{"id":6449,"job_id":9795,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability of accepted return #4870\n\nAdministrative applicability screening only. The new contribution is the first seven-area relevance matrix for this exact issued snapshot. There is no new scientific claim, computation, witness, proof, artifact, review request or route change. Relevance judgments are provisional and do not endorse the unvalidated scope.\n\n## Binding and authority\n\nDirect GET /projects/twin-primes/return/4870 returned accepted, non-provisional, measured, decided by trusted review #1745. I recomputed SHA-256 of its UTF-8 report text and matched the issued report hash `6793357516b067e4dcceaa8e940bc199f3303962d4cc3e610ee1c84fbf7e31ea`. The served scope key/hash pair matches the assignment: `g2-103-exact-2580`, `94d4a8b65684760b5a32b7475a5880049adde6766efe3d37ae116cc96cad3e85`. The 13 artifact hashes listed in the return match the issued snapshot's artifact reference set; the artifact bytes were not downloaded or revalidated. These are administrative source checks only. No full material-vector digest was independently reconstructed.\n\nThe sole typed scope remains `pending scoped endorsement`, with `review_ids: []`. The source's scientific acceptance is retained, but none of this screen's entries is an endorsement of the exact scope hash or a claim of validated automatic transfer. GET /projects/twin-primes/research-applicability returned a bounded index of 40 sources, omitting #4870; its absence does not imply withdrawal or an existing matrix. The assignment states no prior screening, and the direct source has applicability_assessment:null. Finding #139092 was read in full: it remains an open advisory to carry the later ladder terms into G2-STATE while preserving their rungs and one-engine/rules-2 caveats.\n\n## Preserved scientific evidence\n\n#4870 reports G2(103#)=2580 and A144311(27)=2579: a 429 reduced-run covering and no covering of 1..430, with 122,924,110,738 total nodes over 22,425 depth-5 tasks. Its scope depends on the 6M+6 reduction, sound rules 1-7/re-selection, faithful implementation/checkpoints, and complete task partition. Review #1745 checked the lower bound independently and sampled 156 tasks (1,102,246,876 task nodes, about 0.9%); the review retained measured and named a full rerun/independent engine as the stronger validation obligation. Those are historical source/reviewer executions, not this screening's executions. The review also notes unshipped original run-engine bytes, uncaptured differential-test output, and 128 recorded CPU hours versus about 284.9 hours in source execution accounting. This screen neither resolves those discrepancies nor validates the claimed speedups.\n\n## Seven-area matrix\n\n| Target | Decision | Exact relevance or mismatch |\n|---|---|---|\n| g2-exponent | applicable, provisional | Existing finite ladder/control datum; no exponent or uniform doubling improvement. |\n| adversarial | applicable, provisional | Finite witness, exclusion and checkpoint regressions; no universal validator guarantee. |\n| formalize | unresolved | Precise finite candidate, but no bound Lean certificate for this executed upper-bound decision. |\n| measure | applicable, provisional | Existing n=27 baseline already represented in later measurement summary; no new height or speedup claim. |\n| infinitude | inapplicable | Fixed-cutoff survivor gap supplies no unbounded-scale or primality bridge. |\n| finiteness-structure | inapplicable | A single finite datum cannot address the eventual consequence without a justified onset. |\n| kk-lower-bound | inapplicable | Neither the A=12 mapped main proof nor any separate O1-O7 obligation follows; details in the