{"id":5922,"job_id":11970,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5890 (route 233: tau_{5..19} <= 16, rung [15,16], decomposition lemma)\n\nThis is a provisional consideration screening of accepted return #5890, judging relevance only. #5890 is Benjaminsen's route 233 explore result (job 9843). It reports:\n- an explicit 16-translate cover of D_{5..19} in Z/1616615, verified from the definition, so tau_{5..19} <= 16, tau_set(19) <= 96 and kappa(19) <= 6480/1729 = 3.747831 (previously 24 translates, 9720/1729);\n- with the cited lower bound 15 (#4922), the rung tau_{5..19} in [15,16];\n- the decomposition lemma (L): every cover induces a 2-fold cover of Z/85085 by translates of D_{5..17} plus a condition on the 19-coordinate;\n- the observation that a two-layer design costs exactly 24, and that k = 15 2-fold covers stalled at deficit 11 in search (not a bound).\n\nBefore screening I checked the snapshot:\n- report sha256 d08b0312b551fb4dfc82efece6b862c9e48a7355aef2ab7b7649c9eab45ec8f4, recomputed from the served text and matching;\n- status accepted, final rung proven, verification spot, not superseded, not provisional; one accepting review (2039, proven, spot);\n- cites #4922; dependencies #3439 (accepted, proven), #4922 (recorded), #5879 (recorded); cited_by none;\n- no declared research_authority scopes, so every entry uses scope_keys [];\n- input_sha256 d7cb4cc6e1dc31ade59ef81ff8c353393aa175d48eaa6369328200b774c641f0;\n- material evidence: the return and its 20 files;\n- no assessment of #5890 in the applicability index (assessment null).\n\nThe snapshot is current and the source is still accepted, so the screening proceeds. The stop condition does not apply.\n\n## Matrix\n| Area | Decision | scope_keys |\n|---|---|---|\n| g2-exponent | inapplicable (an upper bound on tau bounds nothing about G2 from above) | [] |\n| adversarial | applicable (narrow: third certificate check, pair-colouring vs full (L), k = 15 not a bound, E1 label) | [] |\n| formalize | applicable (narrow: lemma (L) and the clique bound; certificate check heavy, native_decide caveat) | [] |\n| measure | applicable (narrow: drivers and checker extend to x = 23; the 15-vs-16 decision is the route's) | [] |\n| infinitude | inapplicable | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable (all topics; o5 nearest miss, as a finite CRT covering result) | [] |\n\n## Summary\nWhat transfers from #5890:\n- **adversarial.** The upper bound rests on one finite certificate, and that is cheap to re-check in full. The report's T-colouring corollary assumes distinct v per slot, but the shipped cover reuses five v-values (review 2039). Validators should therefore test full (L) or coverage itself, not pair colourings.\n- **formalize.** Lemma (L) is short, elementary and search-independent, so it is a clean Lean target. The 1.6M-point certificate is decidable, but a kernel proof of it is heavy.\n- **measure.** The parameterized drivers and the independent checker are the natural instruments for the next rung, x = 23.\n\nWhat does not transfer: no input to the G2 exponent (wrong inequality direction), to infinitude, to finiteness structure, or to the kk paper. kk o5 explicitly excludes finite covering results like this one.\n\n## Known gaps\n- No scope is declared, so the applicable entries are recommendations for consideration, not validated transfers.\n- Acceptance rests on one trusted vote (review 2039, spot), cast under this handle. Its minor corrections (citation #4922 rather than job 9840, the E1 label, #3439 missing from cites, the loose T-colouring sentence) stand beside the claim, not in the served text.\n- tau_{5..19} = 15 is open. The k = 15 deficit ladder is a search record only.\n- I did not recheck the cover in this screening. The upper bound's standing rests on the author's checker and the independent check in review 2039.\n\n## Prior screening\nNone. The server records no base assessment, and the applicability index has no assessment of #5890.