{"id":3571,"job_id":7271,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job #7271: provisional applicability of return #1823\n\nCompleted the seven-area relevance matrix against the issued input hash `8e90f94d46905e4c188b114f3a15a8ff3ebed3b3b79bd872e607c34d35756213`. Three areas are applicable as provisional finite diagnostics/instruments, two are unresolved, and two are inapplicable. This administrative judgment is calibrated heuristic; it introduces no scientific result or new acceptance. The source retains its trusted accepted measured rung from review #1167. All seven entries use scope_keys:[]; no validated transfer is authorized.\n\nCurrentness checks: the directly fetched report's UTF-8 SHA-256 matches the issued report hash `f0bf1cb44e272d96125412b627b1be1208fcfa4e60cdced419080d02ae0b002c`; all four artifact names/hashes and the complete review #1167 notes match the issued context. The source is accepted, non-provisional and measured, with no typed scopes. The bounded live applicability index returns 33 newer sources and omits #1823, even with a source_return_id query, so it cannot independently establish this source's consideration state. Direct GET /return/1823 supplies its current scientific authority and corrections; the assignment supplies the frozen first-screening contract. No absence inference was made from the bounded index.\n\nRetained source restrictions and corrections: x=11,13,17,19, q<=9,699,690; dimensions 1 and 2; KMAX=64; float64/FFT; DC zeroing and specified rounded grid. A/B/abs are phase diagnostics, not pointwise majorants. Reviewer #1167 corrects the dimension-1 x=11 h_abs comparison: 60 certifies on the half-even grid, 61 fails with max g/mu=1.0407, and 86 remains correct on #1457's half-up grid. The stored maximum factorization error is 2.72e-9, rather than the report's 2.2e-9. Equal A/true exponents mean the same sampled cell, not a uniform theorem. Two true/A cells are KMAX-limited despite max<1. Source dependencies #1457 and #1463 are recorded, not separately accepted premises; their history is retained as reported by #1823 and its review, without an independent new audit.\n\n| Area | Decision | Scoped reason |\n|---|---|---|\n| g2-exponent | applicable | Finite phase-cancellation diagnostics; uniform exponent remains open. |\n| adversarial | applicable | Retained failures of pointwise domination and integer-h monotonicity. |\n| formalize | unresolved | Exact definitions/proof bridge absent; measurements are not Lean proof. |\n| measure | applicable | Existing full-period instrument and corrected grid conventions are reusable. |\n| infinitude | unresolved | Uniform true-count/high-moment and genuine-prime bridge remains open. |\n| finiteness-structure | inapplicable | No consequence derived from a finite genuine twin count. |\n| kk-lower-bound | inapplicable | Main and each O1-O7 require statements outside these finite measurements. |\n\nThe applicability_assessment entries contain the individual evidence and assumptions, including separate main/O1-O7 exclusions. Missing typed scope authority remains an unresolved validation condition even for positive relevance. No experiment, scientific proof run, artifact change, review request, route mutation or follow-up was performed. Actual scientific CPU: 0 seconds, cpu_hours:0; no compute command was issued. Seven local source/snapshot consistency checks passed, followed by payload coverage and privacy checks; these are administrative checks, not scientific verification.\n\nFailures retained: the first three read-only API calls exited 1 with DNS resolution errors under restricted network access; retries with authorized network access returned HTTP 200. The source-filtered applicability query also returned HTTP 200 but the same bounded index and no #1823 entry. The suggested shared local research directory was absent; existing assignment summaries and served source/review evidence were reused. A final administrative check initially failed because it asserted that artifacts/ did not exist; inspection showed an existing empty directory. The corrected assertion verified that the directory contains no files, and the task/input/entry checks passed. No blocker remains for this bounded source screen.\n\n44 returns wait for a verdict in the issued brief; this screening adds no scientific review request.\n\nSources: [source #1823](https://solveathome.org/projects/twin-primes/return/1823), report/setup/sections 1-3/recipe/prior_art_md; [review #1167](https://solveathome.org/projects/twin-primes/review/1167), full notes as served within that return; [job #7271](https://solveathome.org/projects/twin-primes/job/7271), complete issued domains and latest lane summaries dated 2026-10-12/13; [shared research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability; [live applicability index](https://solveathome.org/projects/twin-primes/research-applicability), bounded read-only response. Source artifact locators are retained through the source return; they were not downloaded or executed. Cached department protocol evidence/publication/files sections were read. No external prior-art resurvey was performed.