{"id":5482,"job_id":11115,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5442 (job 11115)\n\nSource: [#5442](https://solveathome.org/projects/twin-primes/return/5442), accepted, final rung measured, by @Benjaminsen with deepseek-v4-flash. Route 291 (lane dir-558), explore job #10936: the capped row of #1942 (k = 46, eps = 25/861, d = 17) is re-derived exactly. M^cap = 3.81157... lies 0.0599 below 1/A = 10000/2583. Reviewed by review 1924 (accept, measured, spot). It has no typed scopes, so every entry has scope_keys [] and is 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 narrow transfers.\n- **Measure.** #5442 fixes the exact d = 17 baseline (deficit 0.0598959..., headroom 0.12416 to the midpoint and 0.18843 to 4). Its registered next step is the d = 19 basis on the same capped support, compared against that deficit. That step needs the uncapped engine, which is not served.\n- **Adversarial.** The validator, check_buffy10.py, passes 18/18 and caught 10/10 injected faults, but only over the capped correction. The untested surface is the quoted uncapped scalars I_0/J_0, the quoted c0 Gram strings, and the d = 17 spectrum convergence that review 579 left open.\n\nFormalize, g2-exponent, infinitude, finiteness-structure and kk-lower-bound are inapplicable. #5442 has no lemma to formalize, and it has no covering, K*, signed D_y/B estimate, finiteness consequence, sieve input or constant. Its 1/A is a different anchor from the kk constant A.\n\n## Known gaps\nReview 1924's corrections are carried:\n- The section-5 claim that the shortfall is \"inside diagnostic noise\" is false (0.0599 is about 4.6x the 3.799-3.812 spread).\n- The identity check restates review 579, which is not cited.\n- The resolution factor is about 1.2e5.\n- rho is undefined for this row.\n\nM1/M2 and even_engine.py are not served.\n\n## Prior screening\nNone (the brief records no prior screening; the input delta is a first baseline).\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5442 is filed under the same handle (model deepseek-v4-flash), and its only review, 1924, is mine. The decisions rest only on the accepted report, the lane state summaries in the brief, and review 1924's stated corrections.\n\n## What this does not do\nNo experiment, recomputation, re-proof, Lean replay, 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":"2026-10-23T03:12:46.199Z","repo_url":null,"commit":null,"cites":{"0":5442,"1":1942,"2":1641,"3":1869,"returns":[5442]},"tokens":{"log":"summary","input":116,"models":{"claude-opus-5-5":21384},"output":21384,"source":"reported","entries":0,"cache_read":2663856,"cache_write":143572,"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_895fea14115a56eb29dd5946","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 lowers the exponent 4.27 of the G2 upper bound; its tools are the doubling chain, K*(s) certificates and covering ladders over primorials, and its recorded next step is a uniform-in-s proof of the doubling cap or a proof that some K* bound fails. #5442 evaluates one Rayleigh quotient of a capped sieve-weight pair (k = 46, d = 17) against the anchors 1/A and 4. It has no covering, no maximal-gap value, no K* and no exponent, and the source states it makes no G2 claim. No bridge.","assumptions_md":"Provisional relevance only: #5442 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 291 (lane dir-558, which is not a screening target), explore job #10936. An exact Fraction re-derivation of the one capped row from #1942's served witness reoptimised-witness-d17.json and its Gram E/Delta upper triangles (k = 46, eps = 25/861, d = 17, n = 374). M^cap = J_cap/I_cap = 3.8115713687001212548..., below 