{"id":3655,"job_id":7312,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of return #1918 — job #7312\n\nAdministrative relevance judgment only. Source #1918 remains trusted-accepted, non-provisional, at **verified**. This screening is calibrated as **heuristic** for possible transfer relevance; it neither changes the source rung nor endorses a new scientific claim.\n\nThe live report SHA-256 is `7deb4f75046c2186b72b881c369c8b80e38ba511b683451adf4ef158dd85da32`, matching the issued snapshot. All 12 source artifact hashes match its pinned artifact set. Review #1191's verdict, rung, trust, notes, reassessment flag and scope assessment match the issued context; there are no typed source scopes. The seven live target domains match the issued domains. The bounded live applicability index omits #1918; adding source_return_id=1918 returned the identical 32-source index, so that response cannot establish a source-specific currentness flag. Direct source and issued scientific review checks establish the unchanged evidence actually used; no validated transfer eligibility is claimed.\n\n| Area | Decision | Reason at the issued domain |\n|---|---|---|\n| g2-exponent | inapplicable | No upper-bound inequality or worst-position bridge; fixed-gap statistics are diagnostic context only. |\n| adversarial | applicable, provisional | Existing CRT counts provide bounded oracles for histogram/repeat validators. |\n| formalize | applicable, provisional | Finite CRT/inclusion-exclusion statements and a reviewed fixed-gap argument provide possible formalization targets; no Lean execution is present. |\n| measure | applicable, provisional | The HV128 T37 instrument and selected T41-T47 IE counts bear directly on extending measurements. |\n| infinitude | inapplicable | No unbounded genuine-prime consequence or sufficient signed/G2 bound. |\n| finiteness-structure | inapplicable | No finite-twin hypothesis or quantified conditional consequence. |\n| kk-lower-bound | inapplicable | Neither the mapped main theorem nor any of the distinct O1-O7 obligations is established. |\n\nAll entries use scope_keys=[] and retain explicit conditions in applicability_assessment. Three possible applicable entries and four inapplicable entries cover all seven configured targets. Missing exact scope authority remains an unresolved validation condition for every proposed reuse; no automatic transfer or additional experiment is authorized by this matrix.\n\nExisting source evidence: T37 D=217,929,355,875, h60=9,831,828,408, R60=100,535,086; rho1(60,T37)=0.226655 (review), and L(60)=0.462542. Source repayment at p=29/31/41/43 is 0.4609/0.4067/0.6231/0.6878. The fold-level Lambda1 limit is open. Review #1191 did not independently recount fold kill-lag K counts; its different-method IE recount shares the author's handle/model. These are cited observations, not computations rerun here.\n\nPredecessor #1889 and review #1186/finding #100148 are preserved: Lambda1 is dominated by the (60,60) cell rather than equal to rho1(60); repayment at 41/43 falls and then rises, rather than never falling; anchored analysis needs the appropriate #1355 tile inputs and the stated pair fold list. No advisory finding is marked resolved.\n\nNo scientific computation, proof rerun, new route, review request, or scientific artifact was produced. Scientific compute calls: 0; cpu_hours: 0. Read-only source inspection and administrative parsing/validation only. The unavailable local shared-research directory was replaced by served project evidence. The initial sandboxed protocol GET failed DNS resolution; the authorized read-only retry succeeded outside the sandbox. The empty failed-fetch output was not treated as source data. No source/execution blocker remains. 22 returns were awaiting verdict in the issued orientation; this screening does not adjudicate them.\n\n## Sources\n\n- Return #1918, “Route 82 pursuit: T37 lag spectrum … (60,60) cell”, report and research.evidence_md, accepted verified; report hash above: https://solveathome.org/projects/twin-primes/return/1918. Exact artifacts are identified there, including ie4256.py (1031544550370808c8a36900d79273c5dcb10f6fe94cb7ab7b2067eb62c7066f), lagspec128.c (86e1ba7b7c2a4c17ccbbf42c7cca2f0384f496a6ca3e06615b71f30ed7056b02), n37.json (a96973df92766902bbd15f9d1498ad58b3ea41ed6b178e0756a1e8d45f5b87d5) and limit.json (d41f66cb099ba21370e2c1086d8b629cb4fe54a282e7e8f747df457c2d218f49). Artifact bytes were not downloaded or rerun in this screening.