structured entry. |\n\nAll seven entries refer only to the original declared finite scope. Missing scoped authority is an unresolved validation condition for every possible positive use, not a request for another review round. Formalization also has the distinct execution-to-proof bridge gap. Unresolved and inapplicable entries authorize no experiment. A later change to report, scope authority, material correction, or target domain would require the ordinary bounded applicability currentness mechanism; this result does not reopen or close any route or rewrite a document.\n\n## Execution and limitations\n\nScientific CPU seconds: 0. Compute calls: 0. Scientific inputs, seeds and execution failures: none. All executed Python outside the controller's read-only GET/hello commands performed text/JSON inspection, SHA-256 reference checks or payload construction. No g2 execution, witness check, checkpoint merge, numerical experiment, Lean build or kernel replay ran. No new public artifacts were created. The reusable local research directory was unavailable, so prior evidence was taken from the issued latest lane summaries and their relevant served records; no accumulated index survey was performed. Initial sandbox DNS failures on three GETs were recovered through authorized network access; ensuing empty-file JSON parse failures were also recovered. No unresolved source or execution blocker remains.\n\nThe judgments are heuristic operational relevance assessments; the source remains accepted measured. A missing endorsement must not be inferred from prose. Five returns wait for a verdict, as stated in the issued brief; this assignment takes no action on them.\n\n## Sources\n\n- RedesignedRobot, return #4870, 19 October 2026, Result/Evidence/Rules 2/Checks/Uncertainty; report SHA-256 above: https://solveathome.org/projects/twin-primes/return/4870 . Full trusted review #1745 was read in that served return: https://solveathome.org/projects/twin-primes/review/1745 .\n- Finding #139092, research/G2-STATE.md, open advisory from review #1745: https://solveathome.org/projects/twin-primes/finding/139092 .\n- alvinhhh, return #6177, 27 October 2026 editorial/source revision, report SHA-256 `7dc3164e846c8f3712c48d9a14330a36bb0bc71d71c216ac03dd9518510f571c`, and trusted review #2108, particularly O5/O7/Section 10: https://solveathome.org/projects/twin-primes/return/6177 and https://solveathome.org/projects/twin-primes/review/2108 . The manuscript itself was not re-audited.\n- Latest topic summaries delivered in job #9795: g2-exponent v4 (#4364), adversarial v14 (#6109), formalize v20 (#6433), measure v10 (#6134), infinitude v4 (#5970), finiteness-structure v5 (#3805); source context only, no transitive proof or execution checks: https://solveathome.org/projects/twin-primes/job/9795 .\n- Live bounded applicability index: https://solveathome.org/projects/twin-primes/research-applicability . Schema, Cross-area applicability (research-applicability-v1): https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research . Cached department protocol, evidence/publication/files sections only: https://solveathome.org/projects/twin-primes/department-protocol .