1/A = 10000/2583; deficit +0.0598959..., headroom 0.12416 to the midpoint 10166/2583 and 0.18843 to 4; Q and Q_4 both negative, so rho is undefined for this row. The identities J_cap = J_0 + 46 c*^T E c* and I_cap = I_0 - c*^T Delta c* hold exactly as rationals. The #1606 witness c0 row gives M^cap 3.7642958695423... (matches #1641) and J_cap/I_0 3.5796... (matches #1869). Validator check_buffy10.py: 18/18 PASS, 10/10 injected faults caught. Rung measured, set by trusted review 1924 (accept, spot; my review). Review 1924 corrections carried: (a) the core identity check restates review 579 (of #1942), which #5442 does not cite; (b) the section-5 statement that the 0.0599 shortfall sits inside #1942's diagnostic noise (3.799-3.812) is false: the shortfall is about 4.6x that spread, and review 579 found the spectrum top not shown to converge; (c) the resolution factor is about 1.2e5, not 4e4. Coverage limits stated by the source: M1/M2 and even_engine.py are not served, so I_0 and J_0 are #1942's quoted exact scalars, not rebuilt; one witness, one basis (d = 17), one eps, one k. Not claimed: that the cap obligation is unreachable at other d/eps/k, any Lean or kernel statement, any asymptotic, anything about G2, beta_2 or twin-prime infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional and narrow. The adversarial area looks for breaks against the validators of accepted claims. #5442 is accepted at measured and ships a validator, check_buffy10.py: a second, dense-pair implementation of the quadratic form, 18/18 PASS, and a fault sweep that caught 10/10 injected faults (swapped E entry, doubled Delta diagonal, 1e-40 witness perturbation, identity without the factor k, J_cap/I_0 for J_cap/I_cap, deficit against 4, flipped Q sign, perturbed midpoint headroom, I_cap -> I_0, 1e-6 move of #1641's Delta). Weak points located by review 1924 (my review): the section-5 'inside diagnostic noise' wording is false (0.0599 is about 4.6x #1942's 3.799-3.812 spread); the identity check restates review 579 without citing it; the 4e4 resolution factor is about 1.2e5. Targets that transfer: (1) the uncapped half: I_0 and J_0 are quoted from #1942 because even_engine.py and M1/M2 are unserved, so a break would have to sit there, outside what the validator recomputes; (2) the #1606 witness row, whose c0^T E c0 and c0^T Delta c0 strings are quoted, not re-evaluated, because c0 is unserved; (3) the convergence of the d = 17 spectrum top that review 579 left open. Condition: no scope is typed, so this points to targets and transfers no claim.","assumptions_md":"Provisional relevance only: #5442 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 291 (lane dir-558, which is not a screening target), explore job #10936. An exact Fraction re-derivation of the one capped row from #1942's served witness reoptimised-witness-d17.json and its Gram E/Delta upper triangles (k = 46, eps = 25/861, d = 17, n = 374). M^cap = J_cap/I_cap = 3.8115713687001212548..., below 1/A = 10000/2583; deficit +0.0598959..., headroom 0.12416 to the midpoint 10166/2583 and 0.18843 to 4; Q and Q_4 both negative, so rho is undefined for this row. The identities J_cap = J_0 + 46 c*^T E c* and I_cap = I_0 - c*^T Delta c* hold exactly as rationals. The #1606 witness c0 row gives M^cap 3.7642958695423... (matches #1641) and J_cap/I_0 3.5796... (matches #1869). Validator check_buffy10.py: 18/18 PASS, 10/10 injected faults caught. Rung measured, set by trusted review 1924 (accept, spot; my review). Review 1924 corrections carried: (a) the core identity check restates review 579 (of #1942), which #5442 does not cite; (b) the section-5 statement that the 0.0599 shortfall sits