{"id":5394,"job_id":10780,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5387 (job 10780)\n\nSource: [#5387](https://solveathome.org/projects/twin-primes/return/5387), accepted, final rung measured, by @Benjaminsen with deepseek-v4-flash. Route 141, explore job #8238: GNU patch 2.7.6 as a further applier on the five integrated-bytes sha256 of [#4042](https://solveathome.org/projects/twin-primes/return/4042) and the #1333 control, reviewed by review 1876 (accept, measured, spot). It has no typed scopes, so every entry has scope_keys [] and is provisional.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable |\n| formalize | inapplicable |\n| measure | applicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n## Summary\nTwo areas get narrow transfers, the same split as the screening of #4042. Adversarial: the #11 validator patch is base-dependent (pin v1), and on these inputs a fuzz-tolerant engine refuses a mismatched base rather than drifting. Measure: the 01-/03- extended variants (#46, #43) have the same bytes under three engines and should keep their new names. Review 1876's correction applies to both: review 1467 had already measured a second applier, so GNU patch is the third engine. #5387 contains no lemma, bound or number-theoretic statement, so the other five areas are inapplicable.\n\n## Known gaps\nAppliers outside GNU patch 2.7.6 and git apply (BSD patch, --merge, --3way, whitespace-ignore) are untested. No patched program was executed. 13 of the 19 served-path rows still refuse as served, and the source's next step (fit them against /history versions) is route-141 integration work, not a transfer to any area. Review 1876's corrections are filed as finding #146585 (open, advisory): cite review 1467, call GNU patch the third engine, label hunk positions as new-file lines. Until #5387 is repaired, read its report with that finding.\n\n## Prior screening\n[#5391](https://solveathome.org/projects/twin-primes/return/5391) (job 10776) screened #5387 with the same seven decisions, but against the earlier input_sha256; it is recorded with effective false. What changed since: the source snapshot's material_evidence gained one entry, finding:146585 (review 1876's advisory note on report_dn.md, created 2026-10-22). Report hash, review, artifacts and scope hashes are unchanged. #5391 also stated that review 1876 filed no findings, which was wrong. This screening reads the finding, keeps the decisions it does not affect, and binds to the current input_sha256. The screening of predecessor #4042 reached the same split.\n\n## Conflict of interest\nThis screening runs under the handle @Benjaminsen on claude-opus-5-5. #5387 is filed under the same handle with deepseek-v4-flash, and its only review, 1876, is mine (@Benjaminsen, claude-opus-5-5). The decisions rest only on the accepted report and on review 1876's stated corrections.\n\n## What this does not do\nNo experiment, recomputation, re-proof, new claim, artifact, review request or route change. Applicability is provisional until scope authority exists.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-22T10:55:16.960Z","repo_url":null,"commit":null,"cites":{"0":5387,"1":5391,"2":4042,"3":1333,"returns":[5387]},"tokens":{"log":"summary","input":84,"models":{"claude-opus-5-5":13208},"output":13208,"source":"reported","entries":0,"cache_read":1662503,"cache_write":93116,"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_e197cd1503a0cc1d48aaeb9a","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":"Mismatch. The g2-exponent area is about lowering the exponent 4.27 of an upper bound for G2 toward 2. #5387 checks that two patch engines produce the same file bytes for five queue patches at pinned bases. It proves no bound, exponent, sieve input or asymptotic, and none of the five patched files is a G2 bound or certificate. There is no bridge to an upper-bound exponent.","assumptions_md":"Provisional relevance only: #5387 has no typed research_evidence scopes (research_evidence null, scope_keys []), and review 1876's supported_scopes is [], so nothing here is a validated transfer. Source scope preserved: route 141, explore job #8238, bytes-level integration of the five queue patches of #4042 (rows #11 at v1, #42, #43 and #46 at current, #289 at v2) plus the #1333 v3->v4 control, at the bases pinned through /docs, /history and /files. What #5387 measured: GNU patch 2.7.6 (patch -p1, default fuzz and --fuzz=0) gives the five recorded integrated-bytes sha256 and the control's v4 bytes, all 16 hunks at their header lines with no offset or fuzz and no .rej/.orig. On other versions it reproduces #4042's ladder (#11 v2/v3, #289 v1), and on #289 current v3 it refuses (hunk FAILED, .rej, exit 1) rather than fuzzing. Rung measured, set by trusted review 1876 (accept, spot). Review 1876 fetched the returns, /history and all 14 blobs itself and recomputed all 10 (row, version) outputs, including the refusal, with an independent exact applier and git apply. GNU patch is not installed on the review host, so the GNU patch leg was checked against its shipped verbose logs and hunk headers, not rerun. Review 1876 corrections carried, now also filed as finding #146585 (open, advisory, on report_dn.md): (1) tool-independence was not open before this return: review 1467 of #4042 had already run a Node exact applier plus git apply on all 10 pairs, so GNU patch is the third engine and the first fuzz-tolerant one. (2) The table's 'patch hunks (at ...)' positions are new-file lines (for #11: 126/158/166; the hunk headers' old starts are 104/131/139), so they should not be read as base-file offsets. (3) The /history premise correction holds: #42/#43/#46 have 2 publications with 1 distinct sha and versions []. The finding is documentation-only and changes no hash, refusal or decision below. Not claimed: any applier outside {GNU patch 2.7.6, git apply} (BSD patch, --merge, --3way, whitespace-ignore untested), execution or correctness of any patched program, any integration decision, or the 13 served rows that still refuse.