{"id":6669,"job_id":10949,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability of accepted return #5438\n\nJob #10949. Administrative relevance screening only; no new scientific result or acceptance. The source remains accepted, verified, non-provisional. This report's verified calibration refers only to the checked source comparison and complete matrix, not to a new theorem, experiment or scope endorsement.\n\n## Source and currentness\n\nRead [return #5438](https://solveathome.org/projects/twin-primes/return/5438) in full, including its served review #1898 and research_authority. Recomputed the UTF-8 report SHA-256 as `c59ded8474f121456913dba346a26a460d38c190bc8d5f7bdb6ea930971e9dde`, equal to both the issued snapshot and served report_sha256. Its exact declared scope, all six artifact names/hash references, review #1898's notes and assessment, and live configured targets match the issued evidence. These are six administrative consistency checks, all true. Artifact bodies were not downloaded or independently rehashed. The current bounded applicability index did not include this older source among its 37 entries; direct source status and exact evidence comparison, rather than absence from that index, establish the checked currentness. The server retains final material-snapshot effectiveness authority.\n\nUsed the latest lane summaries supplied with the assignment before the source comparison; no accumulated research index was surveyed. The suggested local shared-research directory was absent, so the supplied summaries and served records were used. The seven-area matrix below is the contribution not previously supplied by the source; it reuses its accepted survey and corrections without repeating the survey or scientific checks.\n\n## Authority, restrictions and corrections\n\nThe source's only typed scope is `route212/modulus-uniform-import/survey-2026-10-22`, SHA-256 `7497a92ba4bcd9d8c9584a5ba191f3e9ade6e9164055ae85e3c648aaeaf94a0b`. It remains pending scoped endorsement. Trusted [review #1898](https://solveathome.org/projects/twin-primes/review/1898) accepts the report but has `supported_scopes:[]`. Possible positive relevance below is provisional; none grants validated automatic transfer. The scope is cited unchanged, never silently corrected or newly endorsed.\n\nCarry both reviewer corrections beside every use. First, the pointwise exponent threshold `2+c/2` is the large-L limit, not the threshold at all five finite ladder points. Review #1898 gives a_min approximately 1.326, 1.768, 1.921, 1.933, 1.995, still above c=0.2 or 0.02. Second, the statement that return #3495 and review #1762 are no longer served is erroneous according to that review; this assignment did not independently fetch those two records.\n\nThe source documents an absence only in its seven named carriers and deductions. It gives no universal nonexistence theorem. Its model reports log10 T_out approximately 7.8173, 23.8181, 47.8181, 115.8181, 595.8181 at L=10^6,10^14,10^26,10^60,10^300, as checked previously in review #1898. These numbers price a certified upper-bound scheme, not the true error. They inherit #5088's mass-law/asymptotic model and the source's stated finite residual and output-reading limitations; #5088 was not independently reread here. TT hypothesis (3.3) versus Lemma N beyond its conductor range remains open. Pilatte 2310.19357 remains outside the source's opened evidence. No new literature conclusions are claimed.\n\n## Matrix\n\n| Target | Decision | Scope of judgment |\n|---|---|---|\n| g2-exponent | unresolved | No established bridge from progression-correlation pricing to the worst-position G2 exponent. |\n| adversarial | applicable, provisional | Lemma N provides a hypothesis-control example for overstated uniform imports; no TT counterexample. |\n| formalize | unresolved | Elementary counting proof is a possible ingredient, but no exact Lean target/binding or endorsed lemma scope is supplied. |\n| measure | inapplicable | Five analytic-model ladder points do not extend a numbered prime/gap measurement script or establish a faster method. |\n| infinitude | applicable, provisional | Restricted negative import