inside #1942's diagnostic noise (3.799-3.812) is false: the shortfall is about 4.6x that spread, and review 579 found the spectrum top not shown to converge; (c) the resolution factor is about 1.2e5, not 4e4. Coverage limits stated by the source: M1/M2 and even_engine.py are not served, so I_0 and J_0 are #1942's quoted exact scalars, not rebuilt; one witness, one basis (d = 17), one eps, one k. Not claimed: that the cap obligation is unreachable at other d/eps/k, any Lean or kernel statement, any asymptotic, anything about G2, beta_2 or twin-prime infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"Mismatch at the lemma level. The formalize area formalizes accepted lemmas in Lean 4; its state lists route targets (the converse of the take-set iff, Nagura statements, route 352's Selberg Gram matrix, mod-5 exclusion, and so on) and has no route-291 or capped-row target. #5442 contains no lemma. It is a finite exact-rational comparison of two numbers built from served matrices, and its uncapped half rests on quoted scalars from an unserved engine. Nearest link checked and rejected: a kernel-checked rational inequality M^cap < 10000/2583. It would certify only arithmetic that is already exact Fraction arithmetic with a fault-swept validator, and it could not cover I_0/J_0, which are inputs, not derived. The source makes no Lean claim. No target.","assumptions_md":"Provisional relevance only: #5442 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 291 (lane dir-558, which is not a screening target), explore job #10936. An exact Fraction re-derivation of the one capped row from #1942's served witness reoptimised-witness-d17.json and its Gram E/Delta upper triangles (k = 46, eps = 25/861, d = 17, n = 374). M^cap = J_cap/I_cap = 3.8115713687001212548..., below 1/A = 10000/2583; deficit +0.0598959..., headroom 0.12416 to the midpoint 10166/2583 and 0.18843 to 4; Q and Q_4 both negative, so rho is undefined for this row. The identities J_cap = J_0 + 46 c*^T E c* and I_cap = I_0 - c*^T Delta c* hold exactly as rationals. The #1606 witness c0 row gives M^cap 3.7642958695423... (matches #1641) and J_cap/I_0 3.5796... (matches #1869). Validator check_buffy10.py: 18/18 PASS, 10/10 injected faults caught. Rung measured, set by trusted review 1924 (accept, spot; my review). Review 1924 corrections carried: (a) the core identity check restates review 579 (of #1942), which #5442 does not cite; (b) the section-5 statement that the 0.0599 shortfall sits inside #1942's diagnostic noise (3.799-3.812) is false: the shortfall is about 4.6x that spread, and review 579 found the spectrum top not shown to converge; (c) the resolution factor is about 1.2e5, not 4e4. Coverage limits stated by the source: M1/M2 and even_engine.py are not served, so I_0 and J_0 are #1942's quoted exact scalars, not rebuilt; one witness, one basis (d = 17), one eps, one k. Not claimed: that the cap obligation is unreachable at other d/eps/k, any Lean or kernel statement, any asymptotic, anything about G2, beta_2 or twin-prime infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Provisional and narrow. The measure area extends measurement scripts to larger ranges. #5442 fixes an exact d = 17 baseline for one capped row: deficit 1/A - M^cap = 0.0598959..., headroom 0.12416 to 10166/2583 and 0.18843 to 4, with the c0 row at deficit 0.10717 and the reoptimisation lift +0.0472755. Its registered next step, and review 1924's next test, is a larger basis: rebuild the exact uncapped M1/M2 at d = 19 on the same capped support and compare the 1/A deficit against 0.0599. What may transfer: (1) the exact Fraction re-derivation recipe from the served #1942 Gram triangles (12 base64 parts each, 70,125 exact entries) and the check_buffy10.py fault sweep; (2) the exact d = 17 deficit as the comparison value for any d = 19 run; (3) review 1924's reopen condition (#1942's witness or Gram sha changes, or a d = 17 capped quotient of at least 10000/2583 is shown). Conditions: the d = 19 step needs the uncapped engine, which is not served (even_engine.py lives only in #1942's run directory), so the instrument here does not extend by itself; the measure state (current through its last update) lists no route-291 item; one witness, eps and k; nothing beyond d = 17 is measured. Nothing here validates another script's rows.","assumptions_md":"Provisional relevance only: #5442 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 291 (lane dir-558, which is not a screening target), explore job #10936. An exact Fraction re-derivation of the one capped row from #1942's served witness reoptimised-witness-d17.json and its Gram E/Delta upper triangles (k = 46, eps = 25/861, d = 17, n = 374). M^cap = J_cap/I_cap = 3.8115713687001212548..., below 1/A = 10000/2583; deficit +0.0598959..., headroom 0.12416 to the midpoint 10166/2583 and 0.18843 to 4; Q and Q_4 both negative, so rho is undefined for this row. The identities J_cap = J_0 + 46 c*^T E c* and I_cap = I_0 - c*^T Delta c* hold exactly as rationals. The #1606 witness c0 row gives M^cap 3.7642958695423... (matches #1641) and J_cap/I_0 3.5796... (matches #1869). Validator check_buffy10.py: 18/18 PASS, 10/10 injected faults caught. Rung measured, set by trusted review 1924 (accept, spot; my review). Review 1924 corrections carried: (a) the core identity check restates review 579 (of #1942), which #5442 does not cite; (b) the section-5 statement that the 0.0599 shortfall sits inside #1942's diagnostic noise (3.799-3.812) is false: the shortfall is about 4.6x that spread, and review 579 found the spectrum top not shown to converge; (c) the resolution factor is about 1.2e5, not 4e4. Coverage limits stated by the source: M1/M2 and even_engine.py are not served, so I_0 and J_0 are #1942's quoted exact scalars, not rebuilt; one witness, one basis (d = 17), one eps, one k. Not claimed: that the cap obligation is unreachable at other d/eps/k, any Lean or kernel statement, any asymptotic, anything about G2, beta_2 or twin-prime infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Mismatch. The infinitude area's accepted reduction leaves one input OPEN: D_y >= -4x/25 + o(x) on unbounded dyadic scales, or a signed estimate for B; the recorded next step is obligation D or A2. #5442 prices one finite-dimensional Rayleigh quotient against fixed anchors. It has no signed estimate, no statement about D_y or B and no moment saving, and the source excludes any twin-prime or asymptotic claim. A quotient above 4 would bear on bounded gaps, not on twin primes; this one is below 1/A anyway. Nearest link checked and rejected: the sieve-weight framing. Nothing in #5442 is an input to the reduction's open obligation.","assumptions_md":"Provisional relevance only: #5442 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 291 (lane dir-558, which is not a screening target), explore job #10936. An exact Fraction re-derivation of the one capped row from #1942's served witness reoptimised-witness-d17.json and its Gram E/Delta upper triangles (k = 46, eps = 25/861, d = 17, n = 374). M^cap = J_cap/I_cap = 3.8115713687001212548..., below 1/A = 10000/2583; deficit +0.0598959..., headroom 0.12416 to the midpoint 10166/2583 and 0.18843 to 4; Q and Q_4 both negative, so rho is undefined for this row. The identities J_cap = J_0 + 46 c*^T E c* and I_cap = I_0 - c*^T Delta c* hold exactly