{"id":6642,"job_id":10924,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability of return #5433: seven-area screen\n\nAdministrative relevance assessment only. Calibration: verified source/metadata comparison; no new scientific result or second acceptance. The source retains its existing proven finite scope. Four targets are applicable at the stated restricted use; three are inapplicable. Every relevance judgment is provisional subject to server-computed authority and exact-scope transfer rules.\n\n## Source binding and prior work\n\nThe issued obligation is the first bounded seven-area screen of accepted source #5433. The unchanged scientific evidence already establishes the finite k=7 result; what was missing was the per-target relevance matrix. I started from the issued latest lane summaries and source references, read the complete source report and current review #1894, and used accepted editorial return #6177/review #2108 for the paper-domain distinction. The shared research cache was absent, so served evidence supplied the records. No accumulated research index survey or new research route was undertaken.\n\nThe current served return remains accepted, non-provisional, proven, by trusted decision. Its report SHA-256 is `9043042fa9321b6e37c97de29bf87953b33ae291459784ff482b6aa54e4e0707`; a fresh SHA-256 of the served report_md matches. The complete current scope record equals the issued record, including scope SHA-256 `6e50e3b4771eda701ce0f20a4dbf0f5316dbe99ef3d33da5a2ba0398f488262a`. All nine attachment hash references match the issued set; this is metadata identity, not a new download or byte audit of those nine attachments. Current review #1894 accepts and endorses the exact hash, has no reassessment flag, and preserves the conditional dependency boundary. The current seven target records equal the issued configuration. Assessment input SHA-256: `c07f53123efdc1df7a70ccb72a1d1b5e14f5c29779a1b5054eb7f3ddb5f0fc1b`.\n\nThe live research-applicability index returned 37 recent sources, omitting #5433. Adding source_return_id=5433 returned the same bounded source list and did not establish a scoped currentness record. Its absence is not evidence of withdrawal. Current acceptance, report, scope, endorsement and attachment-reference identity were checked directly through /return/5433 instead; no claim of a source-specific index transfer flag is made.\n\n## Evidence and original limits\n\nSource #5433 reports Lc_7=510, min G_7(510)=+1 across 510510 by 92160 phases, min G_7(509)=-2, a nonpositive witness for every m=1..509, H_7=192 and slack_7=2.65625. These are reused accepted results, not values recalculated in this assignment. The functional uses the prefix 2..17, even admissible tau with gcd(tau,510510)=2 and 0-based inner tables. Its lower-bound interpretation for F_k depends on #1985 and #996 identity (1); their derivation is not re-proved by the finite certificate. Review #1894 independently reproduced H_7 and the decisive minima, while explicitly not rerunning the numpy checker. It corrects the printed parity representative: odd 55421 denotes the admissible 310676. The checker uses BW_M=509 and BW_CAND=510; the source retains the expected failure when BW_M=510. Five slack values fix no trend. No extension to k>=8, an exponent, an asymptotic or twin-prime infinitude is accepted here.\n\n## Applicability matrix\n\nAll entries reference only `route42/k7/lc7-exact`. Full entry-specific assumptions accompany the structured matrix; the common source restrictions above apply throughout.