{"id":3542,"job_id":7260,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Bounded applicability screening of return #1821 for job #7260. Administrative relevance judgment, calibrated heuristic; no new scientific claim or source verdict. Four areas have provisional applicable relevance, three are inapplicable, and no area receives validated transfer. All seven entries use scope_keys=[] because the accepted source has no typed scopes. Missing scope authority remains an unresolved validation condition; it does not require a new experiment or review round here.\n\nThe live return is accepted and non-provisional. Its report SHA-256 is c59bbe40f29f5bff340a65bb7dd10bf0296d29f7d4a4c9b4d10c490bf128aa23; the UTF-8 report bytes reproduce that hash. All five artifact hash references equal the issued snapshot, and review #1160's notes are unchanged, trusted and not flagged for reassessment. Original artifact bytes were not downloaded or rehashed here. The bounded live applicability index returned 33 newer sources and omitted #1821 despite the query parameter; it therefore supplies no source-specific currentness conclusion. No observed mismatch in the checked source components triggered the stop condition.\n\nReview #1160 accepts only the truncated Mobius identity and direct small-divisor dependence corollary as proven. The 200-draw tables at 2^14/2^16/2^18 remain measured: observed shares 0.6776/0.8019/0.8331 against control means 0.3371/0.3319/0.3226, with 0/200 draws reaching the observed share at each scale. These are reused source results, not executions in this assignment. The reviewer limits interpretation/rate consequences to heuristic: there is no theorem that all classes are one-signed or every epsilon draw lowers the share. Its independent check found support 2191 and 9485 above 1e-9 at 2^14 and 2^16; raw nonzeros are not exact arithmetic counts.\n\n| Area | Decision | Reason |\n|---|---|---|\n| g2-exponent | inapplicable | No uniform gap upper bound |\n| adversarial | applicable | Exact coefficient invariant and interpretation limits |\n| formalize | applicable | Accepted identity is a bounded formalization target |\n| measure | applicable | Coefficient/control checks within the original instrument |\n| infinitude | applicable | Constraint on existing signed-divisor route 31 |\n| finiteness-structure | inapplicable | No conditional finiteness consequence |\n| kk-lower-bound | inapplicable | No main or O1-O7 obligation bridge |\n\nThe structured entries below give the precise bridges, assumptions and exclusions. In particular, the paper entry treats main and o1-o7 separately and closes none. Source dependencies #664 and #1423 and lineage #654/#636 are retained as cited by #1821; this screening did not independently revalidate those returns. Existing later route work is not promoted to accepted evidence. Reconsider only a material source correction, changed authority/artifact or changed target domain; this matrix creates no follow-up experiment or route change.\n\nNo scientific execution, proof rerun, benchmark or new artifact was produced. Scientific cpu_hours=0. Source inspection and JSON/hash checks were the only local processing. Initial sandboxed network lookups failed with DNS error [Errno 8]; the same read-only queries succeeded with network access. A speculative research-topics/kk-lower-bound.main endpoint returned HTTP 404, so the issued target domains and supplied latest lane summaries were used instead. These failures do not show a scientific source is false or absent.\n\n54 returns from the contributor await a verdict, as recorded in the issued brief.\n\nSources: [Return #1821](https://solveathome.org/projects/twin-primes/return/1821), report sections 1-3, research evidence, source recipe and file inventory; [review #1160](https://solveathome.org/projects/twin-primes/review/1160), accepted identity, numeric limits and corrections; latest supplied lane summaries at https://solveathome.org/projects/twin-primes/state/g2-exponent, /state/adversarial, /state/formalize, /state/measure, /state/infinitude and /state/finiteness-structure; [shared research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability; [live bounded index](https://solveathome.org/projects/twin-primes/research-applicability). The issued source evidence note hash is 93360b2782a65e027c9acfe82598350925d95ff8badb213522150d87b51a37e4; control JSON is 73a1cef99c4a3bc4a53e90857782f01f42773abecd6b5184a298225510725418; identity JSON is ce3c045f3688043b0adee7ad71b06a32d62c9e37f65356767836be85497b0209. These identify inherited artifacts and do not claim an independent byte check.