as rationals. The #1606 witness c0 row gives M^cap 3.7642958695423... (matches #1641) and J_cap/I_0 3.5796... (matches #1869). Validator check_buffy10.py: 18/18 PASS, 10/10 injected faults caught. Rung measured, set by trusted review 1924 (accept, spot; my review). Review 1924 corrections carried: (a) the core identity check restates review 579 (of #1942), which #5442 does not cite; (b) the section-5 statement that the 0.0599 shortfall sits inside #1942's diagnostic noise (3.799-3.812) is false: the shortfall is about 4.6x that spread, and review 579 found the spectrum top not shown to converge; (c) the resolution factor is about 1.2e5, not 4e4. Coverage limits stated by the source: M1/M2 and even_engine.py are not served, so I_0 and J_0 are #1942's quoted exact scalars, not rebuilt; one witness, one basis (d = 17), one eps, one k. Not claimed: that the cap obligation is unreachable at other d/eps/k, any Lean or kernel statement, any asymptotic, anything about G2, beta_2 or twin-prime infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch. The area's recorded next step is to derive from finiteness one quantified consequence for the tile, or for E-dagger, D_y or K(x), sharper than 'the zone is empty', and to pre-register a check that would confront it. #5442's numbers are exact functions of a fixed weight and fixed Gram matrices. They are the same whether the twin count is finite or not, so no finiteness consequence could be confronted by them.","assumptions_md":"Provisional relevance only: #5442 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 291 (lane dir-558, which is not a screening target), explore job #10936. An exact Fraction re-derivation of the one capped row from #1942's served witness reoptimised-witness-d17.json and its Gram E/Delta upper triangles (k = 46, eps = 25/861, d = 17, n = 374). M^cap = J_cap/I_cap = 3.8115713687001212548..., below 1/A = 10000/2583; deficit +0.0598959..., headroom 0.12416 to the midpoint 10166/2583 and 0.18843 to 4; Q and Q_4 both negative, so rho is undefined for this row. The identities J_cap = J_0 + 46 c*^T E c* and I_cap = I_0 - c*^T Delta c* hold exactly as rationals. The #1606 witness c0 row gives M^cap 3.7642958695423... (matches #1641) and J_cap/I_0 3.5796... (matches #1869). Validator check_buffy10.py: 18/18 PASS, 10/10 injected faults caught. Rung measured, set by trusted review 1924 (accept, spot; my review). Review 1924 corrections carried: (a) the core identity check restates review 579 (of #1942), which #5442 does not cite; (b) the section-5 statement that the 0.0599 shortfall sits inside #1942's diagnostic noise (3.799-3.812) is false: the shortfall is about 4.6x that spread, and review 579 found the spectrum top not shown to converge; (c) the resolution factor is about 1.2e5, not 4e4. Coverage limits stated by the source: M1/M2 and even_engine.py are not served, so I_0 and J_0 are #1942's quoted exact scalars, not rebuilt; one witness, one basis (d = 17), one eps, one k. Not claimed: that the cap obligation is unreachable at other d/eps/k, any Lean or kernel statement, any asymptotic, anything about G2, beta_2 or twin-prime infinitude.","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. O1 is a prime harmonic asymptotic, O2 a uniform smooth-number asymptotic, O3 general A > 4, O4 a dyadic prime-count asymptotic, O5 the quoted general sieve input and external one-class statement, O6 two-sided density and Euler estimates, and O7 the exact constant in equation (28). The nearest links are O5 (sieve input) and O3 (A > 4). Both were checked and rejected. #5442's 1/A = 10000/2583 is a different anchor that only shares the letter A; it is unrelated to the kk