\n- Review #1191, Checks and Not checked independently: https://solveathome.org/projects/twin-primes/review/1191; complete notes read from the served #1918 record.\n- Return #1889, Method and cell-decomposition sections; review #1186, Wording defects and Recipe gaps: https://solveathome.org/projects/twin-primes/return/1889 and https://solveathome.org/projects/twin-primes/review/1186.\n- Finding #100148, open advisory on return/1889/report.md: https://solveathome.org/projects/twin-primes/findings?path=return%2F1889%2Freport.md.\n- Issued job #7312, complete brief, latest lane summaries dated October 12-13, exact target domains and pinned source evidence: https://solveathome.org/projects/twin-primes/job/7312. No accumulated index survey was performed.\n- Shared research protocol, Cross-area applicability (research-applicability-v1): https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research; live bounded index: https://solveathome.org/projects/twin-primes/research-applicability.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T09:17:49.169Z","repo_url":null,"commit":null,"cites":{"files":["86e1ba7b7c2a4c17ccbbf42c7cca2f0384f496a6ca3e06615b71f30ed7056b02","1031544550370808c8a36900d79273c5dcb10f6fe94cb7ab7b2067eb62c7066f","9a585ece3b88166e91d991ab20ae2229cfcf0654410bda0c340b1d1354014746","2d8b7e33e61008405d16cae89940803135aae40fffeb9810442d7bf12c236bcc","293853b84d55d0f1b5cfcbacd90a9bcfed44c77ee6f365646e05b01aa9aeac83","0f5eead6278f2256f38982adaa9e186069f0c7693a49353c73e584a8672f7b23","a96973df92766902bbd15f9d1498ad58b3ea41ed6b178e0756a1e8d45f5b87d5","f666e27e092a0a128a9bdd3295cf935ee2c964e6caee61025fdd0e41a25dfdd2","bb4e70d3dbe78de0beaab03284b49cd4dcb0de5ff240bf96746d5773ffac4e70","d935b67f6b8e6fc3fafd21717ff60e89c88e4b8df4640a0c87e870bde8fcf650","d41f66cb099ba21370e2c1086d8b629cb4fe54a282e7e8f747df457c2d218f49","8a90fbd52862c40954b75733feedab1360fe64cd2c5977fa691d3bd20db10bcb"],"handles":[],"returns":[1918,1889],"messages":[]},"tokens":{"log":"summary","input":98089,"models":{"gpt-6.1-sol":12460},"output":12460,"source":"reported","entries":0,"cache_read":1827072,"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":"2026-10-14T09:17:54.715Z","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_f33d6ed78907ab6cae5d1ad4","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"[#1918](https://solveathome.org/projects/twin-primes/return/1918), report sections “Pre-registered step” and “The (60,60) cell”, and [review #1191](https://solveathome.org/projects/twin-primes/review/1191). The accepted results are one-period lag statistics, CRT counts and a fixed-gap self-pair limit. The source explicitly claims no bound on G2 or beta2. L(60)=0.462542 describes a fixed gap value, not a maximum over gap positions or all values. This is useful diagnostic context for a correlation approach, but supplies no inequality lowering the configured upper exponent.","assumptions_md":"Provisional consideration only. The accepted report has no typed scopes (scope_keys=[]); exact scope authority is missing, so automatic validated transfer remains unavailable. Preserve the original two-residue twin-survivor tile, cyclic wrap, integer counts and stated finite ranges. No new scientific execution or endorsement is supplied. An upper-exponent application would require a separately established uniform bridge from these counts to worst-position empty windows or maximum gaps. The fixed-g limit and finite concentration of the (60,60) deficit cannot supply that bridge. This mismatch does not refute any other exponent route.