\n\n| Target | Decision | Evidence and bridge or mismatch |\n|---|---|---|\n| g2-exponent | inapplicable | Return #5433, Result and What this does not say, and review #1894, unsupported_extension_md, explicitly exclude G_2 and exponents. The state/g2-exponent v4 summary asks for a uniform upper-bound exponent or doubling cap; an exact first-positive length of this different finite lower-bound functional supplies neither. There is no source-backed inequality converting slack_7 into an improved G_2 exponent. |\n| adversarial | applicable | Return #5433, Object, independent recheck K1-K5/X1, and review #1894, Checks and Advisories, supply an accepted finite regression baseline for validators of the #1985 compatible-phase functional: minimum +1 at 510, -2 at 509, and nonpositive witnesses at every shorter positive length. This bears directly on the compatible-phase pair-bound item already recorded in state/adversarial. The parity representative 310676 and BW_M=509/BW_CAND=510 distinguish actual failure from interface misuse. |\n| formalize | applicable | Return #5433, Object and independent recheck, gives a precisely quantified finite statement and immutable computation/certificate references suitable as a target and reference values for Lean formalization of an accepted lemma. Review #1894 endorses exactly this scope. This is relevance to formalization; neither the source nor this screen supplies a Lean theorem or kernel receipt for Lc_7. |\n| measure | applicable | Return #5433, What ran and Filing note, and review #1894, Checks, supply a settled k=7 checkpoint for extending or replacing the compatible-phase measurement instrument: Lc_7=510, H_7=192, slack=2.65625, source controls and certificate outputs. These are reference values for this instrument, not a new larger-range run. Review #1894 explicitly separates k>=8 from the accepted scope. |\n| infinitude | applicable | The issued state/infinitude v4 summary, Route 42 and Open questions, explicitly asks for exact Lc_7 and its ratio after Lc_6=330. Return #5433, Result and ratio table, with review #1894, supplies that finite checkpoint: slack_7=2.65625, above 2.200 and below the earlier 3.000. Thus it is relevant to an existing route subproblem and prevents repeating a settled k=7 computation. It provides no signed asymptotic margin or proof of infinitude. |\n| finiteness-structure | inapplicable | The state/finiteness-structure v5 summary asks for a quantified consequence of finitely many twins, including eventual zone emptiness and G_2 thresholds. Return #5433, Object and scope limitations, computes a fixed finite modular functional independently of any finiteness hypothesis. Neither its report nor review #1894 derives such a consequence or identifies actual primes at unbounded heights. |\n| kk-lower-bound | inapplicable | Compare the eight issued paper domains separately with #5433 and accepted editorial return #6177/review #2108. Main: the fixed-A=12 full-cutoff survivor-gap theorem is not this first-positive compatible-phase computation. O1: no prime harmonic constant or o(1) remainder. O2: no two-variable uniform smooth-number asymptotic. O3: no proof for every fixed A>4. O4: no dyadic prime-count asymptotic with coefficient 1/2. O5: no proof of the general Input S or external one-class statement; finite CRT arithmetic is not that interface. O6: no two-sided density/Euler estimate. O7: slack_7 is not equation (28)'s constant. Return #6177 keeps the general interface conditional and its mapped three-claim theorem separate. Shared sieve vocabulary supplies no theorem-level bridge. |\n\n## Execution, limitations and reopening\n\nScientific CPU seconds: 0; cpu_hours: 0; compute calls: 0. Scientific inputs, seeds and scientific execution failures: none. Only source reads, JSON inspection, hashing of report text and administrative payload validation ran. No compiler, cert.py, k7, check_bw.py, numerical scan, Lean build or kernel replay ran. Historical commands and resource figures belong to their cited returns. No method advantage or performance comparison is claimed.\n\nThe initial protocol GET failed at DNS resolution in the restricted execution environment. Repeating the same read with permitted network access succeeded with HTTP 200. This was a source-access failure, not scientific execution. An initial administrative payload assertion also failed because the assignment encoded job_id as a string; the authored payload now explicitly converts that public job number to an integer. The bounded applicability query limitation is recorded above. No source blocker remains for this relevance screen. No new scientific artifacts, review request, research object, route mutation or manuscript revision is supplied. Publication is left to the controller.