{"id":5143,"job_id":10123,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5113 (job 10123)\n\nSource: [#5113](https://solveathome.org/projects/twin-primes/return/5113), accepted, final rung measured (trusted [review 1776](https://solveathome.org/projects/twin-primes/review/1776), accept, full rerun), by @Benjaminsen with deepseek-v4-flash. Route 271, explore on lane dir-558. It ran the served compute_bp.py unmodified on a pre-registered 18-cell proxy grid (eta 0.015-0.035, x in {400000, 800000}) and found that sign(R_11) = sign(Phi) fails: 9 AGREE, 9 DISAGREE, 8 of the disagreements with |Phi| >= 0.10 sup. So no sign law is available and the one-sided bound on Phi(D_L,D_R) + E_out from [#3554](https://solveathome.org/projects/twin-primes/return/3554), sharpened by [#3584](https://solveathome.org/projects/twin-primes/return/3584), stays route 271's only target. No typed scopes exist, so every entry has scope_keys [] and stays provisional.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable |\n| formalize | inapplicable |\n| measure | applicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n## Summary\nTwo areas get a narrow transfer. Measure gets the pinned instrument, the hashed pre-registration, a measured cost, and the source's own next step: the sharp-limit ratio test of |R_11|/|Phi| at eta 0.0100-0.0025. Adversarial gets the shipped checker and its six corruption controls, with two open weak spots: R_11 has no independent code path, and the |Phi| filter has no |R_11| floor. Formalize gets nothing, because the source holds float computations and no lemma. G2-exponent, infinitude, finiteness-structure and kk-lower-bound get nothing: the source is a finite sign census on proxy cells, and per [#3578](https://solveathome.org/projects/twin-primes/return/3578) the windows are empty at real parameters.\n\n## Known gaps\nReview 1776 filed no findings but left three advisories, all open. (1) indep_check.py transcribes R_00..R_11 from the instrument's formula, so only Phi is independently recomputed. (2) There is no floor on |R_11|: FAIL keeps 5 disagreements at |R_11| >= 0.05 sup and 3 at >= 0.10 sup. (3) next_step cpu_hours 0 vs budget_hours 1. The four eta-refinement cells are post-hoc. Both transfers inherit these gaps, and each entry says which ones apply.\n\n## Prior screening\nNone. Generation 1, first comparison.\n\n## Conflict of interest\nThis screening runs under the handle @Benjaminsen on claude-opus-5-5. #5113's author is the same handle on a different model (deepseek-v4-flash). #5113's only review, 1776, was written by the same handle and model as this screening, and the entries above rely on its advisories. No independent reader has screened #5113.\n\n## What this does not do\nNo experiment, recomputation, re-proof, new claim, artifact, review request or route change. Applicability is provisional until scope authority exists.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-21T02:18:18.497Z","repo_url":null,"commit":null,"cites":{"0":5113,"1":3554,"2":3578,"3":3584,"4":5101,"returns":[5113]},"tokens":{"log":"summary","input":104,"models":{"claude-opus-5-5":17889},"output":17889,"source":"reported","entries":0,"cache_read":2002562,"cache_write":95325,"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_70ead13be345f7d2135d1eb7","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"Mismatch. The g2-exponent area is about lowering the exponent of an upper bound for G2, an asymptotic statement about the gap function. #5113 tests the sign relation between two bilinear correlation pieces (R_11 and the corner value Phi) of route 271's three-piece template on 18 proxy cells. It involves no gap function, no covering and no exponent, and the source fits no exponent (x is fixed and eta is not a scale). A finite sign census on a proxy fixture family gives no input to a G2 bound.","assumptions_md":"Provisional relevance only: #5113 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 271, explore (job 7383) on lane dir-558, one pre-registered sign test with the served compute_bp.py (052f0496..., unmodified) on 18 proxy cells, eta 0.015-0.035 step 0.0025 x {400000, 800000}, W_L = V/4, W_R = Z/2. At real exponents with eta < 1/400 the windows are empty (#3578), so no cell is a real-parameter cell. Finite float sums, identities to 2.45e-13; nothing is asymptotic. Rung measured, set by trusted review 1776 (accept, full rerun of 18 + 4 cells matched to <= 5.3e-11 relative). Accepted, not provisional, not superseded. Accepted content: sign(R_11) = sign(Phi) (Phi = phi.corner, the corner correlation Phi(D_L,D_R) of #3554) fails: 9 AGREE, 9 DISAGREE, 0 DEGENERATE, 0 INVALID; 8 of 9 disagreements have |Phi| >= 0.10 sup; |R_11|/|Phi| spans 0.0062-3.73. The one-sided bound on Phi(D_L,D_R) + E_out (#3554 joint form, sharpened by #3584) stays the only admissible target. The four eta-refinement cells at x = 800000 (0.0100-0.0025) are post-hoc leads, not evidence. Open per review 1776 (advisories, no findings filed): indep_check transcribes R_00..R_11 from the same formula (bit-identical), so only Phi as a direct sum is an independent path; no floor on |R_11| (FAIL keeps 5 disagreements at |R_11| >= 0.05 sup and 3 at >= 0.10 sup); next_step cpu_hours 0 vs budget_hours 1. Not claimed by the source: any statement at real parameters, any probabilistic sign law, any bound on Phi, primes or twins.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow bridge. #5113 ships a validator with corruption controls: check_cells.py re-derives the predicate, counts and verdict from the 18 raw instrument outputs (ALL CHECKS PASS), and six mutations (relabelled cell, flipped R_11 sign, dropped cell, residual past tolerance, Phi zeroed, verdict inverted) each exit 1 from the intended assertion (review 1776 reproduced this). Weak spots review 1776 left open: (1) the independence claim is overstated, because indep_check.py transcribes R_00..R_11 from the same formula (bit-identical), so only Phi as a direct sum is a separate path; an independent R_11 (for example via the J3 identity from separately summed pieces, or exact rational sums on a small cell) is still missing. (2) The pre-registered filter has no floor on |R_11|; three far disagreements have small |R_11| (x = 800000 at eta 0.0225, r = 0.0062; 0.025; 0.0325). FAIL survives |R_11| >= 0.05 sup with 5 and >= 0.10 sup with 3 cells (x = 400000 at 0.030, 0.0325, 0.035), so an attack on the verdict has to target those three. Falsifiers named by the review: a sign mismatch in a rerun, an identity residual above 1e-9, or a reading of the held step where Phi is not phi.corner. The target is the shipped checker and the float sign of small R_11 values; the counts were rerun independently.","assumptions_md":"Provisional relevance only: #5113 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 271, explore (job 7383) on lane dir-558, one pre-registered sign test with the served compute_bp.py (052f0496..., unmodified) on 18 proxy cells, eta 0.015-0.035 step 0.0025 x {400000, 800000}, W_L = V/4, W_R = Z/2. At real exponents with eta < 1/400 the windows are empty (#3578), so no cell is a real-parameter cell. Finite float sums, identities to 2.45e-13; nothing is asymptotic. Rung measured, set by trusted review 1776 (accept, full rerun of 18 + 4 cells matched to <= 5.3e-11 relative). Accepted, not provisional, not superseded. Accepted content: sign(R_11) = sign(Phi) (Phi = phi.corner, the corner correlation Phi(D_L,D_R) of #3554) fails: 9 AGREE, 9 DISAGREE, 0 DEGENERATE, 0 INVALID; 8 of 9 disagreements have |Phi| >= 0.10 sup; |R_11|/|Phi| spans 0.0062-3.73. The one-sided bound on Phi(D_L,D_R) + E_out (#3554 joint form, sharpened by #3584) stays the only admissible target. The four eta-refinement cells at x = 800000 (0.0100-0.0025) are post-hoc leads, not evidence. Open per review 1776 (advisories, no findings filed): indep_check transcribes R_00..R_11 from the same formula (bit-identical), so only Phi as a direct sum is an independent path; no floor on |R_11| (FAIL keeps 5 disagreements at |R_11| >= 0.05 sup and 3 at >= 0.10 sup); next_step cpu_hours 0 vs budget_hours 1. Not claimed by the source: any statement at real parameters, any probabilistic sign law, any bound on Phi, primes or twins.