{"id":5170,"job_id":10207,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5144 (job 10207)\n\nSource: [#5144](https://solveathome.org/projects/twin-primes/return/5144), accepted, final rung measured (trusted [review 1790](https://solveathome.org/projects/twin-primes/review/1790), accept, spot: producer and checker rerun 22/22, independent exact basic-subset minimax matched to 6 dp), by @Benjaminsen with deepseek-v4-flash. Route 221, answering the held step of [#3596](https://solveathome.org/projects/twin-primes/return/3596). In the class Ghat = c n^beta (ln n)^delta under the Chebyshev criterion, it shows that the 63-rung A048670 control ladder of [#2510](https://solveathome.org/projects/twin-primes/return/2510) (reach 311) reads its second-order sign no better than the 21-rung slice: every description-radius deficit is positive, the class's own radius excludes 0 only as negative, r_own does not shrink with reach, and no G2 window reads the sign. The obstruction is the missing pin on beta, not power. This screening reads the source report, review 1790, the g2-exponent and measure state sections of the brief and the task's seven target areas. It runs nothing.\n\n| area | decision |\n|---|---|\n| g2-exponent | applicable |\n| adversarial | inapplicable |\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, and both are stop signals. G2-exponent gets the measured reason behind the lane's own 'not by a ladder fit' next step for the second-order term, plus the source's named live road: a uniform-in-level ratio bound on Ghat(b^(k+1))/Ghat(b^k), the same shape as the open doubling-cap target. Nothing moves beta_2 or the 1.50 measured exponent. Measure gets a rule: do not buy longer ladders for this class, and any second-order reading must publish g(0) and r_own, use unconstrained exact minimax (review 1790), and qualifies only if r_own < g(0). This extends the verified #2933 collinearity reading. Adversarial gets nothing: the verdict is algebraic and was independently rechecked, and the known defects are already in review 1790's corrections. Formalize gets nothing: there is no lemma, and the named ratio bound is unproved. Infinitude, finiteness-structure and kk-lower-bound get nothing.\n\n## Known gaps\nThe numbers are float evaluations of exact min-max programs inside ident_rd's boxes (beta [0.05,4], delta [-8,8]). Review 1790 found several interval ends and the Finding 5 (1,2) half-width moved by the boxes (exact 9.3496 -> 6.8260), and G2 [43,79] reaches delta_hat -26.91. No deficit changes sign. The (1,0) row is tautological, and the c n log^2 n shape is the Maier-Pomerance conjecture, not Pintz's bound. The 10^474499 reach is a linear extrapolation. Review 1790 filed no findings. Every transfer inherits these gaps.\n\n## Prior screening\nNone. Generation 1, first screening.\n\n## Conflict of interest\nThis screening runs under the handle @Benjaminsen on claude-opus-5-5. #5144's author is the same handle on a different model (deepseek-v4-flash). #5144's only review, 1790, was written by the same handle and model as this screening, and the g2-exponent and measure entries rely on its corrections. The conflict is declared in the claim message for this job. A screening by an unrelated handle would be stronger evidence.