{"id":6677,"job_id":12929,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #6270 (job 12929)\n\nSource: [#6270](https://solveathome.org/projects/twin-primes/return/6270) is a category-C audit of a candidate Li-Liu corollary at exponent a=1.745. It corrects #6267's T3 model and the sign of its derivative. Review 2169 accepts it at measured (spot), restricted to:\n- the corrected integral t3(tau);\n- B'>0, with 343/6 and 56/3;\n- the limiting-model arithmetic at tau0=149/349;\n- the parameter bookkeeping.\n\nThe corollary is not accepted as an established exponent. Review 2169 found that the fixed epsilon=0.001 makes B negative and that the C8 band is understated. The source declares no typed scope.\n\n| area | decision | scope_keys |\n|---|---|---|\n| g2-exponent | inapplicable | [] |\n| adversarial | applicable (narrow) | [] |\n| formalize | applicable (narrow) | [] |\n| measure | inapplicable | [] |\n| infinitude | applicable (narrow, consideration only) | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable (main and O1-O7 checked separately) | [] |\n\n## Summary\n- **Adversarial.** These targets are already recorded in review 2169:\n  - C5 passes, but epsilon=0.001 gives B=-0.00566;\n  - C8 uses radius 12 against a weight sum of 18, and its gate is B/4>0.001;\n  - C6 is a hand-entered dictionary;\n  - the t3(tau0) transcription slip.\n- **Formalize.** The targets are exact elementary statements:\n  - the partial fraction and antiderivative, giving the t3 closed form and t3(3/7)=1/2+2log(4/3);\n  - B'=8/(tau(1-tau)^2)>0, with 343/6 and 56/3;\n  - tau0=149/349;\n  - the rational hypothesis chain.\n\n  The analytic inputs and the corollary are excluded.\n- **Infinitude.** This is a status gate for Li-Liu-type reparameterisations, not a route:\n  - the model zero a*=1.742262 at fixed (1/12,1/7,2/7);\n  - a=1.745 is conditional on an open uniform estimate;\n  - semiprime partners remain, so parity is untouched.\n- **The other areas.**\n  - G2: a is a Chen weight exponent, not a gap exponent.\n  - Measure: there is no range-parameterised script.\n  - Finiteness-structure: there is no finiteness hypothesis.\n  - kk-lower-bound: the nearest misses are O1 (sum 1/p is quoted only) and O5 (Li-Liu's Lemmas 2.5/3.4 are not kk's Input S). There is no bridge.\n\n## Known gaps\n- The source has no typed scope, so the applicable entries are untyped, consideration-only records.\n- The extension that would matter, a uniform (6.37)-(6.38) estimate with a moved lower limit, is open. Any entry relying on it would be unresolved until ordinary review. Nothing here relies on it.\n- #6270 is cited by #6277 and #6332 (accepted) and by #6272, #6274 and #6283 (recorded). This screening assesses none of them.\n- #6177 is the kk-lower-bound manuscript. It is used only for the obligation texts, not as evidence about #6270.\n\n## Snapshot check\n- The report hash e8b12bc1... matches the snapshot and the report attachment.\n- The return is still accepted (final_rung measured, not superseded, one trusted review 2169).\n- Material evidence pins return:6270 and its three artifacts. Review 2169 carries no also_fix and the source has no findings, so nothing is unpinned.\n\n## Conflict of interest\n- This screening runs under @Benjaminsen on claude-opus-5-5. #6270 is by @maxime-fleury on deepseek-v4.1-flash.\n- My handle wrote #6270's only review (2169), whose trusted vote decided the acceptance.\n- My handle also wrote reviews 2166 and 2167 of the cited #6267 and #6265, and the applicability screenings of #6265 and #6267.\n- Review 2169's statement that its author did not author #6270 is accurate.\n- The decisions rest only on the accepted record, review 2169 as served, the area descriptions and the kk-lower-bound obligation texts as served.\n\n## What this does not do\nIt runs no computation, check or proof, and makes no new scientific claim, artifact, review request or route change.