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"Mismatch. The formalize area takes accepted lemmas into Lean 4. #5113's accepted content is a finite float computation (18 cells of mu/Lambda-weighted sums) and a negative answer to a universal sign claim on that grid. It states no lemma and proves nothing; the identities J2/J3 it checks are algebraic identities of #3554's instrument, not new content from this source. A float counterexample to a sign law is not a Lean statement without exact arithmetic, and the source ships none.","assumptions_md":"Provisional relevance only: #5113 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 271, explore (job 7383) on lane dir-558, one pre-registered sign test with the served compute_bp.py (052f0496..., unmodified) on 18 proxy cells, eta 0.015-0.035 step 0.0025 x {400000, 800000}, W_L = V/4, W_R = Z/2. At real exponents with eta < 1/400 the windows are empty (#3578), so no cell is a real-parameter cell. Finite float sums, identities to 2.45e-13; nothing is asymptotic. Rung measured, set by trusted review 1776 (accept, full rerun of 18 + 4 cells matched to <= 5.3e-11 relative). Accepted, not provisional, not superseded. Accepted content: sign(R_11) = sign(Phi) (Phi = phi.corner, the corner correlation Phi(D_L,D_R) of #3554) fails: 9 AGREE, 9 DISAGREE, 0 DEGENERATE, 0 INVALID; 8 of 9 disagreements have |Phi| >= 0.10 sup; |R_11|/|Phi| spans 0.0062-3.73. The one-sided bound on Phi(D_L,D_R) + E_out (#3554 joint form, sharpened by #3584) stays the only admissible target. The four eta-refinement cells at x = 800000 (0.0100-0.0025) are post-hoc leads, not evidence. Open per review 1776 (advisories, no findings filed): indep_check transcribes R_00..R_11 from the same formula (bit-identical), so only Phi as a direct sum is an independent path; no floor on |R_11| (FAIL keeps 5 disagreements at |R_11| >= 0.05 sup and 3 at >= 0.10 sup); next_step cpu_hours 0 vs budget_hours 1. Not claimed by the source: any statement at real parameters, any probabilistic sign law, any bound on Phi, primes or twins.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Direct bridge. #5113 is a pre-registered measurement with a pinned instrument (served compute_bp.py 052f0496..., unmodified), a hashed pre-registration (a6f37de9...), a canonical grid (7db0a81d...), raw cells and a measured cost (18 cells in 174 s, peak 2.94 GB, one core; review 1776 reran in 182 s). The extension is named by the source: a pre-registered sharp-limit test of r = |R_11|/|Phi| at eta 0.0100/0.0075/0.0050/0.0025, x in {400000, 800000}, with cells |Phi| < 0.10 sup recorded but excluded from the ratio test. Failure (r bounded below) keeps only the one-sided bound on Phi(D_L,D_R) + E_out; success (r -> 0) drops the mixed line from the template. The post-hoc refinement already hints at failure (eta 0.0050 has r = 57 at |Phi|/sup 0.003; 0.0025 disagrees). A rerun should pre-register a floor on |R_11| as well as on |Phi| (review 1776 advisory 2), set next_step cpu_hours consistent with budget_hours (advisory 3), and keep the proxy-regime limit: at real exponents with eta < 1/400 the windows are empty (#3578), so no measure result here transfers to real parameters.","assumptions_md":"Provisional relevance only: #5113 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 271, explore (job 7383) on lane dir-558, one pre-registered sign test with the served compute_bp.py (052f0496..., unmodified) on 18 proxy cells, eta 0.015-0.035 step 0.0025 x {400000, 800000}, W_L = V/4, W_R = Z/2. At real exponents with eta < 1/400 the windows are empty (#3578), so no cell is a real-parameter cell. Finite float sums, identities to 2.45e-13; nothing is asymptotic. Rung measured, set by trusted review 1776 (accept, full rerun of 18 + 4 cells matched to <= 5.3e-11 relative). Accepted, not provisional, not superseded. Accepted content: sign(R_11) = sign(Phi) (Phi = phi.corner, the corner correlation Phi(D_L,D_R) of #3554) fails: 9 AGREE, 9 DISAGREE, 0 DEGENERATE, 0 INVALID; 8 of 9 disagreements have |Phi| >= 0.10 sup; |R_11|/|Phi| spans 0.0062-3.73. The one-sided bound on Phi(D_L,D_R) + E_out (#3554 joint form, sharpened by #3584) stays the only admissible target. The four eta-refinement cells at x = 800000 (0.0100-0.0025) are post-hoc leads, not evidence. Open per review 1776 (advisories, no findings filed): indep_check transcribes R_00..R_11 from the same formula (bit-identical), so only Phi as a direct sum is an independent path; no floor on |R_11| (FAIL keeps 5 disagreements at |R_11| >= 0.05 sup and 3 at >= 0.10 sup); next_step cpu_hours 0 vs budget_hours 1. Not claimed by the source: any statement at real parameters, any probabilistic sign law, any bound on Phi, primes or twins.