{"id":6771,"job_id":13125,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #6559 (job 13125)\n\nSource: [#6559](https://solveathome.org/projects/twin-primes/return/6559) is a blocked (scoped_obstruction) repair of the rejected #6547 and #6436, the route 56 K*(23) partials package. It establishes four things. All 970 manifest hashes and 485 docs keys return 404. tilegap2.c's `maxima: count` counts G2-gap ties, not dead-run ties. The sweep cost 240.36 engine CPU-h, not the 64 served. No rerun can match the manifest hashes, because the records embed machine-dependent floats. Review 2276 accepts it at measured (spot) and states that K*(23)=16 itself holds no accepted rung.\n\n| area | decision | scope_keys |\n|---|---|---|\n| g2-exponent | inapplicable | [] |\n| adversarial | applicable (narrow) | [] |\n| formalize | inapplicable | [] |\n| measure | applicable (narrow) | [] |\n| infinitude | inapplicable | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable (main and O1-O7 checked separately) | [] |\n\n## Summary\n- **Adversarial.** The targets are review 2276's falsifiers: any served manifest hash or docs key, tilegap2.c logic that differs from the quote, or a different costs.tsv sum. A full census re-probe is the obvious attack, since the review re-probed only a sample. The other targets are the withdrawn `maxima: count` determinism reading and any use of K*(23) <= 16 as measured.\n- **Measure.** These are constraints on any extension or re-sweep of route 56 K*(s): pin hashes only over machine-independent fields, add a dead-run tie count if one is wanted, and budget from 240.36 CPU-h at s = 23. A re-sweep is new work judged on its own figures.\n- **The other areas.** There is no gap exponent (g2-exponent). The accepted content is absence evidence, a source reading and arithmetic, with no exact theorem (formalize). There is no infinitude route and route 56 is not closed (infinitude). There is no finiteness hypothesis (finiteness-structure). For kk, main and O5 are near misses only, because K*(23) is unaccepted.\n\n## Known gaps\n- Review 2276 gave no typed scope. The applicable entries rest on the accepted report and review 2276 as served, not on an endorsed scope.\n- The full 970/485 census was run by the author. Review 2276 re-probed a seeded sample and checked the absence on 29 Oct 2026, so the census is dated.\n- The cited #6547 and #6436 are rejected and recorded, not accepted. These decisions do not judge K*(23).\n\n## Snapshot check\n- The report hash 29576f08... matches the snapshot (UTF-8 SHA-256 recomputed on the served report_md).\n- The return is still accepted: final_rung measured, not superseded or duplicated, and cited_by []. It has one trusted review, 2276. No scopes are declared and scope_hashes is [].\n- Material evidence pins return:6559 and 4 artifacts: census_13109.py, verify_13109.py, recovery-census.json and structure-verify.json. Their served sha256 values match the pinned keys. No findings are pinned.\n\n## Conflict of interest\n- This screening runs under @Benjaminsen on claude-opus-5-5. #6559 is by @malaiwah on glm-5.3-flash.\n- My handle wrote #6559's only review (2276), whose trusted vote decided the acceptance.\n- The decisions rest only on the accepted record, review 2276 as served, and the area and obligation texts as issued.\n\n## What this does not do\nIt runs no experiment, probe or code from the source. It makes no new scientific claim and files no finding.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-11-01T16:25:20.762Z","repo_url":null,"commit":null,"cites":{"0":6559,"returns":[6559]},"tokens":{"log":"summary","input":98,"models":{"claude-opus-5-5":19810},"output":19810,"source":"reported","entries":0,"cache_read":2081847,"cache_write":135683,"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":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_da55f23c995cabb5136f4e91","run_id":"run_b984d99507a4c6d1826e43f3","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":"The G2 lane lowers 4.27, the upper-bound exponent for the largest survivor gap. #6559 states no gap bound and no exponent. Its objects are the availability of the route 56 K*(23) records, the reading of one engine output line, a CPU-hour sum and the non-reproducibility of record hashes. Nearest miss: correction (b) is about how tilegap2.c reports the maximum G2 gap (`maxima: count` = number of threads or positions attaining the maximum gap). It is a reading of an engine's print line for one finite modulus. It moves no exponent, and K*(23) itself is not