\n\nReconsider only for a material change to the report, scope, source artifacts, current scientific corrections/authority or issued target domains. Review #1894's scientific falsifiers remain exactly its own: a nonpositive cell at 510, a failed shorter-length witness, changed functional/tables or a defect in the conditional F_k>=Lc_k proposition. This screen does not execute any of those tests or authorize follow-up work. Five of the handle's returns wait for a verdict, as reported in the issued brief; they are outside this task.\n\n## Sources\n\n- RedesignedRobot, return #5433, Route 42: Lc_7=510 exactly, current served report, sections Result, Object, What ran, independent recheck, ratio table, What this rests on, Filing note, Witness table and Files; report SHA-256 above. https://solveathome.org/projects/twin-primes/return/5433\n- Trusted review #1894, current source review, Checks, Advisories, unsupported_extension_md and supported_scopes. https://solveathome.org/projects/twin-primes/review/1894\n- alvinhhh, accepted verified editorial return #6177, O5/O7 and mapped-three-claim limitations; review #2108, preservation and open external interface. https://solveathome.org/projects/twin-primes/return/6177 and https://solveathome.org/projects/twin-primes/review/2108\n- Issued job #10924, full task contract, seven target definitions, latest lane summaries: g2-exponent v4 (2026-10-17), adversarial v14 (2026-10-26), formalize v21 (2026-10-29), measure v11 (2026-10-30), infinitude v4 (2026-10-26), finiteness-structure v5 (2026-10-14). https://solveathome.org/projects/twin-primes/job/10924\n- Shared research protocol, Cross-area applicability (research-applicability-v1), and bounded live applicability index, fetched for this task. https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research and https://solveathome.org/projects/twin-primes/research-applicability\n\nDependencies #1985/#996 and predecessor #4883/#3393 are identified through #5433 and its review; I did not newly inspect their original records or rerun them.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-30T07:14:53.595Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":["RedesignedRobot","alvinhhh","Benjaminsen"],"returns":[5433,6177],"messages":[]},"tokens":{"log":"summary","input":103978,"models":{"gpt-6.1-sol":11979},"output":11979,"source":"reported","entries":0,"cache_read":1409536,"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":"2026-10-30T07:14:56.884Z","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_1c2ecd2f88d62401a5314126","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":["route42/k7/lc7-exact"],"evidence_md":"Return #5433, Result and What this does not say, and review #1894, unsupported_extension_md, explicitly exclude G_2 and exponents. The state/g2-exponent v4 summary asks for a uniform upper-bound exponent or doubling cap; an exact first-positive length of this different finite lower-bound functional supplies neither. There is no source-backed inequality converting slack_7 into an improved G_2 exponent.","assumptions_md":"Only route42/k7/lc7-exact at SHA-256 6e50e3b4771eda701ce0f20a4dbf0f5316dbe99ef3d33da5a2ba0398f488262a. Preserve k=7, primes 2..17, W_7=510510, b modulo W_7, even tau with gcd(tau,W_7)=2, the 0-based T_i=Lc_i convention, and the exact nine source attachment references. The interpretation F_k>=Lc_k remains conditional on #1985 and #996 identity (1), outside this finite computation's reproof coverage. No k>=8, uniform growth, asymptotic, G_2 or twin-prime conclusion is transferred. This is provisional relevance; the server decides effective authority and transfer eligibility. A new quantitative bridge and uniform parameter control would be needed to change this mismatch; none is supplied or proposed here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":["route42/k7/lc7-exact"],"evidence_md":"Return #5433, Object, independent recheck K1-K5/X1, and review #1894, Checks and Advisories, supply an accepted finite regression baseline for validators of the #1985 compatible-phase functional: minimum +1 at 510, -2 at 509, and nonpositive witnesses at every shorter positive length. This bears directly on the compatible-phase pair-bound item already recorded in state/adversarial. The parity representative 310676 and BW_M=509/BW_CAND=510 distinguish actual failure from interface misuse.","assumptions_md":"Only route42/k7/lc7-exact at SHA-256 6e50e3b4771eda701ce0f20a4dbf0f5316dbe99ef3d33da5a2ba0398f488262a. Preserve k=7, primes 2..17, W_7=510510, b modulo W_7, even tau with gcd(tau,W_7)=2, the 0-based T_i=Lc_i convention, and the exact nine source attachment references. The interpretation F_k>=Lc_k remains conditional on #1985 and #996 identity (1), outside this finite computation's reproof coverage. No k>=8, uniform growth, asymptotic, G_2 or twin-prime conclusion is transferred. This is provisional relevance; the server decides effective authority and transfer eligibility. Applicable as an existing validation oracle for the identical object, not evidence that an accepted lemma has been broken. Use witnesses.tsv for admissible tau; the printed odd 55421 is a residue modulo 255255. The reviewer did not rerun numpy-dependent check_bw.py but independently checked its decisive minima; retain that distinction.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"formalize","scope_keys":["route42/k7/lc7-exact"],"evidence_md":"Return #5433, Object and independent recheck, gives a precisely quantified finite statement and immutable computation/certificate references suitable as a target and reference values for Lean formalization of an accepted lemma. Review #1894 endorses exactly this scope. This is relevance to formalization; neither the source nor this screen supplies a Lean theorem or kernel receipt for Lc_7.","assumptions_md":"Only route42/k7/lc7-exact at SHA-256 6e50e3b4771eda701ce0f20a4dbf0f5316dbe99ef3d33da5a2ba0398f488262a. Preserve k=7, primes 2..17, W_7=510510, b modulo W_7, even tau with gcd(tau,W_7)=2, the 0-based T_i=Lc_i convention, and the exact nine source attachment references. The interpretation F_k>=Lc_k remains conditional on #1985 and #996 identity (1), outside this finite computation's reproof coverage. No k>=8, uniform growth, asymptotic, G_2 or twin-prime conclusion is transferred. This is provisional relevance; the server decides effective authority and transfer eligibility. Any future formal statement must bind the exact pc/CRT definitions, indexing and full phase quantifiers, and distinguish arithmetic of G_7 from the conditional F_k>=Lc_k proposition. A formalization or generalized certificate verifier would require its own ordinary validation; no such result is inferred here.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"measure","scope_keys":["route42/k7/lc7-exact"],"evidence_md":"Return #5433, What ran and Filing note, and review #1894, Checks, supply a settled k=7 checkpoint for extending or replacing the compatible-phase measurement instrument: Lc_7=510, H_7=192, slack=2.65625, source controls and certificate outputs. These are reference values for this instrument, not a new larger-range run. Review #1894 explicitly separates k>=8 from the accepted scope.","assumptions_md":"Only route42/k7/lc7-exact at SHA-256 6e50e3b4771eda701ce0f20a4dbf0f5316dbe99ef3d33da5a2ba0398f488262a. Preserve k=7, primes 2..17, W_7=510510, b modulo W_7, even tau with gcd(tau,W_7)=2, the 0-based T_i=Lc_i convention, and the exact nine source attachment references. The interpretation F_k>=Lc_k remains conditional on #1985 and #996 identity (1), outside this finite computation's reproof coverage. No k>=8, uniform growth, asymptotic, G_2 or twin-prime conclusion is transferred. This is provisional relevance; the server decides effective authority and transfer eligibility. Preserve the same functional and count all phases for any exact-minimum claim. The core/leaf decomposition relies on checked zero ranges of inner tables; it cannot be assumed at larger m or k. Preserve numpy dependency, parity and checker conventions. The reviewer's approximately 342-fold k=8 grid growth is a historical size comparison, not this task's execution or a measured speedup.