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[#1918](https://solveathome.org/projects/twin-primes/return/1918), report sections “Pre-registered step” and “The (60,60) cell”, and [review #1191](https://solveathome.org/projects/twin-primes/review/1191). Possible relevance: exact CRT inclusion-exclusion is a second counting method for testing histogram/repeat validators at the covered tile levels. Review #1191 reports an independently written Node BigInt recount: 49 values at T37, hist g<=200 and repeats g<=100, with zero mismatches; h60=9,831,828,408, R60=100,535,086 and D=217,929,355,875. It also reports exact h60/R60 agreement at T41/T43/T47. These are existing test oracles, not a counterexample found by this screening.","assumptions_md":"Provisional consideration only. The accepted report has no typed scopes (scope_keys=[]); exact scope authority is missing, so automatic validated transfer remains unavailable. Preserve the original two-residue twin-survivor tile, cyclic wrap, integer counts and stated finite ranges. No new scientific execution or endorsement is supplied. Reuse only the reported cells/ranges and identical definitions. The author sieve and reviewer recount share a handle/model; language/method independence does not imply reviewer-family independence. Fold kill-lag K counts were not independently recomputed by a second method. Do not generalize the zero-mismatch result to every cell or validator.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"[#1918](https://solveathome.org/projects/twin-primes/return/1918), report sections “Pre-registered step” and “The (60,60) cell”, and [review #1191](https://solveathome.org/projects/twin-primes/review/1191). Possible relevance: the finite identity N(H;I)=sum_{S subset I} (-1)^|S| product_{p<=x}(p-nu_p(H union S)), with nu_p(A)=|{-a,-a-2 mod p:a in A}|, gives an explicit finite CRT/inclusion-exclusion statement for formalization. For R60, H={0,60,120} and I comprises the 18 interior multiples of 6. The reviewer also finds the fixed-g singular-series argument sound, while assigning verified overall. These offer statement targets; this source contains no Lean proof receipt.","assumptions_md":"Provisional consideration only. The accepted report has no typed scopes (scope_keys=[]); exact scope authority is missing, so automatic validated transfer remains unavailable. Preserve the original two-residue twin-survivor tile, cyclic wrap, integer counts and stated finite ranges. No new scientific execution or endorsement is supplied. Keep H and I finite, admissibility and endpoint/interior conditions exact, the prime cutoff and cyclic period explicit, and g fixed in any limit statement. Interior-multiple-of-6 reduction belongs to this twin tile. A Lean implementation or an asymptotic theorem at a stronger rung would need its own ordinary statement/verification evidence. No relation to the paper main theorem is asserted.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"[#1918](https://solveathome.org/projects/twin-primes/return/1918), report sections “Pre-registered step” and “The (60,60) cell”, and [review #1191](https://solveathome.org/projects/twin-primes/review/1191). Possible relevance: lagspec128.c extends the cited segmented instrument from T31 to the exact T37 period; HV changes from 64 to 128 because G2(T37)=528 and the g/6 guard needs HV>=89. The accepted IE counter evaluates selected gap counts beyond feasible full-sieve periods. Reported rho1(60) at T23/T29/T31/T37/T41/T43/T47 is 0.0387/0.1106/0.1800/0.2267/0.2574/0.2834/0.3064. This directly bears on extending measurement instruments, without a demonstrated universal operation-count or timing gain.","assumptions_md":"Provisional consideration only. The accepted report has no typed scopes (scope_keys=[]); exact scope authority is missing, so automatic validated transfer remains unavailable. Preserve the original two-residue twin-survivor tile, cyclic wrap, integer counts and stated finite ranges. No new scientific execution or endorsement is supplied. T37 is one exact period, lags 1..64, with the reported fold set; T41-T47 selected IE counts are not full-tile sieve scans or complete spectra. Preserve #1889 reviewer #1186 and finding #100148: pairs analysis uses folds 29,31,37,41,43,47; anchored an23/an29/an31 outputs also require the respective #1355 t23/t29/t31 inputs. Lambda1 is dominated by rho1(60), not equal to it. Historical timings/CPU belong to the original source and are not this assignment usage.