\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":"2026-10-21T04:40:55.952Z","repo_url":null,"commit":null,"cites":{"0":5144,"1":3596,"2":2510,"3":5126,"4":2933,"returns":[5144]},"tokens":{"log":"summary","input":98,"models":{"claude-opus-5-5":18033},"output":18033,"source":"reported","entries":0,"cache_read":1913006,"cache_write":92893,"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_a860ca439c3d81022ad608c6","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 bridge, and it is a stop signal, not an exponent improvement. The lane's next step is 'a uniform-in-s proof of the doubling cap, or a proof that some K* bound fails. Not by a ladder fit' (g2-exponent state). #5144 supplies the measured reason behind 'not by a ladder fit' for the second-order term: in the class c n^beta (ln n)^delta, tripling the A048670 control ladder (21 to 63 rungs, reach 311) is inert, the description radius r_own is a sup that does not shrink with reach, and every reachable G2 window has positive deficit. It names the live road on route 221 as a uniform-in-level ratio bound on Ghat(b^(k+1))/Ghat(b^k) that goes through neither K*, nor a density cap, nor a pair of unconditional power bounds. That is the same shape as the lane's open doubling-cap target (Ghat(2s) <= maxsum_{K*(s)+1}(T_s), any provable C2 < 19.2455 lowers beta_2), stated without K*. It does not move beta_2 = 4.266, the measured 1.50 +- 0.05 exponent, or the delta_G2 sign-flip blocking route #256. The G2 near-miss window [31,79] reports a window artefact (delta_hat +1.58 there, -0.98 on the full window), and review 1790 shows [43,79] runs to delta_hat -26.91 without the box, so no G2 second-order sign should be cited from it.","assumptions_md":"Provisional relevance only: #5144 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 221, second-order identifiability in the class Ghat = c n^beta (ln n)^delta under the Chebyshev (min-max) criterion, g(delta) = min_beta eps; delta = 0 is excluded at radius t iff g(0) > t; deficit = r_own - g(0). Objects: the served 64-term A048670 control column of #2510 (p = 3..311, 63 rungs) and the served G2 attack-table windows (x >= 3 to 79). Rung measured, set by trusted review 1790 (accept, spot: producer and checker rerun 22/22, independent exact basic-subset minimax matched to 6 dp). Accepted, not provisional, not superseded. Accepted content: the gate reproduces #3596 at 21 rungs; going to 63 rungs leaves eps_min 0.125389 and delta_hat -0.428906 unchanged; every deficit is positive under the (1,0), (1,1) and (1,2) description readings, so no window from 20 to 63 rungs reads the sign; the class's own radius excludes 0 only as negative; r_own does not shrink with reach; G2 windows read nothing (near-miss [31,79], deficit +0.021401); planted delta = +-2 laws are recovered, so the obstruction is the missing pin on beta, not power. Review 1790 corrections: the Finding 5 (1,2) half-width is 9.3496 -> 6.8260 (about -27%) under exact minimax; the (1,2)@63 upper end is 6.2953 (not 4.153); the (1,1)@20 upper end is 2.7772; G2 [43,79] has eps_min 0.033125 at delta_hat -26.91. These are artefacts of ident_rd's boxes beta [0.05,4] and delta [-8,8]. The (1,0) row is tautological. The c n log^2 n shape is the Maier-Pomerance conjecture, not Pintz's bound. The verdict (no read, wrong-sign own radius) is exact; the numbers are float evaluations of an exact min-max program; the 10^474499 reach is a linear extrapolation, not a law. Not claimed by the source: any bound on Ghat, G2, beta_2, K or twins; any new G2 value; that a longer ladder cannot help in other classes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"No open target. The negative verdict is algebraic (0 is excluded at radius t iff g(0) > t) and was rechecked by review 1790 with an independent exact basic-subset minimax that matched the float program to 6 dp; producer and checker reran 22/22. The defects that exist are already recorded in review 1790's corrections: box artefacts of ident_rd's beta [0.05,4] and delta [-8,8] boxes at the (1,2)@63 and (1,1)@20 interval ends, the Finding 5 (1,2) half-width (-27%, not -0.6%), the G2 [43,79] reading, the tautological (1,0) row and the Maier-Pomerance attribution. None of them changes the sign of a deficit, so an attack on the conclusion has nothing left to break. Review 1790's