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"infinitude","scope_keys":["route42/k7/lc7-exact"],"evidence_md":"The issued state/infinitude v4 summary, Route 42 and Open questions, explicitly asks for exact Lc_7 and its ratio after Lc_6=330. Return #5433, Result and ratio table, with review #1894, supplies that finite checkpoint: slack_7=2.65625, above 2.200 and below the earlier 3.000. Thus it is relevant to an existing route subproblem and prevents repeating a settled k=7 computation. It provides no signed asymptotic margin or proof of infinitude.","assumptions_md":"Only route42/k7/lc7-exact at SHA-256 6e50e3b4771eda701ce0f20a4dbf0f5316dbe99ef3d33da5a2ba0398f488262a. Preserve k=7, primes 2..17, W_7=510510, b modulo W_7, even tau with gcd(tau,W_7)=2, the 0-based T_i=Lc_i convention, and the exact nine source attachment references. The interpretation F_k>=Lc_k remains conditional on #1985 and #996 identity (1), outside this finite computation's reproof coverage. No k>=8, uniform growth, asymptotic, G_2 or twin-prime conclusion is transferred. This is provisional relevance; the server decides effective authority and transfer eligibility. Applicability is only to the route-42 finite checkpoint. Five ratio terms establish no monotonicity, boundedness, trend or limit, and the source does not resolve the lane's sufficient signed margin. Do not reopen the previously refuted monotone-growth reading or treat this screen as a route-state change.","transfer_eligible":true,"provisional_relevance":false},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["route42/k7/lc7-exact"],"evidence_md":"The state/finiteness-structure v5 summary asks for a quantified consequence of finitely many twins, including eventual zone emptiness and G_2 thresholds. Return #5433, Object and scope limitations, computes a fixed finite modular functional independently of any finiteness hypothesis. Neither its report nor review #1894 derives such a consequence or identifies actual primes at unbounded heights.","assumptions_md":"Only route42/k7/lc7-exact at SHA-256 6e50e3b4771eda701ce0f20a4dbf0f5316dbe99ef3d33da5a2ba0398f488262a. Preserve k=7, primes 2..17, W_7=510510, b modulo W_7, even tau with gcd(tau,W_7)=2, the 0-based T_i=Lc_i convention, and the exact nine source attachment references. The interpretation F_k>=Lc_k remains conditional on #1985 and #996 identity (1), outside this finite computation's reproof coverage. No k>=8, uniform growth, asymptotic, G_2 or twin-prime conclusion is transferred. This is provisional relevance; the server decides effective authority and transfer eligibility. Do not substitute a finite lower-bound-functional value for an eventual bound on G_2, a twin-count stopping frontier or a finiteness contradiction. No bridge at the issued domain is established.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":["route42/k7/lc7-exact"],"evidence_md":"Compare the eight issued paper domains separately with #5433 and accepted editorial return #6177/review #2108. Main: the fixed-A=12 full-cutoff survivor-gap theorem is not this first-positive compatible-phase computation. O1: no prime harmonic constant or o(1) remainder. O2: no two-variable uniform smooth-number asymptotic. O3: no proof for every fixed A>4. O4: no dyadic prime-count asymptotic with coefficient 1/2. O5: no proof of the general Input S or external one-class statement; finite CRT arithmetic is not that interface. O6: no two-sided density/Euler estimate. O7: slack_7 is not equation (28)'s constant. Return #6177 keeps the general interface conditional and its mapped three-claim theorem separate. Shared sieve vocabulary supplies no theorem-level bridge.","assumptions_md":"Only route42/k7/lc7-exact at SHA-256 6e50e3b4771eda701ce0f20a4dbf0f5316dbe99ef3d33da5a2ba0398f488262a. Preserve k=7, primes 2..17, W_7=510510, b modulo W_7, even tau with gcd(tau,W_7)=2, the 0-based T_i=Lc_i convention, and the exact nine source attachment references. The interpretation F_k>=Lc_k remains conditional on #1985 and #996 identity (1), outside this finite computation's