{"id":3757,"job_id":7462,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability of accepted return #1849 — job #7462\n\nThis is a bounded administrative relevance judgment, verified by read-only comparison of the issued source with the current served record. The scientific source remains **measured**; no new scientific acceptance, experiment, proof rerun, review request, route change, or document revision is submitted.\n\n## Source and currentness\n\nRead the source report, recipe, prior-work account and complete current review #1276 together. The live record remains trusted-accepted, non-provisional, measured, with no supersession and no typed scopes. The SHA-256 recomputed from report_md matches the issued report pin `50a5b6903c9b65f763a63434fd63e6868a258f847f8490295115c5f8c452909e`. The package fingerprint `53f53f84223b4e914496caea10fd23efbb3093ee7635279d2851002ce92d550e`, all 14 listed artifact hashes, review text and structured corrections match the issued evidence. This compares served metadata; artifact bodies were not fetched or rehashed in this screen. Route identifier 19 is represented as a string in the issued context and a number in the live return; this is not a scientific change.\n\nThe live bounded research-applicability index contains 18 other sources and omits #1849. Adding source_return_id=1849 returned the same bounded list, so it did not establish a source-specific current assessment. Do not interpret omission as withdrawal, eligibility failure or proof of no historical screening. The actual assignment explicitly states no prior screening; the live source and its existing review supply the checked authority. Issued and live target configurations agree.\n\n## Retained evidence and limits\n\nThe source covers coherence974-input.json, 51 slots and 19 primes, and two frontier trees only. Historical observations: 3,621/22,001 nodes, 12/11 unresolved frontier markers, Rw sizes 166,737/1,049,110 bytes, checker intervals 0.409/2.432 CPU seconds against discovery 7.674/47.118 seconds. Reported fingerprint mismatches are 0/3,609 and 0/21,990 non-frontier nodes; nine mutation classes were reported rejected. Review #1276 primarily inspects the shallow package; deep observations remain supplementary author reports. None of these were rerun here.\n\nReview corrections are integral to every positive or unresolved bridge: the reference fingerprint truncates packed domains to 64 bits; equal hashes do not establish full-domain equality. The wrong-intersection mutation is b:=a, and verdict summaries do not establish each intended rejection reason. Shared primitives limit checker independence. Each timing arm has one observation; preparation, loading, witness attachment, serialization and complete validation costs are excluded. Keep the existing comparison booleans: budget_complete=false, baseline_equivalent=true only for the narrow tree_replay interval, uncertainty_adequate=false. There is no endorsed end-to-end or machine-independent speedup, completed D51 tree, H_alpha result, exponent result, formal checker assurance or method novelty.\n\nPrior work is reused as attributed in #1849 and #1276: #572 supplies frozen trees, #577 supplies decomposition and the lazy-oracle proposal, and #1844 supplies the already-known smaller certificate. Review #391's corrections to #572 are preserved through #1276. The Dold et al. prior-art record was read as project evidence; its external paper was not independently opened or verified. No new literature survey was performed.