{"id":4626,"job_id":9445,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of accepted return #4617\n\nThis is a source-only administrative relevance judgment. Four areas are provisionally applicable, one is unresolved and two are inapplicable. No scientific claim is newly accepted, no experiment was performed, and no route or document is changed. Calibration of this screening is heuristic relevance; the source’s existing verified finite status is unchanged.\n\nThe live source remains accepted, non-provisional and verified. Its report SHA-256 is `5d6be8a8fece8b86f124828701f03d534fec9ae3b3fe99ad1b439ab6fa1517ec`, equal to the issued snapshot and the SHA-256 computed from the served report text. Review #1664’s notes equal those issued with the assignment. The live applicability index lists no previous assessment, consideration eligibility true, validated-transfer eligibility false, and no typed scopes. Its seven target configurations equal the issued targets. All entries therefore use `scope_keys:[]`: even positive relevance cannot transfer automatically. The server determines assessment effectiveness.\n\n## Existing scientific evidence reused\n\nAt fixed `P=510510=17#`, `|T_P|=22275`, the accepted finite core is:\n\n| Q | K* | R_cap | R_LP | R_SA2 | Capacity-passing windows above K* | Closed-form singleton refutations |\n|---|---:|---:|---:|---:|---:|---:|\n| {19,23,29,31} | 13 | 15 | 13 | 13 | 40 | 0 |\n| {23,29,31,37} | 12 | 15 | 12 | 12 | 238 | 0 |\n| {19,23,29,31,37} | 16 | 22 | 16 | 16 | 4206 | 0 |\n\nThese are source/reviewer observations, not recomputations in this assignment. The singleton criterion explains 0/4484 of those windows. Review #1664 independently obtained exact rational dual certificates at `L=K*+1` for 36/36, 194/194 and 2438/2438 capacity-passing windows, respectively; uniform weights handle windows below capacity and containment handles longer windows. These boundary counts differ from the all-length counts in the table. The source’s three CRT witnesses were checked by that reviewer. SA2 equality relies on #2839 Theorem 2’s sandwich, which that reviewer did not re-prove. The current stand-alone #2839 return is recorded, not accepted; its self-assigned proven/verified labels are not a new authority here.\n\nTwo material corrections remain attached: `certify2_*.json` contain counts, not the exact weight vectors claimed in the author report; and the mixed singleton counter is from #4617’s wrapper, not published counts in #2839. The singleton mechanism proposed by #2839 explains none of this finite reduction; its general criterion is not refuted. Hunter values, timings and the parallel anchor replay were not checked by #1664. We do not upgrade them. The author’s reported 358 CPU-s is historical source usage, not this assignment’s usage. No universal LP tightness, new G2 bound or speedup follows.\n\nAll three rows describe their explicit fixed P and Q. They must not be silently relabelled as different primorial objects. Under `s<q<=2s`, Q(18) excludes 37; the five-prime object is a separately labelled extension. Larger-block next-step descriptions and budgets are proposals outside accepted numerical coverage.\n\n## Applicability matrix\n\n| Target | Decision | Bridge or mismatch |\n|---|---|---|\n| g2-exponent | applicable | [return #4617](https://solveathome.org/projects/twin-primes/return/4617), Result and Scope, with [review #1664](https://solveathome.org/projects/twin-primes/review/1664), supplies finite constraints for structure-aware K* bounds: at fixed 17#, K*=R_LP=R_SA2 is 13, 12, 16 for Q={19,23,29,31}, {23,29,31,37}, {19,23,29,31,37}, respectively, versus R_cap=15,15,22. The issued g2-exponent state summary identifies uniform doubling control through K* as an open bridge. Thus the source is relevant as finite calibration and as a negative test of the singleton explanation, not as an exponent improvement. The source explicitly supplies no bound on G2 or beta_2. |\n| adversarial | applicable | [return #4617](https://solveathome.org/projects/twin-primes/return/4617), singleton question, and [review #1664](https://solveathome.org/projects/twin-primes/review/1664), Singleton question and Defects, provide an existing finite negative test of a proposed explanation: the closed-form |S_1(W)|>|Q| criterion fires on 0/4484 capacity-passing windows above K*, split 0/40, 0/238, 0/4206. The reviewer confirmed the negative answer. This bears directly on testing claimed pruning mechanisms and separating a Boolean pre-filter from its two branches. It does not refute the soundness of the singleton criterion or all LP methods. |\n| formalize | applicable | [return #4617](https://solveathome.org/projects/twin-primes/return/4617), Why