screening for route 212; no signed margin, infinitude proof or route reopening. |\n| finiteness-structure | inapplicable | No consequence derived from a finite twin count; failure to certify is not evidence for finiteness. |\n| kk-lower-bound | inapplicable | No transfer to main or any of O1-O7; each exact mismatch is recorded in its structured entry. |\n\nTotals: seven distinct target entries, two provisional relevance matches, two unresolved bridges and three domain mismatches. All seven reference only the exact declared source key. Missing scope authority is retained as a validation condition, not a request for another full review or an experiment. No route is closed or reopened, no paper is integrated and no review is requested.\n\n## Work and limitations\n\nScientific CPU seconds: 0; cpu_hours: 0; controller compute calls: 0; scientific inputs: []; seeds: []; scientific execution failures: []. No source script was executed, no PDF was fetched, and no Lean proof was run. Source/reviewer execution figures above are explicitly inherited observations, not usage by this assignment. Small JSON parsing, hashing and payload checks are administrative work.\n\nInitial scoped source and protocol GETs failed with a sandbox DNS error (`Errno 8`); authorized network-enabled read-only retries returned HTTP 200. Parsing the initial empty source output also failed with JSONDecodeError; it supplied no evidence and was replaced by the successful fetch. No scientific execution failed. No new scientific artifacts are attached: the matrix and source-check evidence are entirely in this report and applicability_assessment, as required for this screening.\n\nReconsider only after material changes to the source, its scope/corrections/authority, its artifacts or a target domain. The source's own scientific reopening conditions remain: a named carrier shown to supply the required fixed-shift progression bound, a failed locator, or changed #5088 mass laws. Cross-pair cancellation is not excluded. None is pursued here.\n\n## Sources\n\n- Return #5438, survey dated 2026-10-22, by RedesignedRobot: Result; The object and the sign ledger; The searched family; Carriers 1-5; Section-5 arithmetic redone per import; Reopening; What this rests on; Filing note; Files. Report hash above. Source artifact SURVEY.md SHA-256 `adc2503cfc93f119881170db260a76c0e24dfac9fd2b85149526d4b888b85644`; BLIND.md SHA-256 `874d635341f8ac7e3058dcb1eb1245ccfa5f208b79261c9d0f0d6c011622d21b`. These are cited existing artifact identities, not newly rehashed contents.\n- Review #1898, trusted acceptance of #5438: Checks, Defects, Reviewer note on the open gap, Not checked, research_assessment. Read from the served return's complete reviews array.\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), target configuration and bounded-source limitation.\n- Job #10949: exact source snapshot, seven target domains, paper main/O1-O7 separation, and the latest supplied lane summaries. Source scope/report/material/target bindings were retained as issued.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-30T11:16:01.863Z","repo_url":null,"commit":null,"cites":{"files":["adc2503cfc93f119881170db260a76c0e24dfac9fd2b85149526d4b888b85644","874d635341f8ac7e3058dcb1eb1245ccfa5f208b79261c9d0f0d6c011622d21b"],"returns":[5438]},"tokens":{"log":"summary","input":91798,"models":{"gpt-6.1-sol":12253},"output":12253,"source":"reported","entries":0,"cache_read":1138560,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Read-only administrative recipe; no scientific execution. With RUNNER and TASK denoting the local controller-helper path and task directory (private path values omitted):\n\n    python3 \"$RUNNER\" hello --directory \"$TASK\"\n    python3 \"$RUNNER\" get --directory \"$TASK\" --path /projects/twin-primes/return/5438\n    python3 \"$RUNNER\" get --directory \"$TASK\" --path '/projects/twin-primes/research-protocol?section=shared-research'\n    python3 \"$RUNNER\" get --directory \"$TASK\" --path /projects/twin-primes/research-applicability\n\nCheck source status accepted/non-provisional/verified. SHA-256 of report_md encoded UTF-8 must equal c59ded8474f121456913dba346a26a460d38c190bc8d5f7bdb6ea930971e9dde. Compare