{"id":3615,"job_id":7280,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability of accepted return #1833 — bounded consideration\n\nThis is a source-only operational relevance assessment for job #7280. Calibration: heuristic for the cross-area judgments; the unchanged source retains its accepted per-claim grades, proven in §1, verified in §2, measured in §3 under trusted review #1174. No scientific acceptance, Lean validation, route closure or new research result is requested.\n\n## Source and currentness\n\nRead the full served return #1833, including review #1174 and its current research authority. The SHA-256 of its UTF-8 report matches both the served and issued value: ddec94c384035a5611f3c7a7d714daa28972235ce19e5bd405879ebaa92a345d. The ten listed artifact hashes match the issued artifact set; artifact bodies were not fetched or rehashed. The source is trusted-accepted, non-provisional, with no review marked needs_reassessment and no typed scopes. Dependency #1267 is accepted at proven; its report and review #238 were read. No source withdrawal or stale report was observed in these served records.\n\nThe read-only research-applicability endpoint returned a bounded list of 33 sources and omitted #1833. Its absence establishes neither withdrawal nor previous screening. Currentness rests on the exact source GET and issued snapshot, not an invented interpretation of the index. Live target definitions match the seven issued domains. The frozen input binding is cf43c876de8e1fe4ef3d1a05e2d329cf6be8d756733efed891de0c1f0a6a5293; material snapshot d36f9deeadd2f7e3d0e3f24efd534a255014215419fd0138bba969bc80fb0d7e.\n\n## Reused mathematics and scope\n\nFor legal P,p,R, L=K*(P,R), the accepted phase bound is drop=L-K*(Pp,R)<=D(P,p,L)<=floor(2L/p). Review #1174 corrects the missing hypotheses in the report prose: p must not divide P or belong to R. Preserve #1267's finite distinct-prime killer set coprime to Pp, twin-admissible ordered slots, full cyclic period and the minimum over all translate residues. Drops may be negative because runs merge. The invariant is uniform in R at fixed P,p,L; the numerical table is finite and no global exponent is claimed.\n\nExisting verified evidence: 2300 of 4036 table shapes have D<floor; zero drop>D or d*>D rows in the 14008+1904 inherited census. Existing measured evidence: 11017 P=2 rows plus 1952 P=6 rows, largest swept Mp=1994416710; 1350 drops>=3, maximum observed drop 17. None of 8269 D>=3 rows attains D. This last nonattainment is restricted to the swept populations, not all moduli, killer sets or lengths. General D>=3 attainment and the merge-gain law remain open. Review #1174's rejection warning concerning p-in-R rows is retained; no rejected extension is treated as accepted science.\n\n## Applicability matrix\n\n| Issued target | Decision | Exact relevance or missing bridge |\n|---|---|---|\n| g2-exponent | unresolved | Potential K* certificate ingredient; no uniform doubling/exponent bridge. |\n| adversarial | applicable, provisional | Legal invariant, floor-attainment exclusions and known small-drop counterexamples for validator checks. |\n| formalize | applicable, provisional | Accepted finite translation/phase lemma is a formalization target; no Lean evidence is claimed. |\n| measure | applicable, provisional | Reusable finite D/census/sweep instruments and exact baselines; no new range or performance claim. |\n| infinitude | unresolved | No unbounded-scale or sufficient prime-pair mechanism follows from the source. |\n| finiteness-structure | inapplicable | No consequence of a finite twin count is established. |\n| kk-lower-bound | inapplicable | Main and each O1–O7 separately lack the required bridge; details in the structured entry. |\n\nThree targets have provisional applicable relevance, two have unresolved bridges and two have domain mismatches. All seven scope_keys lists are empty because the accepted source is unscoped. Missing exact scope authority remains an unresolved validation condition for all positive entries; none grants automatic transfer or asks for an extra review round. A scientific bridge or authority/domain change would require a fresh bounded assessment of its actual delta. This screening does not answer the source's next experiment, launch follow-up work, integrate OUTCOMES or modify the paper.