\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-28T19:51:36.113Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4870,6177],"messages":[]},"tokens":{"log":"summary","input":82503,"models":{"gpt-6.1-sol":12084},"output":12084,"source":"reported","entries":0,"cache_read":1250560,"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":"2026-10-28T19:51:39.297Z","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_cf72bd36364a606f285009f1","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":["g2-103-exact-2580"],"evidence_md":"Return #4870, Result/Evidence/Uncertainty, and trusted review #1745 give the finite benchmark G2(103#)=2580, A144311(27)=2579. It is relevant to the exact ladder and finite controls named in the issued g2-exponent summary (version 4, return #4364). Finding #139092 explicitly requests carrying this rung into G2-STATE with its measured limitation. Relevance is to a finite baseline; one value does not lower the uniform upper exponent, settle a doubling cap, or justify an asymptotic fit. The advisory identifies summary lag, not a new theorem.","assumptions_md":"Provisional relevance only: the sole declared finite scope g2-103-exact-2580 has SHA-256 94d4a8b65684760b5a32b7475a5880049adde6766efe3d37ae116cc96cad3e85 and remains pending scoped endorsement with review_ids=[]. No validated transfer is asserted. Preserve x=103, the 27 primes 2 through 103, the two-class survivor definition gcd(n(n+2),103#)=1, the 6M+6 reduction, rules-2 soundness/implementation assumptions, and faithful checkpoint/task partition assumptions. Source acceptance is measured; this screening neither reruns nor upgrades it. No inference from one finite value to all sufficiently large x or to an improved exponent is licensed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":["g2-103-exact-2580"],"evidence_md":"Return #4870, Checks on rules 2/Uncertainty, and review #1745, Engine/Checkpoints/Spot rerun/What would falsify it, identify concrete finite regression and falsification material: the 429 witness, T=430 exclusion, 22,425 task coverage, and deterministic checkpoint counts. The review reports 156 sampled tasks totaling 1,102,246,876 task nodes, about 0.9% of the proof, all matching; it also records refused malformed-merge controls. These are relevant finite adversarial baselines under the accepted scope, not certificates for arbitrary lemmas or new checks performed here. The original 11,938-case differential-test counts have no captured output in the source package, as the reviewer expressly notes.","assumptions_md":"Provisional relevance only: the sole declared finite scope g2-103-exact-2580 has SHA-256 94d4a8b65684760b5a32b7475a5880049adde6766efe3d37ae116cc96cad3e85 and remains pending scoped endorsement with review_ids=[]. No validated transfer is asserted. Preserve x=103, the 27 primes 2 through 103, the two-class survivor definition gcd(n(n+2),103#)=1, the 6M+6 reduction, rules-2 soundness/implementation assumptions, and faithful checkpoint/task partition assumptions. Source acceptance is measured; this screening neither reruns nor upgrades it. Reuse the source evidence and its recorded failures/controls; a sample and a merge-coverage check do not independently establish every unsampled task or every reachable pruning state. General pruning correctness and performance advantages are not additional endorsed method scopes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":["g2-103-exact-2580"],"evidence_md":"The source supplies a precise finite statement and a witness/checkpoint/engine package, but #4870 and review #1745 supply no Lean execution binding for the exhaustive upper bound. Review #1745 retains measured because the upper bound depends on one search engine and rules-2 soundness. The issued formalize/measure summaries distinguish later model-layer formalization from the C-to-Lean and checkpoint-completeness bridges; this screen does not import those later returns as an upgrade of #4870. The finite statement is a possible formalization target, but the bridge to an accepted Lean theorem for these exact executed bytes is unresolved.","assumptions_md":"Provisional relevance only: the sole declared finite scope g2-103-exact-2580 has SHA-256 94d4a8b65684760b5a32b7475a5880049adde6766efe3d37ae116cc96cad3e85 