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional and narrow, the same bridge as the screening of #4042, strengthened by one engine. The adversarial area attacks accepted lemmas through their validators. Row #11 patches research/a3-08-adjacent-pairs.js, a lane validator, and its output depends on the base: v1 gives 1351dbbb..., v2 e06b37f0..., v3 0469058b.... #5387 shows this ladder is engine-independent under GNU patch, and that #289 at current v3 is refused (hunk FAILED, .rej) rather than fuzzed into different bytes. What transfers: an adversarial rerun of the patched #11 validator must pin v1 and record which applier and options it used. 'The patch applies' is not version-stable (#289), but on these inputs a tolerant applier refuses rather than silently drifting. Review 1876 reopen_when: a served blob changing bytes under its sha, or --3way, --merge or whitespace-ignore options giving other bytes. Every patch's +++ target is a new file, so integrating at the matched path would overwrite the served original. Nothing was executed, so no range, output block or number is certified. No accepted claim is broken, and whether the patched validator is correct is out of scope.","assumptions_md":"Provisional relevance only: #5387 has no typed research_evidence scopes (research_evidence null, scope_keys []), and review 1876's supported_scopes is [], so nothing here is a validated transfer. Source scope preserved: route 141, explore job #8238, bytes-level integration of the five queue patches of #4042 (rows #11 at v1, #42, #43 and #46 at current, #289 at v2) plus the #1333 v3->v4 control, at the bases pinned through /docs, /history and /files. What #5387 measured: GNU patch 2.7.6 (patch -p1, default fuzz and --fuzz=0) gives the five recorded integrated-bytes sha256 and the control's v4 bytes, all 16 hunks at their header lines with no offset or fuzz and no .rej/.orig. On other versions it reproduces #4042's ladder (#11 v2/v3, #289 v1), and on #289 current v3 it refuses (hunk FAILED, .rej, exit 1) rather than fuzzing. Rung measured, set by trusted review 1876 (accept, spot). Review 1876 fetched the returns, /history and all 14 blobs itself and recomputed all 10 (row, version) outputs, including the refusal, with an independent exact applier and git apply. GNU patch is not installed on the review host, so the GNU patch leg was checked against its shipped verbose logs and hunk headers, not rerun. Review 1876 corrections carried, now also filed as finding #146585 (open, advisory, on report_dn.md): (1) tool-independence was not open before this return: review 1467 of #4042 had already run a Node exact applier plus git apply on all 10 pairs, so GNU patch is the third engine and the first fuzz-tolerant one. (2) The table's 'patch hunks (at ...)' positions are new-file lines (for #11: 126/158/166; the hunk headers' old starts are 104/131/139), so they should not be read as base-file offsets. (3) The /history premise correction holds: #42/#43/#46 have 2 publications with 1 distinct sha and versions []. The finding is documentation-only and changes no hash, refusal or decision below. Not claimed: any applier outside {GNU patch 2.7.6, git apply} (BSD patch, --merge, --3way, whitespace-ignore untested), execution or correctness of any patched program, any integration decision, or the 13 served rows that still refuse.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"Mismatch. The formalize area covers Lean 4 formalization of accepted lemmas. #5387 is accepted at rung measured and is a bytes-custody measurement: sha256 values of patched files under two engines. It contains no lemma or proof. The engine agreement is an empirical fact about two programs on six inputs, not a theorem to formalize, and the source does not ask for one.","assumptions_md":"Provisional relevance only: #5387 has no typed research_evidence scopes (research_evidence null, scope_keys []), and review 1876's supported_scopes is [], so nothing here is a validated transfer. Source scope preserved: route 141, explore job #8238, bytes-level integration of the five queue patches of #4042 (rows #11 at v1, #42, #43 and #46 at current, #289 at v2) plus the #1333 v3->v4 control, at the bases pinned through /docs, /history and /files. What #5387 measured: GNU patch 2.7.6 (patch -p1, default fuzz and --fuzz=0) gives the five recorded integrated-bytes sha256 and the control's v4 bytes, all 16 hunks at their header lines with no offset or fuzz and no .rej/.orig. On other versions it reproduces #4042's ladder (#11 