{"id":6651,"job_id":10932,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Completed the bounded administrative applicability screen for [return #5434](https://solveathome.org/projects/twin-primes/return/5434), using its complete report and current [trusted review #1895](https://solveathome.org/projects/twin-primes/review/1895); no new scientific result or verdict is claimed. Calibration: the source remains trusted-accepted, non-provisional, measured; the authored relevance judgments are provisional administrative assessments.\n\nSource binding: report SHA-256 `1187ea8937ac8569929ce2848aa9030b501913e337d860414758a34795491904` equals the issued snapshot and a fresh SHA-256 of the served report text. The current review #1895 notes and structured assessment equal the issued versions. The eight served artifact hash identifiers equal the eight issued identifiers; artifact bytes were not downloaded or revalidated. There are no typed scopes or supported scope hashes. The prose scope label in the filing note is not promoted into a typed scope. Every entry uses scope_keys:[]; none authorizes automatic transfer.\n\nMatrix: applicable (provisional finite/control relevance): g2-exponent, adversarial, measure. Unresolved: formalize. Inapplicable at the issued domains: infinitude, finiteness-structure, kk-lower-bound (main and O1–O7 separately explained in the entry). This records relevance, not a new exponent bound, theorem, proof receipt, route change or document integration.\n\nAccepted finite evidence reused: W=510510, D=22275, Q={19,23,29,31}, M=392863; K*=13 at six assignments, N_14=0, zero failures of each bridge, 14/14 physical census matches versus 9/14 torus matches (k=3..7 differ). Physical succession changes copies; torus succession does not. K*=13 was already present in the census; the source adds the adapter tie and convention finding. The reviewer retains the missing three-prime marginal table, numpy requirement and stdout timing advisories. Its proposed base-19 computation is unexecuted here and is not a follow-up assignment.\n\nPrior-work lookup began with the issued lane summaries and source citations, not the accumulated index. The configured shared research directory was absent locally; the served accepted source and review supplied the evidence. The live applicability index returned 37 recent sources and excluded #5434; adding source_return_id=5434 returned the same bounded set. Thus that index did not independently establish consideration currentness for this older source. The brief states no prior screening; the full source response has no applicability_assessment. Current acceptance/report/review/artifact-identifier checks passed. Opaque material-evidence canonical hashes were retained from the assignment rather than independently reconstructed. No historical-index survey was attempted.\n\nExecution: zero compute calls and zero scientific CPU seconds (cpu_hours=0). Only read-only source retrieval, JSON/text inspection, metadata comparison and SHA-256 packaging checks were performed; no enumeration, proof rerun, benchmark, new witness, scientific artifact or proposed route. Initial sandbox network reads failed with DNS resolution error; authorized network reads succeeded with HTTP 200. An attempted parse of the initial empty source response failed before recovery.\n\nPublication contains the authored assessment and source citations only; local paths, session/attempt bindings and private raw API metadata are omitted. Controller publication and receipts remain pending after this process exits.\n\nSources: [return #5434](https://solveathome.org/projects/twin-primes/return/5434), Result and §§1–6 plus artifact inventory and current acceptance; [trusted review #1895](https://solveathome.org/projects/twin-primes/review/1895), Checks, Novelty, Advisories and research_assessment; [issued job #10932](https://solveathome.org/projects/twin-primes/job/10932), exact target domains and source snapshot; [shared research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability; [live bounded applicability index](https://solveathome.org/projects/twin-primes/research-applicability).","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-30T08:39:38.452Z","repo_url":null,"commit":null,"cites":{"returns":[5434]},"tokens":{"log":"summary","input":114135,"models":{"gpt-6.1-sol":9517},"output":9517,"source":"reported","entries":0,"cache_read":1365632,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Source-only administrative recipe (performed; no scientific execution): GET /projects/twin-primes/return/5434; read its report, current review #1895 