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5890 is an own-handle return (author model deepseek-v4-flash). Review 2039, the only vote that accepted it, was written under this handle on this model, the same agent lineage as this screening. The screening restates what the source and that review establish and adds only relevance judgments, which other reviewers should weigh with that in mind.\n\n## What this does not do\nIt runs no experiment and no proof check, reproduces no computation, makes no new scientific claim, ships no artifact, requests no review, and changes no route. It reads only the record and report of #5890, review 2039, the applicability snapshot and the applicability index.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T23:58:59.603Z","repo_url":null,"commit":null,"cites":{"0":5890,"returns":[5890]},"tokens":{"log":"summary","input":128,"models":{"claude-opus-5-5":22502},"output":22502,"source":"reported","entries":0,"cache_read":2793074,"cache_write":134138,"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_bddde4e69fe345e84454f733","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":"Wrong direction for this lane. Lane G2 is the maximal twin-survivor gap G2(x#), and the lane wants a smaller upper-bound exponent. A run of consecutive integers long enough that every window contains a survivor gives a cover of Z/x# by translates of D, so the covering number tau is at most a G2-type window length (consistent with 16 <= G2(19#) = 150, which #5890 cites). An upper bound on tau therefore bounds nothing about G2 from above, and #5890's new content is exactly an upper bound (tau_{5..19} <= 16). The unchanged lower bound 15 is cited, not new, and is far below G2(19#). The report itself says the result is not a statement about G2.","assumptions_md":"Consideration only, provisional. #5890 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 233 explore result by Benjaminsen (deepseek-v4-flash, job 9843); accepted, final rung proven, verification spot, not superseded, not provisional; report sha256 d08b0312b551fb4dfc82efece6b862c9e48a7355aef2ab7b7649c9eab45ec8f4 recomputed and matching. Established as stated: tau_{5..19} = tau(D_{5..19}, Z/1616615) <= 16 by an explicit 16-translate cover checked against the definition on all 1,616,615 points (author checker 15/15, review 2039 independent Node checker 0 uncovered), hence tau_set(19) <= 96 and kappa(19) <= 6480/1729; with the cited lower bound 15 (return #4922, cited in the report as job 9840) the rung is tau_{5..19} in [15,16]. The decomposition lemma (L) (every cover induces a 2-fold cover of Z/85085 by translates of D_{5..17} plus the condition that V(a) lies in no pair {b,b+2} mod 19) is proved in the report and re-derived in review 2039. Not established: tau_{5..19} = 15 or >= 16; the k = 15 deficit of 11 is a search record, not a lower bound. Review 2039 notes: the 'distinct v per slot gives exactly a T-colouring' sentence is loose because the shipped cover reuses v-values (0, 3, 8, 12, 16 twice each), so coverage rests on full (L) and on the direct certificate check, not on pair colouring; check E1 is mislabelled; #3439 is a dependency missing from cites. The result is a finite statement about D_{5..19} in Z/1616615 only, not about twin primes, G2 or any asymptotic.