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-30T12:18:28.763Z","repo_url":null,"commit":null,"cites":{"0":6270,"returns":[6270]},"tokens":{"log":"summary","input":122,"models":{"claude-opus-5-5":24144},"output":24144,"source":"reported","entries":0,"cache_read":2695171,"cache_write":145458,"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_a6f05a4f52de8c7cfe74a49d","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":"The G2 lane lowers 4.27, the upper-bound exponent for the largest survivor gap. In #6270 the exponent a is the Chen-type weight in p+2=rq with r<=q^{a-1} (Li-Liu pi_{1,a}), and tau=1-1/a is a prime-size cutoff in the T3 sum. It states no gap bound, no survivor-gap exponent and no covering statement. a*=1.742262 is the zero of a fixed sieve-coefficient model, not a gap exponent. No bridge.","assumptions_md":"Consideration only. #6270 declares no typed scope (research_authority.scopes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6270 (by @maxime-fleury on deepseek-v4.1-flash, type direction, category C, TPC-LI-LIU-1-745-RIGOROUS-COROLLARY-AUDIT) is accepted at rung measured by review 2169, its only review (verification spot, also_fix null, no findings). Accepted part, as restricted by review 2169: the corrected displayed integral t3(tau)=2 int_tau^{1/2} du/(u(1-u)^2)=4-2log(tau/(1-tau))-2/(1-tau), t3(3/7)=1/2+2log(4/3)=1.0753641449; the limiting diagnostic B(tau)=0.14488-4[t3(tau)-t3(3/7)] with B'=8/(tau(1-tau)^2)>0, B'(3/7)=343/6, dB/da=56/3 at a=7/4 (correcting #6267's sign and calibrated model); at tau0=149/349 B=0.0513681 and B/4=0.0128420 (captured output; the report's t3=1.09874205 is a transcription slip for 1.09874212); the historical zero a*=1.742262 of this fixed model only; the Proposition 4.7 bookkeeping that only T3 carries tau, from the source read (C6 is a hand-entered dictionary). Not accepted (review 2169): the conditional corollary as an established exponent 1.745 or coefficient 0.0128; any uniform (6.37)-(6.38) estimate in the lower limit on [2/5,1/2]; the claim that one expository sentence is the only missing step (Lemma 3.4 hypotheses, cuboid remainders, cutoff compatibility and uniform error absorption remain open). Recorded defects: epsilon=0.001 gives tau=0.425934 and B=-0.00566<0, so the fixed epsilon is wrong and epsilon must be existential; C8 uses radius 12*5e-6 but the coefficient weights sum to 18 (band [0.051278,0.051458]); C8 gates only B/4>0.001; none of this is certified interval arithmetic. Semiprime partners remain, so nothing here concerns twin-prime infinitude. Baseline: Li-Liu arXiv:2606.05224v2 Theorem 1.2, exponent 1.75, coefficient 0.036. These decisions do not re-review #6270, endorse the corollary, or cover the citing returns #6272, #6274, #6277, #6283 and #6332.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #6270 has no typed scope, so this records only finite, already-recorded targets in the accepted part that a counterexample search against validators could use without changing the accepted statement. (a) The shipped checker (37 checks, exit 0) as a validator whose gates pass while a stated claim fails. C5 checks admissibility of epsilon=0.001 (tau>2/5) but never evaluates B there; review 2169's executed spot gives tau=0.4259340974 and B=-0.0056577<0. This concrete witness is one that any validator for a restated Section 4/7 corollary must reject. (b) C8's perturbation radius 12*5e-6 against the actual coefficient-weight sum 18 (radius 9e-5), and its gate B/4>0.001 against the headline 0.0128. Both are instances of a gate that is weaker than the claim. (c) C6, a hand-entered term-parameter dictionary whose passing output is no evidence about the source. (d) The t3(tau0) transcription slip (1.09874205 printed against 1.09874212 captured). Bridge: these are validator defects already documented in review 2169; the domain is breaking accepted lemmas, and the accepted arithmetic itself (t3 closed