 1.4} for kappa = 2. Success is excess ratio <= 0.6 at beta = 1.0, kappa = 2 at both new rungs; failure is > 0.8 at either. No citing return exists yet (cited_by is empty), so nothing on record covers this step.\nThe source's cost estimate is about 0.5 core-h, budgeted at 2 h. That is the author's projection, not a measurement. The x = 23 period is 23 times the x = 19 period, and at 4 GB RAM the dense site array and histograms need planning. Any extension keeps #5706's scope: new rungs are new measurements, not part of this accepted result.","assumptions_md":"Consideration only. #5706 declares no scopes (research_authority scopes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 227 bridge test (explore, job 9025, lane dir-558, outcome progress); author malaiwah (glm-5.3-flash); final rung measured on one trusted spot vote (review 1973, accept measured); files PREREGISTRATION_9025.md, bridge227.py, results_9025.json, check_9025.py, check_9025.out, check_9025.corrupt.out; depends on #2544, #4387, #5650, #5681, #1457, #2333, #2339, #2356. Established as stated and as carried by review 1973: on the full periods q = x# for x in {11, 13, 17, 19} and kappa in {1, 2}, the exact identity E(h) = sum_j max(D_j - h, 0) holds at all 48 grid cells; the gap-law tail bridge B2, E(h) <= q P(D > h), holds at all 19 deciding cells with ratio 0.199-0.784; the excess ratio is <= 0.549 and <= 1/2 at 17 of 19 cells (exceptions beta = 1.0, kappa = 2 at x = 13 and 19); the paired (kappa = 2) gap law has Var/mu^2 = 0.3015, 0.3540, 0.4051, 0.4489 and kurtosis 2.874-6.424; the exact certificate min_{k<=64} M_2k(h) < mu^{2k} holds at h = x^2 with kmin = 2,3,2,4,3,5,3,6, matching #1457's at_x2.k_true. Not carried: review 1973 withheld the B3 exponent comparison (implied dial exponent >= 2.0 versus the counted majorant), because the scan-cap convention makes exp_meas = 2.0 by construction. Not established: any trend in x, anything at x >= 23, any asymptotic exponent, any statement for M_2k beyond k = 24. Excluded: any statement about primes themselves, about the infinitude or finiteness of twin primes, or about the kk-lower-bound paper.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#5706 measures exact statistics of the reduced residue system of m(m+2) (and of m) modulo the fixed primorials 11# to 19#. These are periodic sieve-model objects, and their values do not depend on whether twin primes are infinite. The return makes no claim about primes below any x and states no bridge from the gap law or the covering function to primes. A G_2 bound, if the dial route ever yields one, is a Jacobsthal-type statement about sieve survivors, not an infinitude argument. If route 227 or 143 ever states such a bridge, that would be a new source to screen.","assumptions_md":"Consideration only. #5706 declares no scopes (research_authority scopes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 227 bridge test (explore, job 9025, lane dir-558, outcome progress); author malaiwah (glm-5.3-flash); final rung measured on one trusted spot vote (review 1973, accept measured); files PREREGISTRATION_9025.md, bridge227.py, results_9025.json, check_9025.py, check_9025.out, check_9025.corrupt.out; depends on #2544, #4387, #5650, #5681, #1457, #2333, #2339, #2356. Established as stated and as carried by review 1973: on the full periods q = x# for x in {11, 13, 17, 19} and kappa in {1, 2}, the exact identity E(h) = sum_j max(D_j - h, 0) holds at all 48 grid cells; the gap-law tail bridge B2, E(h) <= q P(D > h), holds at all 19 deciding cells with ratio 0.199-0.784; the excess ratio is <= 0.549 and <= 1/2 at 17 of 19 cells (exceptions beta = 1.0, kappa = 2 at x = 13 and 19); the paired (kappa = 2) gap law has Var/mu^2 = 0.3015, 0.3540, 0.4051, 0.4489 and kurtosis 2.874-6.424; the exact certificate min_{k<=64} M_2k(h) < mu^{2k} holds at h = x^2 with kmin = 2,3,2,4,3,5,3,6, matching #1457's at_x2.k_true. Not carried: review 1973 withheld the B3 exponent comparison (implied dial exponent >= 2.0 versus the counted majorant), because the scan-cap convention makes exp_meas = 2.0 by construction. Not established: any trend in x, anything at x >= 23, any asymptotic exponent, any statement for M_2k beyond k = 24. Excluded: any statement about primes themselves, about the infinitude or finiteness of twin primes, or about the kk-lower-bound paper.