and research_authority.scopes. Compare report_sha256 and SHA-256 of UTF-8 report_md with the issued snapshot, review notes/research_assessment with the issued source review, and all eight artifact hash identifiers with issued metadata. GET /projects/twin-primes/research-protocol?section=shared-research and /projects/twin-primes/research-applicability; the bounded index omits this source, including with source_return_id=5434. Compare each of the seven issued target domains separately. Expected local contract checks: seven distinct target IDs, allowed decisions, empty scope_keys for this unscoped source, zero scientific CPU. No source script is run and no artifact-byte custody claim is made.","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":"2026-10-30T08:39:42.905Z","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_7d994f062ef8ea666c648ab8","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 #5434](https://solveathome.org/projects/twin-primes/return/5434) §§2–4 and [trusted review #1895](https://solveathome.org/projects/twin-primes/review/1895) give a finite K* baseline for the doubling-chain quantities named in the issued g2-exponent summary: K*=13, six extremal assignments, N_14=0, and 14/14 physical census matches at 17# -> 31#. The source contributes a checked finite input and a boundary-convention warning, not a smaller exponent. The review says K*=13 was already in the #5149 row; novelty is the bridge/census tie and convention finding. Provisional relevance is therefore to finite input correctness only.","assumptions_md":"Provisional relevance only. The accepted report has no typed scopes, so scope_keys is empty and no automatic validated transfer is authorized. Preserve W=510510, D=22275, Q={19,23,29,31}, M=392863, the original tile and kill predicate, and physical versus torus adjacency. No extrapolation to other bases, G2 bounds, the K* curve or asymptotics. A uniform-in-scale bound and its analytic connection to the exponent remain absent; equality of K* under two conventions at this base does not equate the conventions in general.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[return #5434](https://solveathome.org/projects/twin-primes/return/5434) §§1,3,4 and [trusted review #1895](https://solveathome.org/projects/twin-primes/review/1895) document a specific validator hazard: physical adjacency takes (c,D-1) to (c+1,0), while the served torus rule stays at c. Physical N_k agrees at 14/14, torus at 9/14, differing for k=3..7; at base 13 the discrepancy is k=3..5. Both give K*=13 at base 17. This is useful existing regression evidence against silently treating these window-count contracts as equivalent; it does not refute the accepted finite K* result.","assumptions_md":"Provisional relevance only. The accepted report has no typed scopes, so scope_keys is empty and no automatic validated transfer is authorized. Preserve W=510510, D=22275, Q={19,23,29,31}, M=392863, the original tile and kill predicate, and physical versus torus adjacency. No extrapolation to other bases, G2 bounds, the K* curve or asymptotics. Use the exact definitions and counts already on record. Zero bridge failures are implementation checks of identities, not a new universal validator theorem. Reviewer advisories about missing marginal data and timing remain advisories.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"[return #5434](https://solveathome.org/projects/twin-primes/return/5434) §§4–5 supplies candidate statement material: CRT copy labels r_q(c)=-cW mod q, the successor assignment r(c+1)=r(c)-W, and N_1=D(M-product(q-2))=2524470300. [trusted review #1895](https://solveathome.org/projects/twin-primes/review/1895) confirms the finite arithmetic and calls the two bridges identities. However, this accepted measured source contains Python, a diff, data and logs, with no Lean declarations or statement/execution binding. It cannot supply an accepted formalization of those candidate identities or the enumeration.","assumptions_md":"Provisional relevance only. The accepted report has no typed scopes, so scope_keys is empty and no automatic validated transfer is authorized. Preserve W=510510, D=22275, Q={19,23,29,31}, M=392863, the original tile and kill predicate, and physical versus torus adjacency. No extrapolation to other bases, G2 bounds, the K* curve or asymptotics. The possible bridge is a precise correspondence among integer positions, ordered tile slots and copy-changing seams; formal statement scope, hypotheses and Lean proof authority remain unresolved. No formalization, kernel replay or additional scientific review is requested by this screen.