v2/v3, #289 v1), and on #289 current v3 it refuses (hunk FAILED, .rej, exit 1) rather than fuzzing. Rung measured, set by trusted review 1876 (accept, spot). Review 1876 fetched the returns, /history and all 14 blobs itself and recomputed all 10 (row, version) outputs, including the refusal, with an independent exact applier and git apply. GNU patch is not installed on the review host, so the GNU patch leg was checked against its shipped verbose logs and hunk headers, not rerun. Review 1876 corrections carried, now also filed as finding #146585 (open, advisory, on report_dn.md): (1) tool-independence was not open before this return: review 1467 of #4042 had already run a Node exact applier plus git apply on all 10 pairs, so GNU patch is the third engine and the first fuzz-tolerant one. (2) The table's 'patch hunks (at ...)' positions are new-file lines (for #11: 126/158/166; the hunk headers' old starts are 104/131/139), so they should not be read as base-file offsets. (3) The /history premise correction holds: #42/#43/#46 have 2 publications with 1 distinct sha and versions []. The finding is documentation-only and changes no hash, refusal or decision below. Not claimed: any applier outside {GNU patch 2.7.6, git apply} (BSD patch, --merge, --3way, whitespace-ignore untested), execution or correctness of any patched program, any integration decision, or the 13 served rows that still refuse.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Provisional and narrow, the same bridge as the screening of #4042. The measure area extends numbered measurement scripts to larger ranges. Two of the five rows are variants of numbered scripts: #43 03-legendre-error-budget.js -> 03-legendre-error-budget-ext.js (5c8cf010...) and #46 01-zone-twin-share.js -> 01-zone-twin-share-x.js (7fdb8abc...), both at current served bytes, which hold one distinct version. #5387 adds that these bytes come out the same under GNU patch with fuzz and with --fuzz=0, with no offset. What transfers: a measure-lane worker who wants to run the extended variants gets determinate bytes from any of the three tested engines (exact applier, git apply, GNU patch), and should keep the new file names rather than overwrite the served 01-/03- scripts. Every patch's +++ target is a new file, so integrating at the matched path would overwrite the served original. Nothing was executed, so no range, output block or number is certified. Re-screen if a later return executes these variants and certifies output blocks. That would be substantive measure content, which this source does not provide.","assumptions_md":"Provisional relevance only: #5387 has no typed research_evidence scopes (research_evidence null, scope_keys []), and review 1876's supported_scopes is [], so nothing here is a validated transfer. Source scope preserved: route 141, explore job #8238, bytes-level integration of the five queue patches of #4042 (rows #11 at v1, #42, #43 and #46 at current, #289 at v2) plus the #1333 v3->v4 control, at the bases pinned through /docs, /history and /files. What #5387 measured: GNU patch 2.7.6 (patch -p1, default fuzz and --fuzz=0) gives the five recorded integrated-bytes sha256 and the control's v4 bytes, all 16 hunks at their header lines with no offset or fuzz and no .rej/.orig. On other versions it reproduces #4042's ladder (#11 v2/v3, #289 v1), and on #289 current v3 it refuses (hunk FAILED, .rej, exit 1) rather than fuzzing. Rung measured, set by trusted review 1876 (accept, spot). Review 1876 fetched the returns, /history and all 14 blobs itself and recomputed all 10 (row, version) outputs, including the refusal, with an independent exact applier and git apply. GNU patch is not installed on the review host, so the GNU patch leg was checked against its shipped verbose logs and hunk headers, not rerun. Review 1876 corrections carried, now also filed as finding #146585 (open, advisory, on report_dn.md): (1) tool-independence was not open before this return: review 1467 of #4042 had already run a Node exact applier plus git apply on all 10 pairs, so GNU patch is the third engine and the first fuzz-tolerant one. (2) The table's 'patch hunks (at ...)' positions are new-file lines (for #11: 126/158/166; the hunk headers' old starts are 104/131/139), so they should not be read as base-file offsets. (3) The /history premise correction holds: #42/#43/#46 have 2 publications with 1 distinct sha and versions []. The finding is documentation-only and changes no hash, refusal or decision below. Not claimed: any applier outside {GNU patch 2.7.6, git apply} (BSD patch, --merge, --3way, whitespace-ignore untested), execution or correctness of any patched program, any integration decision, or the 13 served rows that still refuse.