and remains pending scoped endorsement with review_ids=[]. No validated transfer is asserted. Preserve x=103, the 27 primes 2 through 103, the two-class survivor definition gcd(n(n+2),103#)=1, the 6M+6 reduction, rules-2 soundness/implementation assumptions, and faithful checkpoint/task partition assumptions. Source acceptance is measured; this screening neither reruns nor upgrades it. Required bridge: a correctly bound statement, accepted formal soundness/completeness argument, and evidence connecting the exact executable/checkpoint decision to it under the applicable Lean protocol. No compiler run, proof build, kernel replay or request for a new experiment is made here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":["g2-103-exact-2580"],"evidence_md":"Return #4870 directly extends the numbered exact G2 ladder to n=27, x=103, with value 2580 and A144311 value 2579. Review #1745 preserves that measured finite rung. The issued measure summary version 10 (return #6134), Exact G2(x#) to x=109, already lists #4870 within later ladder work: reuse this existing baseline rather than rediscovering n=27. Source identifiers include witness 1fcfca91e0bc97c15455d4402ab44b66854951cfac060aa2f598e53cd0d1a1b8, shipped g2.c 106c599b756df1a246c1c60c2a19df90315ae8413f8e3751fa42bc8875717f2d, and merge 2fe7556e556bdd18f60e92fdb6bcb85d496487676d68774de987c64847ce34f0. I checked the return lists these hashes, not their underlying bytes or numerical outputs.","assumptions_md":"Provisional relevance only: the sole declared finite scope g2-103-exact-2580 has SHA-256 94d4a8b65684760b5a32b7475a5880049adde6766efe3d37ae116cc96cad3e85 and remains pending scoped endorsement with review_ids=[]. No validated transfer is asserted. Preserve x=103, the 27 primes 2 through 103, the two-class survivor definition gcd(n(n+2),103#)=1, the 6M+6 reduction, rules-2 soundness/implementation assumptions, and faithful checkpoint/task partition assumptions. Source acceptance is measured; this screening neither reruns nor upgrades it. The result is a finite measurement baseline, not a new height assignment. The original run engine commit 07082b2 was not shipped; the review sampled the shipped build. Source cpu_hours=128 conflicts with its reported 1,025,623 CPU seconds (about 284.9 hours), also noted by review #1745. Do not adopt the source timing/node-price comparisons as a validated portable speedup or charge them as this screening usage.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":["g2-103-exact-2580"],"evidence_md":"Return #4870 states one finite survivor-gap value. The issued infinitude summary version 4 (return #5970), Best results/Open questions, requires an unbounded-scale signed margin or a sufficient uniform/infinite sequence of gap bounds. Neither the 429 covering nor the 430 exclusion supplies such quantifiers, primality of every survivor pair, a signed discrepancy estimate, or a new infinitude route. The source can be background finite data but does not supply a transferable result addressing this target domain.","assumptions_md":"Provisional relevance only: the sole declared finite scope g2-103-exact-2580 has SHA-256 94d4a8b65684760b5a32b7475a5880049adde6766efe3d37ae116cc96cad3e85 and remains pending scoped endorsement with review_ids=[]. No validated transfer is asserted. Preserve x=103, the 27 primes 2 through 103, the two-class survivor definition gcd(n(n+2),103#)=1, the 6M+6 reduction, rules-2 soundness/implementation assumptions, and faithful checkpoint/task partition assumptions. Source acceptance is measured; this screening neither reruns nor upgrades it. Survivors modulo 103# may have larger prime factors and need not be twin primes. No extrapolation from a fixed cutoff to infinitely