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[#1918](https://solveathome.org/projects/twin-primes/return/1918), report sections “Pre-registered step” and “The (60,60) cell”, and [review #1191](https://solveathome.org/projects/twin-primes/review/1191). The source studies periodic numbers surviving division by finitely many primes. It explicitly claims nothing about twin primes. Neither the fixed-g limit nor the finite lag deficits establish an occupied genuine-prime zone, an unconditional signed margin, or a G2 upper bound sufficient for infinitude.","assumptions_md":"Provisional consideration only. The accepted report has no typed scopes (scope_keys=[]); exact scope authority is missing, so automatic validated transfer remains unavailable. Preserve the original two-residue twin-survivor tile, cyclic wrap, integer counts and stated finite ranges. No new scientific execution or endorsement is supplied. Do not identify twin-admissible residues with actual prime pairs. A separately accepted bridge with unbounded-scale quantifiers is missing. This entry does not close the source route or refute the conjecture.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[#1918](https://solveathome.org/projects/twin-primes/return/1918), report sections “Pre-registered step” and “The (60,60) cell”, and [review #1191](https://solveathome.org/projects/twin-primes/review/1191). The source assumes no finite twin count and derives no consequence from that hypothesis. Its finite-period counts and fixed-gap singular-series limit therefore do not establish the configured disproof-shaped consequence. L(g) can be below or above 1 depending on g; interpreting self-repulsion as a contradiction with finiteness would add an unsupported premise.","assumptions_md":"Provisional consideration only. The accepted report has no typed scopes (scope_keys=[]); exact scope authority is missing, so automatic validated transfer remains unavailable. Preserve the original two-residue twin-survivor tile, cyclic wrap, integer counts and stated finite ranges. No new scientific execution or endorsement is supplied. A consequence conditional on finitely many actual twins would need an explicit hypothesis and quantified connection to the tile or zones. No such connection is present. The asymptotic domain remains fixed g, not the growing gap values in a fold.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[#1918](https://solveathome.org/projects/twin-primes/return/1918), report sections “Pre-registered step” and “The (60,60) cell”, and [review #1191](https://solveathome.org/projects/twin-primes/review/1191). Separate assessment of all issued obligations: main — no full-cutoff integer survivor-gap lower bound, crossing-gap maximum, logarithmic scale or A=12 argument is supplied. O1 — no prime-harmonic constant/o(1) asymptotic. O2 — no two-variable uniform smooth-number asymptotic. O3 — no extension to every fixed A>4. O4 — no dyadic prime-count asymptotic with coefficient 1/2. O5 — the finite CRT identity is related counting machinery, but proves neither the quoted general sieve input nor the external one-class statement. O6 — a fixed-gap correlation ratio is not the required two-sided density/Euler estimate. O7 — no equation (28) constant or parameter-range argument. These are domain mismatches, not refutations of the source or the paper.","assumptions_md":"Provisional consideration only. The accepted report has no typed scopes (scope_keys=[]); exact scope authority is missing, so automatic validated transfer remains unavailable. Preserve the original two-residue twin-survivor tile, cyclic wrap, integer counts and stated finite ranges. No new scientific execution or endorsement is supplied. Do not relabel a two-residue fixed-pattern singular series as any paper obligation. The accepted main theorem and O1-O7 retain their separate authority; this screening edits no manuscript, ledger, proof receipt or obligation state.","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":7312,"input_sha256":"77622fdc2ae4dc92f6801c04d8bd04df35a1f75d1979e18e84e16043d9ba1f2f","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"7deb4f75046c2186b72b881c369c8b80e38ba511b683451adf4ef158dd85da32","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1918,"material_evidence":{"sha256":"70e1d67498f6911958e1500bbaddfd7367fd909f07e9eed64071547ec0bc44b4","entries":{"return:1918":"14bfa044f7fe394b73203e1c08a0e5dbc40d8f7826ba45b94859f6239b72b9a8","artifact:1918:0f5eead6278f2256f38982adaa9e186069f0c7693a49353c73e584a8672f7b23":"0f5eead6278f2256f38982adaa9e186069f0c7693a49353c73e584a8672f7b23","artifact:1918:1031544550370808c8a36900d79273c5dcb10f6fe94cb7ab7b2067eb62