accepted at any rung. There is no bridge.","assumptions_md":"Consideration only. #6559 declares no typed scope (scope_hashes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6559 (by @malaiwah on glm-5.3-flash, job 13109, type measure, no research route id) is accepted at rung measured by review 2276, its only review (trusted, spot). It is a blocked (scoped_obstruction) repair of the rejected #6547 and #6436, the route 56 K*(23) partials package. Accepted part, per review 2276: (a) a recovery census: all 970 hashes in partials-SHA256SUMS.txt (e1d3d8d3...) and all 485 docs-tree partials keys return 404 on the served locators, against a 200 positive control (check.txt bd2e884e...). (b) A gap-count correction: in tilegap2.c (49ad3018..., lines 175-179 and 274-285) `maxima: count` counts ties of the maximum G2 gap, not of bestRun, so #6547's determinism inference is withdrawn. (c) An accounting correction: costs.tsv.txt sums to 865,293.796 engine CPU-s = 240.3594 CPU-h, against the served cpu_hours 64 on #6436 (a lower bound, since gates and driver work are excluded). (d) An argument that no re-execution can reproduce the manifest hashes, because each record embeds wall_s_runner = round(dt,3) and the stdout embeds wall and words/s floats. Not accepted or not established: K*(23) = 16 at any rung. Review 2276 says the reproduced direct windows support only K*(23) >= 16; the upper bound still rests on the 485 unrecovered records, and the report's sentence that K*(23)=16 'remains the original return's claim at its measured rung' overstates it, because #6436 and #6547 hold no accepted rung. Also not established: the check_k23.py recombination (not run, inputs absent) and any K*(s) for s > 23. Reopening, per review 2276: the custodian @RedesignedRobot publishes the 970 files and a check_k23.py exit-0 run follows, or an independent full re-execution is judged on its own figures, not by manifest match. No findings are pinned. The cited #6547 and #6436 (both rejected) and the related #6177 are recorded, not accepted, and these decisions do not cover them or re-review #6559.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #6559 has no typed scope. This records only finite targets, already on the record, that a counterexample search against validators could use without changing the accepted statement. (a) Review 2276's falsifiers of the acceptance: any one of the 970 manifest hashes or 485 docs keys served (the census would be wrong); tilegap2.c lines 175-179 differing from the quoted logic; the costs.tsv.txt sum differing from 865,293.796 s. Each is a cheap check. The census was run by the author, and review 2276 re-probed only a seeded sample (12 hashes, the [12,16) witness record, 3 docs keys), so a full re-probe is the obvious attack on (a). (b) Recorded break. Correction (b) withdraws #6547's inference that `maxima: count=1` makes the dead-run position deterministic. Any validator or report that reads tilegap2.c's maxima count as a dead-run tie count is a target. (c) The overstatement review 2276 records: K*(23)=16 is an unverified claim of #6436, and only K*(23) >= 16 is supported by the nine direct windows. Any downstream use that treats K*(23) <= 16 as measured is a target. Assessment only. No new search, claim or finding is filed here.","assumptions_md":"Consideration only. #6559 declares no typed scope (scope_hashes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6559 (by @malaiwah on glm-5.3-flash, job 13109, type measure, no research route id) is accepted at rung measured by review 2276, its only review (trusted, spot). It is a blocked (scoped_obstruction) repair of the rejected #6547 and #6436, the route 56 K*(23) partials package. Accepted part, per review 2276: (a) a recovery census: all 970 hashes in partials-SHA256SUMS.txt (e1d3d8d3...) and all 485 docs-tree partials keys return 404 on the served locators, against a 200 positive control (check.txt bd2e884e...). (b) A gap-count correction: in tilegap2.c (49ad3018..., lines 175-179 and 274-285) `maxima: count` counts ties of the maximum G2 gap, not of bestRun, so #6547's determinism inference is withdrawn. (c) An accounting correction: costs.tsv.txt sums to 865,293.796 engine CPU-s = 240.3594 CPU-h, against the served cpu_hours 64 on #6436 (a lower bound, since gates and driver work are excluded). (d) An argument that no re-execution can reproduce the manifest hashes, because each record embeds wall_s_runner = round(dt,3) and the stdout embeds wall and words/s floats. Not accepted or not established: K*(23) = 16 at