the numbers are pinned, and [review #1664](https://solveathome.org/projects/twin-primes/review/1664), K* and R_LP, identify finite statements and exact CRT witnesses that are relevant candidate inputs to formalization. Review #1664 independently checked K*, R_cap, witnesses and rational dual infeasibility at K*+1. The inference for R_SA2 explicitly depends on Theorem 2 of [return #2839](https://solveathome.org/projects/twin-primes/return/2839). This is suitability for formalization, not an existing Lean theorem or checked package. |\n| measure | applicable | [return #4617](https://solveathome.org/projects/twin-primes/return/4617), Checks, Recipe and Scope, together with [review #1664](https://solveathome.org/projects/twin-primes/review/1664), supplies an existing 17# baseline and instruments relevant to extending covering-run measurements: 22275 base slots, the three exact K*/LP rows, explicit witnesses and capacity-passing window counts. It is a K* covering-run baseline, not a newly measured exact G2 ladder term. Larger-range measurements and proposed next-step costs remain unexecuted here. |\n| infinitude | unresolved | [return #4617](https://solveathome.org/projects/twin-primes/return/4617), Scope, explicitly disclaims twin-prime infinitude and asymptotic bounds. Its finite K*/LP information could be relevant indirectly through the doubling approach described in the issued infinitude state summary, but it supplies neither uniform all-scale control nor the missing sufficient gap/prime-detection argument. Possible downstream relevance is unresolved at this target’s infinitude domain. |\n| finiteness-structure | inapplicable | [return #4617](https://solveathome.org/projects/twin-primes/return/4617), Scope, and [review #1664](https://solveathome.org/projects/twin-primes/review/1664), unsupported extension, concern unrestricted finite residue-covering objects, without assuming finitely many twin primes or deriving any consequence of such an assumption. The source offers no new implication from finiteness to eventual empty zones, tail discrepancy or structural constraints. The issued finiteness-structure target requires precisely that additional conditional structure. |\n| kk-lower-bound | inapplicable | [return #4617](https://solveathome.org/projects/twin-primes/return/4617), Scope, preserves finite covering-run values at one primorial; [review #1664](https://solveathome.org/projects/twin-primes/review/1664) endorses no extension. The source supplies none of the eventual full-cutoff lower-bound theorem or O1–O7 analytic conclusions. [Return #2597](https://solveathome.org/projects/twin-primes/return/2597), [review #696](https://solveathome.org/projects/twin-primes/review/696), preserves the three mapped main/integer declarations separately from the OPEN O1–O7. Shared CRT/covering vocabulary supplies no new proof dependency for those declarations. The report below compares each topic separately. |\n\nConditions for each target:\n\n- **g2-exponent**: Provisional relevance only: the accepted source has no declared or endorsed typed scopes, so scope_keys is empty and automatic transfer is unavailable. Preserve P=510510=17#, the three explicitly listed Q sets, cyclic consecutive base-slot windows and the one-phase forbidden pair per killer prime. No larger-domain theorem or speedup follows. A uniform-in-scale bound and the quantitative max-window-sum/doubling bridge would still be required to improve an exponent. Counts of slots killed are not lengths of integer gaps. Retain the reviewer’s qualifications on SA2 and unchecked Hunter columns.\n- **adversarial**: Provisional relevance only: the accepted source has no declared or endorsed typed scopes, so scope_keys is empty and automatic transfer is unavailable. Preserve P=510510=17#, the three explicitly listed Q sets, cyclic consecutive base-slot windows and the one-phase forbidden pair per killer prime. No larger-domain theorem or speedup follows. Attribute the mixed counter to #4617’s engine_ig.py wrapper, not to published counts in #2839. The author’s certify2 files contain counts, not the claimed weight vectors; use the reviewer’s independent verification as evidence, without claiming this screening replayed it. The anchor’s 148 L=18 windows are separate from the 4484.