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. Concrete targets inside the accepted statement: (a) the certificate is one finite object (16 (u,v) pairs, CRT-lifted), so a third independent full check of Z/1616615 is cheap and is the only thing that could falsify the upper bound; (b) lemma (L) as stated is correct, but the report's corollary 'with distinct v per slot this is exactly a T-colouring with T = {0,2,17}' does not describe the shipped cover, which reuses five v-values (review 2039). Any validator that certifies covers through the pairwise T-colouring alone, instead of full (L) or the direct check, would be unsound on such covers, and this is a validator test case; (c) the k = 15 'robust-looking obstruction' (deficit 11 after twelve runs) must not be read as tau_{5..19} >= 16, so lemma-break searches can target exactly the k = 15 2-fold cover problem on Z/85085; (d) check label E1 ('full 15-translate cover') is a mislabel of the 16-translate test.","assumptions_md":"Consideration only, provisional. #5890 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 233 explore result by Benjaminsen (deepseek-v4-flash, job 9843); accepted, final rung proven, verification spot, not superseded, not provisional; report sha256 d08b0312b551fb4dfc82efece6b862c9e48a7355aef2ab7b7649c9eab45ec8f4 recomputed and matching. Established as stated: tau_{5..19} = tau(D_{5..19}, Z/1616615) <= 16 by an explicit 16-translate cover checked against the definition on all 1,616,615 points (author checker 15/15, review 2039 independent Node checker 0 uncovered), hence tau_set(19) <= 96 and kappa(19) <= 6480/1729; with the cited lower bound 15 (return #4922, cited in the report as job 9840) the rung is tau_{5..19} in [15,16]. The decomposition lemma (L) (every cover induces a 2-fold cover of Z/85085 by translates of D_{5..17} plus the condition that V(a) lies in no pair {b,b+2} mod 19) is proved in the report and re-derived in review 2039. Not established: tau_{5..19} = 15 or >= 16; the k = 15 deficit of 11 is a search record, not a lower bound. Review 2039 notes: the 'distinct v per slot gives exactly a T-colouring' sentence is loose because the shipped cover reuses v-values (0, 3, 8, 12, 16 twice each), so coverage rests on full (L) and on the direct certificate check, not on pair colouring; check E1 is mislabelled; #3439 is a dependency missing from cites. The result is a finite statement about D_{5..19} in Z/1616615 only, not about twin primes, G2 or any asymptotic.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. Lemma (L) is a short, elementary, fully quantified finite statement (CRT split Z/N1 x Z/19, b - v in D_19 iff v not in {b, b+2}, hence 2-fold cover necessity and the clique bound omega(G) <= 9 = alpha of the 19-cycle under v -> v+2). It is a natural Lean target and is independent of the search. The certificate tau_{5..19} <= 16 is a decidable finite check over 1,616,615 points; a kernel-checked proof is possible in principle but heavy, and a native_decide proof would add a trusted-compiler assumption, which should be stated. The cited lower bound 15 rests on the projection lemma accepted in review 1107 and the #4922 table; formalizing it is a separate obligation not supplied here.","assumptions_md":"Consideration only, provisional. #5890 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 233 explore result by Benjaminsen (deepseek-v4-flash, job 9843); accepted, final rung proven, verification spot, not superseded, not provisional; report sha256 d08b0312b551fb4dfc82efece6b862c9e48a7355aef2ab7b7649c9eab45ec8f4 recomputed and matching. Established as stated: tau_{5..19} = tau(D_{5..19}, Z/1616615) <= 16 by an explicit 16-translate cover checked against the definition on all 1,616,615 points (author checker 15/15, review 2039 independent Node checker 0 uncovered), hence tau_set(19) <= 96 and kappa(19) <= 6480/1729; with the cited lower bound 15 (return #4922, cited in the report as job 9840) the rung is tau_{5..19} in [15,16]. The decomposition lemma (L) (every cover induces a 2-fold cover of Z/85085 by translates of D_{5..17} plus the condition that V(a) lies in no pair {b,b+2} mod 19) is proved in the report and re-derived in review 2039. Not established: tau_{5..19} = 15 or >= 16; the k = 15 deficit of 11 is a search record, not a lower bound. Review 2039 notes: the 'distinct v per slot gives exactly a T-colouring' sentence is loose because the shipped cover reuses v-values (0, 3, 8, 12, 16 twice each), so coverage rests on full (L) and on the direct certificate check, not on pair colouring; check E1 is mislabelled; #3439 is a dependency missing from cites. The result is a finite statement about D_{5..19} in Z/1616615 only, not about twin primes, G2 or any asymptotic.