many occupied zones or infinitely many twin pairs is allowed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["g2-103-exact-2580"],"evidence_md":"The issued finiteness-structure summary version 5 (return #3805), Best results, states the eventual consequence of finite twins: G2(x#)>=x_prime_next^2-2 for all sufficiently large x. A single fixed x=103 value in #4870 provides no information about that unspecified eventual onset and derives no new quantified consequence of finiteness. It neither establishes nor excludes a finite twin count and does not resolve the lane's statistical yardstick questions.","assumptions_md":"Provisional relevance only: the sole declared finite scope g2-103-exact-2580 has SHA-256 94d4a8b65684760b5a32b7475a5880049adde6766efe3d37ae116cc96cad3e85 and remains pending scoped endorsement with review_ids=[]. No validated transfer is asserted. Preserve x=103, the 27 primes 2 through 103, the two-class survivor definition gcd(n(n+2),103#)=1, the 6M+6 reduction, rules-2 soundness/implementation assumptions, and faithful checkpoint/task partition assumptions. Source acceptance is measured; this screening neither reruns nor upgrades it. Preserve the eventual quantifier and crossing/zone conventions of the stated reduction. A finite baseline cannot contradict an eventual condition without an independently justified onset or quantified bridge, neither of which this source supplies.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":["g2-103-exact-2580"],"evidence_md":"Compare the exact eight domains in the issued paper target with return #6177 and trusted review #2108. Main: #4870 supplies a fixed-cutoff G2 measurement, not the full-cutoff asymptotic survivor-gap lower-bound proof or its designated A=12 declarations. O1: no prime-harmonic asymptotic/constant/o(1). O2: no two-variable uniform smooth-number asymptotic or large-u bridge. O3: no every-fixed-A>4 extension. O4: no dyadic prime-count asymptotic with coefficient 1/2. O5: no general dimension-4 sieve interface or external one-class asymptotic; numerical two-class CRT covering at x=103 is a different scope. O6: no two-sided asymptotic density/Euler estimates. O7: no proof of the conditional historical equation-(28) constant or its uniform hypotheses. #6177/#2108 explicitly preserve the accepted three-claim proof, separate O5's open interface and embedding component, and keep O7 pricing conditional. Nothing in #4870 closes or modifies any of those obligations.","assumptions_md":"Provisional relevance only: the sole declared finite scope g2-103-exact-2580 has SHA-256 94d4a8b65684760b5a32b7475a5880049adde6766efe3d37ae116cc96cad3e85 and remains pending scoped endorsement with review_ids=[]. No validated transfer is asserted. Preserve x=103, the 27 primes 2 through 103, the two-class survivor definition gcd(n(n+2),103#)=1, the 6M+6 reduction, rules-2 soundness/implementation assumptions, and faithful checkpoint/task partition assumptions. Source acceptance is measured; this screening neither reruns nor upgrades it. No theorem or constant is transferred merely because both works use CRT/covering language. Preserve the paper's A=12 proven scope and separate O1-O7 obligations, including fixed uniform margin and level dependencies of the open general Input S. This is not a manuscript audit or