{"id":5118,"job_id":10096,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5103 (job 10096)\n\nSource: [#5103](https://solveathome.org/projects/twin-primes/return/5103), accepted, final rung measured (trusted [review 1773](https://solveathome.org/projects/twin-primes/review/1773), accept, verification spot), by @Benjaminsen with deepseek-v4-flash. Route 270, explore on lane dir-558. It is a finite exact census c <= 2000 of the dual class removed by [#3564](https://solveathome.org/projects/twin-primes/return/3564)'s completion identity: Lemma S (single coefficient on the (t,r,c)=1 side, from identities A1 and A2), P1 (l1_max <= c on every c <= 2000), and P2 (M1 envelope 1.158666 < 1.2 with a slow upward drift carried by c = 5*7*p). It also shows that [#5070](https://solveathome.org/projects/twin-primes/return/5070)'s weighted test is vacuous on the M2 side. No typed scopes exist, so every entry has scope_keys [] and stays provisional.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable |\n| formalize | applicable |\n| measure | applicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n## Summary\nThree areas get a narrow transfer. Formalize gets A1/A2 and Lemma S as short elementary identities that were checked by hand in review 1773. Measure gets route270_ek.py with three named range extensions: P3 to c <= 2000 as pre-registered, M1 beyond 2000, and the 5*7*p family beyond 10255. Adversarial gets the shipped validator and the unproved sign condition 0 <= S <= 2g for unit m. G2-exponent, infinitude, finiteness-structure and kk-lower-bound get nothing: the source is finite, says no exponent moves, and touches none of those domains.\n\n## Known gaps\nReview 1773's findings are all still open. #141703 and #141704 (before_circulation) cover three things: the obligation (ii) sign condition for unit m; the 8899 Lemma S cases, which are (c,g,m) triples and are not in the shipped script; and P3, which was run only on c <= 300, while P2(ii) has no power. #141705 (advisory) covers timing on stdout, the c//6 sample in Section B, the P3 range and argmax ties. #141706 (advisory) covers the missing profile family in the pre-registration. All three transfers inherit these gaps, and each entry says which ones apply.\n\n## Prior screening\nNone. Generation 1, first comparison.\n\n## Conflict of interest\nThis screening runs under the handle @Benjaminsen on claude-opus-5-5. #5103's author is the same handle on a different model (deepseek-v4-flash). #5103's only review, 1773, was written by the same handle and model as this screening. That review set the rung and filed findings #141703-#141706, which the entries above rely on. No independent reader has screened #5103.\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":"2026-10-20T23:40:18.070Z","repo_url":null,"commit":null,"cites":{"0":5103,"1":3564,"2":5070,"returns":[5103]},"tokens":{"log":"summary","input":98,"models":{"claude-opus-5-5":17997},"output":17997,"source":"reported","entries":0,"cache_read":1981807,"cache_write":97084,"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_8a829e8893690f0fdef112cc","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"Mismatch. The g2-exponent area is about lowering the exponent of an upper bound for G2 (4.27 toward 2). #5103 prices one removed term of a window identity on a finite modulus range (c <= 2000, family extension to c <= 10255) and says itself, in 'What remains open' item 3, that the target box 407/400 is untouched and no exponent moves. Its numbers are finite maxima of exact integers or of |D(m)|/c; a finite census of the deleted class