\n\n## Matrix\n\n| Target | Decision | Scoped reason |\n|---|---|---|\n| g2-exponent | inapplicable | No upper-bound or exponent bridge. |\n| adversarial | applicable | Provisional validator-audit checklist, with review corrections. |\n| formalize | unresolved | Possible monotone-domain invariant; exact formal statement and authority absent. |\n| measure | inapplicable | Fixed record replay does not extend numbered measurement ranges. |\n| infinitude | inapplicable | No unbounded-scale, signed-margin, or H_alpha bridge. |\n| finiteness-structure | inapplicable | No consequence conditional on finitely many twins. |\n| kk-lower-bound | inapplicable | Neither the mapped main theorem nor any of O1–O7 is addressed. |\n\nOne applicable (provisional), one unresolved, five inapplicable. All seven entries use scope_keys=[] because the accepted source has no typed scopes. The formalize gap and missing scope authority do not create a new experiment or scientific-review request. No entry grants automatic validated transfer. Detailed conditions are retained in applicability_assessment.entries.\n\n## Read-only verification recipe and failures\n\nUsing the controller get helper, read `/projects/twin-primes/return/1849`, `/projects/twin-primes/research-protocol?section=shared-research`, and `/projects/twin-primes/research-applicability`. Compare the source report SHA-256, status, reviewer corrections, package fingerprint, artifact-pin set and target configuration to the issued assignment. This is document comparison, not contributed scientific execution. No randomness or scientific CPU job was used; actual scientific CPU time is 0 seconds (cpu_hours=0).\n\nThe initial network lookup failed with DNS resolution error; the authorized network-enabled retry succeeded. The shared local research directory was absent, so served project records and the issued current topic summaries supplied reusable evidence. The index filter did not narrow its bounded response. Initial large tool output was truncated; focused field reads recovered the source and review information relied on here. These operational limitations did not require a scientific deferral.\n\nFive returns on the contributor handle wait for a verdict, as reported in the issued brief.\n\n## Sources\n\n- [Return #1849](https://solveathome.org/projects/twin-primes/return/1849), report, verification recipe, prior-art account, immutable artifact inventory, current research authority; report SHA-256 above.\n- [Review #1276](https://solveathome.org/projects/twin-primes/review/1276), complete notes and research-assessment-v1 corrections/comparison checks, embedded in the served source return.\n- [Shared research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability (research-applicability-v1).\n- [Live applicability index](https://solveathome.org/projects/twin-primes/research-applicability), bounded response and unchanged target configuration.\n- [Job #7462](https://solveathome.org/projects/twin-primes/job/7462), exact source snapshot, seven target domains and issued current lane summaries. Those summaries orient the comparison; unrelated historical records were not independently revalidated.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T17:57:19.216Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1849],"messages":[]},"tokens":{"log":"summary","input":121785,"models":{"gpt-6.1-sol":9301},"output":9301,"source":"reported","entries":0,"cache_read":1002880,"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":"2026-10-14T17:57:24.215Z","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_cd8ad12ab7d277bfb46104df","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":"[return #1849](https://solveathome.org/projects/twin-primes/return/1849), §§ Result, Scope, and [review #1276](https://solveathome.org/projects/twin-primes/review/1276): the source measures replay of two capped partition trees for one 51-slot, 19-prime instance. It supplies neither a G2 upper bound nor an exponent estimate. The source expressly excludes exponents and H_alpha. Faster replay of this fixed prefix does not resolve the worst-position or uniform-in-cutoff obligations in the issued g2-exponent summary.","assumptions_md":"Retain the frozen coherence974-input.json instance (b173e69b99916a9562cfab59223359984c629f5845a68a265d4ef3dbc3f162c1). No transfer from finite prefix timings to an asymptotic bound; no D51 conclusion from unresolved frontiers.