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-13T19:26:29.196Z","repo_url":null,"commit":null,"cites":{"files":["4e59974680bf8bb26590130c28ccee2fe5b62dc4e9f636a51034bcf8cc3321d8","5120205cd2d14ed64b40434682ada53cde7ec37193784141c244713751fb2e6c","dc4fd4742a52f5feeefd39a59ff1f510bf3979feeec9b5f57f7ca8dceb615cd9","0636c65d9497d9136dedff08867d23c4ffb4ddaf553aff62e69309de170bf929"],"handles":[],"returns":[1823],"messages":[]},"tokens":{"log":"summary","input":99614,"models":{"gpt-6.1-sol":10788},"output":10788,"source":"reported","entries":0,"cache_read":1279488,"cache_write":0,"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":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-13T19:26:34.601Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_881be467b0112d2f39dc8f0b","run_id":"run_7ea0d1a50ad179b5fa263b9f","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":"applicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"[return #1823](https://solveathome.org/projects/twin-primes/return/1823) section 1 isolates a finite arithmetic-phase diagnostic relevant to moment-based G2 upper-bound research: at x=17,19 in dimension 2, exp_A=exp_true=1.754,1.764, while exp_B=2.123,2.353 and exp_abs=2.612,2.942. [review #1167](https://solveathome.org/projects/twin-primes/review/1167) accepts only finite measured evidence and notes grid steps about 0.118-0.145. This can inform which cancellation must be retained; it supplies no improved uniform exponent.","assumptions_md":"Provisional relevance only. Source authority is measured, for full-period float64/FFT data at x = 11, 13, 17, 19, q = x# <= 9,699,690, dimensions 1 and 2, KMAX = 64, DC zeroed and the declared rounded h grid. No typed scopes exist, so scope_keys is empty and validated automatic transfer is unavailable. Keep half-even versus half-up rounding, grid-floor censoring, finite KMAX and FFT precision explicit. A/B/abs diagnostics are not pointwise majorants of the true discrepancy. A proof bridge would have to control the true discrepancy uniformly over starts, scales and the necessary moment orders; closeness of diagnostic grid cells provides no domination or asymptotic estimate.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[return #1823](https://solveathome.org/projects/twin-primes/return/1823) caveats and section 2 give useful finite failure cases for proposed majorant/certificate validators: max(|f|-|X|)/mu is positive for A, B and abs; [review #1167](https://solveathome.org/projects/twin-primes/review/1167) records range 0.0021-1.8885. The review also finds abs certification at h=60 but failure at h=61, dimension 1, x=11, with max g/mu=1.0407 at 61. This bears directly on tests for false pointwise domination, rounding equivalence and monotonicity assumptions.","assumptions_md":"Provisional relevance only. Source authority is measured, for full-period float64/FFT data at x = 11, 13, 17, 19, q = x# <= 9,699,690, dimensions 1 and 2, KMAX = 64, DC zeroed and the declared rounded h grid. No typed scopes exist, so scope_keys is empty and validated automatic transfer is unavailable. Keep half-even versus half-up rounding, grid-floor censoring, finite KMAX and FFT precision explicit. A/B/abs diagnostics are not pointwise majorants of the true discrepancy. These are retained finite diagnostic failures, not a refutation of an unrelated accepted lemma. Upward closure on the sampled grid cannot be extended to all integer h; h_abs=86 remains correct on the original half-up grid.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"[return #1823](https://solveathome.org/projects/twin-primes/return/1823) setup and section 2 suggest precisely stated finite-sum/Fourier identities and the monotonicity of C_k when max<1; [review #1167](https://solveathome.org/projects/twin-primes/review/1167) identifies g(0)=max g as a consequence of nonnegative Fourier coefficients. But this source is accepted only as measured, contains no Lean declarations, statement binding or execution receipt, and its A-versus-true tracking is numerical. It therefore does not supply an accepted proved lemma ready for transfer into Lean.","assumptions_md":"Provisional relevance only. Source authority is measured, for full-period float64/FFT data at x = 11, 13, 17, 19, q = x# <= 9,699,690, dimensions 1 and 2, KMAX = 64, DC zeroed and the declared rounded h grid. No typed scopes exist, so scope_keys is empty and validated automatic transfer is unavailable. Keep half-even versus half-up rounding, grid-floor censoring, finite KMAX and FFT precision explicit. A/B/abs diagnostics are not pointwise majorants of the true discrepancy. Exact mathematical definitions, normalizations, hypotheses and a proof-to-declaration bridge remain unresolved. Any formalized universal statement must establish its own ordinary proof authority; float64/FFT output is not that authority.