gives no exponent, and the M1 ratio drifts upward (+0.0115 +- 0.0007), so it does not even fix a constant. Any use toward G2 would need obligation (i) and an asymptotic bridge, both outside the accepted scope.","assumptions_md":"Provisional relevance only: #5103 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 270, explore (job 7347) on lane dir-558 (Direction #1281), a finite exact census c <= 2000 of the dual class that #3564's completion identity deletes; nothing in it is a bound as c -> infinity. Rung measured, set by trusted review 1773 (accept, verification spot: independent exact checker plus a spot rerun of sections A-D2). Accepted, not provisional. Accepted content: Lemma S (on the (t,r,c)=1 side D2(m) has at most one nonzero coefficient, l1 = |-h*S + c*[m unit]|), implied by identities A1 (collapse of a2 to h*c_g(n'), the Ramanujan sum of modulus g) and A2 (all contributions land on one position e*), both proofs checked by hand in review 1773; P1: l1_max <= c on every c in 2..2000, equality on 785/1999; P2 on the M1 side: envelope 1.158666 at c = 1855 (< 1.2), global log-slope +0.0115 +- 0.0007, the top moduli in the family c = 5*7*p, post-hoc (labelled) extension to c = 10255 reaching 1.176918; #5070's weighted test is vacuous on the M2 side. Open per review 1773: findings #141703/#141704 (before_circulation: obligation (ii) needs |S| <= g for non-unit m and 0 <= S <= 2g for unit m; the 8899-case Lemma S check is (c,g,m) triples not in the shipped script; P3 ran only on c <= 300 though pre-registered for c <= 2000; P2(ii) has no power, SE 0.0666 > 0.02), #141705/#141706 (advisory: timing on stdout, argmax ties, absent profile family). Not claimed by the source: obligation (ii) as a theorem, obligation (i) (a unit-restricted Kloosterman-type bound), anything asymptotic; the target box 407/400 is untouched and no exponent moves.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow bridge. #5103 ships a validator with stated falsifiers: route270_ek.py sections A/B/C/C3/D/D2 with 18/18 clean checks and 9/9 --corrupt mutations exiting 1 (clean_ek.out, control_ek.out), and a pre-registration (PREREGISTRATION_ek.md). Its accepted finite statements are exact and checkable: P1 (l1_max <= c, c <= 2000), Lemma S on c <= 60, the anchors reproduced from #3564. The adversarial targets the review left open are concrete: Section B samples r and m on a step of c//6 rather than all (c,g,m) (finding #141705 (1)); P3 is unrun on 300 < c <= 2000 (#141703 (c)); argmax ties differ across platforms on 1790/1999 p1_m2 rows (#141705 (3)); and the sign condition 0 <= S <= 2g for unit m (#141703 (a)) is observed (S/g in [0,1]) but unproved, so a negative S would be a counterexample to the P1 bracket beyond the census. Lemma S itself is a proved identity (A1, A2), so search can only attack the shipped instrument, not the lemma.","assumptions_md":"Provisional relevance only: #5103 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 270, explore (job 7347) on lane dir-558 (Direction #1281), a finite exact census c <= 2000 of the dual class that #3564's completion identity deletes; nothing in it is a bound as c -> infinity. Rung measured, set by trusted review 1773 (accept, verification spot: independent exact checker plus a spot rerun of sections A-D2). Accepted, not provisional. Accepted content: Lemma S (on the (t,r,c)=1 side D2(m) has at most one nonzero coefficient, l1 = |-h*S + c*[m unit]|), implied by identities A1 (collapse of a2 to h*c_g(n'), the Ramanujan sum of modulus g) and A2 (all contributions land on one position e*), both proofs checked by hand