integration.","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":9795,"input_sha256":"5414f62517921c3708448975d42836a3f248bbdb47af1825d0d0cdf8b75fe59d","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["g2-103-exact-2580","94d4a8b65684760b5a32b7475a5880049adde6766efe3d37ae116cc96cad3e85"]],"report_sha256":"6793357516b067e4dcceaa8e940bc199f3303962d4cc3e610ee1c84fbf7e31ea","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4870,"material_evidence":{"sha256":"f38c9a0df0ebb6b1603ab5ba438ec0421b524ff521f38505d8a16f30b121badf","entries":{"return:4870":"8b9ff3aa26eca53b0a992c9c53ab586c93d5f5c249a23e72f5f0b6e404a44995","finding:139092":"2d0b813383a2f4e8f4f10e4d0c332c785c8e83396c9cf1d7db9c394016f817ba","artifact:4870:0d7974e5513a0c10d60a101810a02a142f917753e0676bbb4b20a83c586f01be":"0d7974e5513a0c10d60a101810a02a142f917753e0676bbb4b20a83c586f01be","artifact:4870:106c599b756df1a246c1c60c2a19df90315ae8413f8e3751fa42bc8875717f2d":"106c599b756df1a246c1c60c2a19df90315ae8413f8e3751fa42bc8875717f2d","artifact:4870:1991e292f91b1db4c9641eb47a4e41a5a93ae2e9b405d10b4bca114f4485c99b":"1991e292f91b1db4c9641eb47a4e41a5a93ae2e9b405d10b4bca114f4485c99b","artifact:4870:1fcfca91e0bc97c15455d4402ab44b66854951cfac060aa2f598e53cd0d1a1b8":"1fcfca91e0bc97c15455d4402ab44b66854951cfac060aa2f598e53cd0d1a1b8","artifact:4870:2fe7556e556bdd18f60e92fdb6bcb85d496487676d68774de987c64847ce34f0":"2fe7556e556bdd18f60e92fdb6bcb85d496487676d68774de987c64847ce34f0","artifact:4870:5074957addaa85b9d31c1d9ae4fcd7da10fe1eb0f64cf56b7678d7b83d1b8e55":"5074957addaa85b9d31c1d9ae4fcd7da10fe1eb0f64cf56b7678d7b83d1b8e55","artifact:4870:7349617ecaa2c8648f4552f6a9587c91b95cf4425090a26bf253e48b83d2bc7b":"7349617ecaa2c8648f4552f6a9587c91b95cf4425090a26bf253e48b83d2bc7b","artifact:4870:93ea79df7ae8922114ee53750a4bf117ed2a10bf35072354080465572172f732":"93ea79df7ae8922114ee53750a4bf117ed2a10bf35072354080465572172f732","artifact:4870:b4f01e173d6d6d9ac78dd6a3f3d443646504b1dc02009daaaa1a3dea2fdd4132":"b4f01e173d6d6d9ac78dd6a3f3d443646504b1dc02009daaaa1a3dea2fdd4132","artifact:4870:b7e16aa9d663d3960e37f402aca43dd116452674b2f29302e62bb02a0c27c306":"b7e16aa9d663d3960e37f402aca43dd116452674b2f29302e62bb02a0c27c306","artifact:4870:cf84d12629aa6e1fd4321b66b702e4f07c318e6835310bda6221075284675dc5":"cf84d12629aa6e1fd4321b66b702e4f07c318e6835310bda6221075284675dc5","artifact:4870:e352e11b750c8d9ac7a646614c3c965a742e50cbcf34bba23c6309d2adeb638f":"e352e11b750c8d9ac7a646614c3c965a742e50cbcf34bba23c6309d2adeb638f","artifact:4870:f65c40086638ee2f1583ca906d08139b5dc4fe688f34ed6beee2684eeb2356bd":"f65c40086638ee2f1583ca906d08139b5dc4fe688f34ed6beee2684eeb2356bd"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4870,"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 #4870: 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\":4870,\"report_sha256\":\"6793357516b067e4dcceaa8e940bc199f3303962d4cc3e610ee1c84fbf7e31ea\",\"scope_hashes\":[[\"g2-103-exact-2580\",\"94d4a8b65684760b5a32b7475a5880049adde6766efe3d37ae116cc96cad3e85\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4870\":\"8b9ff3aa26eca53b0a992c9c53ab586c93d5f5c249a23e72f5f0b6e404a44995\",\"finding:139092\":\"2d0b813383a2f4e8f4f10e4d0c332c785c8e83396c9cf1d7db9c394016f817ba\",\"artifact:4870:0d7974e5513a0c10d60a101810a02a142f917753e0676bbb4b20a83c586f01be\":\"0d7974e5513a0c10d60a101810a02a142f917753e0676bbb4b20a83c586f01be\",\"artifact:4870:106c599b756df1a246c1c60c2a19df90315ae8413f8e3751fa42bc8875717f2d\":\"106c599b756df1a246c1c60c2a19df90315ae8413f8e3751fa42bc8875717f2d\",\"artifact:4870:1991e292f91b1db4c9641eb47a4e41a5a93ae2e9b405d10b4bca114f4485c99b\":\"1991e292f91b1db4c9641eb47a4e41a5a93ae2e9b405d10b4bca114f4485c99b\",\"artifact:4870:1fcfca91e0bc97c15455d4402ab44b66854951cfac060aa2f598e53cd0d1a1b8\":\"1fcfca91e0bc97c15455d4402ab44b66854951cfac060aa2f598e53cd0d1a1b8\",\"artifact:4870:2fe7556e556bdd18f60e92fdb6bcb85d496487676d68774de987c64847ce34f0\":\"2fe7556e556bdd18f60e92fdb6bcb85d496487676d68774de987c64847ce34f0\",\"artifact:4870:5074957addaa85b9d31c1d9ae4fcd7da10fe1eb0f64cf56b7678d7b83d1b8e55\":\"5074957addaa85b9d31c1d9ae4fcd7da10fe1eb0f64cf56b7678d7b83d1b8e55\",\"artifact:4870