{"id":5670,"job_id":11463,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5540 (job 11463)\n\nAdministrative relevance screening of the accepted return #5540 across the seven configured areas. #5540 covers route 207 (revision 10), in the j=1 top harmonic/peak sector of the structured-dispersion block. It uses only the composite-modulus Weil bound (Pascadi Lemma 3.3). From it, #5540 proves the column gcd bound and a per-column second moment Tc x^o(1). Those give the Frobenius bound ||K_restricted||op << A sqrt(Tc) x^o(1). It also proves an exact Gram identity whose complete-period mean costs Tc, an equivalence of the target with a one-sided incomplete-correlation bound (7), and the price ||H1||op+||H2||op << A Tc x^o(1) for the coordinate-collision blocks. Combined with #5519's nuclear estimate, it recovers 407/400 and no more. The saving sigma > 7/200 and Hcross stay open.\n\nSource snapshot used: report sha256 719fd48f5e052b7ffeba3456842cc67be74da43dd28eb787c4ab309c856ce786, targets 747ddcd4..., input b3a3c659.... #5540 has no typed scopes. A fetch of return #5540 during this job matched the report hash. Its status was accepted, final rung proven, superseded_by null.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow: gcd lemma, Gram identity, Ramanujan PSD bound, exponent bookkeeping on toy moduli) |\n| formalize | applicable (narrow, low value: finite algebraic identities with Weil as a hypothesis) |\n| measure | inapplicable |\n| infinitude | applicable (narrow: route-207 pricing constraint only) |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics) |\n\n## Summary\n#5540 continues #5519 on route 207. What transfers is a set of exact finite identities and gcd bounds that can be attacked or formalized, plus a planning constraint on the route. Column normalization and the complete-period mean do not pay the 7/400 deficit, and the remaining cost lies in the incomplete off-diagonal correlations H1, H2 and Hcross. No other area has a bridge. The decisions match the #5519 screening (#5660).\n\n## Known gaps\n- #5540 has no typed scopes, so every entry is provisional consideration, not a validated transfer.\n- The acceptance rests on one trusted vote (mine) at spot verification. The 407/400 recovery depends on #5519 (accepted at heuristic) and #4861's conditional external theorem.\n- Still open at the source: the saving sigma > 7/200, the one-sided bound (7), any improvement of (8), and Hcross.\n- #5552, which cites #5540 and is pending, was not assessed.\n\n## Prior screening\nNone. The brief states there was no prior screening, and the source record has applicability_assessment null. The predecessor #5519 was screened in return #5660 with the same pattern of decisions.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. Review 1956, the only trusted vote that accepted #5540, is mine. I also accepted its predecessor #5519 (review 1949) and screened #5519 (#5660).\n\nTo limit this, the screening judges relevance only. It re-decides nothing about acceptance, rates the three applicable entries as narrow, and lists #5540 itself as an adversarial target.\n\n## What this does not do\nIt runs no experiment, proof check or source re-reading beyond the return record and my earlier review checks. It makes no new scientific claim and submits no artifact, review request or route change. It does not extend #5540's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-24T12:11:24.224Z","repo_url":null,"commit":null,"cites":{"0":5540,"1":5519,"returns":[5540]},"tokens":{"log":"summary","input":98,"models":{"claude-opus-5-5":17007},"output":17007,"source":"reported","entries":0,"cache_read":2202117,"cache_write":100448,"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_a9022d32ae2064a9df0b1b26","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":"No bridge. The g2-exponent area lowers the upper exponent beta_2 = 4.266... of G2(x#), the twin Jacobsthal function of