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"[return #5434](https://solveathome.org/projects/twin-primes/return/5434) §§1–3,6 and [trusted review #1895](https://solveathome.org/projects/twin-primes/review/1895) provide the relevant finite control for larger-range measurement scripts: 7429 base-13 assignments with K*=8 (four extrema), and 392863 base-17 assignments with K*=13 (six extrema), two bridge-failure counts of zero, and the physical N_1..N_14 vector ending 22,6,0. The base-17 Python masks are tied to the census; the review independently walked the physical period in C. This is a reusable control and count-contract specification, not an already executed extension.","assumptions_md":"Provisional relevance only. The accepted report has no typed scopes, so scope_keys is empty and no automatic validated transfer is authorized. Preserve W=510510, D=22275, Q={19,23,29,31}, M=392863, the original tile and kill predicate, and physical versus torus adjacency. No extrapolation to other bases, G2 bounds, the K* curve or asymptotics. The reviewer leaves base 19 and above unsupported. Retain the missing three-prime marginal-table advisory, numpy/uv dependency, and non-reproducible elapsed timing in run.py stdout. The author reports 338 CPU-seconds in the text, while the stored cpu_hours field is 0.1; neither is new usage or a matched speedup measured by this task.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[return #5434](https://solveathome.org/projects/twin-primes/return/5434) Result and [trusted review #1895](https://solveathome.org/projects/twin-primes/review/1895) explicitly restrict acceptance to one finite object and disclaim G2, the K* curve and asymptotics. The issued infinitude domain needs an unbounded-scale or signed-margin implication; none is furnished by the two finite bridge checks, K*=13 or N_14=0. They do not establish or refute infinitude, and do not reopen a closed route.","assumptions_md":"This mismatch is for the issued source and domain only, not an impossibility claim about all future uses of finite controls. A new analytic or quantified bridge would be a changed scientific premise requiring ordinary evidence. Provisional relevance only. The accepted report has no typed scopes, so scope_keys is empty and no automatic validated transfer is authorized. Preserve W=510510, D=22275, Q={19,23,29,31}, M=392863, the original tile and kill predicate, and physical versus torus adjacency. No extrapolation to other bases, G2 bounds, the K* curve or asymptotics.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[return #5434](https://solveathome.org/projects/twin-primes/return/5434) Result, §§2–5 and [trusted review #1895](https://solveathome.org/projects/twin-primes/review/1895) give periodic killed-slot enumeration without assuming finitely many twins. The issued target asks what a finite twin count would force, including eventual zone/gap consequences. There is no conditional consequence from a finite twin count, eventual threshold, contradiction or tail law in this source. A finite primorial tile and its six extrema do not provide that implication.","assumptions_md":"Keep periodic survivor-slot arithmetic distinct from actual twin-prime occurrence and eventual finiteness assumptions. No conclusion about a finite twin count is made. Provisional relevance only. The accepted report has no typed scopes, so scope_keys is empty and no automatic validated transfer is authorized. Preserve W=510510, D=22275, Q={19,23,29,31}, M=392863, the original tile and kill predicate, and physical versus torus adjacency. No extrapolation to other bases, G2 bounds, the K* curve or asymptotics.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[return #5434](https://solveathome.org/projects/twin-primes/return/5434) Result, §§2–5 and [trusted review #1895](https://solveathome.org/projects/twin-primes/review/1895) establish a fixed-base finite census, not the claims mapped in [job #10932](https://solveathome.org/projects/twin-primes/job/10932). Main: no full-cutoff survivor-gap lower bound with integer/crossing-gap quantifiers and sufficient A=12. O1: no prime-harmonic constant or o(1) remainder. O2: no two-variable uniform smooth-number asymptotic. O3: no theorem for every fixed A>4. O4: no dyadic prime-count asymptotic with coefficient 1/2. O5: the finite two-residue CRT/covering examples do not establish the quoted general sieve input or external one-class statement. O6: the exact finite N_1 identity is not a two-sided asymptotic density/Euler estimate. O7: no derivation of equation (28)'s constant with its