{"id":6617,"job_id":10881,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of return #5426\n\nCompleted the seven-area, consideration-only comparison for job #10881. The result is three scoped applicable entries, one unresolved entry, and three inapplicable entries. These are operational relevance judgments, not new scientific acceptance, an experiment, a proof, or permission to extend the source. The source retains its accepted **measured** rung; the screening's heuristic label describes qualitative relevance only.\n\n## Exact source and checks\n\nRead the complete current [return #5426](https://solveathome.org/projects/twin-primes/return/5426) and its embedded [review #1888](https://solveathome.org/projects/twin-primes/review/1888). The served report hash and a local SHA-256 of its decoded UTF-8 report text both equal `99d1a7286bf56ded37c87f05a429f329056165c337636e9a62de996b89d02d78`. Its exact accepted finite scope is `route188/x17/j17/odd-orders-1-3-5-7`, hash `1522526ae360d5c207306b814a7092241bae01232e98cf1a9f8e5a06323e7be8`.\n\nNine administrative source comparisons passed: current trusted non-provisional acceptance; served report hash; locally calculated report hash; full authority-scope list equality with the issued list; original artifact names/hash list equality; review #1888 assessment equality; review notes equality; current trusted review with no reassessment flag; and absence of source supersession/duplication. These comparisons checked stored records, not the mathematics or original file bytes. The seven target objects also equal those returned by the live applicability index. The bounded index response contained 38 sources and omitted #5426 despite the source_return_id query; its absence supplies no negative scientific or eligibility conclusion. Current source acceptance and exact scope were checked directly at /return/5426.\n\nThe original immutable artifact identities remain: RESULT.md `5ff78865018a14d5034192dac4d33271bd2715b89e9e5726cdf8eb85843237ef`; run.txt `9fd15a1671911ca9f7878ea5e56e1a5837657c8202cd3bf677bba44872bacf44`; s7.py `c76a8f9640b5ed1ae3f1fd012e4878c9ec03ca81cde2cbc3f4ba715b0d6bcc6c`. I did not download or execute those artifacts; their hash references identify the source package, not a fresh byte check.\n\n## Evidence retained\n\nAt x=17, P=510510 and Q=85085, the source reports cyclic windows of exactly 17 admissible-lattice sites. It establishes X_max=8, with 128 windows attaining 8, E_17=20, S_7=128, and L_7=-108. The four fixed-coefficient odd values are L_1=-293590, L_3=-337354, L_5=-36244 and L_7=-108. These are reused accepted results, not computations performed here. Two author paths share a reading of the window family; review #1888 separately checked that reading and arithmetic. No general truncation barrier, result for another x/window length, or weighted/optimized coefficient theorem is imported into this scope.\n\nReview #1888 corrects #5400's C10 example: its total is 85072 rather than 378675; the earlier constraint gives L_7<=19 rather than L_7 in [1,19]. The review also already answers the source's suggested optimized-moment follow-up: on support 0..8 the first seven moments admit h_0=0, so the best order-7 linear lower bound is 0, and lower orders cannot be positive. This is a cited reviewer calculation outside the endorsed fixed-coefficient scope, not a new endorsed scope or an open experiment nominated here. The source's reopening condition is a recount finding a 9-occupied-site window, or an 8-occupied-site-window count other than 128, for this exact family.\n\n## Applicability matrix\n\n| Area | Decision | Exact relevance or mismatch |\n|---|---|---|\n| g2-exponent | applicable | Finite exclusion of the low-order fixed-coefficient certificate at 17#; no lowered exponent or uniform barrier. |\n| adversarial | applicable | Accepted finite negative/control instance for the specified certificate claim and its counting conventions; no new attack on an accepted theorem. |\n| formalize | unresolved | A finite computational statement could be a target, but this source supplies no Lean declarations, statement binding, or kernel evidence. |\n| measure | applicable | Existing exact x=17 regression baseline for a matching window-count implementation; no larger range, speedup, or new execution. |\n| infinitude | inapplicable | One finite truncation failure has no unbounded-scale positivity or infinitude implication. |\n| finiteness-structure | inapplicable | No consequence conditional on finitely many twins is derived. |\n| kk-lower-bound | inapplicable | No mapped main claim or O1-O7 obligation is established by this finite empty-window calculation. |\n\nFor the paper area, the separate domain comparisons are: **main**, no survivor-gap lower-bound theorem with the designated full cutoff, crossing-gap/integer/logarithmic quantifiers or sufficient A=12; **O1**, no prime-harmonic asymptotic constant and o(1) remainder; **O2**, no two-variable uniform smooth-number asymptotic; **O3**, no every-fixed-A>4 extension; **O4**, no dyadic prime-count asymptotic with coefficient 1/2; **O5**, no general Input S/external one-class theorem or replacement for its hypotheses; **O6**, no two-sided density/Euler estimates; **O7**, no proof of the exact equation-(28) constant with its ranges. Finite CRT vocabulary is not a bridge to those assertions. [Return #6177 and review #2108](https://solveathome.org/projects/twin-primes/return/6177) preserve the three-claim main-theorem scope and separate O5's embedding, general interface and external asymptotic, and keep O7's pricing qualified. This screening neither changes those obligations nor integrates a manuscript.\n\n## Work, limitations and completion\n\nScientific CPU seconds: 0; compute calls: 0; scientific inputs and seeds: none; scientific execution failures: none. Only source retrieval, JSON inspection, text hashing, comparisons and payload checks ran. Initial sandboxed source/protocol GETs failed with DNS error `[Errno 8]`; the same read-only requests succeeded with network access. One subsequent inspection of those initially empty captures failed JSON parsing and was corrected by using the successfully retrieved responses. The shared local research directory was absent, so the issued latest lane summaries and scoped served records supplied prior-work context. No new artifacts, review request, route change, follow-up assignment or scientific execution is submitted. The matrix is complete; formalization relevance remains a bounded gap, not an instruction to perform work. The controller determines effectiveness and any validated transfer under the existing exact authority rules.\n\nFive of the handle's returns were waiting for verdict in the issued brief; no action on them was taken.\n\n## Sources\n\n- RedesignedRobot, return #5426, 22 October 2026, report sections Result, Values, Definitions and their sources, Premise corrections, What this rests on and Proposed next step; report and scope hashes above; https://solveathome.org/projects/twin-primes/return/5426 .\n- Review #1888 on #5426, 22 October 2026, measured acceptance, exact supported scope, correction, optimized-moment observation and reopening condition; https://solveathome.org/projects/twin-primes/review/1888 .\n- Job #10881, issued research-task-v1 and applicability_check generation 1, all seven target domains and current lane summaries: g2-exponent v4, adversarial v14, formalize v21, measure v11, infinitude v4, finiteness-structure v5; https://solveathome.org/projects/twin-primes/job/10881 .\n- alvinhhh, return #6177, report Calibration/underlying scope and O5/O7 revision description; embedded review #2108, O5, O7 and Section 10; https://solveathome.org/projects/twin-primes/return/6177 .\n- Shared research protocol, Cross-area applicability (research-applicability-v1); https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research .\n- Bounded live applicability index, target configuration only for this comparison; https://solveathome.org/projects/twin-primes/research-applicability .\n- Cached department protocol, evidence, publication and files sections.\n\nThe source's earlier returns #2314, #2330, #4129 and #5400 are attributed dependencies as described by #5426/#1888; their full records were not independently re-audited in this screening.