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Mismatch. The infinitude area wants routes toward infinitely many twin primes outside the refuted registry. #5113 closes a candidate reduction inside route 271 (no sign law of R_11 through Phi on the proxy grid) and leaves the one-sided bound on Phi(D_L,D_R) + E_out as the route's only target. It proves no bound, gives no twin count or density, and its cells are proxy cells, not real-parameter cells. A negative finite answer to a sub-step does not advance an infinitude argument; at most it narrows route 271's template.","assumptions_md":"Provisional relevance only: #5113 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 271, explore (job 7383) on lane dir-558, one pre-registered sign test with the served compute_bp.py (052f0496..., unmodified) on 18 proxy cells, eta 0.015-0.035 step 0.0025 x {400000, 800000}, W_L = V/4, W_R = Z/2. At real exponents with eta < 1/400 the windows are empty (#3578), so no cell is a real-parameter cell. Finite float sums, identities to 2.45e-13; nothing is asymptotic. Rung measured, set by trusted review 1776 (accept, full rerun of 18 + 4 cells matched to <= 5.3e-11 relative). Accepted, not provisional, not superseded. Accepted content: sign(R_11) = sign(Phi) (Phi = phi.corner, the corner correlation Phi(D_L,D_R) of #3554) fails: 9 AGREE, 9 DISAGREE, 0 DEGENERATE, 0 INVALID; 8 of 9 disagreements have |Phi| >= 0.10 sup; |R_11|/|Phi| spans 0.0062-3.73. The one-sided bound on Phi(D_L,D_R) + E_out (#3554 joint form, sharpened by #3584) stays the only admissible target. The four eta-refinement cells at x = 800000 (0.0100-0.0025) are post-hoc leads, not evidence. Open per review 1776 (advisories, no findings filed): indep_check transcribes R_00..R_11 from the same formula (bit-identical), so only Phi as a direct sum is an independent path; no floor on |R_11| (FAIL keeps 5 disagreements at |R_11| >= 0.05 sup and 3 at >= 0.10 sup); next_step cpu_hours 0 vs budget_hours 1. Not claimed by the source: any statement at real parameters, any probabilistic sign law, any bound on Phi, primes or twins.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch. That area asks what structure a finite twin count would force. #5113 makes no assumption on the twin count, finite or infinite; its objects are correlation pieces of a smoothed bilinear form at fixed proxy parameters, and no step is conditioned on twins stopping. The sign disagreement of R_11 and Phi is a property of the instrument's proxy cells, not a forced consequence of finiteness.","assumptions_md":"Provisional relevance only: #5113 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 271, explore (job 7383) on lane dir-558, one pre-registered sign test with the served compute_bp.py (052f0496..., unmodified) on 18 proxy cells, eta 0.015-0.035 step 0.0025 x {400000, 800000}, W_L = V/4, W_R = Z/2. At real exponents with eta < 1/400 the windows are empty (#3578), so no cell is a real-parameter cell. Finite float sums, identities to 2.45e-13; nothing is asymptotic. Rung measured, set by trusted review 1776 (accept, full rerun of 18 + 4 cells matched to <= 5.3e-11 relative). Accepted, not provisional, not superseded. Accepted content: sign(R_11) = sign(Phi) (Phi = phi.corner, the corner correlation Phi(D_L,D_R) of #3554) fails: 9 AGREE, 9 DISAGREE, 0 DEGENERATE, 0 INVALID; 8 of 9 disagreements have |Phi| >= 0.10 sup; |R_11|/|Phi| spans 0.0062-3.73. The one-sided bound on Phi(D_L,D_R) + E_out (#3554 joint form, sharpened by #3584) stays the only admissible target. The four eta-refinement cells at x = 800000 (0.0100-0.0025) are post-hoc leads, not evidence. Open per review 1776 (advisories, no findings filed): indep_check transcribes R_00..R_11 from the same formula (bit-identical), so only Phi as a direct sum is an independent path; no floor on |R_11| (FAIL keeps 5 disagreements at |R_11| >= 0.05 sup and 3 at >= 0.10 sup); next_step cpu_hours 0 vs budget_hours 1. Not claimed by the source: any statement at real parameters, any probabilistic sign law, any bound on Phi, primes or twins.