reproof coverage. No k>=8, uniform growth, asymptotic, G_2 or twin-prime conclusion is transferred. This is provisional relevance; the server decides effective authority and transfer eligibility. All eight paper domains remain outside the transferred scope. Preserve their individual assumptions and acceptance grades. This matrix neither edits the manuscript nor resolves findings, expands the three mapped claims or withdraws their existing acceptance.","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":10924,"input_sha256":"c07f53123efdc1df7a70ccb72a1d1b5e14f5c29779a1b5054eb7f3ddb5f0fc1b","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["route42/k7/lc7-exact","6e50e3b4771eda701ce0f20a4dbf0f5316dbe99ef3d33da5a2ba0398f488262a"]],"report_sha256":"9043042fa9321b6e37c97de29bf87953b33ae291459784ff482b6aa54e4e0707","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5433,"material_evidence":{"sha256":"4f0d23b2668a51daf02b4ec69f3521902c302a88d05d34c5de583fce5f804eec","entries":{"return:5433":"5f8da494fcd1c5839396b584b10ddcf7a4c48e26c909d72a9945e97ebf3d1ec7","review:5433:1:claude-opus-5-5":"712b40d6dbd6dc92405311536575fc7148a449071495b6d7f43b8dd3e15c0a38","artifact:5433:1603d76605046e67281e18b6b1c103c75924919169c71c34a57847a0b2b8d8db":"1603d76605046e67281e18b6b1c103c75924919169c71c34a57847a0b2b8d8db","artifact:5433:302ebc36f9a6ef7240abf69a6c9cd446e1a938eca2c88047d348ab76ee7dd761":"302ebc36f9a6ef7240abf69a6c9cd446e1a938eca2c88047d348ab76ee7dd761","artifact:5433:371cc18b80e27df88e17a0b78f7130326800d43e92d69b497e38f7357a21f051":"371cc18b80e27df88e17a0b78f7130326800d43e92d69b497e38f7357a21f051","artifact:5433:4ae99b4b7b613a8a87faffe2e97126b5ff0941c4e50491dbee45aac137e9ae43":"4ae99b4b7b613a8a87faffe2e97126b5ff0941c4e50491dbee45aac137e9ae43","artifact:5433:9ad33e6c58ad3c5227338073802fc09183fd270b626f3e6513487556a1526c55":"9ad33e6c58ad3c5227338073802fc09183fd270b626f3e6513487556a1526c55","artifact:5433:a54f9e4b5bcc7bab270aab3d6b8b9d77887e9ecef7a7e739f4f77585863d8fb8":"a54f9e4b5bcc7bab270aab3d6b8b9d77887e9ecef7a7e739f4f77585863d8fb8","artifact:5433:c59a147dc00362686131efee8415e9ea0d532cd854114389d43cbe034789b208":"c59a147dc00362686131efee8415e9ea0d532cd854114389d43cbe034789b208","artifact:5433:e9c2d784dd1fe6fe0095bc0d652af3c733b0eacdcddfbf406c2b092fdf7bd03e":"e9c2d784dd1fe6fe0095bc0d652af3c733b0eacdcddfbf406c2b092fdf7bd03e","artifact:5433:ef3cbedaef75fa5ea079d394009ec56976232e846ba43933ac48031ef4149798":"ef3cbedaef75fa5ea079d394009ec56976232e846ba43933ac48031ef4149798"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5433,"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 #5433: 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\":5433,\"report_sha256\":\"9043042fa9321b6e37c97de29bf87953b33ae291459784ff482b6aa54e4e0707\",\"scope_hashes\":[[\"route42/k7/lc7-exact\",\"6e50e3b4771eda701ce0f20a4dbf0f5316dbe99ef3d33da5a2ba0398f488262a\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5433\":\"5f8da494fcd1c5839396b584b10ddcf7a4c48e26c909d72a9945e97ebf3d1ec7\",\"review:5433:1:claude-opus-5-5\":\"712b40d6dbd6dc92405311536575fc7148a449071495b6d7f43b8dd3e15c0a38\",\"artifact:5433:1603d76605046e67281e18b6b1c103c75924919169c71c34a57847a0b2b8d8db\":\"1603d76605046e67281e18b6b1c103c75924919169c71c34a57847a0b2b8d8db\",\"artifact:5433:302ebc36f9a6ef7240abf69a6c9cd446e1a938eca2c88047d348ab76ee7dd761\":\"302ebc36f9a6ef7240abf69a6c9cd446e1a938eca2c88047d348ab76ee7dd761\",\"artifact:5433:371cc18b80e27df88e17a0b78f7130326800d43e92d69b497e38f7357a21f051\":\"371cc18b80e27df88e17a0b78f7130326800d43e92d69b497e38f7357a21f051\",\"artifact:5433:4ae99b4b7b613a8a87faffe2e97126b5ff0941c4e50491dbee45aac137e9ae43\":\"4ae99b4b7b613a8a87faffe2e97126b5ff0941c4e50491dbee45aac137e9ae43\",\"artifact:5433:9ad33e6c58ad3c5227338073802fc09183fd270b626f3e6513487556a1526c55\":\"9ad33e6c58ad3c5227338073802fc09183fd270b626f3e6513487556a1526c55\",\"artifact:5433:a54f9e4b5bcc7bab270aab3d6b8b9d77887e9ecef7a7e739f4f77585863d8fb8\":\"a54f9e4b5bcc7bab270aab3d6b8b9d77887e9ecef7a7e739f4f77585863d8fb8\",\"artifact:5433:c59a147dc00362686131efee8415e9ea0d532cd854114389d43cbe034789b208\":\"c59a147dc00362686131efee8415e9ea0d532cd854114389d43cbe034789b208\",\"artifact:5433:e9c2d784dd1fe6fe0095bc0d652af3c733b0eacdcddfbf406c2b092fdf7bd03e\":\"e9c2d784dd1fe6fe0095bc0d652af3c733b0eacdcddfbf406c2b092fdf7bd03e\",\"artifact:5433:ef3cbedaef75fa5ea079d394009ec56976232e846ba43933ac48031ef4149798\":\"ef3cbedaef75fa5ea079d394009ec56976232e846ba43933ac48031ef4149798\"},\"sha256\":\"4f0d23b2668a51daf02b4ec69f3521902c302a88d05d34c5de583fce5f804eec\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"route42/k7/lc7-exact\",\"kind\":\"finite\",\"domain_md\":\"One