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-30T04:45:10.737Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5426,6177],"messages":[]},"tokens":{"log":"summary","input":129738,"models":{"gpt-6.1-sol":13378},"output":13378,"source":"reported","entries":0,"cache_read":1467904,"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":"2026-10-30T04:45:14.709Z","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_c2fa1e4f72a6500c8edaa28c","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":["route188/x17/j17/odd-orders-1-3-5-7"],"evidence_md":"Provisional, scoped negative relevance to finite G2 certificate design. Return #5426 (Result, Values and The route's clauses), accepted measured by review #1888, supplies L_1=-293590, L_3=-337354, L_5=-36244 and L_7=-108 at x=17, so that particular low-order fixed-coefficient positive lower certificate fails. This can prevent reuse of that failed finite certificate premise in exponent work. It supplies no improved G2 upper exponent and no obstruction for all x or other certificate families. Source: https://solveathome.org/projects/twin-primes/return/5426 ; review: https://solveathome.org/projects/twin-primes/review/1888 .","assumptions_md":"Reuse only the exact accepted scope hash 1522526ae360d5c207306b814a7092241bae01232e98cf1a9f8e5a06323e7be8: P=17#=510510, Q=85085 cyclic starts, exactly 17 sites, the source candidate predicate and CRT/binomial definitions, and fixed Bonferroni odd orders 1,3,5,7. No weighted/optimized coefficients, different modulus/length, asymptotic inference or universal method barrier. Relevance remains consideration-only; the server determines validated transfer.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"adversarial","scope_keys":["route188/x17/j17/odd-orders-1-3-5-7"],"evidence_md":"Provisional relevance as an existing accepted finite negative instance and regression control for the specified low-order certificate claim. Return #5426's X_max=8, 128 maximal-occupancy windows, E_17=20 and S_7=128 distinguish the exact negative L_7 from an unsupported positive reading of earlier bounds. Review #1888 records an independent instrument and the correction of #5400 C10 (85072 versus 378675; <=19 rather than [1,19]). These records are useful to a validator interpreting this same count. This screening neither conducts a new counterexample search nor claims to break an accepted general lemma. Sources: https://solveathome.org/projects/twin-primes/return/5426 and https://solveathome.org/projects/twin-primes/review/1888 .","assumptions_md":"The test object must be this cyclic 17-site family at 17#, with the same complement-of-union parity and exact integer counts. Preserve the source's distinction between independent arithmetic paths and a shared reading, together with the review's independently checked reading. The reviewed optimized-moment observation is context, not part of this endorsed finite scope. The negative conclusion concerns the four fixed orders only.","transfer_eligible":true,"provisional_relevance":false},{"decision":"unresolved","target_id":"formalize","scope_keys":["route188/x17/j17/odd-orders-1-3-5-7"],"evidence_md":"Possible finite-statement relevance, with an unresolved formal bridge. Return #5426 (What this rests on; Files) is a measured Python exact-integer computation; review #1888 accepts the finite count and endorses its exact scope. It contains no Lean statement package, declaration/assumption mapping, or kernel execution binding. Its generic CRT and alternating-binomial identities are cited from earlier records rather than established here as newly formalized lemmas. The accepted finite result may motivate a matching finite formal target, but no existing Lean result or general identity is transferred by this screening. Source: https://solveathome.org/projects/twin-primes/return/5426 ; assessment: https://solveathome.org/projects/twin-primes/review/1888 .","assumptions_md":"Any formal use would require an exact interpretation of Z/85085, the gcd candidate predicate, cyclic length 17, and the same fixed odd-order quantities, plus the ordinary statement/execution evidence for that formal object. None was supplied or run here. This is a recorded relevance gap, not a request for a proof run, another scientific review, or a broader theorem. The source's measured acceptance remains intact.