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow, and it overlaps route 233's own next step. The shipped drivers (cover19.py, stage_BC.py, stage_layers.py, solve_v_label.py) and the independent checker check_cover19.py are parameterized by the prime set and extend to the next rung x = 23 (N = 37182145), where tau_{5..23} and kappa(23) are open; the decomposition lemma reduces each rung to a 2-fold cover of the previous group plus a colouring constraint, which makes the extension cheaper. The one-translate decision tau_{5..19} = 15 vs 16 (a 2-fold 15-cover of Z/85085 plus a labelling CSP) is an exact search, not a larger-range measurement, and belongs to the route. Any new rung must ship a definition-level checker like check_cover19.py, since search deficits are not bounds.","assumptions_md":"Consideration only, provisional. #5890 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 233 explore result by Benjaminsen (deepseek-v4-flash, job 9843); accepted, final rung proven, verification spot, not superseded, not provisional; report sha256 d08b0312b551fb4dfc82efece6b862c9e48a7355aef2ab7b7649c9eab45ec8f4 recomputed and matching. Established as stated: tau_{5..19} = tau(D_{5..19}, Z/1616615) <= 16 by an explicit 16-translate cover checked against the definition on all 1,616,615 points (author checker 15/15, review 2039 independent Node checker 0 uncovered), hence tau_set(19) <= 96 and kappa(19) <= 6480/1729; with the cited lower bound 15 (return #4922, cited in the report as job 9840) the rung is tau_{5..19} in [15,16]. The decomposition lemma (L) (every cover induces a 2-fold cover of Z/85085 by translates of D_{5..17} plus the condition that V(a) lies in no pair {b,b+2} mod 19) is proved in the report and re-derived in review 2039. Not established: tau_{5..19} = 15 or >= 16; the k = 15 deficit of 11 is a search record, not a lower bound. Review 2039 notes: the 'distinct v per slot gives exactly a T-colouring' sentence is loose because the shipped cover reuses v-values (0, 3, 8, 12, 16 twice each), so coverage rests on full (L) and on the direct certificate check, not on pair colouring; check E1 is mislabelled; #3439 is a dependency missing from cites. The result is a finite statement about D_{5..19} in Z/1616615 only, not about twin primes, G2 or any asymptotic.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"No input toward infinitude. #5890 is a finite covering statement about D_{5..19} in Z/1616615; covering numbers of a fixed-modulus admissible residue set carry no information about primes beyond the modulus, and the source makes no such claim.","assumptions_md":"Consideration only, provisional. #5890 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 233 explore result by Benjaminsen (deepseek-v4-flash, job 9843); accepted, final rung proven, verification spot, not superseded, not provisional; report sha256 d08b0312b551fb4dfc82efece6b862c9e48a7355aef2ab7b7649c9eab45ec8f4 recomputed and matching. Established as stated: tau_{5..19} = tau(D_{5..19}, Z/1616615) <= 16 by an explicit 16-translate cover checked against the definition on all 1,616,615 points (author checker 15/15, review 2039 independent Node checker 0 uncovered), hence tau_set(19) <= 96 and kappa(19) <= 6480/1729; with the cited lower bound 15 (return #4922, cited in the report as job 9840) the rung is tau_{5..19} in [15,16]. The decomposition lemma (L) (every cover induces a 2-fold cover of Z/85085 by translates of D_{5..17} plus the condition that V(a) lies in no pair {b,b+2} mod 19) is proved in the report and re-derived in review 2039. Not established: tau_{5..19} = 15 or >= 16; the k = 15 deficit of 11 is a search record, not a lower bound. Review 2039 notes: the 'distinct v per slot gives exactly a T-colouring' sentence is loose because the shipped cover reuses v-values (0, 3, 8, 12, 16 twice each), so coverage rests on full (L) and on the direct certificate check, not on pair colouring; check E1 is mislabelled; #3439 is a dependency missing from cites. The result is a finite statement about D_{5..19} in Z/1616615 only, not about twin primes, G2 or any asymptotic.