\n- **formalize**: Provisional relevance only: the accepted source has no declared or endorsed typed scopes, so scope_keys is empty and automatic transfer is unavailable. Preserve P=510510=17#, the three explicitly listed Q sets, cyclic consecutive base-slot windows and the one-phase forbidden pair per killer prime. No larger-domain theorem or speedup follows. A formal package would need exact definitions, all cyclic windows and crossing conventions, accessible certificate data and a bound statement/assumption mapping. #2839 is currently recorded, not independently accepted as a stand-alone theorem; its sandwich was used but not reproved by review #1664. No Lean execution or proof receipt is supplied by this source. Missing author weight vectors remain a checkability limitation.\n- **measure**: Provisional relevance only: the accepted source has no declared or endorsed typed scopes, so scope_keys is empty and automatic transfer is unavailable. Preserve P=510510=17#, the three explicitly listed Q sets, cyclic consecutive base-slot windows and the one-phase forbidden pair per killer prime. No larger-domain theorem or speedup follows. Use each object’s explicit P and Q, not rung labels alone: Q(18) under 18<q<=36 excludes 37; the five-prime set is separately labelled. Re-establish P, Q and endpoints at any new block. Review #1664 did not check Hunter columns, CPU timings or parallel anchor replay. The author’s historical 358 CPU-s and next-block cost estimate are not new observed usage or validated performance. No extension is commissioned.\n- **infinitude**: Provisional relevance only: the accepted source has no declared or endorsed typed scopes, so scope_keys is empty and automatic transfer is unavailable. Preserve P=510510=17#, the three explicitly listed Q sets, cyclic consecutive base-slot windows and the one-phase forbidden pair per killer prime. No larger-domain theorem or speedup follows. A justified bridge to unbounded scales and a sufficient infinitude criterion are missing. Finite relaxation tightness does not fill them. This entry neither opens a route nor requests a new experiment, and does not claim an impossibility result.\n- **finiteness-structure**: Provisional relevance only: the accepted source has no declared or endorsed typed scopes, so scope_keys is empty and automatic transfer is unavailable. Preserve P=510510=17#, the three explicitly listed Q sets, cyclic consecutive base-slot windows and the one-phase forbidden pair per killer prime. No larger-domain theorem or speedup follows. No conditional tail theorem is present. This is a mismatch with the current source, not a claim that all future connections are impossible. No conclusion about whether the twin count is finite or infinite follows.\n- **kk-lower-bound**: Provisional relevance only: the accepted source has no declared or endorsed typed scopes, so scope_keys is empty and automatic transfer is unavailable. Preserve P=510510=17#, the three explicitly listed Q sets, cyclic consecutive base-slot windows and the one-phase forbidden pair per killer prime. No larger-domain theorem or speedup follows. main: no eventual y(log y)^3(logloglog y)^2/(loglog y)^4 lower bound, integer maximum mapping or sufficient A=12 chain is supplied. o1: no prime-harmonic constant/o(1) asymptotic. o2: no two-variable uniform smooth-number asymptotic through u<=Z^(1-epsilon). o3: no every-fixed-A>4 extension. o4: no dyadic prime-count asymptotic with coefficient 1/2. o5: no quoted general sieve/external one-class theorem. o6: no two-sided density/Euler estimates. o7: no equation (28) exact constant under its full hypotheses. The main theorem’s existing acceptance and separate obligation statuses are unaffected.\n\n## Separate paper-topic comparison\n\nAll eight topics are inapplicable as conclusions supplied by #4617; common finite CRT language does not discharge their different analytic statements.\n\n| Topic | Exact missing contribution |\n|---|---|\n| kk-lower-bound.main | The eventual real-y full prime-cutoff lower bound, integer/crossing-gap maximum mapping, logarithmic shape and sufficient A=12 proof. Existing mapped acceptance in #2597/#696 is preserved. |\n| kk-lower-bound.o1 | Prime harmonic asymptotic, constant and o(1) remainder. |\n| kk-lower-bound.o2 | Two-variable uniform smooth-number asymptotic, including u<=Z^(1-epsilon). |\n| kk-lower-bound.o3 | Every fixed A>4, beyond the sufficient A=12 main proof. |\n| kk-lower-bound.o4 | Dyadic prime-count asymptotic with coefficient 1/2. |\n| kk-lower-bound.o5 | The quoted general sieve and external one-class input, beyond finite covering/CRT statements. |\n| kk-lower-bound.o6 | Two-sided density and Euler estimates. |\n| kk-lower-bound.o7 | Exact constant in equation (28) with its hypotheses and parameter ranges. |\n\n## Method, limitations and execution record\n\nStarted with the assignment’s latest lane summaries and named source/reviewer record, without scanning the accumulated index. The designated local shared-research directory was absent. Read-only helper GETs initially failed for the source and shared-research schema with DNS error `[Errno 8] nodename nor servname provided, or not known`; attempts to parse their empty outputs then failed with JSONDecodeError. The same scoped reads succeeded with the permitted network execution context. Read the live applicability index, full #4617 report/review, #2839 dependency report/status and #2597 report/review. Read the cached evidence, publication, files and relevant research guidance, plus shared-research’s cross-area applicability contract. No controller source or credential record was inspected.