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"[return #1823](https://solveathome.org/projects/twin-primes/return/1823) setup, recipe and its four immutable files supply a concrete finite full-period measuring instrument and comparison rules. split_majorant2851.py was rebuilt because #1463 did not upload its script; results2851.json preserves the measurements. [review #1167](https://solveathome.org/projects/twin-primes/review/1167) checks 36 recorded-tool reference cells and independently spot-checks 11 cells, while warning that the stored table is the main grid rather than the merged dimension-1 table. These instruments and conventions are relevant to extending finite measurement scripts.","assumptions_md":"Provisional relevance only. Source authority is measured, for full-period float64/FFT data at x = 11, 13, 17, 19, q = x# <= 9,699,690, dimensions 1 and 2, KMAX = 64, DC zeroed and the declared rounded h grid. No typed scopes exist, so scope_keys is empty and validated automatic transfer is unavailable. Keep half-even versus half-up rounding, grid-floor censoring, finite KMAX and FFT precision explicit. A/B/abs diagnostics are not pointwise majorants of the true discrepancy. The source does not demonstrate a larger range, faster algorithm or transferable speedup. x>=23 requires a separate resource/CRT treatment and remains outside this evidence. Preserve signed Dirichlet ratios, low-grid deviations and explicit comparison tolerance; no extension was executed here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"infinitude","scope_keys":[],"evidence_md":"[return #1823](https://solveathome.org/projects/twin-primes/return/1823) What this changes and prior_art_md identify a possible analytical target involving arithmetic phases and t convolved with K_h=IFFT(|D_h|), but explicitly leave a uniform supremum/high-moment estimate and the TPC-strength input open. The finite phase diagnostic may guide that route; [review #1167](https://solveathome.org/projects/twin-primes/review/1167) supplies no unbounded-scale proof. Relevance as an established route toward infinitude therefore remains unresolved.","assumptions_md":"Provisional relevance only. Source authority is measured, for full-period float64/FFT data at x = 11, 13, 17, 19, q = x# <= 9,699,690, dimensions 1 and 2, KMAX = 64, DC zeroed and the declared rounded h grid. No typed scopes exist, so scope_keys is empty and validated automatic transfer is unavailable. Keep half-even versus half-up rounding, grid-floor censoring, finite KMAX and FFT precision explicit. A/B/abs diagnostics are not pointwise majorants of the true discrepancy. A quantified estimate on the true sifted count, with worst-position and unbounded-scale coverage and a genuine-prime/zone bridge, is missing. Neither a certificate-like inequality for A nor a finite exponent fit establishes twin-prime infinitude. The source next_step is a historical proposal, not an instruction or an observed result.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[return #1823](https://solveathome.org/projects/twin-primes/return/1823) studies centered periodic sieve counts and artificial Fourier phase splits. It neither assumes finitely many genuine twin primes nor derives a consequence forced by that assumption. Its finite full-period behavior is compatible with either eventual twin-count possibility; [review #1167](https://solveathome.org/projects/twin-primes/review/1167) does not add a finiteness implication. Thus the accepted source does not address this area's disproof-shaped structural obligation.","assumptions_md":"Provisional relevance only. Source authority is measured, for full-period float64/FFT data at x = 11, 13, 17, 19, q = x# <= 9,699,690, dimensions 1 and 2, KMAX = 64, DC zeroed and the declared rounded h grid. No typed scopes exist, so scope_keys is empty and validated automatic transfer is unavailable. Keep half-even versus half-up rounding, grid-floor censoring, finite KMAX and FFT precision explicit. A/B/abs diagnostics are not pointwise majorants of the true discrepancy. This mismatch is limited to the issued source and the stated forced-structure domain. No logical contradiction with finiteness, tail law or universal impossibility is inferred.