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Mismatch with every mapped claim. main is the survivor-gap lower bound with sufficient A = 12 (not infinitude); O1 a prime harmonic asymptotic; O2 a uniform smooth-number asymptotic; O3 every fixed A > 4; O4 a dyadic prime count with coefficient 1/2; O5 the quoted general sieve input and one-class statement; O6 two-sided density and Euler estimates; O7 the exact constant in equation (28). #5113 measures the sign relation between R_11 and the corner correlation Phi on 18 proxy cells. It involves no survivor gap, no smooth-number count, no prime harmonic sum and no sieve constant, and it cites no kk-lower-bound declaration. None of O1-O7 takes a correlation-sign census as input, and a finite float test gives no quantified bound in x.","assumptions_md":"Provisional relevance only: #5113 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 271, explore (job 7383) on lane dir-558, one pre-registered sign test with the served compute_bp.py (052f0496..., unmodified) on 18 proxy cells, eta 0.015-0.035 step 0.0025 x {400000, 800000}, W_L = V/4, W_R = Z/2. At real exponents with eta < 1/400 the windows are empty (#3578), so no cell is a real-parameter cell. Finite float sums, identities to 2.45e-13; nothing is asymptotic. Rung measured, set by trusted review 1776 (accept, full rerun of 18 + 4 cells matched to <= 5.3e-11 relative). Accepted, not provisional, not superseded. Accepted content: sign(R_11) = sign(Phi) (Phi = phi.corner, the corner correlation Phi(D_L,D_R) of #3554) fails: 9 AGREE, 9 DISAGREE, 0 DEGENERATE, 0 INVALID; 8 of 9 disagreements have |Phi| >= 0.10 sup; |R_11|/|Phi| spans 0.0062-3.73. The one-sided bound on Phi(D_L,D_R) + E_out (#3554 joint form, sharpened by #3584) stays the only admissible target. The four eta-refinement cells at x = 800000 (0.0100-0.0025) are post-hoc leads, not evidence. Open per review 1776 (advisories, no findings filed): indep_check transcribes R_00..R_11 from the same formula (bit-identical), so only Phi as a direct sum is an independent path; no floor on |R_11| (FAIL keeps 5 disagreements at |R_11| >= 0.05 sup and 3 at >= 0.10 sup); next_step cpu_hours 0 vs budget_hours 1. Not claimed by the source: any statement at real parameters, any probabilistic sign law, any bound on Phi, primes or twins.","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":10123,"input_sha256":"7ead298ea76a56b4d3a9dc44cf0de1e032e9078e41d94a1085dc6ad03e96d4ee","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"d2f967ec849583bd8b815e5f51a1d27a5aa01ff531b55dd547194397d377896a","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5113,"material_evidence":{"sha256":"1e700390e91b341c58bddfb682900f5357d219e695f1bde3dc9971d4afb909a9","entries":{"return:5113":"853db6f9411a11147f788cbf064b4b53fd95fb185b8a6681e91e46522645142a","artifact:5113:052f0496080f0248c009105750299d47121722907a1a15f90172c53b737aaf99":"052f0496080f0248c009105750299d47121722907a1a15f90172c53b737aaf99","artifact:5113:07005bb189e97693b90b7e39daf7e45a06d019e63f16815ebeb8214628ebe2d4":"07005bb189e97693b90b7e39daf7e45a06d019e63f16815ebeb8214628ebe2d4","artifact:5113:21507f34118d5ba553f2955c23cce9492d5d59de64c524c8ce5712fec3258698":"21507f34118d5ba553f2955c23cce9492d5d59de64c524c8ce5712fec3258698","artifact:5113:234f988665d63755171a84d4250be6590e916b10127fc551b7f892f50ea06671":"234f988665d63755171a84d4250be6590e916b10127fc551b7f892f50ea06671","artifact:5113:2c039b745309e32d9a869bb38d0127e8f657b4bba87367735615dc7e3147ed97":"2c039b745309e32d9a869bb38d0127e8f657b4bba87367735615dc7e3147ed97","artifact:5113:2f2fef2bdfc21d757559b81956caadd41ca1c02f301a768bf76572c127368519":"2f2fef2bdfc21d757559b81956caadd41ca1c02f301a768bf76572c127368519","artifact:5113:3ce6d6e44f11ea82b8cf9d39ab8970a5e06bead0112da96f653242c0efe272fd":"3ce6d6e44f11ea82b8cf9d39ab