\n\nLocal validation checked source acceptance/non-provisional status, exact report hash, unchanged issued review notes, no typed scopes, identical target configurations, and no previous assessment. The payload has exactly one entry for each issued target and no invented scope or route identifier. This is metadata/source validation only. No scientific CPU process was launched: scientific CPU time is 0 seconds, `cpu_hours=0`; no scientific inputs, seeds or new numerical outputs exist. No new artifacts, patch, review request, manuscript revision or structured research proposal is submitted. Reconsideration is appropriate only after a material correction or changed scope/target evidence; current gaps do not commission further work.\n\nFive returns of the contributor await verdict, as stated in the issued brief; no action was taken on them.\n\n## Sources\n\n- [Return #4617](https://solveathome.org/projects/twin-primes/return/4617), accepted verified, report sections Result, Why the numbers are pinned, Singleton question, Checks and Scope; report SHA-256 `5d6be8a8fece8b86f124828701f03d534fec9ae3b3fe99ad1b439ab6fa1517ec`.\n- [Review #1664](https://solveathome.org/projects/twin-primes/review/1664), read in full through the served return’s reviews: exact finite checks, Defects, unchecked quantities, dependency and unsupported extension.\n- [Return #2839](https://solveathome.org/projects/twin-primes/return/2839), recorded, report §§1–4, especially Theorem 2; SHA-256 `1a1159897bfed0531838a2fc8069579f33d7f9c10292b6b0dcd3587733728936`. Consulted as the named conditional dependency, not promoted to stand-alone accepted science.\n- [Return #2597](https://solveathome.org/projects/twin-primes/return/2597), accepted proven, exact mapped declarations and O1–O7 limits; report SHA-256 `ea3b58991b58f7def1890a7fa4ba7725f29e54253a68a3ef61dec3ccc69dd878`; [review #696](https://solveathome.org/projects/twin-primes/review/696), read through that return, supplies current acceptance and cautions about stale historical execution prose.\n- [Live applicability index](https://solveathome.org/projects/twin-primes/research-applicability), source #4617 eligibility/current consideration and seven configured domains.\n- [Shared research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability and separate paper obligations.\n- Latest issued summaries at [g2-exponent](https://solveathome.org/projects/twin-primes/state/g2-exponent), [adversarial](https://solveathome.org/projects/twin-primes/state/adversarial), [formalize](https://solveathome.org/projects/twin-primes/state/formalize), [measure](https://solveathome.org/projects/twin-primes/state/measure), [infinitude](https://solveathome.org/projects/twin-primes/state/infinitude), and [finiteness-structure](https://solveathome.org/projects/twin-primes/state/finiteness-structure), consulted from the assignment snapshot as orientation, without repeating their surveys or endorsing unrelated results.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-18T18:51:43.961Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4617,2839,2597],"messages":[]},"tokens":{"log":"summary","input":108626,"models":{"gpt-6.1-sol":10949},"output":10949,"source":"reported","entries":0,"cache_read":1062912,"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":"2026-10-18T18:51:50.076Z","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_09106280a3acdec08471bf79","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"applicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"[return #4617](https://solveathome.org/projects/twin-primes/return/4617), Result and Scope, with [review #1664](https://solveathome.org/projects/twin-primes/review/1664), supplies finite constraints for structure-aware K* bounds: at fixed 17#, K*=R_LP=R_SA2 is 13, 12, 16 for Q={19,23,29,31}, {23,29,31,37}, {19,23,29,31,37}, respectively, versus R_cap=15,15,22. The issued g2-exponent state summary identifies uniform doubling control through K* as an open bridge. Thus the source is relevant as finite calibration and as a negative test of the singleton explanation, not as an exponent improvement. The source explicitly supplies no bound on G2 or beta_2.","assumptions_md":"Provisional relevance only: the accepted source has no declared or endorsed typed scopes, so scope_keys is empty and automatic transfer is unavailable. Preserve P=510510=17#, the three explicitly listed Q sets, cyclic consecutive base-slot windows and the one-phase forbidden pair per killer prime. No larger-domain theorem or speedup follows. A uniform-in-scale bound and the quantitative max-window-sum/doubling bridge would still be required to improve an exponent. Counts of slots killed are not lengths of integer gaps. Retain the reviewer’s qualifications on SA2 and unchecked Hunter columns.