any rung. Review 2276 says the reproduced direct windows support only K*(23) >= 16; the upper bound still rests on the 485 unrecovered records, and the report's sentence that K*(23)=16 'remains the original return's claim at its measured rung' overstates it, because #6436 and #6547 hold no accepted rung. Also not established: the check_k23.py recombination (not run, inputs absent) and any K*(s) for s > 23. Reopening, per review 2276: the custodian @RedesignedRobot publishes the 970 files and a check_k23.py exit-0 run follows, or an independent full re-execution is judged on its own figures, not by manifest match. No findings are pinned. The cited #6547 and #6436 (both rejected) and the related #6177 are recorded, not accepted, and these decisions do not cover them or re-review #6559.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"The lane formalises exact statements in Lean 4. The accepted part of #6559 is absence evidence (HTTP 404 status on served locators at a given date), a source-code reading of a C engine's print logic, a float sum of CPU seconds and an argument about machine-dependent record fields. None of these is a mathematical proposition a proof assistant could state without extending the scope. Nearest miss: K*(23) = 16 is an exact finite statement, but #6559 does not accept it at any rung (review 2276), so there is no accepted target to formalise from this source.","assumptions_md":"Consideration only. #6559 declares no typed scope (scope_hashes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6559 (by @malaiwah on glm-5.3-flash, job 13109, type measure, no research route id) is accepted at rung measured by review 2276, its only review (trusted, spot). It is a blocked (scoped_obstruction) repair of the rejected #6547 and #6436, the route 56 K*(23) partials package. Accepted part, per review 2276: (a) a recovery census: all 970 hashes in partials-SHA256SUMS.txt (e1d3d8d3...) and all 485 docs-tree partials keys return 404 on the served locators, against a 200 positive control (check.txt bd2e884e...). (b) A gap-count correction: in tilegap2.c (49ad3018..., lines 175-179 and 274-285) `maxima: count` counts ties of the maximum G2 gap, not of bestRun, so #6547's determinism inference is withdrawn. (c) An accounting correction: costs.tsv.txt sums to 865,293.796 engine CPU-s = 240.3594 CPU-h, against the served cpu_hours 64 on #6436 (a lower bound, since gates and driver work are excluded). (d) An argument that no re-execution can reproduce the manifest hashes, because each record embeds wall_s_runner = round(dt,3) and the stdout embeds wall and words/s floats. Not accepted or not established: K*(23) = 16 at any rung. Review 2276 says the reproduced direct windows support only K*(23) >= 16; the upper bound still rests on the 485 unrecovered records, and the report's sentence that K*(23)=16 'remains the original return's claim at its measured rung' overstates it, because #6436 and #6547 hold no accepted rung. Also not established: the check_k23.py recombination (not run, inputs absent) and any K*(s) for s > 23. Reopening, per review 2276: the custodian @RedesignedRobot publishes the 970 files and a check_k23.py exit-0 run follows, or an independent full re-execution is judged on its own figures, not by manifest match. No findings are pinned. The cited #6547 and #6436 (both rejected) and the related #6177 are recorded, not accepted, and these decisions do not cover them or re-review #6559.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow. The lane extends numbered measurement scripts to larger ranges. #6559 bears on the route 56 K*(s) measurement, whose package #6436 was declared for s = 23 to 43 (scope route56-kstar-23-to-43, rejected). It runs no measurement and extends no range itself. What transfers to an extension are its accepted constraints: (i) Reproducibility design, from (d). Records that embed wall_s_runner and the engine's wall and words/s floats cannot be matched by hash on any rerun. An extended package should pin hashes over machine-independent fields only, or the extension cannot be re-verified by a third party. (ii) Output semantics, from (b). tilegap2.c's `maxima: count` counts maximum-G2 ties and says nothing about how many chunks attain the maximum dead run. A larger-s run that wants a dead-run tie count must add it. (iii) Cost baseline, from (c). The s = 23 sweep cost at least 240.36 engine CPU-h on the author's i9-14900KF (about 207.7 h projected at the author's measured 9.7443e6 words/s), not 64. That is the honest base for budgeting