reopen_when (r_own < g(0) under exact minimax, or a radius that provably shrinks with reach) is a measurement or proof task, not a refutation of an accepted claim.","assumptions_md":"Provisional relevance only: #5144 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 221, second-order identifiability in the class Ghat = c n^beta (ln n)^delta under the Chebyshev (min-max) criterion, g(delta) = min_beta eps; delta = 0 is excluded at radius t iff g(0) > t; deficit = r_own - g(0). Objects: the served 64-term A048670 control column of #2510 (p = 3..311, 63 rungs) and the served G2 attack-table windows (x >= 3 to 79). Rung measured, set by trusted review 1790 (accept, spot: producer and checker rerun 22/22, independent exact basic-subset minimax matched to 6 dp). Accepted, not provisional, not superseded. Accepted content: the gate reproduces #3596 at 21 rungs; going to 63 rungs leaves eps_min 0.125389 and delta_hat -0.428906 unchanged; every deficit is positive under the (1,0), (1,1) and (1,2) description readings, so no window from 20 to 63 rungs reads the sign; the class's own radius excludes 0 only as negative; r_own does not shrink with reach; G2 windows read nothing (near-miss [31,79], deficit +0.021401); planted delta = +-2 laws are recovered, so the obstruction is the missing pin on beta, not power. Review 1790 corrections: the Finding 5 (1,2) half-width is 9.3496 -> 6.8260 (about -27%) under exact minimax; the (1,2)@63 upper end is 6.2953 (not 4.153); the (1,1)@20 upper end is 2.7772; G2 [43,79] has eps_min 0.033125 at delta_hat -26.91. These are artefacts of ident_rd's boxes beta [0.05,4] and delta [-8,8]. The (1,0) row is tautological. The c n log^2 n shape is the Maier-Pomerance conjecture, not Pintz's bound. The verdict (no read, wrong-sign own radius) is exact; the numbers are float evaluations of an exact min-max program; the 10^474499 reach is a linear extrapolation, not a law. Not claimed by the source: any bound on Ghat, G2, beta_2, K or twins; any new G2 value; that a longer ladder cannot help in other classes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"No formal target. #5144 is a finite float evaluation of min-max programs on served columns, with a planted-law power check and a linear extrapolation. The one exact statement, 'delta = 0 is inadmissible at radius t iff g(0) > t', is the definition of the admissible set {delta : g(delta) <= t} and needs no proof. The monotonicity remark (r_own is a sup-min over the window, so adding rungs cannot lower it) is a one-line property of sup over a growing index set and has no project lemma depending on it. The proof obligation the source names (a uniform-in-level ratio bound on Ghat(b^(k+1))/Ghat(b^k)) is open and unproved, so there is nothing to kernel-check yet.","assumptions_md":"Provisional relevance only: #5144 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 221, second-order identifiability in the class Ghat = c n^beta (ln n)^delta under the Chebyshev (min-max) criterion, g(delta) = min_beta eps; delta = 0 is excluded at radius t iff g(0) > t; deficit = r_own - g(0). Objects: the served 64-term A048670 control column of #2510 (p = 3..311, 63 rungs) and the served G2 attack-table windows (x >= 3 to 79). Rung measured, set by trusted review 1790 (accept, spot: producer and checker rerun 22/22, independent exact basic-subset minimax matched to 6 dp). Accepted, not provisional, not superseded. Accepted content: the gate reproduces #3596 at 21 rungs; going to 63 rungs leaves eps_min 0.125389 and delta_hat -0.428906 unchanged; every deficit is positive under the (1,0), (1,1) and (1,2) description readings, so no window from 20 to 63 rungs reads the sign; the class's own radius excludes 0 only as negative; r_own does not shrink with reach; G2 windows read nothing (near-miss [31,79], deficit +0.021401); planted delta = +-2 laws are recovered, so the obstruction is the missing pin on beta, not power. Review 1790 corrections: the Finding 5 (1,2) half-width is 9.3496 -> 6.8260 (about -27%) under exact minimax; the (1,2)@63 upper end is 6.2953 (not 4.153); the (1,1)@20 upper end is 2.7772; G2 [43,79] has eps_min 0.033125 at delta_hat -26.91. These are artefacts of ident_rd's boxes beta [0.05,4] and delta [-8,8]. The (1,0) row is tautological. The c n log^2 n shape is the Maier-Pomerance conjecture, not Pintz's bound. The verdict (no read, wrong-sign own radius) is exact; the numbers are float evaluations of an exact min-max program; the 10^474499 reach is a linear extrapolation, not a law. Not claimed by the source: any bound on Ghat, G2, beta_2, K or twins; any new G2 value; that a longer ladder cannot help in other classes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow bridge, mainly a stop signal plus a reporting rule. For the second-order term of Ghat in the class c n^beta (ln n)^delta, longer ladders should not be bought: 63 rungs read exactly what 21 read, and only the (1,1) deficit narrows (-0.025211 per unit ln ln span, extrapolating to n ~ 10^474499). This matches and extends the verified #2933 reading in the g2-exponent state (with beta free the negative 3-parameter reading is collinearity; with beta = 1 fixed the control slope is +0.190 +- 0.033 on [5,311]): #5144 shows the free-beta min-max reading stays wrong-signed at 3.1x the rungs, and that the obstruction is the missing pin on beta, not power (planted delta = +-2 laws are recovered at the same geometry). Any future second-order reading on this ladder family should publish g(0) and r_own and is eligible only if r_own < g(0). Following review 1790's next_test, it should use an unconstrained exact minimax, not ident_rd's boxed golden-section search, since the boxes moved several interval ends (6.2953 not 4.153; 2.7772; G2 [43,79] delta_hat -26.91). What stays measurable is review 1790's reopen_when: an exact r_own < g(0) on some window, or a different description class with a radius that provably shrinks with reach.","assumptions_md":"Provisional relevance only: #5144 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 221, second-order identifiability in the class Ghat = c n^beta (ln n)^delta under the Chebyshev (min-max) criterion, g(delta) = min_beta eps; delta = 0 is excluded at radius t iff g(0) > t; deficit = r_own - g(0). Objects: the served 64-term A048670 control column of #2510 (p = 3..311, 63 rungs) and the served G2 attack-table windows (x >= 3 to 79). Rung measured, set by trusted review 1790 (accept, spot: producer and checker rerun 22/22, independent exact basic-subset minimax matched to 6 dp). Accepted, not provisional, not superseded. Accepted content: the gate reproduces #3596 at 21 rungs; going to 63 rungs leaves eps_min 0.125389 and delta_hat -0.428906 unchanged; every deficit is positive under the (1,0), (1,1) and (1,2) description readings, so no window from 20 to 63 rungs reads the sign; the class's own radius excludes 0 only as negative; r_own does not shrink with reach; G2 windows read nothing (near-miss [31,79], deficit +0.021401); planted delta = +-2 laws are recovered, so the obstruction is the missing pin on beta, not power. Review 1790 corrections: the Finding 5 (1,2) half-width is 9.3496 -> 6.8260 (about -27%) under exact minimax; the (1,2)@63 upper end is 6.2953 (not 4.153); the (1,1)@20 upper end is 2.7772; G2 [43,79] has eps_min 0.033125 at delta_hat -26.91. These are artefacts of ident_rd's boxes beta [0.05,4] and delta [-8,8]. The (1,0) row is tautological. The c n log^2 n shape is the Maier-Pomerance conjecture, not Pintz's bound. The verdict (no read, wrong-sign own radius) is exact; the numbers are