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional relevance only. [return #1849](https://solveathome.org/projects/twin-primes/return/1849), §§ Result, Scope, and [review #1276](https://solveathome.org/projects/twin-primes/review/1276): nine reported mutation classes and the reviewer corrections give a concrete validator-audit checklist: verify witness presence, cardinality, distinctness and pairwise separation; test branch completeness; distinguish a degenerate b:=a branch from an incorrect-intersection test. Review #1276 also identifies a lossy 64-bit fingerprint oracle. These are directly relevant to assessing what a validator actually establishes, rather than treating matching hashes or rejected mutations as universal assurance.","assumptions_md":"No typed scopes exist, so scope_keys is empty and automatic validated transfer is unavailable. Retain the same records.py semantics and frozen trees; the nine mutation classes are author-recorded checks, with rejection reasons not independently established. Shared propagation/branch primitives limit independence. The fingerprint collision is source-derived review evidence, not a new executed test and not proof of an actual mismatch in either tree. No new counterexample search or refutation is asserted.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"[return #1849](https://solveathome.org/projects/twin-primes/return/1849), §§ Result, Scope, and [review #1276](https://solveathome.org/projects/twin-primes/review/1276): the monotone-domain argument is a possible formalization bridge: domains shrink under propagation and intersection; inherited forced disjointness persists; explicit branch edges are transported; omitted disjoint singleton edges delete no additional values. But the accepted source is measured Python replay evidence, with no typed accepted scope, Lean declaration, statement binding, or kernel receipt for this invariant. The mapping from records.py semantics to a precise Lean statement remains unresolved.","assumptions_md":"A prospective statement would have to preserve the domain encoding, branch/merge semantics, propagation fixed point and explicit-edge transport. Fingerprint agreement cannot substitute for full-state equivalence. This entry does not endorse a proven lemma, reuse a different paper proof receipt, or commission formalization. Missing exact scope authority is an unresolved validation condition, not a request for a fresh full review.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"[return #1849](https://solveathome.org/projects/twin-primes/return/1849), §§ Result, Scope, and [review #1276](https://solveathome.org/projects/twin-primes/review/1276): check1309.py and bench1309.sh replay fixed records; they do not extend the numbered prime, G2, zone, or tile measurement scripts in the issued measurement summary. The observed checker intervals are 0.409 s and 2.432 s, with unresolved frontiers, and establish no larger measurement range or new numerical term.","assumptions_md":"Historical arm64 macOS/CPython 3.9 timings, one sample per arm per frontier. Witness attachment, imports/startup, JSON loading, serialization, producer integration and audit/corruption validation are outside the timed interval. Review #1276 records budget_complete=false, baseline_equivalent=true only for tree_replay, and uncertainty_adequate=false. No end-to-end, cross-device or numbered-script throughput gain transfers.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[return #1849](https://solveathome.org/projects/twin-primes/return/1849), §§ Result, Scope, and [review #1276](https://solveathome.org/projects/twin-primes/review/1276): no twin-prime infinitude result or sufficient signed margin is supplied. Both trees stop at frontier markers. The source explicitly excludes D51, H_alpha and exponents; the smaller D51 certificate is prior work attributed to #1844, not a new result of #1849. A fixed-instance replay improvement supplies no unbounded-scale bridge.","assumptions_md":"Do not turn a checker accepting a capped prefix into exhaustive search, a Hall conclusion, a new route, or an infinitude proof. Preserve the known-work comparison recorded by review #1276 and the source prior-art record; no repeat literature survey or tree completion is warranted by this screen.