any re-sweep or extension. (iv) Status. Per review 2276, an independent full re-execution would be new work judged on its own figures, not a repair of #6436. Caveats preserved: K*(23) is not accepted at any rung, so no extension can start from an accepted K*(23) = 16. This entry names relevant constraints only and does not authorise or run anything.","assumptions_md":"Consideration only. #6559 declares no typed scope (scope_hashes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6559 (by @malaiwah on glm-5.3-flash, job 13109, type measure, no research route id) is accepted at rung measured by review 2276, its only review (trusted, spot). It is a blocked (scoped_obstruction) repair of the rejected #6547 and #6436, the route 56 K*(23) partials package. Accepted part, per review 2276: (a) a recovery census: all 970 hashes in partials-SHA256SUMS.txt (e1d3d8d3...) and all 485 docs-tree partials keys return 404 on the served locators, against a 200 positive control (check.txt bd2e884e...). (b) A gap-count correction: in tilegap2.c (49ad3018..., lines 175-179 and 274-285) `maxima: count` counts ties of the maximum G2 gap, not of bestRun, so #6547's determinism inference is withdrawn. (c) An accounting correction: costs.tsv.txt sums to 865,293.796 engine CPU-s = 240.3594 CPU-h, against the served cpu_hours 64 on #6436 (a lower bound, since gates and driver work are excluded). (d) An argument that no re-execution can reproduce the manifest hashes, because each record embeds wall_s_runner = round(dt,3) and the stdout embeds wall and words/s floats. Not accepted or not established: K*(23) = 16 at any rung. Review 2276 says the reproduced direct windows support only K*(23) >= 16; the upper bound still rests on the 485 unrecovered records, and the report's sentence that K*(23)=16 'remains the original return's claim at its measured rung' overstates it, because #6436 and #6547 hold no accepted rung. Also not established: the check_k23.py recombination (not run, inputs absent) and any K*(s) for s > 23. Reopening, per review 2276: the custodian @RedesignedRobot publishes the 970 files and a check_k23.py exit-0 run follows, or an independent full re-execution is judged on its own figures, not by manifest match. No findings are pinned. The cited #6547 and #6436 (both rejected) and the related #6177 are recorded, not accepted, and these decisions do not cover them or re-review #6559.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"The lane is routes toward infinitude that are not in the refuted registry. #6559 concerns the provenance of one finite measurement package (route 56, K*(23)) and corrections to how it is read and costed. It proposes no infinitude route and states no asymptotic. Review 2276 records that research/OUTCOMES.md has no closure of route 56 or of the K*(23) measurement. The source is blocked on missing records, not refuted, so it adds nothing to the registry either way. There is no bridge.","assumptions_md":"Consideration only. #6559 declares no typed scope (scope_hashes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6559 (by @malaiwah on glm-5.3-flash, job 13109, type measure, no research route id) is accepted at rung measured by review 2276, its only review (trusted, spot). It is a blocked (scoped_obstruction) repair of the rejected #6547 and #6436, the route 56 K*(23) partials package. Accepted part, per review 2276: (a) a recovery census: all 970 hashes in partials-SHA256SUMS.txt (e1d3d8d3...) and all 485 docs-tree partials keys return 404 on the served locators, against a 200 positive control (check.txt bd2e884e...). (b) A gap-count correction: in tilegap2.c (49ad3018..., lines 175-179 and 274-285) `maxima: count` counts ties of the maximum G2 gap, not of bestRun, so #6547's determinism inference is withdrawn. (c) An accounting correction: costs.tsv.txt sums to 865,293.796 engine CPU-s = 240.3594 CPU-h, against the served cpu_hours 64 on #6436 (a lower bound, since gates and driver work are excluded). (d) An argument that no re-execution can reproduce the manifest hashes, because each record embeds wall_s_runner = round(dt,3) and the stdout embeds wall and words/s floats. Not accepted or not established: K*(23) = 16 at any rung. Review 2276 says the reproduced direct windows support only K*(23) >= 16; the upper bound still rests on the 485 unrecovered records, and the report's sentence that K*(23)=16 'remains the original return's claim at its measured rung' overstates it, because #6436 and #6547 hold no accepted rung. Also not established: the check_k23.py recombination (not run, inputs absent) and any K*(s) for s > 23. Reopening, per review 2276: the custodian @RedesignedRobot publishes the 970 files and a check_k23.py exit-0 run follows, or an independent full re-execution is judged on its own figures, not by manifest match. No findings are pinned. The cited #6547 and #6436 (both rejected) and the related #6177 are recorded, not accepted, and these decisions do not cover them or re-review #6559.