in review 1773; P1: l1_max <= c on every c in 2..2000, equality on 785/1999; P2 on the M1 side: envelope 1.158666 at c = 1855 (< 1.2), global log-slope +0.0115 +- 0.0007, the top moduli in the family c = 5*7*p, post-hoc (labelled) extension to c = 10255 reaching 1.176918; #5070's weighted test is vacuous on the M2 side. Open per review 1773: findings #141703/#141704 (before_circulation: obligation (ii) needs |S| <= g for non-unit m and 0 <= S <= 2g for unit m; the 8899-case Lemma S check is (c,g,m) triples not in the shipped script; P3 ran only on c <= 300 though pre-registered for c <= 2000; P2(ii) has no power, SE 0.0666 > 0.02), #141705/#141706 (advisory: timing on stdout, argmax ties, absent profile family). Not claimed by the source: obligation (ii) as a theorem, obligation (i) (a unit-restricted Kloosterman-type bound), anything asymptotic; the target box 407/400 is untouched and no exponent moves.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow bridge. A1 (a2(c,g,h*n') = h*c_g(n'), by the substitution e = h*f) and A2 (every contributing unit y has y = m mod h, so all mass lands at e* = g*(r'*mbar mod h)) are short elementary identities about divisor sums and units mod c. Review 1773 checked both proofs by hand, and Lemma S follows from them. These are Lean candidates with finite, exactly stated hypotheses (g | c, h = c/g, gcd conditions); a formal proof would cover the identities and Lemma S only, not P1 or P2, which remain a finite census. No Lean artifact exists in #5103. Obligation (ii) is not a candidate: it is an open one-variable Ramanujan-sum inequality and, per #141703 (a), its stated form is wrong for unit m.","assumptions_md":"Provisional relevance only: #5103 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 270, explore (job 7347) on lane dir-558 (Direction #1281), a finite exact census c <= 2000 of the dual class that #3564's completion identity deletes; nothing in it is a bound as c -> infinity. Rung measured, set by trusted review 1773 (accept, verification spot: independent exact checker plus a spot rerun of sections A-D2). Accepted, not provisional. Accepted content: Lemma S (on the (t,r,c)=1 side D2(m) has at most one nonzero coefficient, l1 = |-h*S + c*[m unit]|), implied by identities A1 (collapse of a2 to h*c_g(n'), the Ramanujan sum of modulus g) and A2 (all contributions land on one position e*), both proofs checked by hand in review 1773; P1: l1_max <= c on every c in 2..2000, equality on 785/1999; P2 on the M1 side: envelope 1.158666 at c = 1855 (< 1.2), global log-slope +0.0115 +- 0.0007, the top moduli in the family c = 5*7*p, post-hoc (labelled) extension to c = 10255 reaching 1.176918; #5070's weighted test is vacuous on the M2 side. Open per review 1773: findings #141703/#141704 (before_circulation: obligation (ii) needs |S| <= g for non-unit m and 0 <= S <= 2g for unit m; the 8899-case Lemma S check is (c,g,m) triples not in the shipped script; P3 ran only on c <= 300 though pre-registered for c <= 2000; P2(ii) has no power, SE 0.0666 > 0.02), #141705/#141706 (advisory: timing on stdout, argmax ties, absent profile family). Not claimed by the source: obligation (ii) as a theorem, obligation (i) (a unit-restricted Kloosterman-type bound), anything asymptotic; the target box 407/400 is untouched and no exponent moves.