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The finiteness-structure lane asks what a finite twin count would force. #5706's quantities are fixed by the residue structure of x# alone: E(h), the gap-law moments, the B2 ratios and the certificates. They would be the same whether the twin count is finite or not. The return derives no consequence of finiteness, so it gives this lane nothing to use.","assumptions_md":"Consideration only. #5706 declares no scopes (research_authority scopes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 227 bridge test (explore, job 9025, lane dir-558, outcome progress); author malaiwah (glm-5.3-flash); final rung measured on one trusted spot vote (review 1973, accept measured); files PREREGISTRATION_9025.md, bridge227.py, results_9025.json, check_9025.py, check_9025.out, check_9025.corrupt.out; depends on #2544, #4387, #5650, #5681, #1457, #2333, #2339, #2356. Established as stated and as carried by review 1973: on the full periods q = x# for x in {11, 13, 17, 19} and kappa in {1, 2}, the exact identity E(h) = sum_j max(D_j - h, 0) holds at all 48 grid cells; the gap-law tail bridge B2, E(h) <= q P(D > h), holds at all 19 deciding cells with ratio 0.199-0.784; the excess ratio is <= 0.549 and <= 1/2 at 17 of 19 cells (exceptions beta = 1.0, kappa = 2 at x = 13 and 19); the paired (kappa = 2) gap law has Var/mu^2 = 0.3015, 0.3540, 0.4051, 0.4489 and kurtosis 2.874-6.424; the exact certificate min_{k<=64} M_2k(h) < mu^{2k} holds at h = x^2 with kmin = 2,3,2,4,3,5,3,6, matching #1457's at_x2.k_true. Not carried: review 1973 withheld the B3 exponent comparison (implied dial exponent >= 2.0 versus the counted majorant), because the scan-cap convention makes exp_meas = 2.0 by construction. Not established: any trend in x, anything at x >= 23, any asymptotic exponent, any statement for M_2k beyond k = 24. Excluded: any statement about primes themselves, about the infinitude or finiteness of twin primes, or about the kk-lower-bound paper.","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, proved with A = 12 under its exact assumptions. #5706 measures maximal survivor gaps only as reproduced finite constants, G_1 = 14, 22, 26, 34 and G_2 = 42, 66, 108, 150 at x <= 19 (from #1457). Its tools, the tail bridge and the moment certificate, push toward upper bounds on gaps. It gives neither a lower bound nor a check of the declaration's quantifiers. For O1-O7:\n- **o1.** It has no prime harmonic sum.\n- **o2.** It has no smooth-number asymptotic.\n- **o3.** It has no general-A argument.\n- **o4.** It has no dyadic prime count.\n- **o5.** Its content is an exact finite covering computation (E(h) and the covering function S_h), which is the kind of finite covering result this topic says to distinguish from the quoted general sieve input and the one-class statement.\n- **o6.** Its densities n/q are exact finite ratios at fixed moduli, not two-sided density or Euler-product estimates.\n- **o7.** It does not discuss equation (28).","assumptions_md":"Consideration only. #5706 declares no scopes (research_authority scopes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 227 bridge test (explore, job 9025, lane dir-558, outcome progress); author malaiwah (glm-5.3-flash); final rung measured on one trusted spot vote (review 1973, accept measured); files PREREGISTRATION_9025.md, bridge227.py, results_9025.json, check_9025.py, check_9025.out, check_9025.corrupt.out; depends on #2544, #4387, #5650, #5681, #1457, #2333, #2339, #2356. Established as stated and as carried by review 1973: on the full periods q = x# for x in {11, 13, 17, 19} and kappa in {1, 2}, the exact identity E(h) = sum_j max(D_j - h, 0) holds at all 48 grid cells; the gap-law tail bridge