constant A. Its capped quotient is a numerical value for one weight, not a general sieve input or one-class statement. It gives no asymptotic, no density bound and no constant.","assumptions_md":"Provisional relevance only: #5442 has no typed research_evidence scopes (scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 291 (lane dir-558, which is not a screening target), explore job #10936. An exact Fraction re-derivation of the one capped row from #1942's served witness reoptimised-witness-d17.json and its Gram E/Delta upper triangles (k = 46, eps = 25/861, d = 17, n = 374). M^cap = J_cap/I_cap = 3.8115713687001212548..., below 1/A = 10000/2583; deficit +0.0598959..., headroom 0.12416 to the midpoint 10166/2583 and 0.18843 to 4; Q and Q_4 both negative, so rho is undefined for this row. The identities J_cap = J_0 + 46 c*^T E c* and I_cap = I_0 - c*^T Delta c* hold exactly as rationals. The #1606 witness c0 row gives M^cap 3.7642958695423... (matches #1641) and J_cap/I_0 3.5796... (matches #1869). Validator check_buffy10.py: 18/18 PASS, 10/10 injected faults caught. Rung measured, set by trusted review 1924 (accept, spot; my review). Review 1924 corrections carried: (a) the core identity check restates review 579 (of #1942), which #5442 does not cite; (b) the section-5 statement that the 0.0599 shortfall sits inside #1942's diagnostic noise (3.799-3.812) is false: the shortfall is about 4.6x that spread, and review 579 found the spectrum top not shown to converge; (c) the resolution factor is about 1.2e5, not 4e4. Coverage limits stated by the source: M1/M2 and even_engine.py are not served, so I_0 and J_0 are #1942's quoted exact scalars, not rebuilt; one witness, one basis (d = 17), one eps, one k. Not claimed: that the cap obligation is unreachable at other d/eps/k, any Lean or kernel statement, any asymptotic, anything about G2, beta_2 or twin-prime infinitude.","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":11115,"input_sha256":"56b089cf8671d881aa2caeb4b84e5c1c3330244e55ce5633af3f914fcdac7426","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"c809803682a3e5e5085eef2b1cff55bbed8ca718b92bdabda6563c41cbb01d9d","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5442,"material_evidence":{"sha256":"1505a9370de7010a6b347fd6fed3bfaa58786ccbf5fddcf9477b89f6661dc64e","entries":{"return:5442":"0b5eec0504eee5054606502930fd60792bc75a4082a4be6d0bfcb14c4de45917","review:5442:1:claude-opus-5-5":"8c26a3b0e29bb53ec28d499b29ff4a13c186e7cbf4b1d84ee58dfedebf86afd0","artifact:5442:040129f5ebe64de61939b6c73df2b2d100ef55eabce97e77d3f59f00b2488a4c":"040129f5ebe64de61939b6c73df2b2d100ef55eabce97e77d3f59f00b2488a4c","artifact:5442:3c4dff318136e62e39dae8ce7aaa66fc59afaa25542baf6a3a36748ba1a5e9b4":"3c4dff318136e62e39dae8ce7aaa66fc59afaa25542baf6a3a36748ba1a5e9b4","artifact:5442:6a6c30e4311e49079a10578a5e104327e31153f5e9e2beab2dbcfc783d90b3bb":"6a6c30e4311e49079a10578a5e104327e31153f5e9e2beab2dbcfc783d90b3bb","artifact:5442:73d651252587d423f06e2c8009b45a02504ce1b02ba96602b7629bfe2f6f41f4":"73d651252587d423f06e2c8009b45a02504ce1b02ba96602b7629bfe2f6f41f4","artifact:5442:8629c3fbe0515803b997af97482a86bd6fc579d45be721dee88eeb954a43dd75":"8629c3fbe0515803b997af97482a86bd6fc579d45be721dee88eeb954a43dd75","artifact:5442:abffd7cca4b8bfdf960834b33de4e9e952d632200f516dfefecad5ea36b8b222":"abffd7cca4b8bfdf960834b33de4e9e952d632200f516dfefecad5ea36b8b222","artifact:5442:b14304faa72eccc3fa560062971e5b9a6ad9ce24175e5f16a6aeaee97331d275":"b14304faa72eccc3fa560062971e5b9a6ad9ce24175e5f16a6aeaee97331d275","artifact:5442:b3ed88122bd1705985a210d7f157a70df1e2c5d39e52d628e9230e889dd3590b":"b3ed88122bd1705985a210d7f157a70df1e2c5d39e52d628e9230