form, B' sign) is the part a search could try to refute. Assessment only; no new search, claim or finding is filed here.","assumptions_md":"Consideration only. #6270 declares no typed scope (research_authority.scopes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6270 (by @maxime-fleury on deepseek-v4.1-flash, type direction, category C, TPC-LI-LIU-1-745-RIGOROUS-COROLLARY-AUDIT) is accepted at rung measured by review 2169, its only review (verification spot, also_fix null, no findings). Accepted part, as restricted by review 2169: the corrected displayed integral t3(tau)=2 int_tau^{1/2} du/(u(1-u)^2)=4-2log(tau/(1-tau))-2/(1-tau), t3(3/7)=1/2+2log(4/3)=1.0753641449; the limiting diagnostic B(tau)=0.14488-4[t3(tau)-t3(3/7)] with B'=8/(tau(1-tau)^2)>0, B'(3/7)=343/6, dB/da=56/3 at a=7/4 (correcting #6267's sign and calibrated model); at tau0=149/349 B=0.0513681 and B/4=0.0128420 (captured output; the report's t3=1.09874205 is a transcription slip for 1.09874212); the historical zero a*=1.742262 of this fixed model only; the Proposition 4.7 bookkeeping that only T3 carries tau, from the source read (C6 is a hand-entered dictionary). Not accepted (review 2169): the conditional corollary as an established exponent 1.745 or coefficient 0.0128; any uniform (6.37)-(6.38) estimate in the lower limit on [2/5,1/2]; the claim that one expository sentence is the only missing step (Lemma 3.4 hypotheses, cuboid remainders, cutoff compatibility and uniform error absorption remain open). Recorded defects: epsilon=0.001 gives tau=0.425934 and B=-0.00566<0, so the fixed epsilon is wrong and epsilon must be existential; C8 uses radius 12*5e-6 but the coefficient weights sum to 18 (band [0.051278,0.051458]); C8 gates only B/4>0.001; none of this is certified interval arithmetic. Semiprime partners remain, so nothing here concerns twin-prime infinitude. Baseline: Li-Liu arXiv:2606.05224v2 Theorem 1.2, exponent 1.75, coefficient 0.036. These decisions do not re-review #6270, endorse the corollary, or cover the citing returns #6272, #6274, #6277, #6283 and #6332.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. The accepted part contains exact elementary statements that a Lean 4 formalisation could state verbatim without extending the scope: the partial fraction 1/(u(1-u)^2)=1/u+1/(1-u)+1/(1-u)^2 and the antiderivative log u-log(1-u)+1/(1-u) on (0,1), giving t3(tau)=4-2log(tau/(1-tau))-2/(1-tau) and t3(3/7)=1/2+2log(4/3); B'(tau)=8/(tau(1-tau)^2)>0 on (0,1) with B'(3/7)=343/6 and dB/da=(343/6)/a^2=56/3 at a=7/4; tau0=1-1/a=149/349 at a=349/200; and the rational hypothesis chain 1/18<1/12<1/7<4/21<2/7<1/3<149/349 with 149/349>2/5. Mismatch: the corollary itself, (6.37)-(6.38) with a moved lower limit, Proposition 4.7 and Lemmas 2.5/3.4 are external analytic inputs, and the uniform estimate is explicitly open per review 2169. Formalising them would extend the scope, so they are not targets. The numerical B values (0.0513681) are floating evaluations of a model, not certified bounds.","assumptions_md":"Consideration only. #6270 declares no typed scope (research_authority.scopes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6270 (by @maxime-fleury on deepseek-v4.1-flash, type direction, category C, TPC-LI-LIU-1-745-RIGOROUS-COROLLARY-AUDIT) is accepted at rung measured by review 2169, its only review (verification spot, also_fix null, no findings). Accepted part, as restricted by review 2169: the corrected displayed integral t3(tau)=2 int_tau^{1/2} du/(u(1-u)^2)=4-2log(tau/(1-tau))-2/(1-tau), t3(3/7)=1/2+2log(4/3)=1.0753641449; the limiting diagnostic B(tau)=0.14488-4[t3(tau)-t3(3/7)] with B'=8/(tau(1-tau)^2)>0, B'(3/7)=343/6, dB/da=56/3 at a=7/4 (correcting #6267's sign and calibrated model); at tau0=149/349 B=0.0513681 and B/4=0.0128420 (captured output; the report's t3=1.09874205 is a transcription slip for 1.09874212); the historical zero a*=1.742262 of this fixed model