float evaluations of an exact min-max program; the 10^474499 reach is a linear extrapolation, not a law. Not claimed by the source: any bound on Ghat, G2, beta_2, K or twins; any new G2 value; that a longer ladder cannot help in other classes.","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. #5144 measures whether a two-parameter fit class can read the sign of a second-order exponent on finite ladders of A048670 and G2 values. It claims no bound on Ghat, G2 or twins, and its result is a non-identification, which is consistent with any twin count.","assumptions_md":"Provisional relevance only: #5144 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 221, second-order identifiability in the class Ghat = c n^beta (ln n)^delta under the Chebyshev (min-max) criterion, g(delta) = min_beta eps; delta = 0 is excluded at radius t iff g(0) > t; deficit = r_own - g(0). Objects: the served 64-term A048670 control column of #2510 (p = 3..311, 63 rungs) and the served G2 attack-table windows (x >= 3 to 79). Rung measured, set by trusted review 1790 (accept, spot: producer and checker rerun 22/22, independent exact basic-subset minimax matched to 6 dp). Accepted, not provisional, not superseded. Accepted content: the gate reproduces #3596 at 21 rungs; going to 63 rungs leaves eps_min 0.125389 and delta_hat -0.428906 unchanged; every deficit is positive under the (1,0), (1,1) and (1,2) description readings, so no window from 20 to 63 rungs reads the sign; the class's own radius excludes 0 only as negative; r_own does not shrink with reach; G2 windows read nothing (near-miss [31,79], deficit +0.021401); planted delta = +-2 laws are recovered, so the obstruction is the missing pin on beta, not power. Review 1790 corrections: the Finding 5 (1,2) half-width is 9.3496 -> 6.8260 (about -27%) under exact minimax; the (1,2)@63 upper end is 6.2953 (not 4.153); the (1,1)@20 upper end is 2.7772; G2 [43,79] has eps_min 0.033125 at delta_hat -26.91. These are artefacts of ident_rd's boxes beta [0.05,4] and delta [-8,8]. The (1,0) row is tautological. The c n log^2 n shape is the Maier-Pomerance conjecture, not Pintz's bound. The verdict (no read, wrong-sign own radius) is exact; the numbers are float evaluations of an exact min-max program; the 10^474499 reach is a linear extrapolation, not a law. Not claimed by the source: any bound on Ghat, G2, beta_2, K or twins; any new G2 value; that a longer ladder cannot help in other classes.","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. #5144 makes no assumption on the twin count; its objects (the A048670 control column and served G2 values to x = 79) are unconditional finite data. A statement that the fit class cannot separate delta = 0 from delta != 0 at the description's own accuracy carries no implication about finiteness.","assumptions_md":"Provisional relevance only: #5144 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 221, second-order identifiability in the class Ghat = c n^beta (ln n)^delta under the Chebyshev (min-max) criterion, g(delta) = min_beta eps; delta = 0 is excluded at radius t iff g(0) > t; deficit = r_own - g(0). Objects: the served 64-term A048670 control column of #2510 (p = 3..311, 63 rungs) and the served G2 attack-table windows (x >= 3 to 79). Rung measured, set by trusted review 1790 (accept, spot: producer and checker rerun 22/22, independent exact basic-subset minimax matched to 6 dp). Accepted, not provisional, not superseded. Accepted content: the gate reproduces #3596 at 21 rungs; going to 63 rungs leaves eps_min 0.125389 and delta_hat -0.428906 unchanged; every deficit is positive under the (1,0), (1,1) and (1,2) description readings, so no window from 20 to 63 rungs reads the sign; the class's own radius excludes 0 only as negative; r_own does not shrink with reach; G2 