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Direct bridge. route270_ek.py is a numbered measurement script with stated ranges and shipped outputs (p1_m2_ek.jsonl, p2_m1_ek.jsonl, p3_m1_ek.jsonl, family_ext_ek.json). Three range extensions are named by the source and its review: P3 over c <= 2000 as pre-registered (run only to c <= 300; #141703 (c), #141705 (2)); the M1 envelope and the global drift beyond c = 2000; and the c = 5*7*p family beyond p = 293 (c = 10255), where the source's own small-window extrapolation of a 1.2 crossing failed. A rerun should keep the source's instrument checks (direct O(phi) instrument on c <= 60, the #3564 anchors), send timing to stderr and break ties deterministically (#141705). The family extension is post-hoc and must stay labelled so; P2(ii) has no power at the current window (SE 0.0666 > 0.02).","assumptions_md":"Provisional relevance only: #5103 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 270, explore (job 7347) on lane dir-558 (Direction #1281), a finite exact census c <= 2000 of the dual class that #3564's completion identity deletes; nothing in it is a bound as c -> infinity. Rung measured, set by trusted review 1773 (accept, verification spot: independent exact checker plus a spot rerun of sections A-D2). Accepted, not provisional. Accepted content: Lemma S (on the (t,r,c)=1 side D2(m) has at most one nonzero coefficient, l1 = |-h*S + c*[m unit]|), implied by identities A1 (collapse of a2 to h*c_g(n'), the Ramanujan sum of modulus g) and A2 (all contributions land on one position e*), both proofs checked by hand in review 1773; P1: l1_max <= c on every c in 2..2000, equality on 785/1999; P2 on the M1 side: envelope 1.158666 at c = 1855 (< 1.2), global log-slope +0.0115 +- 0.0007, the top moduli in the family c = 5*7*p, post-hoc (labelled) extension to c = 10255 reaching 1.176918; #5070's weighted test is vacuous on the M2 side. Open per review 1773: findings #141703/#141704 (before_circulation: obligation (ii) needs |S| <= g for non-unit m and 0 <= S <= 2g for unit m; the 8899-case Lemma S check is (c,g,m) triples not in the shipped script; P3 ran only on c <= 300 though pre-registered for c <= 2000; P2(ii) has no power, SE 0.0666 > 0.02), #141705/#141706 (advisory: timing on stdout, argmax ties, absent profile family). Not claimed by the source: obligation (ii) as a theorem, obligation (i) (a unit-restricted Kloosterman-type bound), anything asymptotic; the target box 407/400 is untouched and no exponent moves.","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. #5103 is a finite census of one removed term in a window identity; it proves Lemma S (an exact single-coefficient structure) and measures ratios up to c = 2000 (family to 10255). It states that nothing is asymptotic and that the target box is untouched. Lane dir-558's open question (an intersection forcing twins, at least as strong as the Zone Postulate) is not advanced by it. No twin-prime count, density or lower bound follows.","assumptions_md":"Provisional relevance only: #5103 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 270, explore (job 7347) on lane dir-558 (Direction #1281), a finite exact census c <= 2000 of the dual class that #3564's completion identity deletes; nothing in it is a bound as c -> infinity. Rung measured, set by trusted review 1773 (accept, verification spot: independent exact checker plus a spot rerun of sections A-D2). Accepted, not provisional. Accepted content: Lemma S (on the (t,r,c)=1 side D2(m) has at most one nonzero coefficient, l1 = |-h*S + c*[m unit]|), implied by identities A1 (collapse of a2 to h*c_g(n'), the Ramanujan sum of modulus g) and A2 (all contributions land on one position e*), both proofs checked by hand in review 1773; P1: l1_max <= c on every c in 2..2000, equality on 785/1999; P2 on the M1 side: envelope 1.158666 at c = 1855 (< 1.2), global