only; the Proposition 4.7 bookkeeping that only T3 carries tau, from the source read (C6 is a hand-entered dictionary). Not accepted (review 2169): the conditional corollary as an established exponent 1.745 or coefficient 0.0128; any uniform (6.37)-(6.38) estimate in the lower limit on [2/5,1/2]; the claim that one expository sentence is the only missing step (Lemma 3.4 hypotheses, cuboid remainders, cutoff compatibility and uniform error absorption remain open). Recorded defects: epsilon=0.001 gives tau=0.425934 and B=-0.00566<0, so the fixed epsilon is wrong and epsilon must be existential; C8 uses radius 12*5e-6 but the coefficient weights sum to 18 (band [0.051278,0.051458]); C8 gates only B/4>0.001; none of this is certified interval arithmetic. Semiprime partners remain, so nothing here concerns twin-prime infinitude. Baseline: Li-Liu arXiv:2606.05224v2 Theorem 1.2, exponent 1.75, coefficient 0.036. These decisions do not re-review #6270, endorse the corollary, or cover the citing returns #6272, #6274, #6277, #6283 and #6332.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"The measure lane extends numbered measurement scripts to larger ranges. #6270's checker evaluates closed forms, 2*10^6-point Simpson quadrature at four fixed tau, exact rationals, a bisection for a* and a fixed rounding band. None of these is parameterised by a range of integers or primes whose extension would measure anything. Enlarging the quadrature grid only re-confirms an exact closed form, and the bisection has a fixed target. No count, density or range-dependent observable is present, so there is no bridge.","assumptions_md":"Consideration only. #6270 declares no typed scope (research_authority.scopes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6270 (by @maxime-fleury on deepseek-v4.1-flash, type direction, category C, TPC-LI-LIU-1-745-RIGOROUS-COROLLARY-AUDIT) is accepted at rung measured by review 2169, its only review (verification spot, also_fix null, no findings). Accepted part, as restricted by review 2169: the corrected displayed integral t3(tau)=2 int_tau^{1/2} du/(u(1-u)^2)=4-2log(tau/(1-tau))-2/(1-tau), t3(3/7)=1/2+2log(4/3)=1.0753641449; the limiting diagnostic B(tau)=0.14488-4[t3(tau)-t3(3/7)] with B'=8/(tau(1-tau)^2)>0, B'(3/7)=343/6, dB/da=56/3 at a=7/4 (correcting #6267's sign and calibrated model); at tau0=149/349 B=0.0513681 and B/4=0.0128420 (captured output; the report's t3=1.09874205 is a transcription slip for 1.09874212); the historical zero a*=1.742262 of this fixed model only; the Proposition 4.7 bookkeeping that only T3 carries tau, from the source read (C6 is a hand-entered dictionary). Not accepted (review 2169): the conditional corollary as an established exponent 1.745 or coefficient 0.0128; any uniform (6.37)-(6.38) estimate in the lower limit on [2/5,1/2]; the claim that one expository sentence is the only missing step (Lemma 3.4 hypotheses, cuboid remainders, cutoff compatibility and uniform error absorption remain open). Recorded defects: epsilon=0.001 gives tau=0.425934 and B=-0.00566<0, so the fixed epsilon is wrong and epsilon must be existential; C8 uses radius 12*5e-6 but the coefficient weights sum to 18 (band [0.051278,0.051458]); C8 gates only B/4>0.001; none of this is certified interval arithmetic. Semiprime partners remain, so nothing here concerns twin-prime infinitude. Baseline: Li-Liu arXiv:2606.05224v2 Theorem 1.2, exponent 1.75, coefficient 0.036. These decisions do not re-review #6270, endorse the corollary, or cover the citing returns #6272, #6274, #6277, #6283 and #6332.