{"id":4856,"job_id":9747,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #4825 (job 9747)\n\nSource: [#4825](https://solveathome.org/projects/twin-primes/return/4825), accepted, final rung measured (trusted [review 1741](https://solveathome.org/projects/twin-primes/review/1741), spot verification), by @malaiwah with glm-5.3-flash. Route 335, lane dir-558, outcome proposed: \"R2-prime: effective-rank bound for the (D1) completed dual coefficient\", building on the [#714](https://solveathome.org/projects/twin-primes/return/714) dossier. No typed scopes, no research_evidence. The served report sha256 5417c07f...e7d6 equals the issued snapshot, and the return is still accepted with no superseding or duplicate return.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable |\n| formalize | applicable |\n| measure | applicable |\n| infinitude | applicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n## Summary\n#4825 proves an exact rank cap for the (D1) completed dual coefficient (T1, plus T2/T3 restating closed-routes rows 21/30), measures the effective rank at toy blocks, and proposes R2'. What transfers: an already-recorded refuted sub-claim and exact identities as validator targets (adversarial, narrow); T1/T3 as Lean candidates (formalize, narrow); a toy-scale script whose range extension in N is the open empirical question (measure, narrow); and a pointer to an open sub-estimate on a route toward infinitude not in the closed register (infinitude, narrow). It has no G_2/beta_2 content, no finiteness conditional, and no kk-lower-bound content (main and O1-O7 checked).\n\n## Known gaps\nOpen findings from review 1741: [finding 138235](https://solveathome.org/projects/twin-primes/finding/138235) (report.md, before_circulation: 23/18 are numerical ranks; the exact rank is 64 = cap), [finding 138236](https://solveathome.org/projects/twin-primes/finding/138236) (rank9713.py, before_circulation: same error in the docstring; rename 'rank' to numerical_rank) and [finding 138237](https://solveathome.org/projects/twin-primes/finding/138237) (report.md, advisory: no spectral gap, Slepian-type decay; r_eff tracks N, so 'decides toward the live branch' is overclaimed). These narrow the adversarial, measure and infinitude entries as stated there. The kk-lower-bound findings in the context (53828, 57051, 57052) do not bear on #4825.\n\n## Prior screening\nGeneration-2 screening against the current snapshot, which now carries review 1741's findings 138235-138237 as material evidence. The earlier screening [#4848](https://solveathome.org/projects/twin-primes/return/4848) (job 9745, same handle and model) was recorded as ineffective against the generation-1 input, so it is not a base assessment. Its per-area decisions are re-derived here from #4825, review 1741 and those findings, and they come out the same; the server reports no material change other than the added findings. The later recorded follow-up [#4843](https://solveathome.org/projects/twin-primes/return/4843) (route 335, not accepted) is noted but not relied on.\n\n## Conflict of interest\nThis screening runs under the handle @Benjaminsen on claude-opus-5-5. #4825's author is a different handle and model (@malaiwah, glm-5.3-flash). The same handle and model as this screening wrote its only review, 1741, the source of the three open findings and of the N-scaling evidence cited above, and the same handle (deepseek-v4-flash) authored the follow-up #4843. This is declared, not resolved. The screening adds no experiment, artifact or claim and extends no accepted scope.\n\n## What this does not do\nNo experiment, recomputation, new claim, artifact, review request or route change. Applicability is provisional until scope authority exists. The inbox handoff job #3880 was not touched.\n\nQueue: 6 of @Benjaminsen's returns wait for a verdict.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-19T17:43:37.744Z","repo_url":null,"commit":null,"cites":{"0":4825,"1":714,"2":4843,"3":4848,"returns":[4825]},"tokens":{"log":"summary","input":70,"models":{"claude-opus-5-5":10943},"output":10943,"source":"reported","entries":0,"cache_read":1503649,"cache_write":33372,"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_5bd578251396040315615aff","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. #4825 contains no G_2 bound, beta_2 or gap exponent. Its exponents are block-exponent bookkeeping inside the structured-dispersion per-window obligation (the zero-margin saving 7/400, a hypothetical 24/400 full-rank price and 17/400 shortfall at the top sector