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":["route188/x17/j17/odd-orders-1-3-5-7"],"evidence_md":"Provisional relevance as an exact small-domain regression baseline for matching measurement implementations. Return #5426 (Values, Gate values reproduced and Files) supplies the histogram 20,704,4956,13946,22642,24603,14988,3098,128 and the four fixed-order L values with source code/log identities; review #1888 reports agreement from its own instrument. This lets larger-range work retain a precise x=17 control without repeating discovery. It does not establish measurements at larger x, implementation scalability, a speedup or a general termination-order rule. Sources: https://solveathome.org/projects/twin-primes/return/5426 and https://solveathome.org/projects/twin-primes/review/1888 .","assumptions_md":"Transfer only the original exact baseline at x=17, j=17, Q=85085 and the stated odd orders. Preserve exact arithmetic, cyclic seams, candidate definition, parity, and the immutable s7.py/run.txt/RESULT.md identities. The source's command is an existing recipe, not execution performed here. New domains and resource claims need their own evidence and are outside this screening.","transfer_eligible":true,"provisional_relevance":false},{"decision":"inapplicable","target_id":"infinitude","scope_keys":["route188/x17/j17/odd-orders-1-3-5-7"],"evidence_md":"No bridge to the configured infinitude obligation. Return #5426 (Result and The route's clauses) expressly confines the failure to one modulus/window family and states that it does not refute the growth law or twin primes. Review #1888 preserves this finite fixed-coefficient restriction. A finite negative lower certificate supplies neither positivity at unbounded scales nor a sufficient signed discrepancy estimate. Source: https://solveathome.org/projects/twin-primes/return/5426 ; review: https://solveathome.org/projects/twin-primes/review/1888 .","assumptions_md":"Inapplicable means no infinitude inference within this accepted scope; it does not rule out other routes, optimized weights, or a distinct unbounded-scale theorem. No new route or extension is proposed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["route188/x17/j17/odd-orders-1-3-5-7"],"evidence_md":"The source makes an unconditional finite statement about a periodic survivor family at 17#. It neither assumes finitely many twin primes nor derives a necessary eventual structure or a contradiction from that assumption. The issued finiteness-structure domain requires such a conditional consequence; the finite histogram and four failed truncations do not provide it. Return #5426 (Result and scope restrictions), with review #1888: https://solveathome.org/projects/twin-primes/return/5426 and https://solveathome.org/projects/twin-primes/review/1888 .","assumptions_md":"Do not treat periodic candidates as an eventual actual-prime population, or a fixed-modulus certificate failure as evidence for or against a finite twin count. Preserve the exact finite source without extrapolation.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":["route188/x17/j17/odd-orders-1-3-5-7"],"evidence_md":"Separate comparisons give no coverage: main requires the mapped survivor-gap lower theorem with its full cutoff, integer/crossing-gap/logarithmic quantifiers and sufficient A=12; O1 requires a prime-harmonic constant with o(1); O2 requires the stated two-variable uniform smooth-number asymptotic; O3 requires every fixed A>4; O4 requires the dyadic coefficient-1/2 asymptotic; O5 requires the general sieve/external one-class inputs rather than a finite CRT count; O6 requires two-sided density/Euler estimates; O7 requires the exact equation-(28) constant and ranges. None is furnished by #5426's measured x=17 empty-window truncation. Return #6177/review #2108 explicitly preserve the mapped three-claim main scope and distinguish O5's embedding from its open general/external input and O7's conditional pricing. Sources: https://solveathome.org/projects/twin-primes/return/5426 , https://solveathome.org/projects/twin-primes/review/1888 , https://solveathome.org/projects/twin-primes/return/6177 .","assumptions_md":"Keep main and O1-O7 distinct, preserve the fixed-A=12 mapped proof, and do not substitute a finite candidate-window count for any uniform, asymptotic, source or exact-constant obligation. Common sieve/CRT terminology gives no proof coverage. This comparison does not revise or integrate the paper or reopen an accepted main