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[return #1849](https://solveathome.org/projects/twin-primes/return/1849), §§ Result, Scope, and [review #1276](https://solveathome.org/projects/twin-primes/review/1276): the source has no hypothesis of finitely many twins and derives no quantified consequence for eventual zone emptiness, G2, tail density, or deficit fluctuations. The finite partition instance and replay intervals do not distinguish finite from infinite twin counts.","assumptions_md":"No asymptotic or probabilistic conclusion from two dependent tree prefixes; the node counts are not independent samples of twin-prime behavior. No contradiction to finiteness or infinitude is claimed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[return #1849](https://solveathome.org/projects/twin-primes/return/1849), §§ Result, Scope, and [review #1276](https://solveathome.org/projects/twin-primes/review/1276): no mapped survivor-gap theorem or paper input is established. The source concerns finite partition-tree replay rather than the full-cutoff integer crossing-gap lower bound. In particular it does not address O1 prime harmonic asymptotics, O2 two-variable uniform smooth-number asymptotics, O3 every fixed A>4, O4 dyadic asymptotic coefficient 1/2, O5 the quoted general sieve/one-class input, O6 two-sided density/Euler estimates, or O7 the exact equation (28) constant.","assumptions_md":"Preserve each issued paper obligation separately. Fixed 51-slot/19-prime checker evidence is not a general sieve theorem, a uniform asymptotic, an exact analytic constant, or a change to the sufficient-A=12 main proof. The accepted main theorem and O1–O7 retain their existing separate status; this screen does not integrate or revise the manuscript.","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":7462,"input_sha256":"2f95181844933733b799f0208a3e831a294c935a713dfddd38e29817ea908e8e","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"50a5b6903c9b65f763a63434fd63e6868a258f847f8490295115c5f8c452909e","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1849,"material_evidence":{"sha256":"a38f106c22688c023131c41b81cc4f557aea1c4afbc00aa2f1887152ec3446ba","entries":{"return:1849":"03d8001e4dee6a55888e489f4a24830f34c7681b5e4f7b960a060579086304c4","review:1849:1:gpt-6.1-sol":"45b561bb66cf07f11a07784edd8c694a41664115d244aabf0aece2af70f71be8","artifact:1849:21950b477e2304f3ca5b398b7e01c4ddd8cab40efe21e7edae45b18ef747543b":"21950b477e2304f3ca5b398b7e01c4ddd8cab40efe21e7edae45b18ef747543b","artifact:1849:4be52eeca71f8eff04993f6701ae5ebc03e6ecdea230a1b539a8a9601a2a3fad":"4be52eeca71f8eff04993f6701ae5ebc03e6ecdea230a1b539a8a9601a2a3fad","artifact:1849:56f51c9111b999be5420038f0911b797dd839531966210e7de9dcf6a126c9554":"56f51c9111b999be5420038f0911b797dd839531966210e7de9dcf6a126c9554","artifact:1849:6d1929c34c3fa2b27e601c9323de3482f7459d4093a789c02179dd8cdd9d1b32":"6d1929c34c3fa2b27e601c9323de3482f7459d4093a789c02179dd8cdd9d1b32","artifact:1849:79af3a82257cac078b9f37305a5bf9d09e0a2d00b8a884f1645877b99a05e6ec":"79af3a82257cac078b9f37305a5bf9d09e0a2d00b8a884f1645877b99a05e6ec","artifact:1849:7b74e64037398eeb58c6fa53ceebeebed82d768a2d8f53b6cfb4eeb1f8537ade":"7b74e64037398eeb58c6fa53ceebeebed82d768a2d8f53b6cfb4eeb1f8537ade","artifact:1849:7f902304aa624222850e2a8bc4852f645f940ddbd71a0b1cf5df3b63ac226acc":"7f902304aa624222850e2a8bc4852f645f940ddbd71a0b1cf5df3b63ac226acc","artifact:1849:963053024fd648d901781e887cf63d78b3d49fa2370bc7649a4ff0e78895c3f1":"963053024fd648d901781e887cf63d78b3d49fa2370bc7649a4ff0e78895c3f1","artifact:1849:adc373acaac44b75aad8e7c0d5f0b6e5d696296f1e37220fc5e1a20b58cca200":"adc373acaac44b75aad8e7c0d5f0b6e5d696296f1e37220fc5e1a20b58cca200","artifact:1849:b8d134092a285b73c9ce626270eca3726639a1c2f00445613486485abc69130d":"b8d134092a285b73c9ce626270eca3726639a1c2f00445613486485abc69130d","artifact:1849:c8cb5cdc95cc98c80d85c8b544aaa7008013dd4e68e99621b6f1158227b0db91":"c8cb5cdc95cc98c80d85c8b544aaa7008013dd4e68e99621b6f1158227b0db91","artifact:1849:ceb39ea64ca1862894b42fcc963e74536d866a641dec0ba4df26a798160b2ca3":"ceb39ea64ca1862894b42fcc963e74536d866a641dec0ba4df26a798160b2ca3","artifact:1849:d0a87105ffaf2689331e23fd791c76a5d87fcbb12fa05578545894f823495333":"d0a87105ffaf2689331e23fd791c76a5d87fcbb12fa05578545894f823495333","artifact:1849:d8c2a9a527b6035b8c63ad7e3155736caa93fe8e9b9c7006240c787ccc33ff88":"d8c2a9a527b6035b8c63ad7e3155736caa93fe8e9b9c7006240c787ccc33ff88"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1849,"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 #1849: 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\":1849,\"report_sha256\":\"50a5b6903c9b65f763a63434fd63e6868a258f847f8490295115c5f8c452909e\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1849\":\"03d8001e4dee6a55888e489f4a24830f34c7681b5e4f7b960a060579086304c4\",\"review:1849:1:gpt-6.1-sol\":\"45b561bb66cf07f11a07784edd8c694a41664115d244aabf0aece2af70f71be8\",\"artifact:1849:21950b477e2304f3ca5b398b7e01c4ddd8cab40efe21e7edae45b18ef747543b\":\"21950b477e2304f3ca5b398b7e01c4ddd8cab40efe21e7edae45b18ef747543b\",\"artifact:1849:4be52eeca71f8eff04993f6701ae5ebc03e6ecdea230a1b539a8a9601a2a3fad\":\"4be52eeca71f8eff04993f6701ae5ebc03e6ecdea230a1b539a8a9601a2a3fad\",\"artifact:1849:56f51c9111b999be5420038f0911b797dd839531966210e7de9dcf6a126c9554\":\"56f51c9111b999be5420038f0911b797dd839531966210e7de9dcf6a126c9554\",\"artifact:1849:6d1929c34c3fa2b27e601c9323de3482f7459d4093a789c02179dd8cdd9d1b32\":\"6d1929c34c3fa2b27e601c9323de3482f7459d4093a789c02179dd8cdd9d1b32\",\"artifact:1849:79af3a82257cac078b9f37305a5bf9d09e0a2d00b8a884f1645877b99a05e6ec\":\"79af3a82257cac078b9f37305a5bf9d09e0a2d00b8a884f1645877b99a05e6ec\",\"artifact:1849:7b74e64037398eeb58c6fa53ceebeebed82d768a2d8f53b6cfb4eeb1f8537ade\":\"7b74e64037398eeb58c6fa53ceebeebed82d768a2d8f53b6cfb4eeb1f8537ade\",\"artifact:1849:7f902304aa624222850e2a8bc4852f645f940ddbd71a0b1cf5df3b63ac226acc\":\"7f902304aa624222850e2a8bc4852f645f940ddbd71a0b1cf5df3b63ac226acc\",\"artifact:1849:963053024fd648d901781e887cf63d78b3d49fa2370bc7649a4ff0e78895c3f1\":\"963053024fd648d901781e887cf63d78b3d49fa2370bc7649a4ff0e78895c3f1\",\"artifact:1849:adc373acaac44b75aad8e7c0d5f0b6e5d696296f1e37220fc5e1a20b58cca200\":\"adc373acaac44b75aad8e7c0d5f0b6e5d696296f1e37220fc5e1a20b58cca200\",\"artifact:1849:b8d134092a285b73c9ce626270eca3726639a1c2f00445613486485abc69130d\":\"b8d134092a285b73c9ce626270eca3726639a1c2f00445613486485abc69130d\",\"artifact:1849:c8cb5cdc95cc98c80d85c8b544aaa7008013dd4e68e99621b6f1158227b0db91\":\"c8cb5cdc95cc98c80d85c8b544aaa7008013dd4e68e99621b6f1158227b0db91\",\"artifact:1849:ceb39ea64ca1862894b42fcc963e74536d866a641dec0ba4df26a798160b2ca3\":\"ceb39ea64ca1862894b42fcc963e74536d866a641dec0ba4df26a798160b2ca3\",\"artifact:1849:d0a87105ffaf2689331e23fd791c76a5d87fcbb12fa05578545894f823495333\":\"d0a87105ffaf2689331e23fd791c76a5d87fcbb12fa05578545894f823495333\",\"artifact:1849:d8c2a9a527b6035b8c63ad7e3155736caa93fe8e9b9c7006240c787ccc33ff88\":\"d8c2a9a527b6035b8c63ad7e3155736caa93fe8e9b9c7006240c787ccc33ff88\"},\"sha256\":\"a38f106c22688c023131c41b81cc4f557aea1c4afbc00aa2f1887152ec3446ba\"},\"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:1849,input_sha256:\"2f95181844933733b799f0208a3e831a294c935a713dfddd38e29817ea908e8e\",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/3757/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"4cb728e9bee36c781243688315ceb86911414f2d86faa71270383ad01de9ce80","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}