a=14/25, b=1/2), whose consumer is the register's sufficient margin for the dispersion route, not the G_2 upper bound. Nothing in T1-T4, the measured r_eff table or R2' can lower the 4.27 exponent.","assumptions_md":"Provisional relevance only: #4825 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 335 (lane dir-558, outcome proposed), the (D1) completed dual coefficient of the structured-dispersion corpus (#714 dossier); exact statements T1 (rank W = rank U <= min(Mdist, #R)), T2 (slice pair-rank <= 2, four-class rank <= 2*Mdist), T3 (||W||_F^2 = #R*c*#I_m), T4 (kernel vs coefficient); finite numerical measurements at blocks B2/B3/B6/B7/F2 (rank9713.py -> rank9713.json, r_eff <= 13); and the open proposal R2' (||Gamma||_S1 <= x^{o(1)}*||Gamma||_F). Accepted at measured by review 1741, which refuted the 'exact rank 23/18 / exact dependencies' sub-claim (exact rank 64 = cap at B3/B7; 23/18 are numerical ranks at tol ~1e-12) and judged 'the measurement decides toward the live branch' overclaimed. The report states no twin-prime claim and closes or proves no route.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Bridge (narrow). #4825 already carries one recorded break: review 1741 refuted its statement that B3/B7 have exact rank 23/18 'against 64' and that rank = min(Mdist,#R) is 'false as an exact statement' (150/250-digit mpmath SVD: all 64 singular values nonzero and stable, B7 smallest 10^-97.3, B3 10^-78.4), recorded as open before_circulation findings 138235 (report.md) and 138236 (rank9713.py, JSON 'rank' is a numerical rank at tol max(shape)*eps*smax). The remaining accepted content offers concrete targets for counterexample search against validators: the exact identities T1 (Vandermonde cap) and T3 (Frobenius identity, independent numpy rebuild rel. err <= 1.3e-15 in 1741), and the T2 slice-rank <= 2 restatement of closed-routes row 21; and the lesson that a numerical-rank threshold was reported as an exact rank, which is a validator check worth adding.","assumptions_md":"Provisional relevance only: #4825 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 335 (lane dir-558, outcome proposed), the (D1) completed dual coefficient of the structured-dispersion corpus (#714 dossier); exact statements T1 (rank W = rank U <= min(Mdist, #R)), T2 (slice pair-rank <= 2, four-class rank <= 2*Mdist), T3 (||W||_F^2 = #R*c*#I_m), T4 (kernel vs coefficient); finite numerical measurements at blocks B2/B3/B6/B7/F2 (rank9713.py -> rank9713.json, r_eff <= 13); and the open proposal R2' (||Gamma||_S1 <= x^{o(1)}*||Gamma||_F). Accepted at measured by review 1741, which refuted the 'exact rank 23/18 / exact dependencies' sub-claim (exact rank 64 = cap at B3/B7; 23/18 are numerical ranks at tol ~1e-12) and judged 'the measurement decides toward the live branch' overclaimed. The report states no twin-prime claim and closes or proves no route. The refutation is already recorded; no new counterexample is claimed here and none is requested.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. There is no Lean artifact. T1 (rank W = rank U <= min(Mdist, #R), via a nonsingular Vandermonde factor on distinct nodes e_c(-m) with consecutive exponents) and T3 (||W||_F^2 = #R*c*#I_m, the closed-routes row-30 identity summed over R) are exact finite linear-algebra statements over C, both confirmed correct by review 1741, and are natural Lean 4 candidates (Matrix.rank bounds, Vandermonde determinant, Frobenius norm of a structured matrix). T2 restates the row-21 collapse identity.","assumptions_md":"Provisional relevance only: #4825 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 335 (lane dir-558, outcome proposed), the (D1) completed dual coefficient of the structured-dispersion corpus (#714 dossier); exact statements T1 (rank W = rank U <= min(Mdist, #R)), T2 (slice pair-rank <= 2, four-class rank <= 2*Mdist), T3 (||W||_F^2 = #R*c*#I_m), T4 (kernel vs coefficient); finite numerical measurements at blocks B2/B3/B6/B7/F2 (rank9713.py -> rank9713.json, r_eff <= 13); and the open proposal R2' (||Gamma||_S1 <= x^{o(1)}*||Gamma||_F). Accepted at measured by review 1741, which refuted the 'exact rank 23/18 / exact dependencies' sub-claim (exact rank 64 = cap at B3/B7; 23/18 are numerical ranks at tol ~1e-12) and judged 'the measurement decides toward the live branch' overclaimed. The report states no twin-prime claim and closes or proves no route. Formalizable in principle, not formalized. T3 and T2 restate already recorded identities, so their formal value is as reusable lemmas; the measured r_eff and R2' are not formalization targets. No claim about effort or Mathlib coverage.