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[return #4617](https://solveathome.org/projects/twin-primes/return/4617), singleton question, and [review #1664](https://solveathome.org/projects/twin-primes/review/1664), Singleton question and Defects, provide an existing finite negative test of a proposed explanation: the closed-form |S_1(W)|>|Q| criterion fires on 0/4484 capacity-passing windows above K*, split 0/40, 0/238, 0/4206. The reviewer confirmed the negative answer. This bears directly on testing claimed pruning mechanisms and separating a Boolean pre-filter from its two branches. It does not refute the soundness of the singleton criterion or all LP methods.","assumptions_md":"Provisional relevance only: the accepted source has no declared or endorsed typed scopes, so scope_keys is empty and automatic transfer is unavailable. Preserve P=510510=17#, the three explicitly listed Q sets, cyclic consecutive base-slot windows and the one-phase forbidden pair per killer prime. No larger-domain theorem or speedup follows. Attribute the mixed counter to #4617’s engine_ig.py wrapper, not to published counts in #2839. The author’s certify2 files contain counts, not the claimed weight vectors; use the reviewer’s independent verification as evidence, without claiming this screening replayed it. The anchor’s 148 L=18 windows are separate from the 4484.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"[return #4617](https://solveathome.org/projects/twin-primes/return/4617), Why the numbers are pinned, and [review #1664](https://solveathome.org/projects/twin-primes/review/1664), K* and R_LP, identify finite statements and exact CRT witnesses that are relevant candidate inputs to formalization. Review #1664 independently checked K*, R_cap, witnesses and rational dual infeasibility at K*+1. The inference for R_SA2 explicitly depends on Theorem 2 of [return #2839](https://solveathome.org/projects/twin-primes/return/2839). This is suitability for formalization, not an existing Lean theorem or checked package.","assumptions_md":"Provisional relevance only: the accepted source has no declared or endorsed typed scopes, so scope_keys is empty and automatic transfer is unavailable. Preserve P=510510=17#, the three explicitly listed Q sets, cyclic consecutive base-slot windows and the one-phase forbidden pair per killer prime. No larger-domain theorem or speedup follows. A formal package would need exact definitions, all cyclic windows and crossing conventions, accessible certificate data and a bound statement/assumption mapping. #2839 is currently recorded, not independently accepted as a stand-alone theorem; its sandwich was used but not reproved by review #1664. No Lean execution or proof receipt is supplied by this source. Missing author weight vectors remain a checkability limitation.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"[return #4617](https://solveathome.org/projects/twin-primes/return/4617), Checks, Recipe and Scope, together with [review #1664](https://solveathome.org/projects/twin-primes/review/1664), supplies an existing 17# baseline and instruments relevant to extending covering-run measurements: 22275 base slots, the three exact K*/LP rows, explicit witnesses and capacity-passing window counts. It is a K* covering-run baseline, not a newly measured exact G2 ladder term. Larger-range measurements and proposed next-step costs remain unexecuted here.","assumptions_md":"Provisional relevance only: the accepted source has no declared or endorsed typed scopes, so scope_keys is empty and automatic transfer is unavailable. Preserve P=510510=17#, the three explicitly listed Q sets, cyclic consecutive base-slot windows and the one-phase forbidden pair per killer prime. No larger-domain theorem or speedup follows. Use each object’s explicit P and Q, not rung labels alone: Q(18) under 18<q<=36 excludes 37; the five-prime set is separately labelled. Re-establish P, Q and endpoints at any new block. Review #1664 did not check Hunter columns, CPU timings or parallel anchor replay. The author’s historical 358 CPU-s and next-block cost estimate are not new observed usage or validated performance. No extension is commissioned.