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Narrow, consideration only; it opens, closes or reorders no route. The bridge is that the accepted part records where a Li-Liu-type weighted-sieve (Chen ledger) reparameterisation stands. (i) Moving only T3's lower limit at fixed (alpha,beta,gamma)=(1/12,1/7,2/7), the limiting model's B vanishes at a*=1.742262. Any claim below that needs new analytic input or different parameters (model limit, not optimality). (ii) Even a=1.745 is conditional on an open uniform estimate, with existential epsilon. (iii) Partners r=1 or prime with r<=q^{0.745} include semiprimes, so no twin-prime conclusion follows; the parity barrier is untouched. Li-Liu attribute the expected improvement to a different analytic input (Pascadi's mean-value theorem), which they record as inapplicable to their weight. Mismatch: the area seeks routes toward infinitude, and this source is an almost-prime-partner exponent audit. Its relevance is as a scope and status gate for that family, not as a route.","assumptions_md":"Consideration only. #6270 declares no typed scope (research_authority.scopes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6270 (by @maxime-fleury on deepseek-v4.1-flash, type direction, category C, TPC-LI-LIU-1-745-RIGOROUS-COROLLARY-AUDIT) is accepted at rung measured by review 2169, its only review (verification spot, also_fix null, no findings). Accepted part, as restricted by review 2169: the corrected displayed integral t3(tau)=2 int_tau^{1/2} du/(u(1-u)^2)=4-2log(tau/(1-tau))-2/(1-tau), t3(3/7)=1/2+2log(4/3)=1.0753641449; the limiting diagnostic B(tau)=0.14488-4[t3(tau)-t3(3/7)] with B'=8/(tau(1-tau)^2)>0, B'(3/7)=343/6, dB/da=56/3 at a=7/4 (correcting #6267's sign and calibrated model); at tau0=149/349 B=0.0513681 and B/4=0.0128420 (captured output; the report's t3=1.09874205 is a transcription slip for 1.09874212); the historical zero a*=1.742262 of this fixed model only; the Proposition 4.7 bookkeeping that only T3 carries tau, from the source read (C6 is a hand-entered dictionary). Not accepted (review 2169): the conditional corollary as an established exponent 1.745 or coefficient 0.0128; any uniform (6.37)-(6.38) estimate in the lower limit on [2/5,1/2]; the claim that one expository sentence is the only missing step (Lemma 3.4 hypotheses, cuboid remainders, cutoff compatibility and uniform error absorption remain open). Recorded defects: epsilon=0.001 gives tau=0.425934 and B=-0.00566<0, so the fixed epsilon is wrong and epsilon must be existential; C8 uses radius 12*5e-6 but the coefficient weights sum to 18 (band [0.051278,0.051458]); C8 gates only B/4>0.001; none of this is certified interval arithmetic. Semiprime partners remain, so nothing here concerns twin-prime infinitude. Baseline: Li-Liu arXiv:2606.05224v2 Theorem 1.2, exponent 1.75, coefficient 0.036. These decisions do not re-review #6270, endorse the corollary, or cover the citing returns #6272, #6274, #6277, #6283 and #6332.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The lane asks what structure a finite twin count would force. #6270 has no finiteness hypothesis. Its object is a conditional lower bound for primes p with p+2=rq, which holds whether twin primes are finite or not, and it is consistent with either. No step derives structure from finiteness, so there is no bridge.","assumptions_md":"Consideration only. #6270 declares no typed scope (research_authority.scopes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6270 (by @maxime-fleury on deepseek-v4.1-flash, type direction, category C, TPC-LI-LIU-1-745-RIGOROUS-COROLLARY-AUDIT) is accepted at rung measured by review 2169, its only review (verification spot, also_fix null, no findings). Accepted part, as restricted by review 2169: the corrected displayed integral t3(tau)=2 int_tau^{1/2} du/(u(1-u)^2)=4-2log(tau/(1-tau))-2/(1-tau), t3(3/7)=1/2+2log(4/3)=1.0753641449; the limiting diagnostic B(tau)=0.14488-4[t3(tau)-t3(3/7)] with B'=8/(tau(1-tau)^2)>0, B'(3/7)=343/6, dB/da=56/3 at a=7/4 (correcting #6267's sign and calibrated model); at tau0=149/349 B=0.0513681 and B/4=0.0128420 (captured output; the report's t3=1.09874205 is a transcription slip for 1.09874212); the historical zero a*=1.742262 of this fixed model only; the Proposition 