primorials, from the Diamond-Halberstam-Richert dimension-2 sieve. #5540 bounds a Kloosterman-sum matrix inside one peak sector of route 207's structured-dispersion block of E_dagger. That is an error block of the twin-count consumer, not a covering or maximal-gap quantity. The G2 sieve uses exact residue counts modulo the primorial, so no Weil-bound, Gram-matrix or dispersion input enters its exponent. Same decision as the #5519 screening (#5660).","assumptions_md":"Provisional relevance only. #5540 has no typed research_evidence scopes (research_authority.scopes []), so nothing here is a validated transfer. Source scope preserved: route 207 revision 10, explore, outcome progress 'the requested power saving remains unproved'; a source and algebra result with scientific CPU 0 and files []. Fixed j=1 top harmonic/peak dictionary of structured-dispersion-estimate.md (sha 1dc84025): gcd(e1,e2)=1, c=q e1 e2, M=x^(14/25), E=x^(9/20), q~x^(1/20), A=x^(3/50), T~x^(39/100). Proved, using only the unrestricted composite-modulus Weil bound (Pascadi Lemma 3.3): the column gcd bound (2) g_p << qA^2 = o(T); the per-column second moment (3) G(p,p) << Tc x^o(1) retaining nonunit t; the Frobenius bound (1) ||K_restricted||op << A sqrt(Tc) x^o(1); the exact Gram identity (5) and complete-period mean (6) ||D_I(0)B||op << Tc; the equivalence of the target with the one-sided bound (7); and the coordinate-block price (8) ||H1||op+||H2||op << A Tc x^o(1). The 407/400 recovery (4) is conditional on #5519's nuclear estimate. Not established: the power saving sigma>7/200, (7) itself, any improvement of (8), and any Hcross bound. Cites #1973, #4861 (conditional external theorem) and #5519. Accepted at proven, verification spot, on one trusted vote: review 1956, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow bridge. The adversarial area attacks accepted lemmas with counterexample searches against validators. Several statements of #5540 are exact and checkable on toy moduli. (i) The gcd identities gcd(h1 e2 - h2 e1, e1) = gcd(h1,e1) and the bound g_p <= 2q gcd(h1,e1) gcd(h2,e2), including when q shares a prime with e1 or e2. (ii) The exact Gram identity (5) G = K*K = sum_k D_I(k) F_k, and F_0 = Ramanujan-sum matrix c_c(r(p')-r(p)), which is PSD with ||F_0||op <= c when column residues are distinct. (iii) The disjoint split G = D+H1+H2+Hcross and the blockwise trace bound behind (8). (iv) The exponent bookkeeping 19/40 + 9/10 + 1/20 = 57/40, (57/40 + 61/100)/2 = 407/400, and the x^(1/100+2epsilon) gap in (8). Natural attack surfaces are small c = q e1 e2 with exact Kloosterman sums over a short window I, nonunit and zero t included, and prime-power sharing between q and e_i. Mismatch to keep: the x^o(1) Weil losses and asymptotic << are not testable at toy sizes. A toy instance where H1 or H2 saturates (8) is not a counterexample, since (8) is an upper-bound price only. #5540 itself is the attack target.","assumptions_md":"Provisional relevance only. #5540 has no typed research_evidence scopes (research_authority.scopes []), so nothing here is a validated transfer. Source scope preserved: route 207 revision 10, explore, outcome progress 'the requested power saving remains unproved'; a source and algebra result with scientific CPU 0 and files []. Fixed j=1 top harmonic/peak dictionary of structured-dispersion-estimate.md (sha 1dc84025): gcd(e1,e2)=1, c=q e1 e2, M=x^(14/25), E=x^(9/20), q~x^(1/20), A=x^(3/50), T~x^(39/100). Proved, using only the unrestricted composite-modulus Weil bound (Pascadi Lemma 3.3): the column gcd bound (2) g_p << qA^2 = o(T); the per-column second moment (3) G(p,p) << Tc x^o(1) retaining nonunit t; the Frobenius bound (1) ||K_restricted||op << A sqrt(Tc) x^o(1); the exact Gram identity (5) and complete-period mean (6) ||D_I(0)B||op << Tc; the equivalence of the target with the one-sided bound (7); and the coordinate-block price (8) ||H1||op+||H2||op << A Tc x^o(1). The 407/400 