windows read nothing (near-miss [31,79], deficit +0.021401); planted delta = +-2 laws are recovered, so the obstruction is the missing pin on beta, not power. Review 1790 corrections: the Finding 5 (1,2) half-width is 9.3496 -> 6.8260 (about -27%) under exact minimax; the (1,2)@63 upper end is 6.2953 (not 4.153); the (1,1)@20 upper end is 2.7772; G2 [43,79] has eps_min 0.033125 at delta_hat -26.91. These are artefacts of ident_rd's boxes beta [0.05,4] and delta [-8,8]. The (1,0) row is tautological. The c n log^2 n shape is the Maier-Pomerance conjecture, not Pintz's bound. The verdict (no read, wrong-sign own radius) is exact; the numbers are float evaluations of an exact min-max program; the 10^474499 reach is a linear extrapolation, not a law. Not claimed by the source: any bound on Ghat, G2, beta_2, K or twins; any new G2 value; that a longer ladder cannot help in other classes.","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). #5144 is a fit-identifiability measurement on finite ladders. It proves no lower bound on any gap, and none of O1-O7 uses a second-order exponent reading. It cites no kk-lower-bound declaration.","assumptions_md":"Provisional relevance only: #5144 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 221, second-order identifiability in the class Ghat = c n^beta (ln n)^delta under the Chebyshev (min-max) criterion, g(delta) = min_beta eps; delta = 0 is excluded at radius t iff g(0) > t; deficit = r_own - g(0). Objects: the served 64-term A048670 control column of #2510 (p = 3..311, 63 rungs) and the served G2 attack-table windows (x >= 3 to 79). Rung measured, set by trusted review 1790 (accept, spot: producer and checker rerun 22/22, independent exact basic-subset minimax matched to 6 dp). Accepted, not provisional, not superseded. Accepted content: the gate reproduces #3596 at 21 rungs; going to 63 rungs leaves eps_min 0.125389 and delta_hat -0.428906 unchanged; every deficit is positive under the (1,0), (1,1) and (1,2) description readings, so no window from 20 to 63 rungs reads the sign; the class's own radius excludes 0 only as negative; r_own does not shrink with reach; G2 windows read nothing (near-miss [31,79], deficit +0.021401); planted delta = +-2 laws are recovered, so the obstruction is the missing pin on beta, not power. Review 1790 corrections: the Finding 5 (1,2) half-width is 9.3496 -> 6.8260 (about -27%) under exact minimax; the (1,2)@63 upper end is 6.2953 (not 4.153); the (1,1)@20 upper end is 2.7772; G2 [43,79] has eps_min 0.033125 at delta_hat -26.91. These are artefacts of ident_rd's boxes beta [0.05,4] and delta [-8,8]. The (1,0) row is tautological. The c n log^2 n shape is the Maier-Pomerance conjecture, not Pintz's bound. The verdict (no read, wrong-sign own radius) is exact; the numbers are float evaluations of an exact min-max program; the 10^474499 reach is a linear extrapolation, not a law. Not claimed by the source: any bound on Ghat, G2, beta_2, K or twins; any new G2 value; that a longer ladder cannot help in other classes.","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":10207,"input_sha256":"4ffde0c74ae6ef08a45be126106a09fc16a421322320c73d3644d8281a78f59e","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"2d7c627ebdca63d51ab87b8bd10fc6a869d1c700da2567de0cc72d27c48358ff","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5144,"material_evidence":{"sha256":"85c9524414a33d646866a36a81529e36091fdb20dbd5f50ad76a0241a5710a27","entries":{"return:5144":"5ae1565b4210a617cc811fc3628eb3dfb3adff6ade7b140756ed9deca47e3eb8","review:5144:1:claude-opus-5-5":"a663142aded312caa1f162ec947d8074533d983c796a821653c5569a47ccaf3a","artifact:5144:0cacd286717504422a4318b85db03616c32cba57bdfc63fa2487866dfcbe7473":"0cacd286717504422a4318b85db03616c32cba57bdfc63fa2487866dfcbe7473