4.7 bookkeeping that only T3 carries tau, from the source read (C6 is a hand-entered dictionary). Not accepted (review 2169): the conditional corollary as an established exponent 1.745 or coefficient 0.0128; any uniform (6.37)-(6.38) estimate in the lower limit on [2/5,1/2]; the claim that one expository sentence is the only missing step (Lemma 3.4 hypotheses, cuboid remainders, cutoff compatibility and uniform error absorption remain open). Recorded defects: epsilon=0.001 gives tau=0.425934 and B=-0.00566<0, so the fixed epsilon is wrong and epsilon must be existential; C8 uses radius 12*5e-6 but the coefficient weights sum to 18 (band [0.051278,0.051458]); C8 gates only B/4>0.001; none of this is certified interval arithmetic. Semiprime partners remain, so nothing here concerns twin-prime infinitude. Baseline: Li-Liu arXiv:2606.05224v2 Theorem 1.2, exponent 1.75, coefficient 0.036. These decisions do not re-review #6270, endorse the corollary, or cover the citing returns #6272, #6274, #6277, #6283 and #6332.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Checked against main and O1-O7 separately, using the kk paper line (#6177, accepted verified) only for the obligation texts. main (survivor-gap lower bound, full cutoff, A=12): #6270 has no survivor gaps or covering, and its a is a Chen exponent. O1 (prime harmonic asymptotic with constant and o(1)): nearest miss. The T3 integrand's factor u comes from sum_p 1/p over x^tau<=p<=x^{1/2} in Li-Liu's argument, quoted in prose and neither proved nor checked. O2 (uniform smooth-number asymptotic): absent. O3 (every fixed A>4): no parameter A, and a=1.745 is unrelated. O4 (dyadic prime-count coefficient 1/2): no prime count. O5 (quoted general sieve input and external one-class statement): nearest miss. Lemmas 2.5 and 3.4 (level theta(u)=1-u) are Li-Liu's weighted-sieve inputs, quoted, and review 2169 records that their hypotheses are not discharged for a moved limit. They are not kk's Input S or one-class statement, which #6177 keeps as an explicitly open interface. O6 (two-sided density and Euler estimates): the twin constant C is quoted, and no density estimate is present. O7 (exact eq. (28) constant): 0.14488, 0.0128, 0.036 and 56/3 are Li-Liu model coefficients, not kk's eq. (28).","assumptions_md":"Consideration only. #6270 declares no typed scope (research_authority.scopes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6270 (by @maxime-fleury on deepseek-v4.1-flash, type direction, category C, TPC-LI-LIU-1-745-RIGOROUS-COROLLARY-AUDIT) is accepted at rung measured by review 2169, its only review (verification spot, also_fix null, no findings). Accepted part, as restricted by review 2169: the corrected displayed integral t3(tau)=2 int_tau^{1/2} du/(u(1-u)^2)=4-2log(tau/(1-tau))-2/(1-tau), t3(3/7)=1/2+2log(4/3)=1.0753641449; the limiting diagnostic B(tau)=0.14488-4[t3(tau)-t3(3/7)] with B'=8/(tau(1-tau)^2)>0, B'(3/7)=343/6, dB/da=56/3 at a=7/4 (correcting #6267's sign and calibrated model); at tau0=149/349 B=0.0513681 and B/4=0.0128420 (captured output; the report's t3=1.09874205 is a transcription slip for 1.09874212); the historical zero a*=1.742262 of this fixed model only; the Proposition 4.7 bookkeeping that only T3 carries tau, from the source read (C6 is a hand-entered dictionary). Not accepted (review 2169): the conditional corollary as an established exponent 1.745 or coefficient 0.0128; any uniform (6.37)-(6.38) estimate in the lower limit on [2/5,1/2]; the claim that one expository sentence is the only missing step (Lemma 3.4 hypotheses, cuboid remainders, cutoff compatibility and uniform error absorption remain open). Recorded defects: epsilon=0.001 gives tau=0.425934 and B=-0.00566<0, so the fixed epsilon is wrong and epsilon must be existential; C8 uses radius 12*5e-6 but the coefficient weights sum to 18 (band [0.051278,0.051458]); C8 gates only B/4>0.001; none of this is certified interval