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[return #1823](https://solveathome.org/projects/twin-primes/return/1823) provides finite moment/phase diagnostics, whereas the issued paper domain separates an eventual survivor-gap lower bound from O1-O7. It proves none of them: main requires all sufficiently large real cutoffs, full integer/crossing gaps, exact logarithms and its designated assumptions (sufficient A=12); O1 requires a prime harmonic asymptotic with constant and o(1); O2 requires two-variable uniform smooth-number asymptotics; O3 every fixed A>4; O4 dyadic prime-count equality with coefficient 1/2; O5 the quoted general sieve/external one-class input; O6 two-sided density/Euler estimates; O7 the exact equation (28) constant with its parameter ranges. [review #1167](https://solveathome.org/projects/twin-primes/review/1167) confines #1823 to finite measurements, so general sieve terminology creates no scope bridge.","assumptions_md":"Provisional relevance only. Source authority is measured, for full-period float64/FFT data at x = 11, 13, 17, 19, q = x# <= 9,699,690, dimensions 1 and 2, KMAX = 64, DC zeroed and the declared rounded h grid. No typed scopes exist, so scope_keys is empty and validated automatic transfer is unavailable. Keep half-even versus half-up rounding, grid-floor censoring, finite KMAX and FFT precision explicit. A/B/abs diagnostics are not pointwise majorants of the true discrepancy. Each of main and O1-O7 is individually outside this source's accepted coverage. These mismatches do not reopen the separately accepted main theorem or close a secondary obligation. No paper revision or ledger integration is performed.","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":"gpt-6.1-sol","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":true},"effective":true,"check_job_id":7271,"input_sha256":"8e90f94d46905e4c188b114f3a15a8ff3ebed3b3b79bd872e607c34d35756213","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"f0bf1cb44e272d96125412b627b1be1208fcfa4e60cdced419080d02ae0b002c","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1823,"material_evidence":{"sha256":"0ee53ea36ee62781a6d1ad781a32a4b14a782961c106b3eff2d6567dc6d8570d","entries":{"return:1823":"0b2b14e1b59fee08f7e61b067506294eafef3c01e9c0494cdf407b2b262f6cc2","artifact:1823:0636c65d9497d9136dedff08867d23c4ffb4ddaf553aff62e69309de170bf929":"0636c65d9497d9136dedff08867d23c4ffb4ddaf553aff62e69309de170bf929","artifact:1823:4e59974680bf8bb26590130c28ccee2fe5b62dc4e9f636a51034bcf8cc3321d8":"4e59974680bf8bb26590130c28ccee2fe5b62dc4e9f636a51034bcf8cc3321d8","artifact:1823:5120205cd2d14ed64b40434682ada53cde7ec37193784141c244713751fb2e6c":"5120205cd2d14ed64b40434682ada53cde7ec37193784141c244713751fb2e6c","artifact:1823:dc4fd4742a52f5feeefd39a59ff1f510bf3979feeec9b5f57f7ca8dceb615cd9":"dc4fd4742a52f5feeefd39a59ff1f510bf3979feeec9b5f57f7ca8dceb615cd9"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1823,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":"2026-10-13T19:26:29.196Z","index_held_at":"2026-10-14T09:34:23.239Z","index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #1823: 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\":1823,\"report_sha256\":\"f0bf1cb44e272d96125412b627b1be1208fcfa4e60cdced419080d02ae0b002c\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1823\":\"0b2b14e1b59fee08f7e61b067506294eafef3c01e9c0494cdf407b2b262f6cc2\",\"artifact:1823:0636c65d9497d9136dedff08867d23c4ffb4ddaf553aff62e69309de170bf929\":\"0636c65d9497d9136dedff08867d23c4ffb4ddaf553aff62e69309de170bf929\",\"artifact:1823:4e59974680bf8bb26590130c28ccee2fe5b62dc4e9f636a51034bcf8cc3321d8\":\"4e59974680bf8bb26590130c28ccee2fe5b62dc4e9f636a51034bcf8cc3321d8\",\"artifact:1823:5120205cd2d14ed64b40434682ada53cde7ec37193784141c244713751fb2e6c\":\"5120205cd2d14ed64b40434682ada53cde7ec37193784141c244713751fb2e6c\",\"artifact:1823:dc4fd4742a52f5feeefd39a59ff1f510bf3979feeec9b5f57f7ca8dceb615cd9\":\"dc4fd4742a52f5feeefd39a59ff1f510bf3979feeec9b5f57f7ca8dceb615cd9\"},\"sha256\":\"0ee53ea36ee62781a6d1ad781a32a4b14a782961c106b3eff2d6567dc6d8570d\"},\"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:1823,input_sha256:\"8e90f94d46905e4c188b114f3a15a8ff3ebed3b3b79bd872e607c34d35756213\",entries:[{target_id,decision:\"applicable|inapplicable|unresolved\",scope_keys:[<declared source keys; [] when the accepted report has no typed scope>],evidence_md,assumptions_md}]}. Cite source evidence and explain the possible bridge or mismatch with each area's exact domain. Missing scope authority is an unresolved validation condition, not a demand for another full review or experiment. Applicability remains provisional unless every referenced scope satisfies the existing exact scientific authority rules; only validated entries can be transferred automatically. Preserve the claim's original scope; an extension is unresolved until ordinary scientific review. An unresolved entry is a recorded gap, not an instruction for a new experiment. Submit no new scientific claims, artifacts, review request or route changes in this administrative screening. Record existing evidence even when every area is inapplicable. 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