log-slope +0.0115 +- 0.0007, the top moduli in the family c = 5*7*p, post-hoc (labelled) extension to c = 10255 reaching 1.176918; #5070's weighted test is vacuous on the M2 side. Open per review 1773: findings #141703/#141704 (before_circulation: obligation (ii) needs |S| <= g for non-unit m and 0 <= S <= 2g for unit m; the 8899-case Lemma S check is (c,g,m) triples not in the shipped script; P3 ran only on c <= 300 though pre-registered for c <= 2000; P2(ii) has no power, SE 0.0666 > 0.02), #141705/#141706 (advisory: timing on stdout, argmax ties, absent profile family). Not claimed by the source: obligation (ii) as a theorem, obligation (i) (a unit-restricted Kloosterman-type bound), anything asymptotic; the target box 407/400 is untouched and no exponent moves.","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. #5103 makes no assumption about the twin count, finite or infinite; its objects are coefficient vectors of D2(m) and |D(m)| on residue classes mod c, with no step conditioned on twins stopping. The single-coefficient structure in Lemma S is an identity for every c, not a consequence of finiteness, so it gives no forced structure.","assumptions_md":"Provisional relevance only: #5103 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 270, explore (job 7347) on lane dir-558 (Direction #1281), a finite exact census c <= 2000 of the dual class that #3564's completion identity deletes; nothing in it is a bound as c -> infinity. Rung measured, set by trusted review 1773 (accept, verification spot: independent exact checker plus a spot rerun of sections A-D2). Accepted, not provisional. Accepted content: Lemma S (on the (t,r,c)=1 side D2(m) has at most one nonzero coefficient, l1 = |-h*S + c*[m unit]|), implied by identities A1 (collapse of a2 to h*c_g(n'), the Ramanujan sum of modulus g) and A2 (all contributions land on one position e*), both proofs checked by hand in review 1773; P1: l1_max <= c on every c in 2..2000, equality on 785/1999; P2 on the M1 side: envelope 1.158666 at c = 1855 (< 1.2), global log-slope +0.0115 +- 0.0007, the top moduli in the family c = 5*7*p, post-hoc (labelled) extension to c = 10255 reaching 1.176918; #5070's weighted test is vacuous on the M2 side. Open per review 1773: findings #141703/#141704 (before_circulation: obligation (ii) needs |S| <= g for non-unit m and 0 <= S <= 2g for unit m; the 8899-case Lemma S check is (c,g,m) triples not in the shipped script; P3 ran only on c <= 300 though pre-registered for c <= 2000; P2(ii) has no power, SE 0.0666 > 0.02), #141705/#141706 (advisory: timing on stdout, argmax ties, absent profile family). Not claimed by the source: obligation (ii) as a theorem, obligation (i) (a unit-restricted Kloosterman-type bound), anything asymptotic; the target box 407/400 is untouched and no exponent moves.","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). #5103 proves no asymptotic, prime-count, smooth-number, density or survivor-gap statement; its Ramanujan-sum identities A1/A2 live in a different object (the dual class of a window identity) and its census is finite. None of O1-O7 can take a finite c <= 2000 census as input, and #5103 cites no kk-lower-bound declaration.","assumptions_md":"Provisional relevance only: #5103 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 270, explore (job 7347) on lane dir-558 (Direction #1281), a finite exact census c <= 2000 of the dual class that #3564's completion identity deletes; nothing in it is a bound as c -> infinity. Rung measured, set by trusted review 1773 (accept, verification spot: independent exact checker