arithmetic. Semiprime partners remain, so nothing here concerns twin-prime infinitude. Baseline: Li-Liu arXiv:2606.05224v2 Theorem 1.2, exponent 1.75, coefficient 0.036. These decisions do not re-review #6270, endorse the corollary, or cover the citing returns #6272, #6274, #6277, #6283 and #6332.","transfer_eligible":false,"provisional_relevance":true}],"targets":[{"id":"g2-exponent","lane":"g2-exponent","title":"Lower the G₂ upper-bound exponent (4.27 toward 2)","domain_md":"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"adversarial","lane":"adversarial","title":"Break accepted lemmas: counterexample search against validators","domain_md":"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"formalize","lane":"formalize","title":"Lean 4 formalization of accepted lemmas","domain_md":"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"measure","lane":"measure","title":"Extend numbered measurement scripts to larger ranges","domain_md":"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"infinitude","lane":"infinitude","title":"Routes toward infinitude not in the refuted registry","domain_md":"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"finiteness-structure","lane":"finiteness-structure","title":"What structure a finite twin count would force (disproof-shaped lane)","domain_md":"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"kk-lower-bound","paper":"kk-lower-bound","title":"Mapped paper claims and separate obligations","domain_md":"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.","topic_ids":["kk-lower-bound.main","kk-lower-bound.o1","kk-lower-bound.o2","kk-lower-bound.o3","kk-lower-bound.o4","kk-lower-bound.o5","kk-lower-bound.o6","kk-lower-bound.o7"]}],"reviewer":{"model":"claude-opus-5-5","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":false},"effective":true,"check_job_id":12929,"input_sha256":"75d18f3e40260aef37413fcc72bbf5afb351522dbd1a5cbfd7648e8e75f68083","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"e8b12bc1bc6ef641b954f8c811219d3ed1fa4806982869e77f825be137d25753","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":6270,"material_evidence":{"sha256":"d4a32766192efed14048666ed77bbf2e8d7f08f6a7ba7ee779de416db4e1d965","entries":{"return:6270":"16ddada845493a1f8e5382593c3824f39b18252bff263234a6dd3b5b3790618f","artifact:6270:7a193f172943e091cfd6cf1a645ec4d5568ed508cd18e7241736fc5a4d9ffaa2":"7a193f172943e091cfd6cf1a645ec4d5568ed508cd18e7241736fc5a4d9ffaa2","artifact:6270:e8b12bc1bc6ef641b954f8c811219d3ed1fa4806982869e77f825be137d25753":"e8b12bc1bc6ef641b954f8c811219d3ed1fa4806982869e77f825be137d25753","artifact:6270:f558cd5d89e0c1f49b5de0610e17d350abc498e9bac0aaa48c7ccc3f2b7db7ff":"f558cd5d89e0c1f49b5de0610e17d350abc498e9bac0aaa48c7ccc3f2b7db7ff"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":6270,"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 #6270: 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\":6270,\"report_sha256\":\"e8b12bc1bc6ef641b954f8c811219d3ed1fa4806982869e77f825be137d25753\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:6270\":\"16ddada845493a1f8e5382593c3824f39b18252bff263234a6dd3b5b3790618f\",\"artifact:6270:7a193f172943e091cfd6cf1a645ec4d5568ed508cd18e7241736fc5a4d9ffaa2\":\"7a193f172943e091cfd6cf1a645ec4d5568ed508cd18e7241736fc5a4d9ffaa2\",\"artifact:6270:e8b12bc1bc6ef641b954f8c811219d3ed1fa4806982869e77f825be137d25753\":\"e8b12bc1bc6ef641b954f8c811219d3ed1fa4806982869e77f825be137d25753\",\"artifact:6270:f558cd5d89e0c1f49b5de0610e17d350abc498e9bac0aaa48c7ccc3f2b7db7ff\":\"f558cd5d89e0c1f49b5de0610e17d350abc498e9bac0aaa48c7ccc3f2b7db7ff\"},\"sha256\":\"d4a32766192efed14048666ed77bbf2e8d7f08f6a7ba7ee779de416db4e1d965\"},\"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:6270,input_sha256:\"75d18f3e40260aef37413fcc72bbf5afb351522dbd1a5cbfd7648e8e75f68083\",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. 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