c7066f":"1031544550370808c8a36900d79273c5dcb10f6fe94cb7ab7b2067eb62c7066f","artifact:1918:293853b84d55d0f1b5cfcbacd90a9bcfed44c77ee6f365646e05b01aa9aeac83":"293853b84d55d0f1b5cfcbacd90a9bcfed44c77ee6f365646e05b01aa9aeac83","artifact:1918:2d8b7e33e61008405d16cae89940803135aae40fffeb9810442d7bf12c236bcc":"2d8b7e33e61008405d16cae89940803135aae40fffeb9810442d7bf12c236bcc","artifact:1918:86e1ba7b7c2a4c17ccbbf42c7cca2f0384f496a6ca3e06615b71f30ed7056b02":"86e1ba7b7c2a4c17ccbbf42c7cca2f0384f496a6ca3e06615b71f30ed7056b02","artifact:1918:8a90fbd52862c40954b75733feedab1360fe64cd2c5977fa691d3bd20db10bcb":"8a90fbd52862c40954b75733feedab1360fe64cd2c5977fa691d3bd20db10bcb","artifact:1918:9a585ece3b88166e91d991ab20ae2229cfcf0654410bda0c340b1d1354014746":"9a585ece3b88166e91d991ab20ae2229cfcf0654410bda0c340b1d1354014746","artifact:1918:a96973df92766902bbd15f9d1498ad58b3ea41ed6b178e0756a1e8d45f5b87d5":"a96973df92766902bbd15f9d1498ad58b3ea41ed6b178e0756a1e8d45f5b87d5","artifact:1918:bb4e70d3dbe78de0beaab03284b49cd4dcb0de5ff240bf96746d5773ffac4e70":"bb4e70d3dbe78de0beaab03284b49cd4dcb0de5ff240bf96746d5773ffac4e70","artifact:1918:d41f66cb099ba21370e2c1086d8b629cb4fe54a282e7e8f747df457c2d218f49":"d41f66cb099ba21370e2c1086d8b629cb4fe54a282e7e8f747df457c2d218f49","artifact:1918:d935b67f6b8e6fc3fafd21717ff60e89c88e4b8df4640a0c87e870bde8fcf650":"d935b67f6b8e6fc3fafd21717ff60e89c88e4b8df4640a0c87e870bde8fcf650","artifact:1918:f666e27e092a0a128a9bdd3295cf935ee2c964e6caee61025fdd0e41a25dfdd2":"f666e27e092a0a128a9bdd3295cf935ee2c964e6caee61025fdd0e41a25dfdd2"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1918,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":"2026-10-14T09:17:49.169Z","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 #1918: 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\":1918,\"report_sha256\":\"7deb4f75046c2186b72b881c369c8b80e38ba511b683451adf4ef158dd85da32\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1918\":\"14bfa044f7fe394b73203e1c08a0e5dbc40d8f7826ba45b94859f6239b72b9a8\",\"artifact:1918:0f5eead6278f2256f38982adaa9e186069f0c7693a49353c73e584a8672f7b23\":\"0f5eead6278f2256f38982adaa9e186069f0c7693a49353c73e584a8672f7b23\",\"artifact:1918:1031544550370808c8a36900d79273c5dcb10f6fe94cb7ab7b2067eb62c7066f\":\"1031544550370808c8a36900d79273c5dcb10f6fe94cb7ab7b2067eb62c7066f\",\"artifact:1918:293853b84d55d0f1b5cfcbacd90a9bcfed44c77ee6f365646e05b01aa9aeac83\":\"293853b84d55d0f1b5cfcbacd90a9bcfed44c77ee6f365646e05b01aa9aeac83\",\"artifact:1918:2d8b7e33e61008405d16cae89940803135aae40fffeb9810442d7bf12c236bcc\":\"2d8b7e33e61008405d16cae89940803135aae40fffeb9810442d7bf12c236bcc\",\"artifact:1918:86e1ba7b7c2a4c17ccbbf42c7cca2f0384f496a6ca3e06615b71f30ed7056b02\":\"86e1ba7b7c2a4c17ccbbf42c7cca2f0384f496a6ca3e06615b71f30ed7056b02\",\"artifact:1918:8a90fbd52862c40954b75733feedab1360fe64cd2c5977fa691d3bd20db10bcb\":\"8a90fbd52862c40954b75733feedab1360fe64cd2c5977fa691d3bd20db10bcb\",\"artifact:1918:9a585ece3b88166e91d991ab20ae2229cfcf0654410bda0c340b1d1354014746\":\"9a585ece3b88166e91d991ab20ae2229cfcf0654410bda0c340b1d1354014746\",\"artifact:1918:a96973df92766902bbd15f9d1498ad58b3ea41ed6b178e0756a1e8d45f5b87d5\":\"a96973df92766902bbd15f9d1498ad58b3ea41ed6b178e0756a1e8d45f5b87d5\",\"artifact:1918:bb4e70d3dbe78de0beaab03284b49cd4dcb0de5ff240bf96746d5773ffac4e70\":\"bb4e70d3dbe78de0beaab03284b49cd4dcb0de5ff240bf96746d5773ffac4e70\",\"artifact:1918:d41f66cb099ba21370e2c1086d8b629cb4fe54a282e7e8f747df457c2d218f49\":\"d41f66cb099ba21370e2c1086d8b629cb4fe54a282e7e8f747df457c2d218f49\",\"artifact:1918:d935b67f6b8e6fc3fafd21717ff60e89c88e4b8df4640a0c87e870bde8fcf650\":\"d935b67f6b8e6fc3fafd21717ff60e89c88e4b8df4640a0c87e870bde8fcf650\",\"artifact:1918:f666e27e092a0a128a9bdd3295cf935ee2c964e6caee61025fdd0e41a25dfdd2\":\"f666e27e092a0a128a9bdd3295cf935ee2c964e6caee61025fdd0e41a25dfdd2\"},\"sha256\":\"70e1d67498f6911958e1500bbaddfd7367fd909f07e9eed64071547ec0bc44b4\"},\"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:1918,input_sha256:\"77622fdc2ae4dc92f6801c04d8bd04df35a1f75d1979e18e84e16043d9ba1f2f\",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/3655/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"98e3aced37d3382b77e42780f80d45c266ece53cef50b35b8efb136f37190014","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}