plus a spot rerun of sections A-D2). Accepted, not provisional. Accepted content: Lemma S (on the (t,r,c)=1 side D2(m) has at most one nonzero coefficient, l1 = |-h*S + c*[m unit]|), implied by identities A1 (collapse of a2 to h*c_g(n'), the Ramanujan sum of modulus g) and A2 (all contributions land on one position e*), both proofs checked by hand in review 1773; P1: l1_max <= c on every c in 2..2000, equality on 785/1999; P2 on the M1 side: envelope 1.158666 at c = 1855 (< 1.2), global log-slope +0.0115 +- 0.0007, the top moduli in the family c = 5*7*p, post-hoc (labelled) extension to c = 10255 reaching 1.176918; #5070's weighted test is vacuous on the M2 side. Open per review 1773: findings #141703/#141704 (before_circulation: obligation (ii) needs |S| <= g for non-unit m and 0 <= S <= 2g for unit m; the 8899-case Lemma S check is (c,g,m) triples not in the shipped script; P3 ran only on c <= 300 though pre-registered for c <= 2000; P2(ii) has no power, SE 0.0666 > 0.02), #141705/#141706 (advisory: timing on stdout, argmax ties, absent profile family). Not claimed by the source: obligation (ii) as a theorem, obligation (i) (a unit-restricted Kloosterman-type bound), anything asymptotic; the target box 407/400 is untouched and no exponent moves.","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":10096,"input_sha256":"ce647fe93dc5d540096da52eba49a0077d27d384ac72d17c8c6220c92b8d6d92","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"e5d28fc926f544967db97d8ff267b03846424c61e548370c7c38ab4c252f04cf","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5103,"material_evidence":{"sha256":"3331f86d65f9027890ae91e4762a8636ddb9dc1c4b765ebcc305cab4d1f55af1","entries":{"return:5103":"c09597775bbd69c2625c18d9be3f0d2abf8f0020ea1bae6ae9483d021e8b4996","finding:141703":"abb26df66e52e6d9bfc165ed97f640414a4275355317145b387d451ac57e620b","finding:141704":"50ea190bbed0b01683e77c6ccc2c924b82acbe22d275e9f327b5bdde8a4acc2a","finding:141705":"76c271a4da5b91bc833b9b18e0e222104e8165e42994f4a02a1dcc5a8dba5e77","finding:141706":"25d7c0ad5e349c105ea380460a664527a1fdd1f55c5785d039491b030c333171","artifact:5103:11daa6a80eab316f04a41d6b4c0f72d8e78ecc045726a905b4c0214f1766c69b":"11daa6a80eab316f04a41d6b4c0f72d8e78ecc045726a905b4c0214f1766c69b","artifact:5103:27b17bb9a6fdbe0463c11452f3d790b434003c4744c21aaed46e5d4785f7ba16":"27b17bb9a6fdbe0463c11452f3d790b434003c4744c21aaed46e5d4785f7ba16","artifact:5103:2f5e5b88f5f08b3475f5a7f1d3d8f1ae2bc23ef5704a7bf8f1d487c5a55c54cb":"2f5e5b88f5f08b3475f5a7f1d3d8f1ae2bc23ef5704a7bf8f1d487c5a55c54cb","artifact:5103:55e76cbfb50a6f6bd91a24d41b7bfdd883df570e5722d112b28f30f132a6c63a":"55e76cbfb50a6f6bd91a24d41b7bfdd883df570e5722d112b28f30f132a6c63a","artifact:5103:564fbd741e7535d9c9d9bf3842bc07855fbe402a8bfb70d0921c73744a459464":"564fbd741e7535d9c9d9bf3842bc07855fbe402a8bfb70d0921c73744a459464","artifact:5103:5c8808e9050751f304012b85683cd29c7ab851c940793c2f61a628508557654a":"5c8808e9050751f304012b85683cd29c7ab851c940793c2f61a628508557654a","artifact:5103:653e0b0f02ae8af9c0601c28d593f046a2b592bd8d295a2445974219d5805e21":"653e0b0f02ae8af9c0601c28d593f046a2b592bd8d295a2445974219d5805e21","artifact:5103:8bf416ee632ec707e69aaa5f821b919b83d278df7b3b168f6b5140a714a25e05":"8bf416ee632ec707e69aaa5f821b919b83d278df7b3b168f6b5140a714a25e05","artifact:5103:99e69e2d03d64979f7c80335a565dc5c0b4130ca61d0beec1a6900a143eedc88":"99e69e2d03d64979f7c80335a565dc5c0b4130ca61d0beec1a6900a143eedc88","artifact:5103:9dcc5b3d27a6029bc9a41e717369790a52107ab9a6091eccd64bdcfcde68b335":"9dcc5b3d27a6029bc9a41e717369790a52107ab9a6091eccd64bdcfcde68b335","artifact:5103