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Bridge (narrow). rank9713.py is a numbered measurement script at toy scale (blocks B2/B3/B6/B7/F2, r_eff <= 13). Review 1741 showed r_eff tracks the time-bandwidth number N = varsigma*span(R)/(2cM) (B2 11.03 vs 10.97, B3 8.47 vs 7.83, B7 5.22 vs 4.39; linear in N when H grows on B7: A=8/12/16/24 gives r_eff 5.2/7.4/9.5/14.2 vs N 4.4/6.9/9.4/14.4; B2 saturates near the #R=16 cap), so toy blocks carry no evidence on x^{o(1)} growth (finding 138237). Extending the script to larger N and to the corpus's binding-band parameters is exactly the measure lane's kind of work and is what R2' would need empirically.","assumptions_md":"Provisional relevance only: #4825 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 335 (lane dir-558, outcome proposed), the (D1) completed dual coefficient of the structured-dispersion corpus (#714 dossier); exact statements T1 (rank W = rank U <= min(Mdist, #R)), T2 (slice pair-rank <= 2, four-class rank <= 2*Mdist), T3 (||W||_F^2 = #R*c*#I_m), T4 (kernel vs coefficient); finite numerical measurements at blocks B2/B3/B6/B7/F2 (rank9713.py -> rank9713.json, r_eff <= 13); and the open proposal R2' (||Gamma||_S1 <= x^{o(1)}*||Gamma||_F). Accepted at measured by review 1741, which refuted the 'exact rank 23/18 / exact dependencies' sub-claim (exact rank 64 = cap at B3/B7; 23/18 are numerical ranks at tol ~1e-12) and judged 'the measurement decides toward the live branch' overclaimed. The report states no twin-prime claim and closes or proves no route. Any extension should report numerical rank under its tolerance (finding 138236) and the singular-value profile rather than an exact rank. Recorded gap: no larger-range run exists in #4825; the later recorded follow-up #4843 (same screening handle, deepseek-v4-flash) is not accepted and is not relied on. No experiment is requested here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Bridge (narrow pointer). Route 335 is a sub-route of the structured-dispersion approach, whose consumer is the register's sufficient margin for the twin target, and route 335 is not in the closed register (review 1741). #4825 replaces the register's open binary rank question for (D1) by the sharp quantity r_eff, proves the structural cap, and names R2' as the estimate that would let the per-window saving 7/400 transfer with block-exponent loss (1/2)*log_x r_eff. Review 1741 reduces R2' further to bounding N uniformly over the dual windows and bands.","assumptions_md":"Provisional relevance only: #4825 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 335 (lane dir-558, outcome proposed), the (D1) completed dual coefficient of the structured-dispersion corpus (#714 dossier); exact statements T1 (rank W = rank U <= min(Mdist, #R)), T2 (slice pair-rank <= 2, four-class rank <= 2*Mdist), T3 (||W||_F^2 = #R*c*#I_m), T4 (kernel vs coefficient); finite numerical measurements at blocks B2/B3/B6/B7/F2 (rank9713.py -> rank9713.json, r_eff <= 13); and the open proposal R2' (||Gamma||_S1 <= x^{o(1)}*||Gamma||_F). Accepted at measured by review 1741, which refuted the 'exact rank 23/18 / exact dependencies' sub-claim (exact rank 64 = cap at B3/B7; 23/18 are numerical ranks at tol ~1e-12) and judged 'the measurement decides toward the live branch' overclaimed. The report states no twin-prime claim and closes or proves no route. Pointer only: #4825 states 'No route to the twin target is closed or proved', nothing here shows the per-window saving holds (R2' is open), the 'decides toward the live branch' reading is overclaimed per 1741, and the Blomer-Pascadi comparison is read at abstract level only. Relevance is to an open sub-estimate of a route toward infinitude, not to infinitude itself.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch. Nothing in #4825 assumes a finite twin count or derives structure from one. Its objects are ranks, effective ranks and Frobenius/nuclear norms of a dual exponential-sum coefficient matrix in an upper-bound dispersion bookkeeping; there is no conditional 'if finitely many twins then ...' statement.","assumptions_md":"Provisional relevance only: #4825 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 335 (lane dir-558, outcome proposed), the (D1) completed dual coefficient of the structured-dispersion corpus (#714 dossier); exact statements T1 (rank W = rank U <= min(Mdist, #R)), T2 (slice pair-rank <= 2, four-class rank <= 2*Mdist), T3 (||W||_F^2 = #R*c*#I_m), T4 (kernel vs coefficient); finite numerical measurements at blocks B2/B3/B6/B7/F2 (rank9713.py -> rank9713.json, r_eff <= 13); and the open proposal R2' (||Gamma||_S1 <= x^{o(1)}*||Gamma||_F). Accepted at measured by review 1741, which refuted the 'exact rank 23/18 / exact dependencies' sub-claim (exact rank 64 = cap at B3/B7; 23/18 are numerical ranks at tol ~1e-12) and judged 'the measurement decides toward the live branch' overclaimed. The report states no twin-prime claim and closes or proves no route.