8970a5e06bead0112da96f653242c0efe272fd","artifact:5113:4c975d52eb8b549862d621204841e2ef49c3e79c23c2aa1fb66c728829117407":"4c975d52eb8b549862d621204841e2ef49c3e79c23c2aa1fb66c728829117407","artifact:5113:57d447534c6dca3954c8f7a07c654f560bc941c70bb912f3a38290abc999dfc0":"57d447534c6dca3954c8f7a07c654f560bc941c70bb912f3a38290abc999dfc0","artifact:5113:591f4b5ba2fe140a08c05c5d4a0ef30fbd53fc25fbc880e14f365ac3f5fdb22d":"591f4b5ba2fe140a08c05c5d4a0ef30fbd53fc25fbc880e14f365ac3f5fdb22d","artifact:5113:7bb681601db719d0231af4574aa72e57faa5e10e2dc34fc321861861ccf6bd4b":"7bb681601db719d0231af4574aa72e57faa5e10e2dc34fc321861861ccf6bd4b","artifact:5113:7c02139e5077247f9d123a640c8e71ed9cfc7f4ae1d6f728728e90f6318b4e64":"7c02139e5077247f9d123a640c8e71ed9cfc7f4ae1d6f728728e90f6318b4e64","artifact:5113:8dca8c7117bb65bc32ae73fff3dc969ed3a8e35ac5c0cc2501aefb06db2a5e14":"8dca8c7117bb65bc32ae73fff3dc969ed3a8e35ac5c0cc2501aefb06db2a5e14","artifact:5113:a6f37de9bb76295fd56ac8c34b7afd626f91d1b1d73400972828466d6843ac5d":"a6f37de9bb76295fd56ac8c34b7afd626f91d1b1d73400972828466d6843ac5d","artifact:5113:b6a661938ccd6fd8c1b575b1c53bf60310fc69b92fbbd81409019477e887f78c":"b6a661938ccd6fd8c1b575b1c53bf60310fc69b92fbbd81409019477e887f78c","artifact:5113:d2f967ec849583bd8b815e5f51a1d27a5aa01ff531b55dd547194397d377896a":"d2f967ec849583bd8b815e5f51a1d27a5aa01ff531b55dd547194397d377896a","artifact:5113:dbbc9def408fc261fca8f75b3090b3bf0f07d823f94f2b45fb763d9b71fe3443":"dbbc9def408fc261fca8f75b3090b3bf0f07d823f94f2b45fb763d9b71fe3443","artifact:5113:f2421d32f5451c9c5a8e4f393e0e54be98e0b4bffffc917777ba4552d8c12409":"f2421d32f5451c9c5a8e4f393e0e54be98e0b4bffffc917777ba4552d8c12409","artifact:5113:f723881ddf5bffc3771f8448442103dba25ca30a07cfea696e48404121df8511":"f723881ddf5bffc3771f8448442103dba25ca30a07cfea696e48404121df8511","artifact:5113:fc7228447f3576e6be31b8e50edc342113fcdcc8e48ed3e5cce683c433792625":"fc7228447f3576e6be31b8e50edc342113fcdcc8e48ed3e5cce683c433792625"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5113,"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 #5113: provisional consideration before validated transfer. This is relevance judgment, not another acceptance of the source or endorsement of unvalidated scopes. Do not run experiments, reproduce a computation or re-prove the source. No prior screening. 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Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"adversarial\",\"title\":\"Break accepted lemmas: counterexample search against validators\",\"lane\":\"adversarial\",\"topic_ids\":[],\"domain_md\":\"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"formalize\",\"title\":\"Lean 4 formalization of accepted lemmas\",\"lane\":\"formalize\",\"topic_ids\":[],\"domain_md\":\"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"measure\",\"title\":\"Extend numbered measurement scripts to larger ranges\",\"lane\":\"measure\",\"topic_ids\":[],\"domain_md\":\"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"infinitude\",\"title\":\"Routes toward infinitude not in the refuted registry\",\"lane\":\"infinitude\",\"topic_ids\":[],\"domain_md\":\"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"finiteness-structure\",\"title\":\"What structure a finite twin count would force (disproof-shaped lane)\",\"lane\":\"finiteness-structure\",\"topic_ids\":[],\"domain_md\":\"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"kk-lower-bound\",\"title\":\"Mapped paper claims and separate obligations\",\"paper\":\"kk-lower-bound\",\"topic_ids\":[\"kk-lower-bound.main\",\"kk-lower-bound.o1\",\"kk-lower-bound.o2\",\"kk-lower-bound.o3\",\"kk-lower-bound.o4\",\"kk-lower-bound.o5\",\"kk-lower-bound.o6\",\"kk-lower-bound.o7\"],\"domain_md\":\"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.\"}]\n\nFor each area return applicability_assessment:{source_return_id:5113,input_sha256:\"7ead298ea76a56b4d3a9dc44cf0de1e032e9078e41d94a1085dc6ad03e96d4ee\",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/5143/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"20bd0b22906ce15c90b97b7ab7f2aa6404f66d8ddd467eb4168234d2d249c4cd","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}