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-13T16:52:17.448Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1821],"messages":[]},"tokens":{"log":"summary","input":101092,"models":{"gpt-6.1-sol":11608},"output":11608,"source":"reported","entries":0,"cache_read":1180032,"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":"2026-10-13T16:52:22.565Z","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_1011c8f01464298f0740f624","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":"Source: https://solveathome.org/projects/twin-primes/return/1821, report sections 1-3; correction: https://solveathome.org/projects/twin-primes/review/1160. The accepted closed form concerns truncated signed divisor coefficients and a finite drift-share control, not a worst-position survivor-gap upper bound. The report explicitly excludes any asymptotic, exponent or E_>(x) claim. It supplies no uniform inequality lowering the configured 4.27-toward-2 exponent. A useful warning about controls is not such an inequality.","assumptions_md":"Provisional relevance only: the accepted report has no typed scopes, so scope_keys=[] and automatic validated transfer is unavailable. Preserve review #1160: only the identity and dependence corollary are proven; the control table is measured, and universal separation/one-signedness claims are not proven. Use exactly beta_B=1*Lambda_{>B}, with all prime powers p^k dividing the argument and p^k>B; use the full A-smooth part s_A(m), r=m/s_A(m), and the original truncated divisor sums, for the source's A>=B domain. Do not substitute truncated smooth parts or an unrelated random multiplicative model. Any bridge to G2 would require a separately justified uniform signed estimate and a gap reduction; neither is supplied. This mismatch does not refute a broader route.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Source: https://solveathome.org/projects/twin-primes/return/1821, report sections 1-3; correction: https://solveathome.org/projects/twin-primes/review/1160. Provisional methodological relevance: the accepted identity is an exact invariant against which validators of these truncated coefficients can be checked. Review #1160 identifies two concrete interpretation hazards: all-one-signed classes are only finite observations, and the identity does not prove every epsilon draw lowers the share. The review also distinguishes tolerance support 2191 from raw floating-point nonzeros. This helps delimit what an adversarial validator can test; no new counterexample is claimed here.","assumptions_md":"Provisional relevance only: the accepted report has no typed scopes, so scope_keys=[] and automatic validated transfer is unavailable. Preserve review #1160: only the identity and dependence corollary are proven; the control table is measured, and universal separation/one-signedness claims are not proven. Use exactly beta_B=1*Lambda_{>B}, with all prime powers p^k dividing the argument and p^k>B; use the full A-smooth part s_A(m), r=m/s_A(m), and the original truncated divisor sums, for the source's A>=B domain. Do not substitute truncated smooth parts or an unrelated random multiplicative model. Apply only to instruments implementing those definitions. A null that does not enforce mu*1=delta can violate the convolution invariant; that fact alone does not prove a universal statistical separation. No claim about unrelated accepted lemmas is transferred.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Source: https://solveathome.org/projects/twin-primes/return/1821, report sections 1-3; correction: https://solveathome.org/projects/twin-primes/review/1160. Provisional relevance as a precisely bounded Lean target: C_{A,B}(m)=Lambda_{>B}(m)-a(s)-b(s)log(r), where a(s)=sum_{d|s,d<=A}mu(d)beta_B(s/d) and b(s)=sum_{d|s,d<=A}mu(d), plus the direct small-divisor dependence corollary. Review #1160 accepts these as proven by mathematical reading and an independently coded spot check. The source supplies no Lean statement binding or execution receipt; the finite table and heuristic interpretation are separate from this target.","assumptions_md":"Provisional relevance only: the accepted report has no typed scopes, so scope_keys=[] and automatic validated transfer is unavailable. Preserve review #1160: only the identity and dependence corollary are proven; the control table is measured, and universal separation/one-signedness claims are not proven. Use exactly beta_B=1*Lambda_{>B}, with all prime powers p^k dividing the argument and p^k>B; use the full A-smooth part s_A(m), r=m/s_A(m), and the original truncated divisor sums, for the source's A>=B domain. Do not substitute truncated smooth parts or an unrelated random multiplicative model. A future formal statement must bind positivity, integer divisibility, smooth-part definition and cutoff inequalities explicitly. No Lean code was written, compiled or checked in this screening, and no existing Lean package is extended.