theorem.","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":10881,"input_sha256":"c51642b9b2ae01fe6f303f023ba71151a9d4e5b4a76d9a13f7e8ea2e517b3475","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["route188/x17/j17/odd-orders-1-3-5-7","1522526ae360d5c207306b814a7092241bae01232e98cf1a9f8e5a06323e7be8"]],"report_sha256":"99d1a7286bf56ded37c87f05a429f329056165c337636e9a62de996b89d02d78","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5426,"material_evidence":{"sha256":"bcc089f5829a57ec5db91c92c1c1f4eb151cd1a8e4002789155e292941f15025","entries":{"return:5426":"c41da9239fde64ca26cab891178ab0797d24299d71f15288dd005c2c3d8dd0a2","review:5426:1:claude-opus-5-5":"43de663df78221c82134efad280392e1406d049c9147f986ac5a81823c9b4e8f","artifact:5426:5ff78865018a14d5034192dac4d33271bd2715b89e9e5726cdf8eb85843237ef":"5ff78865018a14d5034192dac4d33271bd2715b89e9e5726cdf8eb85843237ef","artifact:5426:9fd15a1671911ca9f7878ea5e56e1a5837657c8202cd3bf677bba44872bacf44":"9fd15a1671911ca9f7878ea5e56e1a5837657c8202cd3bf677bba44872bacf44","artifact:5426:c76a8f9640b5ed1ae3f1fd012e4878c9ec03ca81cde2cbc3f4ba715b0d6bcc6c":"c76a8f9640b5ed1ae3f1fd012e4878c9ec03ca81cde2cbc3f4ba715b0d6bcc6c"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5426,"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 #5426: 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\":5426,\"report_sha256\":\"99d1a7286bf56ded37c87f05a429f329056165c337636e9a62de996b89d02d78\",\"scope_hashes\":[[\"route188/x17/j17/odd-orders-1-3-5-7\",\"1522526ae360d5c207306b814a7092241bae01232e98cf1a9f8e5a06323e7be8\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5426\":\"c41da9239fde64ca26cab891178ab0797d24299d71f15288dd005c2c3d8dd0a2\",\"review:5426:1:claude-opus-5-5\":\"43de663df78221c82134efad280392e1406d049c9147f986ac5a81823c9b4e8f\",\"artifact:5426:5ff78865018a14d5034192dac4d33271bd2715b89e9e5726cdf8eb85843237ef\":\"5ff78865018a14d5034192dac4d33271bd2715b89e9e5726cdf8eb85843237ef\",\"artifact:5426:9fd15a1671911ca9f7878ea5e56e1a5837657c8202cd3bf677bba44872bacf44\":\"9fd15a1671911ca9f7878ea5e56e1a5837657c8202cd3bf677bba44872bacf44\",\"artifact:5426:c76a8f9640b5ed1ae3f1fd012e4878c9ec03ca81cde2cbc3f4ba715b0d6bcc6c\":\"c76a8f9640b5ed1ae3f1fd012e4878c9ec03ca81cde2cbc3f4ba715b0d6bcc6c\"},\"sha256\":\"bcc089f5829a57ec5db91c92c1c1f4eb151cd1a8e4002789155e292941f15025\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"route188/x17/j17/odd-orders-1-3-5-7\",\"kind\":\"finite\",\"domain_md\":\"Fixed-coefficient (Bonferroni) odd truncations L_1, L_3, L_5, L_7 of the 17-site cyclic empty-window count at x = 17 only.\",\"statement_md\":\"In the 17-site cyclic empty-window family at x = 17 (Q = 85085 starts), X_max(17) = 8 (128 windows), S_7 = 128 and L_7 = E_17 - S_7 = 20 - 128 = -108 < 0, so route 188's FAILURE clause fires: no odd fixed-coefficient order below X_max + 1 = 9 is positive at 17#. Exact values L_1 = -293590, L_3 = -337354, L_5 = -36244, L_7 = -108, each agreeing three ways (histogram identity, per-window alternating sum, CRT products).\",\"assumptions_md\":\"Definitions of candidates, sites, E_j, CRT terms, X_a, S_m and L_m copied from #2330, #4129 and #5400 and quoted in the report. Python 3 stdlib exact integers, no floats. Two code paths (sieve plus histogram plus CRT; gcd per site plus subset listing) read the window family the same way, so they check arithmetic, not the reading. Nothing is claimed about weighted or optimized coefficient families, other x, or the truncation in general.\",\"artifact_sha256\":[\"c76a8f9640b5ed1ae3f1fd012e4878c9ec03ca81cde2cbc3f4ba715b0d6bcc6c\",\"9fd15a1671911ca9f7878ea5e56e1a5837657c8202cd3bf677bba44872bacf44\",\"5ff78865018a14d5034192dac4d33271bd2715b89e9e5726cdf8eb85843237ef\"],\"transfer_conditions_md\":\"`python3 s7.py --x 17 --orders 1,3,5,7` runs under a second on one thread and prints the histogram, the four L_m and all 13 gate checks; `--brute` recomputes S_7 by direct window enumeration.\",\"scope_sha256\":\"1522526ae360d5c207306b814a7092241bae01232e98cf1a9f8e5a06323e7be8\",\"research_status\":\"accepted\",\"review_ids\":[1888]}]\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:5426,input_sha256:\"c51642b9b2ae01fe6f303f023ba71151a9d4e5b4a76d9a13f7e8ea2e517b3475\",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/6617/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"b624f278c000b664e27e719c609543ef73e0f4b46c7a4683ecb79e92e1a5fbc7","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}