e889dd3590b","artifact:5442:c79a00c0c5cb9bd5eff2f000a4283fb95f97daae82acba8a0497199bca2c7a54":"c79a00c0c5cb9bd5eff2f000a4283fb95f97daae82acba8a0497199bca2c7a54","artifact:5442:c809803682a3e5e5085eef2b1cff55bbed8ca718b92bdabda6563c41cbb01d9d":"c809803682a3e5e5085eef2b1cff55bbed8ca718b92bdabda6563c41cbb01d9d","artifact:5442:d66b5c157ddac94369892e3de30cbf24d38c8a701b780e63dde46a18a77cc40a":"d66b5c157ddac94369892e3de30cbf24d38c8a701b780e63dde46a18a77cc40a","artifact:5442:d82ec143d54b882f8b427a82f5afdf2d6057d00c4873762958d16d0507ea6184":"d82ec143d54b882f8b427a82f5afdf2d6057d00c4873762958d16d0507ea6184","artifact:5442:fb9a69d56eef92f0a6816920ac938fe955be4a4c683dd65eb4c8256961b96b71":"fb9a69d56eef92f0a6816920ac938fe955be4a4c683dd65eb4c8256961b96b71"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5442,"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 #5442: 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\":5442,\"report_sha256\":\"c809803682a3e5e5085eef2b1cff55bbed8ca718b92bdabda6563c41cbb01d9d\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5442\":\"0b5eec0504eee5054606502930fd60792bc75a4082a4be6d0bfcb14c4de45917\",\"review:5442:1:claude-opus-5-5\":\"8c26a3b0e29bb53ec28d499b29ff4a13c186e7cbf4b1d84ee58dfedebf86afd0\",\"artifact:5442:040129f5ebe64de61939b6c73df2b2d100ef55eabce97e77d3f59f00b2488a4c\":\"040129f5ebe64de61939b6c73df2b2d100ef55eabce97e77d3f59f00b2488a4c\",\"artifact:5442:3c4dff318136e62e39dae8ce7aaa66fc59afaa25542baf6a3a36748ba1a5e9b4\":\"3c4dff318136e62e39dae8ce7aaa66fc59afaa25542baf6a3a36748ba1a5e9b4\",\"artifact:5442:6a6c30e4311e49079a10578a5e104327e31153f5e9e2beab2dbcfc783d90b3bb\":\"6a6c30e4311e49079a10578a5e104327e31153f5e9e2beab2dbcfc783d90b3bb\",\"artifact:5442:73d651252587d423f06e2c8009b45a02504ce1b02ba96602b7629bfe2f6f41f4\":\"73d651252587d423f06e2c8009b45a02504ce1b02ba96602b7629bfe2f6f41f4\",\"artifact:5442:8629c3fbe0515803b997af97482a86bd6fc579d45be721dee88eeb954a43dd75\":\"8629c3fbe0515803b997af97482a86bd6fc579d45be721dee88eeb954a43dd75\",\"artifact:5442:abffd7cca4b8bfdf960834b33de4e9e952d632200f516dfefecad5ea36b8b222\":\"abffd7cca4b8bfdf960834b33de4e9e952d632200f516dfefecad5ea36b8b222\",\"artifact:5442:b14304faa72eccc3fa560062971e5b9a6ad9ce24175e5f16a6aeaee97331d275\":\"b14304faa72eccc3fa560062971e5b9a6ad9ce24175e5f16a6aeaee97331d275\",\"artifact:5442:b3ed88122bd1705985a210d7f157a70df1e2c5d39e52d628e9230e889dd3590b\":\"b3ed88122bd1705985a210d7f157a70df1e2c5d39e52d628e9230e889dd3590b\",\"artifact:5442:c79a00c0c5cb9bd5eff2f000a4283fb95f97daae82acba8a0497199bca2c7a54\":\"c79a00c0c5cb9bd5eff2f000a4283fb95f97daae82acba8a0497199bca2c7a54\",\"artifact:5442:c809803682a3e5e5085eef2b1cff55bbed8ca718b92bdabda6563c41cbb01d9d\":\"c809803682a3e5e5085eef2b1cff55bbed8ca718b92bdabda6563c41cbb01d9d\",\"artifact:5442:d66b5c157ddac94369892e3de30cbf24d38c8a701b780e63dde46a18a77cc40a\":\"d66b5c157ddac94369892e3de30cbf24d38c8a701b780e63dde46a18a77cc40a\",\"artifact:5442:d82ec143d54b882f8b427a82f5afdf2d6057d00c4873762958d16d0507ea6184\":\"d82ec143d54b882f8b427a82f5afdf2d6057d00c4873762958d16d0507ea6184\",\"artifact:5442:fb9a69d56eef92f0a6816920ac938fe955be4a4c683dd65eb4c8256961b96b71\":\"fb9a69d56eef92f0a6816920ac938fe955be4a4c683dd65eb4c8256961b96b71\"},\"sha256\":\"1505a9370de7010a6b347fd6fed3bfaa58786ccbf5fddcf9477b89f6661dc64e\"},\"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:5442,input_sha256:\"56b089cf8671d881aa2caeb4b84e5c1c3330244e55ce5633af3f914fcdac7426\",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/5482/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"b3e2f9fa5a453007356fca3ccabfccc997b2fde20f34805819b227f4416b8768","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}