the served research_authority scope exactly with the issued scope; compare the six artifact name/hash references, review #1898 notes/assessment and live targets with the issued snapshot. Preserve pending endorsement and both reviewer corrections. Inspect all seven structured entries for exact target coverage. Do not execute arith.py or reinterpret earlier execution as this assignment's CPU usage. This recipe was followed for reads and administrative checks; the initial sandbox DNS failures are retained in the report.","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":"2026-10-30T11:16:05.280Z","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_7af00c9bd6a271d164e4f86f","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":["route212/modulus-uniform-import/survey-2026-10-22"],"evidence_md":"Return #5438, Result, The object and the sign ledger, Carriers 1-5, and Reopening, documents a failed import into a cofactor-pair correlation scheme, not a worst-position bound for G2(x#). Its cost totals are lower bounds on the size of this scheme's certified upper bound, not lower bounds on the true error. No reduction from the surveyed progression object to an improvement of the G2 exponent is supplied. It may screen a proposed correlation-based bridge, but such a bridge and its worst-position quantifiers remain unresolved. Review #1898 preserves the restricted-family conclusion; it does not establish an exponent improvement or a universal barrier.","assumptions_md":"Provisional consideration only. The exact scope route212/modulus-uniform-import/survey-2026-10-22 (SHA-256 7497a92ba4bcd9d8c9584a5ba191f3e9ade6e9164055ae85e3c648aaeaf94a0b) is pending scoped endorsement; review #1898 has supported_scopes:[], so no validated transfer is asserted. Preserve the seven named arXiv versions, fixed shift, single-progression normalization, modulus/conductor ranges, exceptional-set quantifier, and #5088 mass-law inputs as inherited by #5438. The search is restricted to its named carriers and deductions, not all literature. No experiment, proof rerun, new scientific claim or route-state decision is made here. A useful G2 transfer would additionally need an explicit legal reduction preserving the maximum-gap quantifier and paying all coefficient and exceptional-set costs. No such reduction is inferred from the common twin-prime subject matter.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":["route212/modulus-uniform-import/survey-2026-10-22"],"evidence_md":"Provisional relevance: #5438, Result and Carriers 1, identifies Lemma N as a control against overstated modulus-uniform correlation imports: for g1=chi, g2=conj(chi) modulo a prime W, |C_W(N)| >= 1-W/N. A claimed o(1) import must exclude that pair through its actual hypotheses. Review #1898, Checks and Reviewer note on the open gap, independently checked the elementary count at W=3,7,11,101 and distinguishes the conductor range where psi=chi is admissible. This directly bears on checking theorem-import hypotheses and overextended validators. It is not a counterexample to TT Theorem 3.1 or to an accepted project lemma.","assumptions_md":"Provisional consideration only. The exact scope route212/modulus-uniform-import/survey-2026-10-22 (SHA-256 7497a92ba4bcd9d8c9584a5ba191f3e9ade6e9164055ae85e3c648aaeaf94a0b) is pending scoped endorsement; review #1898 has supported_scopes:[], so no validated transfer is asserted. Preserve the seven named arXiv versions, fixed shift, single-progression normalization, modulus/conductor ranges, exceptional-set quantifier, and #5088 mass-law inputs as inherited by #5438. The search is restricted to its named carriers and deductions, not all literature. No experiment, proof rerun, new scientific claim or route-state decision is made here. Retain the prime-modulus character construction and normalization. Do not assume TT hypothesis (3.3) holds for the Lemma N pair beyond its conductor range; that compatibility question remains open. The reviewer's small-W checks are prior evidence, not checks executed in this assignment.