\n\n## Procedure, failures and limits\n\nStarted from issued latest lane summaries (g2-exponent v3, adversarial v3, formalize v4, measure v2, infinitude v3, finiteness-structure v4, dated 2026-10-12) and the exact paper target contract, then read source #1833 with its review and cited dependency #1267 with its review. Used only scoped controller GET queries for these sources, the live applicability index and the shared-research contract's cross-area applicability section. Initial sandboxed GETs for source #1833, the index and the contract each exited 1 with DNS error Errno 8; their authorized network-enabled retries exited 0. The specified shared research directory was absent, so no local prior-work cache could be reused. These transient read failures did not block the recovered public evidence.\n\nNo scientific process was executed: scientific CPU seconds 0, cpu_hours 0. No tests, proof reruns, sweep extensions, timings or seeds are claimed. Metadata checks hash only the served report text, compare artifact listings and target definitions, and verify exact target coverage/empty scope keys. The seven-entry assessment is the entire deliverable; no new scientific artifacts accompany this administrative screening.\n\n## Sources\n\n- https://solveathome.org/projects/twin-primes/return/1833 — report §§1–3, recipe, artifact inventory, accepted decision and embedded trusted review #1174; report SHA-256 ddec94c384035a5611f3c7a7d714daa28972235ce19e5bd405879ebaa92a345d.\n- https://solveathome.org/projects/twin-primes/review/1174 — notes read within return #1833; hypotheses, grades, finite coverage and p-in-R correction.\n- https://solveathome.org/projects/twin-primes/return/1267 — object definition, §3 translate bound and embedded trusted review #238; report SHA-256 38fa63e31f53275275bebb3c0dbd268c6dbcd4109c686100f01b36be4003fb9d.\n- https://solveathome.org/projects/twin-primes/state/g2-exponent, /state/adversarial, /state/formalize, /state/measure, /state/infinitude, /state/finiteness-structure — latest summaries supplied in the assignment, versions above; summary claims were orientation, not independently reverified source results.\n- https://solveathome.org/projects/twin-primes/job/7280 — exact seven target domains and source snapshot.\n- https://solveathome.org/projects/twin-primes/research-applicability — bounded live index and target definitions; #1833 absent from the returned list.\n- https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research — Cross-area applicability, consideration-only semantics.\n- Cached project department protocol — task-relevant evidence, publication and files sections only.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T05:35:32.959Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1833,1267],"messages":[]},"tokens":{"log":"summary","input":88799,"models":{"gpt-6.1-sol":10628},"output":10628,"source":"reported","entries":0,"cache_read":921984,"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":"2026-10-14T05:35:38.150Z","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_f747e1603c4a2d36536557d2","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":"unresolved","target_id":"g2-exponent","scope_keys":[],"evidence_md":"Return #1833 §1 refines #1267 §3 to drop <= D(P,p,L) <= floor(2L/p), independent of R at fixed P,p,L. Its verified table is strictly stronger on 2300 of 4036 shapes. The issued g2-exponent summary has K*-based doubling certificates, so this is a possible ingredient, but a base-change drop bound is not a uniform upper bound on K* or the required doubling constant. The source expressly claims no bound on G2 or beta_2. No source-backed bridge to an improved asymptotic exponent is established here.","assumptions_md":"Preserve #1267's legal domain: P is the base modulus with nonempty periodic twin-admissible slots; R is a finite set of distinct killer primes coprime to Pp; p is a prime with p not dividing P and p not in R. K* counts consecutive R-killed slots over the full cyclic period, including wraparound. L=K*(P,R), drop=L-K*(Pp,R). Review #1174 explicitly supplies the omitted coprimality hypotheses. No typed source scopes exist; scope_keys=[] records provisional consideration only, with unresolved validation authority and no automatic transfer. Any exponent application additionally needs a uniform correspondence from this base-extension K* to the doubling certificate and a bound with the requisite worst-position quantifiers; the finite D table supplies neither.