:aedf255f2336964026f31e7cef25aa07d63eaae52c1be14b62c17737f348f6fd":"aedf255f2336964026f31e7cef25aa07d63eaae52c1be14b62c17737f348f6fd","artifact:5103:cedbe6c1cfb83a109224f4a15e77e9c0189b60da6e764ecae5272abe488e7e98":"cedbe6c1cfb83a109224f4a15e77e9c0189b60da6e764ecae5272abe488e7e98","artifact:5103:e5d28fc926f544967db97d8ff267b03846424c61e548370c7c38ab4c252f04cf":"e5d28fc926f544967db97d8ff267b03846424c61e548370c7c38ab4c252f04cf"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5103,"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 #5103: 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\":5103,\"report_sha256\":\"e5d28fc926f544967db97d8ff267b03846424c61e548370c7c38ab4c252f04cf\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5103\":\"c09597775bbd69c2625c18d9be3f0d2abf8f0020ea1bae6ae9483d021e8b4996\",\"finding:141703\":\"abb26df66e52e6d9bfc165ed97f640414a4275355317145b387d451ac57e620b\",\"finding:141704\":\"50ea190bbed0b01683e77c6ccc2c924b82acbe22d275e9f327b5bdde8a4acc2a\",\"finding:141705\":\"76c271a4da5b91bc833b9b18e0e222104e8165e42994f4a02a1dcc5a8dba5e77\",\"finding:141706\":\"25d7c0ad5e349c105ea380460a664527a1fdd1f55c5785d039491b030c333171\",\"artifact:5103:11daa6a80eab316f04a41d6b4c0f72d8e78ecc045726a905b4c0214f1766c69b\":\"11daa6a80eab316f04a41d6b4c0f72d8e78ecc045726a905b4c0214f1766c69b\",\"artifact:5103:27b17bb9a6fdbe0463c11452f3d790b434003c4744c21aaed46e5d4785f7ba16\":\"27b17bb9a6fdbe0463c11452f3d790b434003c4744c21aaed46e5d4785f7ba16\",\"artifact:5103:2f5e5b88f5f08b3475f5a7f1d3d8f1ae2bc23ef5704a7bf8f1d487c5a55c54cb\":\"2f5e5b88f5f08b3475f5a7f1d3d8f1ae2bc23ef5704a7bf8f1d487c5a55c54cb\",\"artifact:5103:55e76cbfb50a6f6bd91a24d41b7bfdd883df570e5722d112b28f30f132a6c63a\":\"55e76cbfb50a6f6bd91a24d41b7bfdd883df570e5722d112b28f30f132a6c63a\",\"artifact:5103:564fbd741e7535d9c9d9bf3842bc07855fbe402a8bfb70d0921c73744a459464\":\"564fbd741e7535d9c9d9bf3842bc07855fbe402a8bfb70d0921c73744a459464\",\"artifact:5103:5c8808e9050751f304012b85683cd29c7ab851c940793c2f61a628508557654a\":\"5c8808e9050751f304012b85683cd29c7ab851c940793c2f61a628508557654a\",\"artifact:5103:653e0b0f02ae8af9c0601c28d593f046a2b592bd8d295a2445974219d5805e21\":\"653e0b0f02ae8af9c0601c28d593f046a2b592bd8d295a2445974219d5805e21\",\"artifact:5103:8bf416ee632ec707e69aaa5f821b919b83d278df7b3b168f6b5140a714a25e05\":\"8bf416ee632ec707e69aaa5f821b919b83d278df7b3b168f6b5140a714a25e05\",\"artifact:5103:99e69e2d03d64979f7c80335a565dc5c0b4130ca61d0beec1a6900a143eedc88\":\"99e69e2d03d64979f7c80335a565dc5c0b4130ca61d0beec1a6900a143eedc88\",\"artifact:5103:9dcc5b3d27a6029bc9a41e717369790a52107ab9a6091eccd64bdcfcde68b335\":\"9dcc5b3d27a6029bc9a41e717369790a52107ab9a6091eccd64bdcfcde68b335\",\"artifact:5103:aedf255f2336964026f31e7cef25aa07d63eaae52c1be14b62c17737f348f6fd\":\"aedf255f2336964026f31e7cef25aa07d63eaae52c1be14b62c17737f348f6fd\",\"artifact:5103:cedbe6c1cfb83a109224f4a15e77e9c0189b60da6e764ecae5272abe488e7e98\":\"cedbe6c1cfb83a109224f4a15e77e9c0189b60da6e764ecae5272abe488e7e98\",\"artifact:5103:e5d28fc926f544967db97d8ff267b03846424c61e548370c7c38ab4c252f04cf\":\"e5d28fc926f544967db97d8ff267b03846424c61e548370c7c38ab4c252f04cf\"},\"sha256\":\"3331f86d65f9027890ae91e4762a8636ddb9dc1c4b765ebcc305cab4d1f55af1\"},\"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:5103,input_sha256:\"ce647fe93dc5d540096da52eba49a0077d27d384ac72d17c8c6220c92b8d6d92\",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/5118/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"4e3dbe38cc2b553a70a48f8a58dc580608f3853bf88a97dac7212990e1b83ea5","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}