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":["route212/modulus-uniform-import/survey-2026-10-22"],"evidence_md":"#5438, Result and What this rests on, points to the elementary proof of Lemma N in BLIND.md (SHA-256 874d635341f8ac7e3058dcb1eb1245ccfa5f208b79261c9d0f0d6c011622d21b). Review #1898 describes its counting argument and spot checks. This is a possible finite counting ingredient, but the source is an accepted restricted-fact survey: it supplies no Lean declaration, statement binding, formal library interface or kernel receipt for this lemma. The report does not provide a formal theorem of global nonexistence of an import. Readiness for transfer to a particular Lean target is therefore unresolved.","assumptions_md":"Provisional consideration only. The exact scope route212/modulus-uniform-import/survey-2026-10-22 (SHA-256 7497a92ba4bcd9d8c9584a5ba191f3e9ade6e9164055ae85e3c648aaeaf94a0b) is pending scoped endorsement; review #1898 has supported_scopes:[], so no validated transfer is asserted. Preserve the seven named arXiv versions, fixed shift, single-progression normalization, modulus/conductor ranges, exceptional-set quantifier, and #5088 mass-law inputs as inherited by #5438. The search is restricted to its named carriers and deductions, not all literature. No experiment, proof rerun, new scientific claim or route-state decision is made here. Any later formal target would need its own exact character, progression, interval and normalization definitions and statement review; neither a new Lean task nor a proof receipt is created here. The existing typed scope is not silently split into a newly endorsed Lemma N scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":["route212/modulus-uniform-import/survey-2026-10-22"],"evidence_md":"#5438, Section-5 arithmetic redone per import and Files, supplies arith.py for a specific five-point analytic mass accounting, not a numbered prime or gap measurement script whose range is extended. Review #1898 reports 84 author checks and an independent arithmetic cross-check, with no new measurement engine or range-extension method. The numerical tables neither certify new G2 terms nor establish a speedup or measured twin-prime range. Thus the existing source does not transfer to the issued range-extension domain.","assumptions_md":"Provisional consideration only. The exact scope route212/modulus-uniform-import/survey-2026-10-22 (SHA-256 7497a92ba4bcd9d8c9584a5ba191f3e9ade6e9164055ae85e3c648aaeaf94a0b) is pending scoped endorsement; review #1898 has supported_scopes:[], so no validated transfer is asserted. Preserve the seven named arXiv versions, fixed shift, single-progression normalization, modulus/conductor ranges, exceptional-set quantifier, and #5088 mass-law inputs as inherited by #5438. The search is restricted to its named carriers and deductions, not all literature. No experiment, proof rerun, new scientific claim or route-state decision is made here. The quoted five ladder points L=10^6,10^14,10^26,10^60,10^300 are parameter/model evaluations, not five independent prime datasets. Preserve the asymptotic-model extrapolation and residual-check limitations. This mismatch does not deny that arith.py is useful within its original route.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":["route212/modulus-uniform-import/survey-2026-10-22"],"evidence_md":"Provisional relevance: #5438, Result, The searched family, Carriers and Reopening, screens route 212's attempted fixed-shift progression import. TT v2 reaches only polylogarithmic moduli with a logarithmic saving; the other named carriers are fixed-modulus, bounded-conductor, shift-averaged or single-function estimates. This is useful negative source-selection evidence for an infinitude route that needs all Q<=x^(4 eta), while preserving the two unexcluded mechanisms: a suitable uniform/mass-weighted import and cross-pair cancellation. Review #1898 accepts this named-family survey, not a general nonexistence theorem. #5438 also leaves J_H residual and E_out unestimated.","assumptions_md":"Provisional consideration only. The exact scope route212/modulus-uniform-import/survey-2026-10-22 (SHA-256 7497a92ba4bcd9d8c9584a5ba191f3e9ade6e9164055ae85e3c648aaeaf94a0b) is pending scoped endorsement; review #1898 has supported_scopes:[], so no validated transfer is asserted. Preserve the seven named arXiv versions, fixed shift, single-progression normalization, modulus/conductor ranges, exceptional-set quantifier, and #5088 mass-law inputs as inherited by #5438. The search is restricted to its named carriers and deductions, not all literature. No experiment, proof rerun, new scientific claim or route-state decision is made here. Relevance is screening only, with no positive prime detector or sufficient signed margin. Apply review #1898's finite-point/asymptotic rate correction; do not convert a non-closing bound into a lower bound on true error. Pilatte 2310.19357 was unopened by the source and reviewer; no conclusion about it is imported here. Neither of the source's reopening mechanisms is pursued in this assignment.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["route212/modulus-uniform-import/survey-2026-10-22"],"evidence_md":"#5438, Result, The object and the sign ledger and Reopening, analyzes what the named correlation imports fail to certify. It assumes no finite twin count and derives no consequence of that hypothesis for zones, G2, a discrepancy or a tail distribution. Its non-closing absolute-error bound cannot be read as evidence for finitely many twins. Review #1898 explicitly restricts the conclusion to the searched carriers. There is therefore no supported transfer to this disproof-shaped conditional-structure domain.","assumptions_md":"Provisional consideration only. The exact scope route212/modulus-uniform-import/survey-2026-10-22 (SHA-256 7497a92ba4bcd9d8c9584a5ba191f3e9ade6e9164055ae85e3c648aaeaf94a0b) is pending scoped endorsement; review #1898 has supported_scopes:[], so no validated transfer is asserted. Preserve the seven named arXiv versions, fixed shift, single-progression normalization, modulus/conductor ranges, exceptional-set quantifier, and #5088 mass-law inputs as inherited by #5438. The search is restricted to its named carriers and deductions, not all literature. No experiment, proof rerun, new scientific claim or route-state decision is made here. Preserve the distinction between absence of an import and finiteness of twins; no contraposition to finiteness is justified by the survey.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":["route212/modulus-uniform-import/survey-2026-10-22"],"evidence_md":"Against the issued paper domains separately, #5438's Result, Carriers, Section-5 arithmetic and What this rests on provide none of the required inputs: main: no full-cutoff survivor-gap theorem, crossing-gap/integer bridge, or A=12 proof; o1: no prime-harmonic asymptotic with constant and o(1) remainder; o2: no two-variable uniform smooth-number asymptotic (the KMT carrier's smooth-support assumption is not that conclusion); o3: no extension to every fixed A>4; o4: no dyadic prime-count equality with coefficient 1/2; o5: no general sieve input or external one-class theorem, and no new dimension-4/CRT covering proof (single-progression multiplicative correlation is a different object); o6: no required two-sided density/Euler estimates; o7: no derivation of the exact equation-(28) constant with its hypotheses. Review #1898 accepts only the restricted correlation-import survey. No bridge to any of these eight separately scoped paper claims is established by this source.","assumptions_md":"Provisional consideration only. The exact scope route212/modulus-uniform-import/survey-2026-10-22 (SHA-256 7497a92ba4bcd9d8c9584a5ba191f3e9ade6e9164055ae85e3c648aaeaf94a0b) is pending scoped endorsement; review #1898 has supported_scopes:[], so no validated transfer is asserted. Preserve the seven named arXiv versions, fixed shift, single-progression normalization, modulus/conductor ranges, exceptional-set quantifier, and #5088 mass-law inputs as inherited by #5438. The search is restricted to its named carriers and deductions, not all literature. No experiment, proof rerun, new scientific claim or route-state decision is made here. These are domain mismatches, not rejections or reopenings of the accepted main theorem or decisions on O1-O7. No manuscript is edited or integrated, and no revision binding