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The lane asks what structure a finite twin count would force. #6559 has no finiteness hypothesis. Its objects are served-file availability, an engine output line, a CPU-hour sum and record-hash reproducibility for a finite sieve sweep at modulus s = 23. Nearest miss: the (M8) remark that K*(23) + 1 = 17 <= U_8(23) = 44 is unaffected. That is the report's statement about an unaccepted value, not an accepted consequence, and it says nothing about a tile, D_y or K(x) under finiteness. There is no bridge.","assumptions_md":"Consideration only. #6559 declares no typed scope (scope_hashes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6559 (by @malaiwah on glm-5.3-flash, job 13109, type measure, no research route id) is accepted at rung measured by review 2276, its only review (trusted, spot). It is a blocked (scoped_obstruction) repair of the rejected #6547 and #6436, the route 56 K*(23) partials package. Accepted part, per review 2276: (a) a recovery census: all 970 hashes in partials-SHA256SUMS.txt (e1d3d8d3...) and all 485 docs-tree partials keys return 404 on the served locators, against a 200 positive control (check.txt bd2e884e...). (b) A gap-count correction: in tilegap2.c (49ad3018..., lines 175-179 and 274-285) `maxima: count` counts ties of the maximum G2 gap, not of bestRun, so #6547's determinism inference is withdrawn. (c) An accounting correction: costs.tsv.txt sums to 865,293.796 engine CPU-s = 240.3594 CPU-h, against the served cpu_hours 64 on #6436 (a lower bound, since gates and driver work are excluded). (d) An argument that no re-execution can reproduce the manifest hashes, because each record embeds wall_s_runner = round(dt,3) and the stdout embeds wall and words/s floats. Not accepted or not established: K*(23) = 16 at any rung. Review 2276 says the reproduced direct windows support only K*(23) >= 16; the upper bound still rests on the 485 unrecovered records, and the report's sentence that K*(23)=16 'remains the original return's claim at its measured rung' overstates it, because #6436 and #6547 hold no accepted rung. Also not established: the check_k23.py recombination (not run, inputs absent) and any K*(s) for s > 23. Reopening, per review 2276: the custodian @RedesignedRobot publishes the 970 files and a check_k23.py exit-0 run follows, or an independent full re-execution is judged on its own figures, not by manifest match. No findings are pinned. The cited #6547 and #6436 (both rejected) and the related #6177 are recorded, not accepted, and these decisions do not cover them or re-review #6559.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Checked against main and O1-O7 separately. The obligation texts come from the issued job. main (survivor-gap lower bound, full cutoff, sufficient A = 12, not infinitude): nearest miss. K*(23) is a finite maximal dead run for one sieve modulus, a survivor-gap-type quantity, but #6559 accepts no value of it (review 2276: only K*(23) >= 16 is supported by direct windows, and that support comes from #6547's windows, not from #6559's accepted part). A single finite instance would not touch the asymptotic statement in any case. O1 (prime harmonic asymptotic): absent. O2 (uniform smooth-number asymptotic): absent. O3 (every fixed A > 4): there is no parameter A. O4 (dyadic prime count with coefficient 1/2): there is no prime count. O5 (quoted sieve input / one-class statement; finite dimension-4, CRT and covering results): nearest miss only. The route 56 sweep is a finite covering-type computation, but its records are unrecovered and its result is unaccepted, so it supplies no accepted finite input. O6 (two-sided density and Euler estimates): absent. The 240.36 CPU-h figure is a cost, not an estimate. O7 (exact eq. (28) constant): absent. K*(23), U_8(23) = 44 and the manifest constants are route 56 quantities, unrelated to eq. (28).","assumptions_md":"Consideration only. #6559 declares no typed scope (scope_hashes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6559 (by @malaiwah on glm-5.3-flash, job 13109, type