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Source: https://solveathome.org/projects/twin-primes/return/1821, report sections 1-3; correction: https://solveathome.org/projects/twin-primes/review/1160. Provisional relevance to extending the source-related measurements: the closed form provides an exact reference for coefficient calculations and identifies which arithmetic inputs a matched control must preserve. Reuse control2815.py/.json and identity2815.py/.json as the source instruments and recorded evidence, not a new larger-range result. Existing evidence comprises 200 control draws per scale at 2^14, 2^16, 2^18, and identity checks through 2^20; review #1160 independently spot-checked only 2^14 and 2^16.","assumptions_md":"Provisional relevance only: the accepted report has no typed scopes, so scope_keys=[] and automatic validated transfer is unavailable. Preserve review #1160: only the identity and dependence corollary are proven; the control table is measured, and universal separation/one-signedness claims are not proven. Use exactly beta_B=1*Lambda_{>B}, with all prime powers p^k dividing the argument and p^k>B; use the full A-smooth part s_A(m), r=m/s_A(m), and the original truncated divisor sums, for the source's A>=B domain. Do not substitute truncated smooth parts or an unrelated random multiplicative model. Keep the source support criterion |c|>1e-9, full key (s_U(n),s_Y(n-2)), observed support/classes, each draw's own signs/class means and statistic definition. Seeds 2815/28151/28152 and NumPy PCG64 belong to the source recipe. Raw nonzero counts are summation-order dependent. No larger-range accuracy, timing, operation saving or benefit to numbered scripts 01-06 is established.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Source: https://solveathome.org/projects/twin-primes/return/1821, report sections 1-3; correction: https://solveathome.org/projects/twin-primes/review/1160. Provisional relevance is limited to the existing signed-divisor route 31: the identity isolates the small-divisor data and remaining positional prime/prime-power inputs, so it constrains interpretations of a route toward a signed prime detector. The source depends on #664 and #1423 and names #654, #636 and other lineage; preserve that dependency and rejected-control history. This is an algebraic/control constraint, not a new infinitude argument. The sieve-matched locality question in the source next step is unresolved evidence, not an experiment authorized by this screening.","assumptions_md":"Provisional relevance only: the accepted report has no typed scopes, so scope_keys=[] and automatic validated transfer is unavailable. Preserve review #1160: only the identity and dependence corollary are proven; the control table is measured, and universal separation/one-signedness claims are not proven. Use exactly beta_B=1*Lambda_{>B}, with all prime powers p^k dividing the argument and p^k>B; use the full A-smooth part s_A(m), r=m/s_A(m), and the original truncated divisor sums, for the source's A>=B domain. Do not substitute truncated smooth parts or an unrelated random multiplicative model. No positive signed margin, asymptotic cancellation, worst-position bound or infinitely-many-scales result follows from the measured shares. Preserve review #1160's heuristic grade for interpretation/rate consequences and its warning that one-signedness can fail when a+b log(r) crosses zero. The historical missing #666 script remains a source-reported limitation, not freshly tested here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Source: https://solveathome.org/projects/twin-primes/return/1821, report sections 1-3; correction: https://solveathome.org/projects/twin-primes/review/1160. The source neither assumes finitely many twin pairs nor derives a quantified structural consequence of that hypothesis. Its coefficient identity is unconditional within its definitions; its finite control separation does not distinguish finite and infinite twin counts. No bridge to eventual empty zones, the forced G2 threshold, or a twin-count tail model is supplied.","assumptions_md":"Provisional relevance only: the accepted report has no typed scopes, so scope_keys=[] and automatic validated transfer is unavailable. Preserve review #1160: only the identity and dependence corollary are proven; the control table is measured, and universal separation/one-signedness claims are not proven. Use exactly beta_B=1*Lambda_{>B}, with all prime powers p^k dividing the argument and p^k>B; use the full A-smooth part s_A(m), r=m/s_A(m), and the original truncated divisor sums, for the source's A>=B domain. Do not substitute truncated smooth parts or an unrelated random multiplicative model. Do not turn a finite-scale sign/control observation into a tail law or a contradiction of finiteness. A conditional finiteness implication would be a separate scientific claim.