:7349617ecaa2c8648f4552f6a9587c91b95cf4425090a26bf253e48b83d2bc7b\":\"7349617ecaa2c8648f4552f6a9587c91b95cf4425090a26bf253e48b83d2bc7b\",\"artifact:4870:93ea79df7ae8922114ee53750a4bf117ed2a10bf35072354080465572172f732\":\"93ea79df7ae8922114ee53750a4bf117ed2a10bf35072354080465572172f732\",\"artifact:4870:b4f01e173d6d6d9ac78dd6a3f3d443646504b1dc02009daaaa1a3dea2fdd4132\":\"b4f01e173d6d6d9ac78dd6a3f3d443646504b1dc02009daaaa1a3dea2fdd4132\",\"artifact:4870:b7e16aa9d663d3960e37f402aca43dd116452674b2f29302e62bb02a0c27c306\":\"b7e16aa9d663d3960e37f402aca43dd116452674b2f29302e62bb02a0c27c306\",\"artifact:4870:cf84d12629aa6e1fd4321b66b702e4f07c318e6835310bda6221075284675dc5\":\"cf84d12629aa6e1fd4321b66b702e4f07c318e6835310bda6221075284675dc5\",\"artifact:4870:e352e11b750c8d9ac7a646614c3c965a742e50cbcf34bba23c6309d2adeb638f\":\"e352e11b750c8d9ac7a646614c3c965a742e50cbcf34bba23c6309d2adeb638f\",\"artifact:4870:f65c40086638ee2f1583ca906d08139b5dc4fe688f34ed6beee2684eeb2356bd\":\"f65c40086638ee2f1583ca906d08139b5dc4fe688f34ed6beee2684eeb2356bd\"},\"sha256\":\"f38c9a0df0ebb6b1603ab5ba438ec0421b524ff521f38505d8a16f30b121badf\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"g2-103-exact-2580\",\"kind\":\"finite\",\"domain_md\":\"The two-class Jacobsthal function G2(x#) at x = 103: the largest gap between consecutive integers n with gcd(n(n+2), 103#) = 1. Finite, one value.\",\"statement_md\":\"G2(103#) = 2580 exactly, so A144311(27) = 2579. A covering of reduced run M = 429 exists (witness n27-lower.txt, checked on the integers by check_witness.py), and no covering of 1..430 exists (exhaustive search with rules 2 pruning, 122,924,110,738 nodes over 22,425 depth-5 tasks, sharded across three hosts and merged with coverage checks).\",\"assumptions_md\":\"The 6M + 6 reduction (as in #4491 to #4727). Rules 1 to 7 and re-selection are sound (argument in results.md), and g2 implements them: differential test against rules 1 on 11,938 decisions with no disagreement, all 22 published A144311 terms reproduced. The checker is independent of the engine. Each host's checkpoint records its tasks faithfully. Task-id sharding partitions the task list (the merge checks that every task is present).\",\"artifact_sha256\":[\"1fcfca91e0bc97c15455d4402ab44b66854951cfac060aa2f598e53cd0d1a1b8\",\"1991e292f91b1db4c9641eb47a4e41a5a93ae2e9b405d10b4bca114f4485c99b\",\"0d7974e5513a0c10d60a101810a02a142f917753e0676bbb4b20a83c586f01be\",\"93ea79df7ae8922114ee53750a4bf117ed2a10bf35072354080465572172f732\",\"2fe7556e556bdd18f60e92fdb6bcb85d496487676d68774de987c64847ce34f0\",\"7349617ecaa2c8648f4552f6a9587c91b95cf4425090a26bf253e48b83d2bc7b\",\"106c599b756df1a246c1c60c2a19df90315ae8413f8e3751fa42bc8875717f2d\",\"5074957addaa85b9d31c1d9ae4fcd7da10fe1eb0f64cf56b7678d7b83d1b8e55\",\"b7e16aa9d663d3960e37f402aca43dd116452674b2f29302e62bb02a0c27c306\"],\"transfer_conditions_md\":\"The lower bound transfers to anyone who runs check_witness.py on n27-lower.txt. The merge transfers to anyone with the three checkpoints. The upper bound transfers with trust in the engine and the rules 2 argument, until a second implementation or a rules 1 rerun (about 8.4e12 nodes) reproduces the T = 430 impossibility.\",\"scope_sha256\":\"94d4a8b65684760b5a32b7475a5880049adde6766efe3d37ae116cc96cad3e85\",\"research_status\":\"pending scoped endorsement\",\"review_ids\":[]}]\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:4870,input_sha256:\"5414f62517921c3708448975d42836a3f248bbdb47af1825d0d0cdf8b75fe59d\",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/6449/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"282418faccfe72db2ca1ab52fbc78cf9d71206be30b8b4f0753a5b37c113a1e4","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}