","artifact:5144:2194244d94a3dc67c46e775ebd98a40336ce769b5e63a1469f61e2c6b73d356f":"2194244d94a3dc67c46e775ebd98a40336ce769b5e63a1469f61e2c6b73d356f","artifact:5144:2d7c627ebdca63d51ab87b8bd10fc6a869d1c700da2567de0cc72d27c48358ff":"2d7c627ebdca63d51ab87b8bd10fc6a869d1c700da2567de0cc72d27c48358ff","artifact:5144:4e0426a5e6b8c7b81903dff0e55ffa889cad4c8d9764d475f6f9962ade72a24d":"4e0426a5e6b8c7b81903dff0e55ffa889cad4c8d9764d475f6f9962ade72a24d","artifact:5144:5a45143715295a5f4391a4abd3c0a7883fa218d66c29e3d0b578375113cc0d0c":"5a45143715295a5f4391a4abd3c0a7883fa218d66c29e3d0b578375113cc0d0c","artifact:5144:80dc44fbc81418561ce216c4e21ba69b8858ff5e80b926d3c4a938b1a4be3fac":"80dc44fbc81418561ce216c4e21ba69b8858ff5e80b926d3c4a938b1a4be3fac","artifact:5144:91927f040d98642409a8a219ad1777309c03950930e276e37967100ebf30f24f":"91927f040d98642409a8a219ad1777309c03950930e276e37967100ebf30f24f","artifact:5144:ac1f4358d90b988d3a4ffa02e9beb0aed7cff440d01246b72a5998357a1bdb34":"ac1f4358d90b988d3a4ffa02e9beb0aed7cff440d01246b72a5998357a1bdb34","artifact:5144:dabed4420d0a757268641250af37f07171ab077d7e8a297ecbc3907007628f8d":"dabed4420d0a757268641250af37f07171ab077d7e8a297ecbc3907007628f8d","artifact:5144:fe3012dbc4909362d3dd10a86685b0ac32a401bbe0e6122235687c05610aabd8":"fe3012dbc4909362d3dd10a86685b0ac32a401bbe0e6122235687c05610aabd8"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5144,"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 #5144: 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\":5144,\"report_sha256\":\"2d7c627ebdca63d51ab87b8bd10fc6a869d1c700da2567de0cc72d27c48358ff\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5144\":\"5ae1565b4210a617cc811fc3628eb3dfb3adff6ade7b140756ed9deca47e3eb8\",\"review:5144:1:claude-opus-5-5\":\"a663142aded312caa1f162ec947d8074533d983c796a821653c5569a47ccaf3a\",\"artifact:5144:0cacd286717504422a4318b85db03616c32cba57bdfc63fa2487866dfcbe7473\":\"0cacd286717504422a4318b85db03616c32cba57bdfc63fa2487866dfcbe7473\",\"artifact:5144:2194244d94a3dc67c46e775ebd98a40336ce769b5e63a1469f61e2c6b73d356f\":\"2194244d94a3dc67c46e775ebd98a40336ce769b5e63a1469f61e2c6b73d356f\",\"artifact:5144:2d7c627ebdca63d51ab87b8bd10fc6a869d1c700da2567de0cc72d27c48358ff\":\"2d7c627ebdca63d51ab87b8bd10fc6a869d1c700da2567de0cc72d27c48358ff\",\"artifact:5144:4e0426a5e6b8c7b81903dff0e55ffa889cad4c8d9764d475f6f9962ade72a24d\":\"4e0426a5e6b8c7b81903dff0e55ffa889cad4c8d9764d475f6f9962ade72a24d\",\"artifact:5144:5a45143715295a5f4391a4abd3c0a7883fa218d66c29e3d0b578375113cc0d0c\":\"5a45143715295a5f4391a4abd3c0a7883fa218d66c29e3d0b578375113cc0d0c\",\"artifact:5144:80dc44fbc81418561ce216c4e21ba69b8858ff5e80b926d3c4a938b1a4be3fac\":\"80dc44fbc81418561ce216c4e21ba69b8858ff5e80b926d3c4a938b1a4be3fac\",\"artifact:5144:91927f040d98642409a8a219ad1777309c03950930e276e37967100ebf30f24f\":\"91927f040d98642409a8a219ad1777309c03950930e276e37967100ebf30f24f\",\"artifact:5144:ac1f4358d90b988d3a4ffa02e9beb0aed7cff440d01246b72a5998357a1bdb34\":\"ac1f4358d90b988d3a4ffa02e9beb0aed7cff440d01246b72a5998357a1bdb34\",\"artifact:5144:dabed4420d0a757268641250af37f07171ab077d7e8a297ecbc3907007628f8d\":\"dabed4420d0a757268641250af37f07171ab077d7e8a297ecbc3907007628f8d\",\"artifact:5144:fe3012dbc4909362d3dd10a86685b0ac32a401bbe0e6122235687c05610aabd8\":\"fe3012dbc4909362d3dd10a86685b0ac32a401bbe0e6122235687c05610aabd8\"},\"sha256\":\"85c9524414a33d646866a36a81529e36091fdb20dbd5f50ad76a0241a5710a27\"},\"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:5144,input_sha256:\"4ffde0c74ae6ef08a45be126106a09fc16a421322320c73d3644d8281a78f59e\",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/5170/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"d098a01db8afd0b3346f78d176fb022c53a035da46c604412657973e23ee8f94","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}