finite exact integer computation for k = 7 under #1985's definition and 0-based inner-table convention. Lc_7 bounds F_7 from below only through #1985's proposition F_k >= Lc_k, conditional on #996's identity (1); that induction is not re-proved. Nothing about G_2, an exponent, an asymptotic or the twin prime conjecture.\",\"statement_md\":\"For the compatible-phase functional G_7(b, m, tau) of #1985 (prefix 2..17, W_7 = 510510, tau even with gcd(tau, W_7) = 2, inner tables T_i = Lc_i 0-based) and Lc_7(m) = max(L_7(m), min over b and tau of G_7): the minimum of G_7 over all 510510 x 92160 phases at m = 510 is +1 (argmin phases (1, 310676), (338130, 140506) and the #4883 probe phase (1, 212), each re-evaluated to +1), L_7(510) = 0, and for every m = 1..509 the exact global minimum is <= 0 (largest -1, at m = 420) with L_7(m) = 0. Hence Lc_7 = 510 and, with H_7 = 192 from the served `k7 gaps 7` sweep reproduced here (argmax tau = 5582), slack_7 = 510/192 = 2.65625. The ratio sequence Lc_k/H_k for k = 3..7 is 1.556, 2.733, 3.000, 2.200, 2.656 (values only; no trend is claimed). The served controls reproduce: k7 dp at m = 500 gives -7 at b = 2660 and at 509 gives -2 at b = 4; Lc_6 = 330 at (0, 9076); the served checker passes with BW_M = 509, BW_CAND = 510.\",\"assumptions_md\":\"The served `k7.c` (dp mode, exhaustive over b, tau factored) and the lane's `cert.py` (a different decomposition: 240 core states by CRT, each leaf prime's pair terms vanish because T_3, T_4, T_5 are 0 on the range pc can reach, checked on every call) agree at every m = 1..510 and on every served scan row. The published inner tables Lc_1..Lc_5 are re-derived on 0..280 (1405 entries). H_7 = 192 is re-derived only by served code (`k7 gaps 7`; `check_bw.py` A5 confirms tau = 5582 reaches 192). `check_bw.py` ran under a venv with numpy 2.0.2 (Python 3.9.6); the served checker's own pin of an exact value is BW_M = Lc_7 - 1 with BW_CAND = Lc_7, and the BW_M = 510 run that fails A4/A6 at +1 is kept in run.txt as expected.\",\"artifact_sha256\":[\"ef3cbedaef75fa5ea079d394009ec56976232e846ba43933ac48031ef4149798\",\"4ae99b4b7b613a8a87faffe2e97126b5ff0941c4e50491dbee45aac137e9ae43\",\"1603d76605046e67281e18b6b1c103c75924919169c71c34a57847a0b2b8d8db\",\"c59a147dc00362686131efee8415e9ea0d532cd854114389d43cbe034789b208\",\"e9c2d784dd1fe6fe0095bc0d652af3c733b0eacdcddfbf406c2b092fdf7bd03e\",\"371cc18b80e27df88e17a0b78f7130326800d43e92d69b497e38f7357a21f051\",\"302ebc36f9a6ef7240abf69a6c9cd446e1a938eca2c88047d348ab76ee7dd761\",\"9ad33e6c58ad3c5227338073802fc09183fd270b626f3e6513487556a1526c55\",\"a54f9e4b5bcc7bab270aab3d6b8b9d77887e9ecef7a7e739f4f77585863d8fb8\"],\"transfer_conditions_md\":\"With #4883's served files at their sha256 beside them: `./build.sh` (clang or gcc, -O3, native) then `./run.sh > run.txt` reproduces every value (about 3 minutes, 1.1 GB; `k7 gaps 7` is 114 s of it). `python3 cert.py` (stdlib, about 100 s) reproduces cert.out and witnesses.tsv; it overwrites witnesses.tsv at the MMAX it is given, so run it at the default 510.\",\"scope_sha256\":\"6e50e3b4771eda701ce0f20a4dbf0f5316dbe99ef3d33da5a2ba0398f488262a\",\"research_status\":\"accepted\",\"review_ids\":[1894]}]\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:5433,input_sha256:\"c07f53123efdc1df7a70ccb72a1d1b5e14f5c29779a1b5054eb7f3ddb5f0fc1b\",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/6642/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"b0cc149464abe9e9d15973329b3cc23d7cdbdf7bfb4ea8504551d190779f77ad","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}