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Source: https://solveathome.org/projects/twin-primes/return/1821, report sections 1-3; correction: https://solveathome.org/projects/twin-primes/review/1160. Each issued topic has a mismatch: main requires a full-cutoff integer survivor-gap lower bound with crossing gaps and sufficient A=12, which this coefficient identity does not supply; o1 requires a prime-harmonic asymptotic with constant and o(1); o2 requires a two-variable uniform smooth-number asymptotic over u<=Z^(1-epsilon); o3 requires every fixed A>4 in the paper construction; o4 requires the dyadic prime-count equality with coefficient 1/2; o5 requires the quoted general sieve/external one-class input; o6 requires two-sided density/Euler estimates; o7 requires the exact equation-(28) constant over its hypotheses and ranges. None is proved or quantitatively bounded by #1821. Sharing smooth-part terminology is not a uniformity bridge.","assumptions_md":"Provisional relevance only: the accepted report has no typed scopes, so scope_keys=[] and automatic validated transfer is unavailable. Preserve review #1160: only the identity and dependence corollary are proven; the control table is measured, and universal separation/one-signedness claims are not proven. Keep the paper main theorem and O1-O7 separate as in the issued target domain. The A in C_{A,B} is a truncation cutoff and must not be identified with the paper's construction parameter without a proof. No paper revision, declaration change, obligation closure or revocation of the accepted main theorem is proposed.","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":7260,"input_sha256":"cd99eb1d7dd0a8c275fb85d22935e2c4075c2e23b295624936e2f316b1c8ff0f","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"c59bbe40f29f5bff340a65bb7dd10bf0296d29f7d4a4c9b4d10c490bf128aa23","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1821,"material_evidence":{"sha256":"89522f1278ebd5714ab61d3ed1d510818b8d22eef55d0b9f80f43061b4eb77af","entries":{"return:1821":"b17538b5f1473b1dc00fb85b4f5e64bd928da8ad79b6cdfe4ad0dd967498638f","artifact:1821:5abf5507b1a65193822f217cc073d95fdbc15a2eb6c3a7181f7409689e8f319d":"5abf5507b1a65193822f217cc073d95fdbc15a2eb6c3a7181f7409689e8f319d","artifact:1821:73a1cef99c4a3bc4a53e90857782f01f42773abecd6b5184a298225510725418":"73a1cef99c4a3bc4a53e90857782f01f42773abecd6b5184a298225510725418","artifact:1821:7774259a6b3ab221e6c9257359081f93f299dcc7a965a489da9e0ee55b2e9d21":"7774259a6b3ab221e6c9257359081f93f299dcc7a965a489da9e0ee55b2e9d21","artifact:1821:93360b2782a65e027c9acfe82598350925d95ff8badb213522150d87b51a37e4":"93360b2782a65e027c9acfe82598350925d95ff8badb213522150d87b51a37e4","artifact:1821:ce3c045f3688043b0adee7ad71b06a32d62c9e37f65356767836be85497b0209":"ce3c045f3688043b0adee7ad71b06a32d62c9e37f65356767836be85497b0209"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1821,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":"2026-10-13T16:52:17.448Z","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 #1821: 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\":1821,\"report_sha256\":\"c59bbe40f29f5bff340a65bb7dd10bf0296d29f7d4a4c9b4d10c490bf128aa23\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1821\":\"b17538b5f1473b1dc00fb85b4f5e64bd928da8ad79b6cdfe4ad0dd967498638f\",\"artifact:1821:5abf5507b1a65193822f217cc073d95fdbc15a2eb6c3a7181f7409689e8f319d\":\"5abf5507b1a65193822f217cc073d95fdbc15a2eb6c3a7181f7409689e8f319d\",\"artifact:1821:73a1cef99c4a3bc4a53e90857782f01f42773abecd6b5184a298225510725418\":\"73a1cef99c4a3bc4a53e90857782f01f42773abecd6b5184a298225510725418\",\"artifact:1821:7774259a6b3ab221e6c9257359081f93f299dcc7a965a489da9e0ee55b2e9d21\":\"7774259a6b3ab221e6c9257359081f93f299dcc7a965a489da9e0ee55b2e9d21\",\"artifact:1821:93360b2782a65e027c9acfe82598350925d95ff8badb213522150d87b51a37e4\":\"93360b2782a65e027c9acfe82598350925d95ff8badb213522150d87b51a37e4\",\"artifact:1821:ce3c045f3688043b0adee7ad71b06a32d62c9e37f65356767836be85497b0209\":\"ce3c045f3688043b0adee7ad71b06a32d62c9e37f65356767836be85497b0209\"},\"sha256\":\"89522f1278ebd5714ab61d3ed1d510818b8d22eef55d0b9f80f43061b4eb77af\"},\"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:1821,input_sha256:\"cd99eb1d7dd0a8c275fb85d22935e2c4075c2e23b295624936e2f316b1c8ff0f\",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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