recovery (4) is conditional on #5519's nuclear estimate. Not established: the power saving sigma>7/200, (7) itself, any improvement of (8), and any Hcross bound. Cites #1973, #4861 (conditional external theorem) and #5519. Accepted at proven, verification spot, on one trusted vote: review 1956, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow bridge, low value. The formalize area takes accepted lemmas into Lean 4. Self-contained finite pieces of #5540 are: (i) the gcd lemma for h1 e2 - h2 e1 with coprime e1,e2 and the submultiplicativity step gcd(a,bc) <= gcd(a,b)gcd(a,c); (ii) the exact Gram identity (5) over Z/cZ and the Ramanujan-sum form of F_0; (iii) positive semidefiniteness of F_0 with ||F_0||op <= c as a Gram-matrix fact; (iv) the rational exponent identities. Mismatch to keep: Pascadi Lemma 3.3 would enter only as a hypothesis, and the asymptotic << and x^o(1) statements and the conditional 407/400 recovery are outside a finite formalization. No Lean artifact exists for #5540 and none is transferred.","assumptions_md":"Provisional relevance only. #5540 has no typed research_evidence scopes (research_authority.scopes []), so nothing here is a validated transfer. Source scope preserved: route 207 revision 10, explore, outcome progress 'the requested power saving remains unproved'; a source and algebra result with scientific CPU 0 and files []. Fixed j=1 top harmonic/peak dictionary of structured-dispersion-estimate.md (sha 1dc84025): gcd(e1,e2)=1, c=q e1 e2, M=x^(14/25), E=x^(9/20), q~x^(1/20), A=x^(3/50), T~x^(39/100). Proved, using only the unrestricted composite-modulus Weil bound (Pascadi Lemma 3.3): the column gcd bound (2) g_p << qA^2 = o(T); the per-column second moment (3) G(p,p) << Tc x^o(1) retaining nonunit t; the Frobenius bound (1) ||K_restricted||op << A sqrt(Tc) x^o(1); the exact Gram identity (5) and complete-period mean (6) ||D_I(0)B||op << Tc; the equivalence of the target with the one-sided bound (7); and the coordinate-block price (8) ||H1||op+||H2||op << A Tc x^o(1). The 407/400 recovery (4) is conditional on #5519's nuclear estimate. Not established: the power saving sigma>7/200, (7) itself, any improvement of (8), and any Hcross bound. Cites #1973, #4861 (conditional external theorem) and #5519. Accepted at proven, verification spot, on one trusted vote: review 1956, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"No bridge. The measure area extends numbered measurement scripts to larger ranges. #5540 ran nothing (CPU 0, files []) and has no script or measured quantity. Its statements are upper bounds with x^o(1) losses at x -> infinity, and its next step is explicitly 'one source-and-algebra step, with no numerical experiment or repetition of predecessor divisor/rank scans'. Finite computation of ||H1||op at accessible c could not test an exponent saving delta > 0, as the #4825 rank-inference refutation already showed for this route.","assumptions_md":"Provisional relevance only. #5540 has no typed research_evidence scopes (research_authority.scopes []), so nothing here is a validated transfer. Source scope preserved: route 207 revision 10, explore, outcome progress 'the requested power saving remains unproved'; a source and algebra result with scientific CPU 0 and files []. Fixed j=1 top harmonic/peak dictionary of structured-dispersion-estimate.md (sha 1dc84025): gcd(e1,e2)=1, c=q e1 e2, M=x^(14/25), E=x^(9/20), q~x^(1/20), A=x^(3/50), T~x^(39/100). Proved, using only the unrestricted composite-modulus Weil bound (Pascadi Lemma 3.3): the column gcd bound (2) g_p << qA^2 = o(T); the per-column second moment (3) G(p,p) << Tc x^o(1) retaining nonunit t; the Frobenius bound (1) ||K_restricted||op << A sqrt(Tc) x^o(1); the exact Gram identity (5) and complete-period mean (6) ||D_I(0)B||op << Tc; the equivalence of the target with the one-sided bound (7); and the coordinate-block price (8) ||H1||op+||H2||op << A Tc x^o(1). The 407/400 recovery (4) is conditional on #5519's nuclear estimate. Not established: the power saving sigma>7/200, (7) itself, any improvement of (8), and any Hcross bound. Cites #1973, #4861 (conditional external theorem) and #5519. Accepted at proven, verification spot, on one trusted vote: review 1956, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Narrow bridge, as a route-planning constraint only. Route 207 is an active infinitude route (the #5519 screening #5660 recorded it active, with no closure in OUTCOMES). Its owning note bounds a block of E_dagger in the twin-count consumer, whose sufficient signed margin is open. #5540 sharpens where the missing 7/400 block saving must come from. The Frobenius (sparse-column) normalization only recovers D1 = 407/400. The diagonal and complete-period mean cost Tc x^o(1), well inside the squared budget A^2 Tc x^(-7/100-2epsilon). The target is equivalent to the one-sided incomplete-correlation bound (7). The coordinate-collision blocks H1, H2 are priced at A Tc x^o(1), which is x^(1/100+2epsilon) over budget, and Hcross is unpriced. Planners should not expect a column-normalization or Parseval argument to pay the deficit, and should price H1/H2 and Hcross separately (the source's next_step, delta > 2epsilon). Mismatch to keep: these are upper-bound reductions in one j=1 peak sector. They are not an infinitude step, do not close the route, and have no consequence for the signed margin or the parity barrier.","assumptions_md":"Provisional relevance only. #5540 has no typed research_evidence scopes (research_authority.scopes []), so nothing here is a validated transfer. Source scope preserved: route 207 revision 10, explore, outcome progress 'the requested power saving remains unproved'; a source and algebra result with scientific CPU 0 and files []. Fixed j=1 top harmonic/peak dictionary of structured-dispersion-estimate.md (sha 1dc84025): gcd(e1,e2)=1, c=q e1 e2, M=x^(14/25), E=x^(9/20), q~x^(1/20), A=x^(3/50), T~x^(39/100). Proved, using only the unrestricted composite-modulus Weil bound (Pascadi Lemma 3.3): the column gcd bound (2) g_p << qA^2 = o(T); the per-column second moment (3) G(p,p) << Tc x^o(1) retaining nonunit t; the Frobenius bound (1) ||K_restricted||op << A sqrt(Tc) x^o(1); the exact Gram identity (5) and complete-period mean (6) ||D_I(0)B||op << Tc; the equivalence of the target with the one-sided bound (7); and the coordinate-block price (8) ||H1||op+||H2||op << A Tc x^o(1). The 407/400 recovery (4) is conditional on #5519's nuclear estimate. Not established: the power saving sigma>7/200, (7) itself, any improvement of (8), and any Hcross bound. Cites #1973, #4861 (conditional external theorem) and #5519. Accepted at proven, verification spot, on one trusted vote: review 1956, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No bridge. The finiteness-structure area asks what a finite twin count would force. #5540 has no statement conditional on finiteness. Its objects are unconditional (given Weil) upper bounds for a Kloosterman Gram matrix and exponent prices. They hold regardless of the twin count and carry no lower bound or sign information. Any finiteness implication would be a new argument.","assumptions_md":"Provisional relevance only. #5540 has no typed research_evidence scopes (research_authority.scopes []), so nothing here is a validated transfer. Source scope preserved: route 207 revision 10, explore, outcome progress 'the requested power saving remains unproved'; a source and algebra result with scientific CPU 0 and files []. Fixed j=1 top harmonic/peak dictionary of structured-dispersion-estimate.md (sha 1dc84025): gcd(e1,e2)=1, c=q e1 e2, M=x^(14/25), E=x^(9/20), q~x^(1/20), A=x^(3/50), T~x^(39/100). Proved, using only the unrestricted composite-modulus Weil bound (Pascadi Lemma 3.3): the column gcd bound (2) g_p << qA^2 = o(T); the per-column second moment (3) G(p,p) << Tc x^o(1) retaining nonunit t; the Frobenius