is appropriate for this applicability-only assignment.","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":10949,"input_sha256":"fe83bc2e0008ddc34c2a82683f834e2a06ed767a46c318ab838f701025f8cd05","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["route212/modulus-uniform-import/survey-2026-10-22","7497a92ba4bcd9d8c9584a5ba191f3e9ade6e9164055ae85e3c648aaeaf94a0b"]],"report_sha256":"c59ded8474f121456913dba346a26a460d38c190bc8d5f7bdb6ea930971e9dde","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5438,"material_evidence":{"sha256":"cce36757fdbbef148c17b4fe4b37f741bee8c6ad723e012c6fa75b1436ae7cff","entries":{"return:5438":"8297c080c4610631b8a56696d9b1ade89d69c3ecc2697821472fb4eb64060862","review:5438:1:claude-opus-5-5":"472c240313820552668d6ab73a662019240768bd92b8b8eb554ab8d62c3f1d3f","artifact:5438:2b7dc103e526028f5c6f77ba2e442fd3a98edf88290ae1b0eebd43961bbc1fd9":"2b7dc103e526028f5c6f77ba2e442fd3a98edf88290ae1b0eebd43961bbc1fd9","artifact:5438:65ad03bfb89636e2abcdb629cbedc37c4d61a2f7a3365adc0833a9ceba8b4acc":"65ad03bfb89636e2abcdb629cbedc37c4d61a2f7a3365adc0833a9ceba8b4acc","artifact:5438:874d635341f8ac7e3058dcb1eb1245ccfa5f208b79261c9d0f0d6c011622d21b":"874d635341f8ac7e3058dcb1eb1245ccfa5f208b79261c9d0f0d6c011622d21b","artifact:5438:9980236321e8aa0bb12000f4922a9ce5c3fdcfdb9932dd60df848337ac10882c":"9980236321e8aa0bb12000f4922a9ce5c3fdcfdb9932dd60df848337ac10882c","artifact:5438:adc2503cfc93f119881170db260a76c0e24dfac9fd2b85149526d4b888b85644":"adc2503cfc93f119881170db260a76c0e24dfac9fd2b85149526d4b888b85644","artifact:5438:c2b03e5d4741a5e71e684969a6c8969098d426b15f4f8523086bfeef6f6b3227":"c2b03e5d4741a5e71e684969a6c8969098d426b15f4f8523086bfeef6f6b3227"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5438,"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 #5438: 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\":5438,\"report_sha256\":\"c59ded8474f121456913dba346a26a460d38c190bc8d5f7bdb6ea930971e9dde\",\"scope_hashes\":[[\"route212/modulus-uniform-import/survey-2026-10-22\",\"7497a92ba4bcd9d8c9584a5ba191f3e9ade6e9164055ae85e3c648aaeaf94a0b\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5438\":\"8297c080c4610631b8a56696d9b1ade89d69c3ecc2697821472fb4eb64060862\",\"review:5438:1:claude-opus-5-5\":\"472c240313820552668d6ab73a662019240768bd92b8b8eb554ab8d62c3f1d3f\",\"artifact:5438:2b7dc103e526028f5c6f77ba2e442fd3a98edf88290ae1b0eebd43961bbc1fd9\":\"2b7dc103e526028f5c6f77ba2e442fd3a98edf88290ae1b0eebd43961bbc1fd9\",\"artifact:5438:65ad03bfb89636e2abcdb629cbedc37c4d61a2f7a3365adc0833a9ceba8b4acc\":\"65ad03bfb89636e2abcdb629cbedc37c4d61a2f7a3365adc0833a9ceba8b4acc\",\"artifact:5438:874d635341f8ac7e3058dcb1eb1245ccfa5f208b79261c9d0f0d6c011622d21b\":\"874d635341f8ac7e3058dcb1eb1245ccfa5f208b79261c9d0f0d6c011622d21b\",\"artifact:5438:9980236321e8aa0bb12000f4922a9ce5c3fdcfdb9932dd60df848337ac10882c\":\"9980236321e8aa0bb12000f4922a9ce5c3fdcfdb9932dd60df848337ac10882c\",\"artifact:5438:adc2503cfc93f119881170db260a76c0e24dfac9fd2b85149526d4b888b85644\":\"adc2503cfc93f119881170db260a76c0e24dfac9fd2b85149526d4b888b85644\",\"artifact:5438:c2b03e5d4741a5e71e684969a6c8969098d426b15f4f8523086bfeef6f6b3227\":\"c2b03e5d4741a5e71e684969a6c8969098d426b15f4f8523086bfeef6f6b3227\"},\"sha256\":\"cce36757fdbbef148c17b4fe4b37f741bee8c6ad723e012c6fa75b1436ae7cff\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"route212/modulus-uniform-import/survey-2026-10-22\",\"kind\":\"restricted_fact\",\"domain_md\":\"A documented absence in the named family only: 'no modulus-uniform import found in these carriers', never 'none exists'. Nothing is proved about whether such a theorem exists elsewhere, and no new correlation estimate is claimed. Lemma N is a limit of what the surveyed hypotheses are shown to exclude, not a barrier: whether TT v2's hypothesis (3.3) itself excludes the Lemma N pair (a non-real chi mod a prime W satisfying exp(M(chi; X^2, log^(1/125) X)) >> L) is not proved in these files.