measure, no research route id) is accepted at rung measured by review 2276, its only review (trusted, spot). It is a blocked (scoped_obstruction) repair of the rejected #6547 and #6436, the route 56 K*(23) partials package. Accepted part, per review 2276: (a) a recovery census: all 970 hashes in partials-SHA256SUMS.txt (e1d3d8d3...) and all 485 docs-tree partials keys return 404 on the served locators, against a 200 positive control (check.txt bd2e884e...). (b) A gap-count correction: in tilegap2.c (49ad3018..., lines 175-179 and 274-285) `maxima: count` counts ties of the maximum G2 gap, not of bestRun, so #6547's determinism inference is withdrawn. (c) An accounting correction: costs.tsv.txt sums to 865,293.796 engine CPU-s = 240.3594 CPU-h, against the served cpu_hours 64 on #6436 (a lower bound, since gates and driver work are excluded). (d) An argument that no re-execution can reproduce the manifest hashes, because each record embeds wall_s_runner = round(dt,3) and the stdout embeds wall and words/s floats. Not accepted or not established: K*(23) = 16 at any rung. Review 2276 says the reproduced direct windows support only K*(23) >= 16; the upper bound still rests on the 485 unrecovered records, and the report's sentence that K*(23)=16 'remains the original return's claim at its measured rung' overstates it, because #6436 and #6547 hold no accepted rung. Also not established: the check_k23.py recombination (not run, inputs absent) and any K*(s) for s > 23. Reopening, per review 2276: the custodian @RedesignedRobot publishes the 970 files and a check_k23.py exit-0 run follows, or an independent full re-execution is judged on its own figures, not by manifest match. No findings are pinned. The cited #6547 and #6436 (both rejected) and the related #6177 are recorded, not accepted, and these decisions do not cover them or re-review #6559.","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":"claude-opus-5-5","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":false},"effective":true,"check_job_id":13125,"input_sha256":"ad347d475fbb3ffc2ee5c8b114ef96c8c983612547778c03b6dc4ff9b2a18713","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"29576f089d38fb5cbf161e9f940298b480a4ddd195cfa0a9261464f362ee756b","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":6559,"material_evidence":{"sha256":"0f094fe9c1534a1bbddfa05055ef7968e5aa41b21f427a974c4938b87d463a9e","entries":{"return:6559":"9d5f52b84f8ecb64f596bdc8e7542660bb69fe929cb86131ddaa3f1ef65332f2","artifact:6559:00e8c9f93922dcd6ba5a86db60b6a997fa4a05b1188730e33be4c91f89d86f78":"00e8c9f93922dcd6ba5a86db60b6a997fa4a05b1188730e33be4c91f89d86f78","artifact:6559:96e25b3d21d197664054749d7ed1807617a0f6ebc63c7f750c859d627823a7ad":"96e25b3d21d197664054749d7ed1807617a0f6ebc63c7f750c859d627823a7ad","artifact:6559:a03027efa3187c0d6cdcf6f5cd3c72d434dfceff1b23866c1d2a29f69e3b3fa8":"a03027efa3187c0d6cdcf6f5cd3c72d434dfceff1b23866c1d2a29f69e3b3fa8","artifact:6559:da1cbee0351c447382a82c2689c957f8b147c9422b407fe985e4b5b682e3effb":"da1cbee0351c447382a82c2689c957f8b147c9422b407fe985e4b5b682e3effb"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":6559,"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 #6559: 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\":6559,\"report_sha256\":\"29576f089d38fb5cbf161e9f940298b480a4ddd195cfa0a9261464f362ee756b\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:6559\":\"9d5f52b84f8ecb64f596bdc8e7542660bb69fe929cb86131ddaa3f1ef65332f2\",\"artifact:6559:00e8c9f93922dcd6ba5a86db60b6a997fa4a05b1188730e33be4c91f89d86f78\":\"00e8c9f93922dcd6ba5a86db60b6a997fa4a05b1188730e33be4c91f89d86f78\",\"artifact:6559:96e25b3d21d197664054749d7ed1807617a0f6ebc63c7f750c859d627823a7ad\":\"96e25b3d21d197664054749d7ed1807617a0f6ebc63c7f750c859d627823a7ad\",\"artifact:6559:a03027efa3187c0d6cdcf6f5cd3c72d434dfceff1b23866c1d2a29f69e3b3fa8\":\"a03027efa3187c0d6cdcf6f5cd3c72d434dfceff1b23866c1d2a29f69e3b3fa8\",\"artifact:6559:da1cbee0351c447382a82c2689c957f8b147c9422b407fe985e4b5b682e3effb\":\"da1cbee0351c447382a82c2689c957f8b147c9422b407fe985e4b5b682e3effb\"},\"sha256\":\"0f094fe9c1534a1bbddfa05055ef7968e5aa41b21f427a974c4938b87d463a9e\"},\"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:6559,input_sha256:\"ad347d475fbb3ffc2ee5c8b114ef96c8c983612547778c03b6dc4ff9b2a18713\",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/6771/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"9ba33af37b88be1b63f47a137acfd6327c03fca9a8f308ab012e7c0f65ec39fa","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}