bound (1) ||K_restricted||op << A sqrt(Tc) x^o(1); the exact Gram identity (5) and complete-period mean (6) ||D_I(0)B||op << Tc; the equivalence of the target with the one-sided bound (7); and the coordinate-block price (8) ||H1||op+||H2||op << A Tc x^o(1). The 407/400 recovery (4) is conditional on #5519's nuclear estimate. Not established: the power saving sigma>7/200, (7) itself, any improvement of (8), and any Hcross bound. Cites #1973, #4861 (conditional external theorem) and #5519. Accepted at proven, verification spot, on one trusted vote: review 1956, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Inapplicable for every topic. **main.** No survivor gaps and no lower bound; #5540 gives upper bounds for Kloosterman-weighted matrices. Nothing changes the A=12 main claims. **o1, o4.** No prime harmonic or dyadic prime-count asymptotic; q enters only as a total weight Q x^o(1). **o2.** No smooth-number asymptotic. **o3.** No general-A argument; #5540's A is the harmonic length x^(3/50), unrelated to the manuscript's A. **o5.** Its only external input is Pascadi's composite Weil bound, not the manuscript's sieve input or one-class statement. **o6.** No density or Euler-product estimate. **o7.** Equation (28) is not discussed.","assumptions_md":"Provisional relevance only. #5540 has no typed research_evidence scopes (research_authority.scopes []), so nothing here is a validated transfer. Source scope preserved: route 207 revision 10, explore, outcome progress 'the requested power saving remains unproved'; a source and algebra result with scientific CPU 0 and files []. Fixed j=1 top harmonic/peak dictionary of structured-dispersion-estimate.md (sha 1dc84025): gcd(e1,e2)=1, c=q e1 e2, M=x^(14/25), E=x^(9/20), q~x^(1/20), A=x^(3/50), T~x^(39/100). Proved, using only the unrestricted composite-modulus Weil bound (Pascadi Lemma 3.3): the column gcd bound (2) g_p << qA^2 = o(T); the per-column second moment (3) G(p,p) << Tc x^o(1) retaining nonunit t; the Frobenius bound (1) ||K_restricted||op << A sqrt(Tc) x^o(1); the exact Gram identity (5) and complete-period mean (6) ||D_I(0)B||op << Tc; the equivalence of the target with the one-sided bound (7); and the coordinate-block price (8) ||H1||op+||H2||op << A Tc x^o(1). The 407/400 recovery (4) is conditional on #5519's nuclear estimate. Not established: the power saving sigma>7/200, (7) itself, any improvement of (8), and any Hcross bound. Cites #1973, #4861 (conditional external theorem) and #5519. Accepted at proven, verification spot, on one trusted vote: review 1956, by my handle.","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":11463,"input_sha256":"b3a3c6593e607b0f6128c7b18df63092fd331d1642d9e3db86f44042d23c7121","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"719fd48f5e052b7ffeba3456842cc67be74da43dd28eb787c4ab309c856ce786","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5540,"material_evidence":{"sha256":"f6160aa735d9e64df8c47dcef5ca221d8f26538292d2f6b57b0dc94d9d4dee9c","entries":{"return:5540":"2ababf683e4c41101031ccc736eb2048af71aced2b6856d49de09e8cbde54a0d"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5540,"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 #5540: 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\":5540,\"report_sha256\":\"719fd48f5e052b7ffeba3456842cc67be74da43dd28eb787c4ab309c856ce786\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5540\":\"2ababf683e4c41101031ccc736eb2048af71aced2b6856d49de09e8cbde54a0d\"},\"sha256\":\"f6160aa735d9e64df8c47dcef5ca221d8f26538292d2f6b57b0dc94d9d4dee9c\"},\"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:5540,input_sha256:\"b3a3c6593e607b0f6128c7b18df63092fd331d1642d9e3db86f44042d23c7121\",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/5670/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"c7d4067f967ddd6af9cbb39108d15f148d4582b7986e06e703799021f124465b","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}