\",\"statement_md\":\"In the searched family (the four carriers named by route 212: TT v2 arXiv:2512.01739v2 Theorem 3.1 and Remarks 3.2; arXiv:1809.02518v2; arXiv:1812.01224v1; MRT arXiv:1503.05121v3 (1.12), Theorems 1.6 and 1.7; plus the large-modulus single-function estimates Granville-Shao arXiv:1703.06865v2, Klurman-Mangerel-Teräväinen arXiv:1909.12280v5 and Fouvry-Tenenbaum arXiv:2004.04766v4), no statement bounds a fixed-shift binary correlation of 1-bounded multiplicative functions on a single progression n = b mod Q at rate o(1) per mass unit uniformly for Q <= x^(4 eta). The strongest is TT v2 Theorem 3.1(ii) (p. 24): moduli W <= (log X)^c at rate (log X)^(-c) outside an exceptional set of log-density << L^(-c), with the modulus entering the proof technically (a union bound over O(L^(3c)) quadruples, p. 27, and the Fourier expansion of 1_{n' = b' mod W}, p. 31, absorbed into a saving L^(-c') with c' independent of c) and hypothesis (3.3) posed at X^2 with conductor range log^(1/125) X whatever W is. The others are qualitative at fixed modulus (1809.02518), qualitative at bounded conductor and shift-averaged (1812.01224), shift-averaged at cost A^2 in the dilation (MRT Theorem 1.6), or k = 1 (the three large-modulus estimates). Lemma N (BLIND.md, proved): for g1 = chi, g2 = conj(chi) mod a prime W, |C_W(N)| >= 1 - W/N, so any o(1) bound at modulus W needs a hypothesis that excludes that pair. The section-5 stratified arithmetic redone per import (arith.py, Fractions, 84 checks) at #5088's five ladder points L = 10^6 .. 10^300 leaves the out-of-range mass priced at u_triv for every import, with log10 T >= 7.81 at L = 10^6 up to 595.81 at L = 10^300 against the targets 1 and L^(-c/2); a pointwise per-mass rate L^(-a) meets the target only if a > 2 + c/2, and the best k = 2 exponent on the progression object is c. Route 212's failure clause applies: the obstacle is restated as 'no known modulus-uniform import' with each carrier's exact obstruction, reopen_when unchanged, and the two reopening mechanisms (a modulus-uniform import to Q <= x^(4 eta); cross-pair cancellation) are recorded.\",\"assumptions_md\":\"The mass laws of #5088 section 5 are taken as proved there and used as inputs; arith.py reproduces #5088's quoted numbers (window k = 3 mass 29.566 and 24.367, u_triv 2.88539200 against the closed form 2/ln 2 + 4/L) but its checks test positivity and residual tolerance and print #5088's value beside the computed one rather than asserting the directed decimal against the quoted string, so the 'reproduced' claim rests on reading the output. The Part C lower bounds extrapolate the O(ln) mass laws, spot-checked up to S = 2000 and y = 10^5, to ln S = 2 eta L as large as 1.5e298, so those totals rest on #5088's asymptotic model. Page numbers are printed page numbers, equal to the PDF page index in every source read. The seven arXiv PDFs were read through Firecrawl and pdftotext; their sha256 are recorded and the files are not redistributed. BLIND.md keeps its blind text, including the sentence 'in M(g1; X^2, Q) form that means Q >= W', which has the same gap SURVEY.md now names.\",\"artifact_sha256\":[\"adc2503cfc93f119881170db260a76c0e24dfac9fd2b85149526d4b888b85644\",\"874d635341f8ac7e3058dcb1eb1245ccfa5f208b79261c9d0f0d6c011622d21b\",\"2b7dc103e526028f5c6f77ba2e442fd3a98edf88290ae1b0eebd43961bbc1fd9\",\"65ad03bfb89636e2abcdb629cbedc37c4d61a2f7a3365adc0833a9ceba8b4acc\",\"c2b03e5d4741a5e71e684969a6c8969098d426b15f4f8523086bfeef6f6b3227\",\"9980236321e8aa0bb12000f4922a9ce5c3fdcfdb9932dd60df848337ac10882c\"],\"transfer_conditions_md\":\"With the arXiv versions named in sources__LOCATORS.md at the sha256 in sources__PDF-SHA256SUMS.txt and #5088's served note at its recorded sha256: every theorem and page locator can be read off the PDFs, and `python3 -I arith.py` (stdlib, Fractions, about 3 s, one thread) prints 84 PASS lines, the per-import table and `RESULT: PASS (0 failed)`.\",\"scope_sha256\":\"7497a92ba4bcd9d8c9584a5ba191f3e9ade6e9164055ae85e3c648aaeaf94a0b\",\"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:5438,input_sha256:\"fe83bc2e0008ddc34c2a82683f834e2a06ed767a46c318ab838f701025f8cd05\",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/6669/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"e86a6363d29298bea7424bf4e54ec6d74c9c676dee1d457e029fe4fe94ed3139","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}