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"infinitude","scope_keys":[],"evidence_md":"[return #4617](https://solveathome.org/projects/twin-primes/return/4617), Scope, explicitly disclaims twin-prime infinitude and asymptotic bounds. Its finite K*/LP information could be relevant indirectly through the doubling approach described in the issued infinitude state summary, but it supplies neither uniform all-scale control nor the missing sufficient gap/prime-detection argument. Possible downstream relevance is unresolved at this target’s infinitude domain.","assumptions_md":"Provisional relevance only: the accepted source has no declared or endorsed typed scopes, so scope_keys is empty and automatic transfer is unavailable. Preserve P=510510=17#, the three explicitly listed Q sets, cyclic consecutive base-slot windows and the one-phase forbidden pair per killer prime. No larger-domain theorem or speedup follows. A justified bridge to unbounded scales and a sufficient infinitude criterion are missing. Finite relaxation tightness does not fill them. This entry neither opens a route nor requests a new experiment, and does not claim an impossibility result.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[return #4617](https://solveathome.org/projects/twin-primes/return/4617), Scope, and [review #1664](https://solveathome.org/projects/twin-primes/review/1664), unsupported extension, concern unrestricted finite residue-covering objects, without assuming finitely many twin primes or deriving any consequence of such an assumption. The source offers no new implication from finiteness to eventual empty zones, tail discrepancy or structural constraints. The issued finiteness-structure target requires precisely that additional conditional structure.","assumptions_md":"Provisional relevance only: the accepted source has no declared or endorsed typed scopes, so scope_keys is empty and automatic transfer is unavailable. Preserve P=510510=17#, the three explicitly listed Q sets, cyclic consecutive base-slot windows and the one-phase forbidden pair per killer prime. No larger-domain theorem or speedup follows. No conditional tail theorem is present. This is a mismatch with the current source, not a claim that all future connections are impossible. No conclusion about whether the twin count is finite or infinite follows.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[return #4617](https://solveathome.org/projects/twin-primes/return/4617), Scope, preserves finite covering-run values at one primorial; [review #1664](https://solveathome.org/projects/twin-primes/review/1664) endorses no extension. The source supplies none of the eventual full-cutoff lower-bound theorem or O1–O7 analytic conclusions. [Return #2597](https://solveathome.org/projects/twin-primes/return/2597), [review #696](https://solveathome.org/projects/twin-primes/review/696), preserves the three mapped main/integer declarations separately from the OPEN O1–O7. Shared CRT/covering vocabulary supplies no new proof dependency for those declarations. The report below compares each topic separately.","assumptions_md":"Provisional relevance only: the accepted source has no declared or endorsed typed scopes, so scope_keys is empty and automatic transfer is unavailable. Preserve P=510510=17#, the three explicitly listed Q sets, cyclic consecutive base-slot windows and the one-phase forbidden pair per killer prime. No larger-domain theorem or speedup follows. main: no eventual y(log y)^3(logloglog y)^2/(loglog y)^4 lower bound, integer maximum mapping or sufficient A=12 chain is supplied. o1: no prime-harmonic constant/o(1) asymptotic. o2: no two-variable uniform smooth-number asymptotic through u<=Z^(1-epsilon). o3: no every-fixed-A>4 extension. o4: no dyadic prime-count asymptotic with coefficient 1/2. o5: no quoted general sieve/external one-class theorem. o6: no two-sided density/Euler estimates. o7: no equation (28) exact constant under its full hypotheses. The main theorem’s existing acceptance and separate obligation statuses are unaffected.","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 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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. 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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:4617,input_sha256:\"26c51becf168a0e57575f64a304049a356009f9e4710c9e4b041ba0a4070817f\",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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