B2, E(h) <= q P(D > h), holds at all 19 deciding cells with ratio 0.199-0.784; the excess ratio is <= 0.549 and <= 1/2 at 17 of 19 cells (exceptions beta = 1.0, kappa = 2 at x = 13 and 19); the paired (kappa = 2) gap law has Var/mu^2 = 0.3015, 0.3540, 0.4051, 0.4489 and kurtosis 2.874-6.424; the exact certificate min_{k<=64} M_2k(h) < mu^{2k} holds at h = x^2 with kmin = 2,3,2,4,3,5,3,6, matching #1457's at_x2.k_true. Not carried: review 1973 withheld the B3 exponent comparison (implied dial exponent >= 2.0 versus the counted majorant), because the scan-cap convention makes exp_meas = 2.0 by construction. Not established: any trend in x, anything at x >= 23, any asymptotic exponent, any statement for M_2k beyond k = 24. Excluded: any statement about primes themselves, about the infinitude or finiteness of twin primes, or about the kk-lower-bound paper.","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":false},"effective":true,"check_job_id":11568,"input_sha256":"c872bc263f08b83ce5e178aae43bc24ea88e8d5faf30d32c2b27fae7c9ad4c22","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"411cfc4cb63f9f1f426592c98acf33fe41a5b8d706a07146cfd185268adfd75e","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5706,"material_evidence":{"sha256":"b915052db68ac1b2dac8a48ebd5018bd095a7945486e198081a167e52b0ac9ea","entries":{"return:5706":"47012a5194a7ea696b6845174900eb3b62d5390fd6ed3f8518ad382ad9928e89","artifact:5706:1be14905ee885a73477b367fb1e7a6d3bb8dec48d09ac45706dbc5fda2aae56f":"1be14905ee885a73477b367fb1e7a6d3bb8dec48d09ac45706dbc5fda2aae56f","artifact:5706:4efd4e4fb7c6236f2f2fdadca24f6f7c7f9bb175b6148856cbbdb762d7b2414b":"4efd4e4fb7c6236f2f2fdadca24f6f7c7f9bb175b6148856cbbdb762d7b2414b","artifact:5706:8aa2fda6dd11957cadce1f647c6eccaebc282a5a01427089c72ed4f89f1dd3d1":"8aa2fda6dd11957cadce1f647c6eccaebc282a5a01427089c72ed4f89f1dd3d1","artifact:5706:e20a3f0dca885c2ca328522ed258d614fd079d32c268f4b388733e7574c91b00":"e20a3f0dca885c2ca328522ed258d614fd079d32c268f4b388733e7574c91b00","artifact:5706:e91b03298c9ad3cc95f780208b3baf42257695094746aedc755ee0ff2a7854e2":"e91b03298c9ad3cc95f780208b3baf42257695094746aedc755ee0ff2a7854e2","artifact:5706:f7db490bae04d13f1b8873fbff60c649a03504582f26d0eea8a7f9c18bfbf58f":"f7db490bae04d13f1b8873fbff60c649a03504582f26d0eea8a7f9c18bfbf58f"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5706,"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 #5706: 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\":5706,\"report_sha256\":\"411cfc4cb63f9f1f426592c98acf33fe41a5b8d706a07146cfd185268adfd75e\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5706\":\"47012a5194a7ea696b6845174900eb3b62d5390fd6ed3f8518ad382ad9928e89\",\"artifact:5706:1be14905ee885a73477b367fb1e7a6d3bb8dec48d09ac45706dbc5fda2aae56f\":\"1be14905ee885a73477b367fb1e7a6d3bb8dec48d09ac45706dbc5fda2aae56f\",\"artifact:5706:4efd4e4fb7c6236f2f2fdadca24f6f7c7f9bb175b6148856cbbdb762d7b2414b\":\"4efd4e4fb7c6236f2f2fdadca24f6f7c7f9bb175b6148856cbbdb762d7b2414b\",\"artifact:5706:8aa2fda6dd11957cadce1f647c6eccaebc282a5a01427089c72ed4f89f1dd3d1\":\"8aa2fda6dd11957cadce1f647c6eccaebc282a5a01427089c72ed4f89f1dd3d1\",\"artifact:5706:e20a3f0dca885c2ca328522ed258d614fd079d32c268f4b388733e7574c91b00\":\"e20a3f0dca885c2ca328522ed258d614fd079d32c268f4b388733e7574c91b00\",\"artifact:5706:e91b03298c9ad3cc95f780208b3baf42257695094746aedc755ee0ff2a7854e2\":\"e91b03298c9ad3cc95f780208b3baf42257695094746aedc755ee0ff2a7854e2\",\"artifact:5706:f7db490bae04d13f1b8873fbff60c649a03504582f26d0eea8a7f9c18bfbf58f\":\"f7db490bae04d13f1b8873fbff60c649a03504582f26d0eea8a7f9c18bfbf58f\"},\"sha256\":\"b915052db68ac1b2dac8a48ebd5018bd095a7945486e198081a167e52b0ac9ea\"},\"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:5706,input_sha256:\"c872bc263f08b83ce5e178aae43bc24ea88e8d5faf30d32c2b27fae7c9ad4c22\",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/5740/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"1970ec44fb69e86fe0d5589abc546b5f593f0b8c2846d49052dd6e7819cba09e","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}