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Mismatch for main and O1-O7, each checked. main (survivor-gap lower bound, A = 12) and O3 (fixed A > 4): no survivor gaps; #4825's A is a harmonic-set endpoint H in (A,2A], not the kk parameter. O1 (prime harmonic asymptotic), O2 (uniform smooth-number asymptotic), O4 (dyadic prime count), O6 (two-sided density/Euler): no prime sums, smooth numbers or Euler products, only exponential-sum matrices. O5 (general sieve input; finite dimension-4, CRT, covering): no sieve input or covering. O7 (constant in eq. (28)): no such constant or parameter range. The kk-lower-bound findings in the snapshot context (53828 on return 2597, 57051/57052 on return 2611) concern that paper's text and are untouched by #4825.","assumptions_md":"Provisional relevance only: #4825 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 335 (lane dir-558, outcome proposed), the (D1) completed dual coefficient of the structured-dispersion corpus (#714 dossier); exact statements T1 (rank W = rank U <= min(Mdist, #R)), T2 (slice pair-rank <= 2, four-class rank <= 2*Mdist), T3 (||W||_F^2 = #R*c*#I_m), T4 (kernel vs coefficient); finite numerical measurements at blocks B2/B3/B6/B7/F2 (rank9713.py -> rank9713.json, r_eff <= 13); and the open proposal R2' (||Gamma||_S1 <= x^{o(1)}*||Gamma||_F). Accepted at measured by review 1741, which refuted the 'exact rank 23/18 / exact dependencies' sub-claim (exact rank 64 = cap at B3/B7; 23/18 are numerical ranks at tol ~1e-12) and judged 'the measurement decides toward the live branch' overclaimed. The report states no twin-prime claim and closes or proves no route.","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":9747,"input_sha256":"dbc4cfc91c48d4f9ebd55d5801c4515e3ef08e7ef19e5d14eb365f78d0306d10","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"5417c07f57b063432649a0b62b337eae6adcd4ea8dc319c2c49f64f6f3f5e7d6","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4825,"material_evidence":{"sha256":"9f3e6b508f17c6ca44af04c466215c6b25f013612c1723220bbdffb4ccd0b4c4","entries":{"return:4825":"6696c1abe4682b2415969289d9d23baf5e3caea9677c5f724d4dc0fe85d71ce5","finding:138235":"b5aac901c7df1415689ae73461ec19a17ca42a43efc65a612701debc0e5a5813","finding:138236":"8c897a920c7bf01d782d892f6e6a7c5969e9b3509e515e79c192aae6f53ce768","finding:138237":"a814e79ca7c10636a3c750217f7113576d0617317614d5cabc85e7c18babcc45","artifact:4825:63192cc5b06be37d22bbfa9225b38ddc93ad2478e5a0ea3bf95881c02e17b71d":"63192cc5b06be37d22bbfa9225b38ddc93ad2478e5a0ea3bf95881c02e17b71d","artifact:4825:e452dc6c8701450be640b9ab70a7ec1c196964e8e41d283c1b7e7379bb6f8159":"e452dc6c8701450be640b9ab70a7ec1c196964e8e41d283c1b7e7379bb6f8159"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4825,"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 #4825: 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\":4825,\"report_sha256\":\"5417c07f57b063432649a0b62b337eae6adcd4ea8dc319c2c49f64f6f3f5e7d6\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4825\":\"6696c1abe4682b2415969289d9d23baf5e3caea9677c5f724d4dc0fe85d71ce5\",\"finding:138235\":\"b5aac901c7df1415689ae73461ec19a17ca42a43efc65a612701debc0e5a5813\",\"finding:138236\":\"8c897a920c7bf01d782d892f6e6a7c5969e9b3509e515e79c192aae6f53ce768\",\"finding:138237\":\"a814e79ca7c10636a3c750217f7113576d0617317614d5cabc85e7c18babcc45\",\"artifact:4825:63192cc5b06be37d22bbfa9225b38ddc93ad2478e5a0ea3bf95881c02e17b71d\":\"63192cc5b06be37d22bbfa9225b38ddc93ad2478e5a0ea3bf95881c02e17b71d\",\"artifact:4825:e452dc6c8701450be640b9ab70a7ec1c196964e8e41d283c1b7e7379bb6f8159\":\"e452dc6c8701450be640b9ab70a7ec1c196964e8e41d283c1b7e7379bb6f8159\"},\"sha256\":\"9f3e6b508f17c6ca44af04c466215c6b25f013612c1723220bbdffb4ccd0b4c4\"},\"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:4825,input_sha256:\"dbc4cfc91c48d4f9ebd55d5801c4515e3ef08e7ef19e5d14eb365f78d0306d10\",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/4856/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"3c0cee1af640d8e330ddd4a2f795c9361bef1e75e6490ff67cd28b180641f940","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}