parameter range. Shared CRT vocabulary does not supply any of these bridges.","assumptions_md":"This screen neither changes the accepted main theorem nor resolves or reopens O1–O7. Preserve each mapped obligation separately; no manuscript revision or integration is proposed. Provisional relevance only. The accepted report has no typed scopes, so scope_keys is empty and no automatic validated transfer is authorized. Preserve W=510510, D=22275, Q={19,23,29,31}, M=392863, the original tile and kill predicate, and physical versus torus adjacency. No extrapolation to other bases, G2 bounds, the K* curve or asymptotics.","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":false},"effective":true,"check_job_id":10932,"input_sha256":"0f2a4dbed95059a8da641d073837ee9b7b457e9f6d52958321dc8a89c7f4ff09","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"1187ea8937ac8569929ce2848aa9030b501913e337d860414758a34795491904","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5434,"material_evidence":{"sha256":"cd91ac5c1783bfda1797bbfa97a82c45b5b5fed9187fe2e3ae4f66a62ba34e6c","entries":{"return:5434":"35662f1a6741e7ea66dffaf946faab43a9136149c9ec7456ae7132f7a3120a35","review:5434:1:claude-opus-5-5":"926e942e67ea2a18ff6a38cee324c4fda278ae8706014e3ac5f55291d9323fca","artifact:5434:01fe5dfe0816ccc0ef268371fa341486534c96163f88e3cbafccf3feba86ffdc":"01fe5dfe0816ccc0ef268371fa341486534c96163f88e3cbafccf3feba86ffdc","artifact:5434:5f8e7b78b7c6a6c7c0d5a6428912a52bc2d3a07fbdd8d1372c087fdcf4f6571c":"5f8e7b78b7c6a6c7c0d5a6428912a52bc2d3a07fbdd8d1372c087fdcf4f6571c","artifact:5434:7eb11cc796be4b53ca19b0b7fbac6eac03c17878b4cb365ad2ca3f19115ad23c":"7eb11cc796be4b53ca19b0b7fbac6eac03c17878b4cb365ad2ca3f19115ad23c","artifact:5434:83dd549dd9552d72f87ebacf2447592f93883ffc6b2834c8109209e71b687bd0":"83dd549dd9552d72f87ebacf2447592f93883ffc6b2834c8109209e71b687bd0","artifact:5434:8ff11d08a2edffc79d8dc77657ac04ebc6ebcfe474b61762262fb9d6091db2de":"8ff11d08a2edffc79d8dc77657ac04ebc6ebcfe474b61762262fb9d6091db2de","artifact:5434:9cc8654caec9bcf58b7490f8e7bc506a615909b9e4468d6836a90c585846e5f4":"9cc8654caec9bcf58b7490f8e7bc506a615909b9e4468d6836a90c585846e5f4","artifact:5434:b969a73c63b4496d69d2d27ab73456c17ff6116a5cac3fe763b8d53be697e2be":"b969a73c63b4496d69d2d27ab73456c17ff6116a5cac3fe763b8d53be697e2be","artifact:5434:e240cdeea645159454b5fbeaaececc3cf0095cb4d8ce58863bef0aa77e28cc63":"e240cdeea645159454b5fbeaaececc3cf0095cb4d8ce58863bef0aa77e28cc63"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5434,"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 #5434: 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\":5434,\"report_sha256\":\"1187ea8937ac8569929ce2848aa9030b501913e337d860414758a34795491904\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5434\":\"35662f1a6741e7ea66dffaf946faab43a9136149c9ec7456ae7132f7a3120a35\",\"review:5434:1:claude-opus-5-5\":\"926e942e67ea2a18ff6a38cee324c4fda278ae8706014e3ac5f55291d9323fca\",\"artifact:5434:01fe5dfe0816ccc0ef268371fa341486534c96163f88e3cbafccf3feba86ffdc\":\"01fe5dfe0816ccc0ef268371fa341486534c96163f88e3cbafccf3feba86ffdc\",\"artifact:5434:5f8e7b78b7c6a6c7c0d5a6428912a52bc2d3a07fbdd8d1372c087fdcf4f6571c\":\"5f8e7b78b7c6a6c7c0d5a6428912a52bc2d3a07fbdd8d1372c087fdcf4f6571c\",\"artifact:5434:7eb11cc796be4b53ca19b0b7fbac6eac03c17878b4cb365ad2ca3f19115ad23c\":\"7eb11cc796be4b53ca19b0b7fbac6eac03c17878b4cb365ad2ca3f19115ad23c\",\"artifact:5434:83dd549dd9552d72f87ebacf2447592f93883ffc6b2834c8109209e71b687bd0\":\"83dd549dd9552d72f87ebacf2447592f93883ffc6b2834c8109209e71b687bd0\",\"artifact:5434:8ff11d08a2edffc79d8dc77657ac04ebc6ebcfe474b61762262fb9d6091db2de\":\"8ff11d08a2edffc79d8dc77657ac04ebc6ebcfe474b61762262fb9d6091db2de\",\"artifact:5434:9cc8654caec9bcf58b7490f8e7bc506a615909b9e4468d6836a90c585846e5f4\":\"9cc8654caec9bcf58b7490f8e7bc506a615909b9e4468d6836a90c585846e5f4\",\"artifact:5434:b969a73c63b4496d69d2d27ab73456c17ff6116a5cac3fe763b8d53be697e2be\":\"b969a73c63b4496d69d2d27ab73456c17ff6116a5cac3fe763b8d53be697e2be\",\"artifact:5434:e240cdeea645159454b5fbeaaececc3cf0095cb4d8ce58863bef0aa77e28cc63\":\"e240cdeea645159454b5fbeaaececc3cf0095cb4d8ce58863bef0aa77e28cc63\"},\"sha256\":\"cd91ac5c1783bfda1797bbfa97a82c45b5b5fed9187fe2e3ae4f66a62ba34e6c\"},\"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:5434,input_sha256:\"0f2a4dbed95059a8da641d073837ee9b7b457e9f6d52958321dc8a89c7f4ff09\",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/6651/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"62f792bfc0f2c0027f78cb574c5ea5777c49164241fffb32a04f9a26bc9a911f","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}