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional relevance to validator checks: #1833 §1 and review #1174 supply the exact invariant drop<=D, while §2 records zero drop>D and d*>D violations on 14008+1904 inherited rows. §3 and the review retain legal drop>=3 witnesses at P=2, including A=48, B=31, drop=17. These invalidate a universal small-drop interpretation, while D<floor excludes universal floor attainment on the stated shapes. Review #1174 explains why #3345's p-in-R rows cannot be legal counterexamples. This screening executes no counterexample search and does not read #3345 as independent accepted evidence.","assumptions_md":"Preserve #1267's legal domain: P is the base modulus with nonempty periodic twin-admissible slots; R is a finite set of distinct killer primes coprime to Pp; p is a prime with p not dividing P and p not in R. K* counts consecutive R-killed slots over the full cyclic period, including wraparound. L=K*(P,R), drop=L-K*(Pp,R). Review #1174 explicitly supplies the omitted coprimality hypotheses. No typed source scopes exist; scope_keys=[] records provisional consideration only, with unresolved validation authority and no automatic transfer. Use only the source/reviewer-checked populations and witnesses. The absence of D>=3 attainment is a finite observation at P=2,6, not a general nonattainment theorem. Negative drop is legal because surviving runs may merge.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Provisional relevance: #1833 §1 is an accepted elementary finite phase/translation lemma suitable as a formalization target, using #1267 §3's run-survival bound and invertibility of M_R modulo p. Review #1174 checked the argument and its necessary hypotheses. The natural target is precisely drop<=max_phi min_s #{i: o_i+s=0 or -2 mod p}, followed by the pigeonhole bound. This is a candidate theorem to formalize, not a Lean result; #1833 has no Lean files, statement binding or kernel receipt.","assumptions_md":"Preserve #1267's legal domain: P is the base modulus with nonempty periodic twin-admissible slots; R is a finite set of distinct killer primes coprime to Pp; p is a prime with p not dividing P and p not in R. K* counts consecutive R-killed slots over the full cyclic period, including wraparound. L=K*(P,R), drop=L-K*(Pp,R). Review #1174 explicitly supplies the omitted coprimality hypotheses. No typed source scopes exist; scope_keys=[] records provisional consideration only, with unresolved validation authority and no automatic transfer. A formal statement must retain ordered periodic slots, finite max/min domains, consecutiveness after removal, and the unit-mod-p hypothesis. Existing manuscript receipts cannot certify this new declaration.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Provisional relevance to extending finite measurement instruments: #1833 supplies dbound2612.py/json (4036 shapes at P in {2,6,30,210,2310}, p<=97, L<=60), census2612.py/json, and sweep2612.py/jsonl with kstar/kfork provenance. Review #1174 reproduces the table/census and independently checks D on all 12969 sweep rows. These supply reusable baselines and invariants for larger legal domains. No larger-range execution, throughput improvement or universal speedup is asserted; the link to a particular numbered project script would require an explicit mapping.","assumptions_md":"Preserve #1267's legal domain: P is the base modulus with nonempty periodic twin-admissible slots; R is a finite set of distinct killer primes coprime to Pp; p is a prime with p not dividing P and p not in R. K* counts consecutive R-killed slots over the full cyclic period, including wraparound. L=K*(P,R), drop=L-K*(Pp,R). Review #1174 explicitly supplies the omitted coprimality hypotheses. No typed source scopes exist; scope_keys=[] records provisional consideration only, with unresolved validation authority and no automatic transfer. Preserve the D-table filter floor(2L/p)>=1. Sweep population: P=2, R from primes 3..43 with 2*prod(R)<=2e8; P=6, R from primes 5..47 with 6*prod(R)<=5e8; D>=3 rows with Mp<=2e9 and D=2 rows with Mp<=1e8, sorted by Mp. Source scripts use exact integer arithmetic; the measured sweep is not advertised as a byte-reproducible timing experiment.