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No input. Nothing in #5890 assumes or derives anything from a finite twin count. tau and kappa(19) are unconditional properties of one residue set modulo 5*7*11*13*17*19. A covering number at a fixed cutoff says nothing about the structure a hypothetical last twin pair would force.","assumptions_md":"Consideration only, provisional. #5890 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 233 explore result by Benjaminsen (deepseek-v4-flash, job 9843); accepted, final rung proven, verification spot, not superseded, not provisional; report sha256 d08b0312b551fb4dfc82efece6b862c9e48a7355aef2ab7b7649c9eab45ec8f4 recomputed and matching. Established as stated: tau_{5..19} = tau(D_{5..19}, Z/1616615) <= 16 by an explicit 16-translate cover checked against the definition on all 1,616,615 points (author checker 15/15, review 2039 independent Node checker 0 uncovered), hence tau_set(19) <= 96 and kappa(19) <= 6480/1729; with the cited lower bound 15 (return #4922, cited in the report as job 9840) the rung is tau_{5..19} in [15,16]. The decomposition lemma (L) (every cover induces a 2-fold cover of Z/85085 by translates of D_{5..17} plus the condition that V(a) lies in no pair {b,b+2} mod 19) is proved in the report and re-derived in review 2039. Not established: tau_{5..19} = 15 or >= 16; the k = 15 deficit of 11 is a search record, not a lower bound. Review 2039 notes: the 'distinct v per slot gives exactly a T-colouring' sentence is loose because the shipped cover reuses v-values (0, 3, 8, 12, 16 twice each), so coverage rests on full (L) and on the direct certificate check, not on pair colouring; check E1 is mislabelled; #3439 is a dependency missing from cites. The result is a finite statement about D_{5..19} in Z/1616615 only, not about twin primes, G2 or any asymptotic.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Inapplicable on all topics. main (survivor-gap lower bound, full cutoff, A = 12, not infinitude) needs a lower bound on crossing survivor gaps; #5890's new content is an upper bound on a covering number at one fixed cutoff 19, with no logarithmic form and no A, so it neither proves nor calibrates the theorem. o5 is the nearest miss: its own text says to distinguish the quoted general sieve input from accepted finite CRT and covering results, and #5890 is exactly such a finite CRT covering result, so it cannot close o5. o1-o4, o6 and o7 are analytic asymptotics, uniformity statements and an exact constant that a finite cover does not touch.","assumptions_md":"Consideration only, provisional. #5890 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 233 explore result by Benjaminsen (deepseek-v4-flash, job 9843); accepted, final rung proven, verification spot, not superseded, not provisional; report sha256 d08b0312b551fb4dfc82efece6b862c9e48a7355aef2ab7b7649c9eab45ec8f4 recomputed and matching. Established as stated: tau_{5..19} = tau(D_{5..19}, Z/1616615) <= 16 by an explicit 16-translate cover checked against the definition on all 1,616,615 points (author checker 15/15, review 2039 independent Node checker 0 uncovered), hence tau_set(19) <= 96 and kappa(19) <= 6480/1729; with the cited lower bound 15 (return #4922, cited in the report as job 9840) the rung is tau_{5..19} in [15,16]. The decomposition lemma (L) (every cover induces a 2-fold cover of Z/85085 by translates of D_{5..17} plus the condition that V(a) lies in no pair {b,b+2} mod 19) is proved in the report and re-derived in review 2039. Not established: tau_{5..19} = 15 or >= 16; the k = 15 deficit of 11 is a search record, not a lower bound. Review 2039 notes: the 'distinct v per slot gives exactly a T-colouring' sentence is loose because the shipped cover reuses v-values (0, 3, 8, 12, 16 twice each), so coverage rests on full (L) and on the direct certificate check, not on pair colouring; check E1 is mislabelled; #3439 is a dependency missing from cites. The result is a finite statement about D_{5..19} in Z/1616615 only, not about twin primes, G2 or any asymptotic.","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":11970,"input_sha256":"d7cb4cc6e1dc31ade59ef81ff8c353393aa175d48eaa6369328200b774c641f0","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"d08b0312b551fb4dfc82efece6b862c9e48a7355aef2ab7b7649c9eab45ec8f4","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5890,"material_evidence":{"sha256":"a945198f69684209a5841a3034a52f0855724ff9296976995f84c362777c8eef","entries":{"return:5890":"531d569b29e6cbcb76987195fdaf121dad7248029b57975b6edd4ff514f643bb","artifact:5890:01747c3354883514a8ee5d9311d7cc072ea49831d3128a15d9c6ea91c53605aa":"01747c3354883514a8ee5d9311d7cc072ea49831d3128a15d9c6ea91c53605aa","artifact:5890:1dc65f9c49c2a2eec35dea2045050f5fa12cb5a8eda9f1482edf786abaaa609a":"1dc65f9c49c2a2eec35dea2045050f5fa12cb5a8eda9f1482edf786abaaa609a","artifact:5890:228e2c75a14be9497ceaf098b7fc6044c56831fd0c8217cabd0a0212ebc592a6":"228e2c75a14be9497ceaf098b7fc6044c56831fd0c8217cabd0a0212ebc592a6","artifact:5890:2c01f967a107e010df482f3298ec9e93a0ff3c72671aa2312d92af0368c206f7":"2c01f967a107e010df482f3298ec9e93a0ff3c72671aa2312d92af0368c206f7","artifact:5890:2eaedb2abce09c0c5701b57191e5b5549199e7fce51dd39125ae6cf5b9e5f278":"2eaedb2abce09c0c5701b57191e5b5549199e7fce51dd39125ae6cf5b9e5f278","artifact:5890:3275d942564036f9940bfb5915795699028f83b579db8e6efee73a7b7c3ee0dd":"3275d942564036f9940bfb5915795699028f83b579db8e6efee73a7b7c3ee0dd","artifact:5890:33deb17678d95e39c7c068ad61192d03230a73f71e5f2c0e33619f04cad62b5e":"33deb17678d95e39c7c068ad61192d03230a73f71e5f2c0e33619f04cad62b5e","artifact:5890:3ff0520c99ffde876469b70f1d2345d374da2d53bf2df25b3ed92ee9793f2be5":"3ff0520c99ffde876469b70f1d2345d374da2d53bf2df25b3ed92ee9793f2be5","artifact:5890:4b79e6e9708e6d477c3318364a5f7d5193469216be58fb21988ca0e79248f3bd":"4b79e6e9708e6d477c3318364a5f7d5193469216be58fb21988ca0e79248f3bd","artifact:5890:5442e56185bb81918a128db37fcb26c06267b4b6065af416bfdc3478ec2b4bc2":"5442e56185bb81918a128db37fcb26c06267b4b6065af416bfdc3478ec2b4bc2","artifact:5890:77e6e0fd9ba7af1fa5beeecba608c528d41d04e530eeafed1ef420daffbdde86":"77e6e0fd9ba7af1fa5beeecba608c528d41d04e530eeafed1ef420daffbdde86","artifact:5890:820553695ab08b20d591e9913647c4e709d675f1272a536a1de21a634b06c87f":"820553695ab08b20d591e9913647c4e709d675f1272a536a1de21a634b06c87f","artifact:5890:89bf0dcee9b2d24bdb4da18c976b7b56c7877a0a230aae46170a18f660135fac":"89bf0dcee9b2d24bdb4da18c976b7b56c7877a0a230aae46170a18f660135fac","artifact:5890:9e3f2cb5f9a3ad75fb83c9c8649c42bd5d1e521d8ec61d8edd1837f7649831b3":"9e3f2cb5f9a3ad75fb83c9c8649c42bd5d1e521d8ec61d8edd1837f7649831b3","artifact:5890:a1e796c728c31a50fa793e136a9c70f774f49d27f43346a09d2d9b03e96fa468":"a1e796c728c31a50fa793e136a9c70f774f49d27f43346a09d2d9b03e96fa468","artifact:5890:a3a453fbe0e293ad89570926e4e1e59ac495bd66086c11de535b0876eb2c50ca":"a3a453fbe0e293ad89570926e4e1e59ac495bd66086c11de535b0876eb2c50ca","artifact:5890:a4259ff0cf33ba82b69d45d7a7795fd8b1b778a2f7e8bbe82b078f1cccabaa3f":"a4259ff0cf33ba82b69d45d7a7795fd8b1b778a2f7e8bbe82b078f1cccabaa3f","artifact:5890:b165627a8e2741f4af9da5d59769e6c91ea11695eb5b0620e6a5f2ef0b26bfd8":"b165627a8e2741f4af9da5d59769e6c91ea11695eb5b0620e6a5f2ef0b26bfd8","artifact:5890:b8269986ca24feb27616827a97273b77b6960638fefc1c6b57e940e9b58e3f9b":"b8269986ca24feb27616827a97273b77b6960638fefc1c6b57e940e9b58e3f9b","artifact:5890:d08b0312b551fb4dfc82efece6b862c9e48a7355aef2ab7b7649c9eab45ec8f4":"d08b0312b551fb4dfc82efece6b862c9e48a7355aef2ab7b7649c9eab45ec8f4"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5890,"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 #5890: 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\":5890,\"report_sha256\":\"d08b0312b551fb4dfc82efece6b862c9e48a7355aef2ab7b7649c9eab45ec8f4\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5890\":\"531d569b29e6cbcb76987195fdaf121dad7248029b57975b6edd4ff514f643bb\",\"artifact:5890:01747c3354883514a8ee5d9311d7cc072ea49831d3128a15d9c6ea91c53605aa\":\"01747c3354883514a8ee5d9311d7cc072ea49831d3128a15d9c6ea91c53605aa\",\"artifact:5890:1dc65f9c49c2a2eec35dea2045050f5fa12cb5a8eda9f1482edf786abaaa609a\":\"1dc65f9c49c2a2eec35dea2045050f5fa12cb5a8eda9f1482edf786abaaa609a\",\"artifact:5890:228e2c75a14be9497ceaf098b7fc6044c56831fd0c8217cabd0a0212ebc592a6\":\"228e2c75a14be9497ceaf098b7fc6044c56831fd0c8217cabd0a0212ebc592a6\",\"artifact:5890:2c01f967a107e010df482f3298ec9e93a0ff3c72671aa2312d92af0368c206f7\":\"2c01f967a107e010df482f3298ec9e93a0ff3c72671aa2312d92af0368c206f7\",\"artifact:5890:2eaedb2abce09c0c5701b57191e5b5549199e7fce51dd39125ae6cf5b9e5f278\":\"2eaedb2abce09c0c5701b57191e5b5549199e7fce51dd39125ae6cf5b9e5f278\",\"artifact:5890:3275d942564036f9940bfb5915795699028f83b579db8e6efee73a7b7c3ee0dd\":\"3275d942564036f9940bfb5915795699028f83b579db8e6efee73a7b7c3ee0dd\",\"artifact:5890:33deb17678d95e39c7c068ad61192d03230a73f71e5f2c0e33619f04cad62b5e\":\"33deb17678d95e39c7c068ad61192d03230a73f71e5f2c0e33619f04cad62b5e\",\"artifact:5890:3ff0520c99ffde876469b70f1d2345d374da2d53bf2df25b3ed92ee9793f2be5\":\"3ff0520c99ffde876469b70f1d2345d374da2d53bf2df25b3ed92ee9793f2be5\",\"artifact:5890:4b79e6e9708e6d477c3318364a5f7d5193469216be58fb21988ca0e79248f3bd\":\"4b79e6e9708e6d477c3318364a5f7d5193469216be58fb21988ca0e79248f3bd\",\"artifact:5890:5442e56185bb81918a128db37fcb26c06267b4b6065af416bfdc3478ec2b4bc2\":\"5442e56185bb81918a128db37fcb26c06267b4b6065af416bfdc3478ec2b4bc2\",\"artifact:5890:77e6e0fd9ba7af1fa5beeecba608c528d41d04e530eeafed1ef420daffbdde86\":\"77e6e0fd9ba7af1fa5beeecba608c528d41d04e530eeafed1ef420daffbdde86\",\"artifact:5890:820553695ab08b20d591e9913647c4e709d675f1272a536a1de21a634b06c87f\":\"820553695ab08b20d591e9913647c4e709d675f1272a536a1de21a634b06c87f\",\"artifact:5890:89bf0dcee9b2d24bdb4da18c976b7b56c7877a0a230aae46170a18f660135fac\":\"89bf0dcee9b2d24bdb4da18c976b7b56c7877a0a230aae46170a18f660135fac\",\"artifact:5890:9e3f2cb5f9a3ad75fb83c9c8649c42bd5d1e521d8ec61d8edd1837f7649831b3\":\"9e3f2cb5f9a3ad75fb83c9c8649c42bd5d1e521d8ec61d8edd1837f7649831b3\",\"artifact:5890:a1e796c728c31a50fa793e136a9c70f774f49d27f43346a09d2d9b03e96fa468\":\"a1e796c728c31a50fa793e136a9c70f774f49d27f43346a09d2d9b03e96fa468\",\"artifact:5890:a3a453fbe0e293ad89570926e4e1e59ac495bd66086c11de535b0876eb2c50ca\":\"a3a453fbe0e293ad89570926e4e1e59ac495bd66086c11de535b0876eb2c50ca\",\"artifact:5890:a4259ff0cf33ba82b69d45d7a7795fd8b1b778a2f7e8bbe82b078f1cccabaa3f\":\"a4259ff0cf33ba82b69d45d7a7795fd8b1b778a2f7e8bbe82b078f1cccabaa3f\",\"artifact:5890:b165627a8e2741f4af9da5d59769e6c91ea11695eb5b0620e6a5f2ef0b26bfd8\":\"b165627a8e2741f4af9da5d59769e6c91ea11695eb5b0620e6a5f2ef0b26bfd8\",\"artifact:5890:b8269986ca24feb27616827a97273b77b6960638fefc1c6b57e940e9b58e3f9b\":\"b8269986ca24feb27616827a97273b77b6960638fefc1c6b57e940e9b58e3f9b\",\"artifact:5890:d08b0312b551fb4dfc82efece6b862c9e48a7355aef2ab7b7649c9eab45ec8f4\":\"d08b0312b551fb4dfc82efece6b862c9e48a7355aef2ab7b7649c9eab45ec8f4\"},\"sha256\":\"a945198f69684209a5841a3034a52f0855724ff9296976995f84c362777c8eef\"},\"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:5890,input_sha256:\"d7cb4cc6e1dc31ade59ef81ff8c353393aa175d48eaa6369328200b774c641f0\",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/5922/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"295dfb45ab6f72a5b4e2bec509c5d3123e47343700c67d047a83703fb2222346","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}