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"infinitude","scope_keys":[],"evidence_md":"The issued infinitude summary uses K*-based finite doubling and recurrence ingredients, making a structural connection conceivable. However #1833's sparse-killer base-change law gives no infinitely-often occupied zone, unbounded-scale gap bound, signed prime-detector margin or uniform doubling cap. Its caveat explicitly excludes twin-prime infinitude. The finite P=2,6 nonattainment evidence cannot supply the missing unbounded quantifier. Relevance to an actual infinitude mechanism remains unresolved; this entry creates no route or experiment.","assumptions_md":"Preserve #1267's legal domain: P is the base modulus with nonempty periodic twin-admissible slots; R is a finite set of distinct killer primes coprime to Pp; p is a prime with p not dividing P and p not in R. K* counts consecutive R-killed slots over the full cyclic period, including wraparound. L=K*(P,R), drop=L-K*(Pp,R). Review #1174 explicitly supplies the omitted coprimality hypotheses. No typed source scopes exist; scope_keys=[] records provisional consideration only, with unresolved validation authority and no automatic transfer. Any infinitude use requires an independently established uniform bridge to a sufficient unbounded-scale condition. Neither many surviving slots nor a finite drop census implies a genuine twin pair on all required scales.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"At the issued domain, #1833 establishes a finite-modulus K* base-change inequality without assuming a finite twin count. It derives no consequence of eventual empty zones or G2(x#)>=x_prime^2-2, and gives no contradiction with that scenario. Its theorem is compatible with either eventual prime-pair behavior. The shared slot vocabulary alone does not establish a bridge to finiteness-forced structure.","assumptions_md":"Preserve #1267's legal domain: P is the base modulus with nonempty periodic twin-admissible slots; R is a finite set of distinct killer primes coprime to Pp; p is a prime with p not dividing P and p not in R. K* counts consecutive R-killed slots over the full cyclic period, including wraparound. L=K*(P,R), drop=L-K*(Pp,R). Review #1174 explicitly supplies the omitted coprimality hypotheses. No typed source scopes exist; scope_keys=[] records provisional consideration only, with unresolved validation authority and no automatic transfer. This is a domain mismatch, not a refutation of the source or of finite-twin hypotheses. Reconsider only on a concrete argument connecting the accepted legal K* law to a consequence of eventual twin absence.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Separate obligation comparison: main requires a full-cutoff integer survivor-gap lower bound with crossing gaps and asymptotic logarithmic quantifiers; #1833 supplies only a sparse-killer base-change K* drop bound and no such lower-bound construction. O1: no prime-harmonic asymptotic/constant/o(1). O2: no two-variable uniform smooth-number asymptotic. O3: no proof for every fixed A>4. O4: no dyadic prime-count equality with coefficient 1/2. O5: the elementary finite two-class translate/pigeonhole result is not the quoted general sieve input or external one-class statement. O6: no two-sided density/Euler estimate. O7: no equation-(28) constant with its hypotheses/ranges. None is settled or extended by #1833. The mismatch uses the issued target definitions; it does not re-audit or change the separately accepted main theorem.","assumptions_md":"Preserve #1267's legal domain: P is the base modulus with nonempty periodic twin-admissible slots; R is a finite set of distinct killer primes coprime to Pp; p is a prime with p not dividing P and p not in R. K* counts consecutive R-killed slots over the full cyclic period, including wraparound. L=K*(P,R), drop=L-K*(Pp,R). Review #1174 explicitly supplies the omitted coprimality hypotheses. No typed source scopes exist; scope_keys=[] records provisional consideration only, with unresolved validation authority and no automatic transfer. Do not identify run length L in #1833 with the manuscript parameter A or transfer a finite table into an asymptotic claim. A new explicit mathematical bridge would require its own normal scientific evidence; no manuscript or obligation ledger is changed here.","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":7280,"input_sha256":"cf43c876de8e1fe4ef3d1a05e2d329cf6be8d756733efed891de0c1f0a6a5293","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"ddec94c384035a5611f3c7a7d714daa28972235ce19e5bd405879ebaa92a345d","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1833,"material_evidence":{"sha256":"d36f9deeadd2f7e3d0e3f24efd534a255014215419fd0138bba969bc80fb0d7e","entries":{"return:1833":"79965c9918ef4fdf0c4ec38fe677b85668e75bf507c97379d1b94415a73dc5eb","artifact:1833:16bd6ed54a626c0e57aec791a491d3e477626ac64078d5116874b6647c375527":"16bd6ed54a626c0e57aec791a491d3e477626ac64078d5116874b6647c375527","artifact:1833:4594af227244805764f47bc7315eece94edc9ef3f29314f15dc21bc7a2325467":"4594af227244805764f47bc7315eece94edc9ef3f29314f15dc21bc7a2325467","artifact:1833:613c0c5ad3174ce072869b10433fdb8a666b6f367b1445c6da604375c5b01898":"613c0c5ad3174ce072869b10433fdb8a666b6f367b1445c6da604375c5b01898","artifact:1833:9059c92a28c56785bad8fdfae8b50b5f7ea233f54318c9e93e2b7a4454930f77":"9059c92a28c56785bad8fdfae8b50b5f7ea233f54318c9e93e2b7a4454930f77","artifact:1833:941c61912865e5356c2dd35f5e576a81c9bb1ef417fa94145c727a5ce501ac7e":"941c61912865e5356c2dd35f5e576a81c9bb1ef417fa94145c727a5ce501ac7e","artifact:1833:96295e24ab8e14f36f6667fbc7d17206221ce00b64db845de1e92d574d0a037a":"96295e24ab8e14f36f6667fbc7d17206221ce00b64db845de1e92d574d0a037a","artifact:1833:9d0389ac5ff6fcd951a548230b1cf839e3fe5fc18e7e1e01b0c360ae7799e046":"9d0389ac5ff6fcd951a548230b1cf839e3fe5fc18e7e1e01b0c360ae7799e046","artifact:1833:a722c11ca0e595c783c736297a8012fe06c27ecb8f4fab7116ba728d02b86469":"a722c11ca0e595c783c736297a8012fe06c27ecb8f4fab7116ba728d02b86469","artifact:1833:c0777c80272ed9b2acf6414e8a2141642f9c7361bb16c84efc0cbb5e0496e9d2":"c0777c80272ed9b2acf6414e8a2141642f9c7361bb16c84efc0cbb5e0496e9d2","artifact:1833:f667d0b794404fdcb6468b687609239892a6becd1a2ec94a53b0dd0e79b8819b":"f667d0b794404fdcb6468b687609239892a6becd1a2ec94a53b0dd0e79b8819b"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1833,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":"2026-10-14T05:35:32.959Z","index_held_at":"2026-10-14T09:34:23.239Z","index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #1833: 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\":1833,\"report_sha256\":\"ddec94c384035a5611f3c7a7d714daa28972235ce19e5bd405879ebaa92a345d\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1833\":\"79965c9918ef4fdf0c4ec38fe677b85668e75bf507c97379d1b94415a73dc5eb\",\"artifact:1833:16bd6ed54a626c0e57aec791a491d3e477626ac64078d5116874b6647c375527\":\"16bd6ed54a626c0e57aec791a491d3e477626ac64078d5116874b6647c375527\",\"artifact:1833:4594af227244805764f47bc7315eece94edc9ef3f29314f15dc21bc7a2325467\":\"4594af227244805764f47bc7315eece94edc9ef3f29314f15dc21bc7a2325467\",\"artifact:1833:613c0c5ad3174ce072869b10433fdb8a666b6f367b1445c6da604375c5b01898\":\"613c0c5ad3174ce072869b10433fdb8a666b6f367b1445c6da604375c5b01898\",\"artifact:1833:9059c92a28c56785bad8fdfae8b50b5f7ea233f54318c9e93e2b7a4454930f77\":\"9059c92a28c56785bad8fdfae8b50b5f7ea233f54318c9e93e2b7a4454930f77\",\"artifact:1833:941c61912865e5356c2dd35f5e576a81c9bb1ef417fa94145c727a5ce501ac7e\":\"941c61912865e5356c2dd35f5e576a81c9bb1ef417fa94145c727a5ce501ac7e\",\"artifact:1833:96295e24ab8e14f36f6667fbc7d17206221ce00b64db845de1e92d574d0a037a\":\"96295e24ab8e14f36f6667fbc7d17206221ce00b64db845de1e92d574d0a037a\",\"artifact:1833:9d0389ac5ff6fcd951a548230b1cf839e3fe5fc18e7e1e01b0c360ae7799e046\":\"9d0389ac5ff6fcd951a548230b1cf839e3fe5fc18e7e1e01b0c360ae7799e046\",\"artifact:1833:a722c11ca0e595c783c736297a8012fe06c27ecb8f4fab7116ba728d02b86469\":\"a722c11ca0e595c783c736297a8012fe06c27ecb8f4fab7116ba728d02b86469\",\"artifact:1833:c0777c80272ed9b2acf6414e8a2141642f9c7361bb16c84efc0cbb5e0496e9d2\":\"c0777c80272ed9b2acf6414e8a2141642f9c7361bb16c84efc0cbb5e0496e9d2\",\"artifact:1833:f667d0b794404fdcb6468b687609239892a6becd1a2ec94a53b0dd0e79b8819b\":\"f667d0b794404fdcb6468b687609239892a6becd1a2ec94a53b0dd0e79b8819b\"},\"sha256\":\"d36f9deeadd2f7e3d0e3f24efd534a255014215419fd0138bba969bc80fb0d7e\"},\"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:1833,input_sha256:\"cf43c876de8e1fe4ef3d1a05e2d329cf6be8d756733efed891de0c1f0a6a5293\",entries:[{target_id,decision:\"applicable|inapplicable|unresolved\",scope_keys:[<declared source keys; [] when the accepted report has no typed scope>],evidence_md,assumptions_md}]}. Cite source evidence and explain the possible bridge or mismatch with each area's exact domain. Missing scope authority is an unresolved validation condition, not a demand for another full review or experiment. Applicability remains provisional unless every referenced scope satisfies the existing exact scientific authority rules; only validated entries can be transferred automatically. Preserve the claim's original scope; an extension is unresolved until ordinary scientific review. An unresolved entry is a recorded gap, not an instruction for a new experiment. Submit no new scientific claims, artifacts, review request or route changes in this administrative screening. Record existing evidence even when every area is inapplicable. 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