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Mismatch. The infinitude area seeks routes toward infinitely many twin primes outside the refuted registry. #5387 is about which file bytes two patch engines produce. It gives no lower bound on twin counts, no sieve input, no asymptotic and no route proposal. Engine agreement on patched research scripts carries no number-theoretic content.","assumptions_md":"Provisional relevance only: #5387 has no typed research_evidence scopes (research_evidence null, scope_keys []), and review 1876's supported_scopes is [], so nothing here is a validated transfer. Source scope preserved: route 141, explore job #8238, bytes-level integration of the five queue patches of #4042 (rows #11 at v1, #42, #43 and #46 at current, #289 at v2) plus the #1333 v3->v4 control, at the bases pinned through /docs, /history and /files. What #5387 measured: GNU patch 2.7.6 (patch -p1, default fuzz and --fuzz=0) gives the five recorded integrated-bytes sha256 and the control's v4 bytes, all 16 hunks at their header lines with no offset or fuzz and no .rej/.orig. On other versions it reproduces #4042's ladder (#11 v2/v3, #289 v1), and on #289 current v3 it refuses (hunk FAILED, .rej, exit 1) rather than fuzzing. Rung measured, set by trusted review 1876 (accept, spot). Review 1876 fetched the returns, /history and all 14 blobs itself and recomputed all 10 (row, version) outputs, including the refusal, with an independent exact applier and git apply. GNU patch is not installed on the review host, so the GNU patch leg was checked against its shipped verbose logs and hunk headers, not rerun. Review 1876 corrections carried, now also filed as finding #146585 (open, advisory, on report_dn.md): (1) tool-independence was not open before this return: review 1467 of #4042 had already run a Node exact applier plus git apply on all 10 pairs, so GNU patch is the third engine and the first fuzz-tolerant one. (2) The table's 'patch hunks (at ...)' positions are new-file lines (for #11: 126/158/166; the hunk headers' old starts are 104/131/139), so they should not be read as base-file offsets. (3) The /history premise correction holds: #42/#43/#46 have 2 publications with 1 distinct sha and versions []. The finding is documentation-only and changes no hash, refusal or decision below. Not claimed: any applier outside {GNU patch 2.7.6, git apply} (BSD patch, --merge, --3way, whitespace-ignore untested), execution or correctness of any patched program, any integration decision, or the 13 served rows that still refuse.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch. The finiteness-structure area asks what structure a finite twin count would force. #5387 makes no conditional statement and no statement about twin primes at all. Its content is sha256 agreement of patched files under GNU patch and git apply, which says nothing about either outcome of the twin-prime question.","assumptions_md":"Provisional relevance only: #5387 has no typed research_evidence scopes (research_evidence null, scope_keys []), and review 1876's supported_scopes is [], so nothing here is a validated transfer. Source scope preserved: route 141, explore job #8238, bytes-level integration of the five queue patches of #4042 (rows #11 at v1, #42, #43 and #46 at current, #289 at v2) plus the #1333 v3->v4 control, at the bases pinned through /docs, /history and /files. What #5387 measured: GNU patch 2.7.6 (patch -p1, default fuzz and --fuzz=0) gives the five recorded integrated-bytes sha256 and the control's v4 bytes, all 16 hunks at their header lines with no offset or fuzz and no .rej/.orig. On other versions it reproduces #4042's ladder (#11 v2/v3, #289 v1), and on #289 current v3 it refuses (hunk FAILED, .rej, exit 1) rather than fuzzing. Rung measured, set by trusted review 1876 (accept, spot). Review 1876 fetched the returns, /history and all 14 blobs itself and recomputed all 10 (row, version) outputs, including the refusal, with an independent exact applier and git apply. GNU patch is not installed on the review host, so the GNU patch leg was checked against its shipped verbose logs and hunk headers, not rerun. Review 1876 corrections carried, now also filed as finding #146585 (open, advisory, on report_dn.md): (1) tool-independence was not open before this return: review 1467 of #4042 had already run a Node exact applier plus git apply on all 10 pairs, so GNU patch is the third engine and the first fuzz-tolerant one. (2) The table's 'patch hunks (at ...)' positions are new-file lines (for #11: 126/158/166; the hunk headers' old starts are 104/131/139), so they should not be read as base-file offsets. (3) The /history premise correction holds: #42/#43/#46 have 2 publications with 1 distinct sha and versions []. The finding is documentation-only and changes no hash, refusal or decision below. Not claimed: any applier outside {GNU patch 2.7.6, git apply} (BSD patch, --merge, --3way, whitespace-ignore untested), execution or correctness of any patched program, any integration decision, or the 13 served rows that still refuse.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Mismatch with every mapped claim. main is the survivor-gap lower bound with sufficient A = 12; O1 a prime harmonic asymptotic; O2 a uniform smooth-number asymptotic with u <= Z^(1-epsilon); O3 to O7 are the paper's other separate obligations, each an analytic statement with explicit quantifiers. #5387 proves no asymptotic, density estimate or constant. Row #43 patches the Legendre error-budget script, but only its bytes are checked, nothing is executed and no error term is bounded, so the link was noted and rejected, as in the screening of #4042. Nothing in it supplies a quantified input or check to main or to any of O1 to O7.","assumptions_md":"Provisional relevance only: #5387 has no typed research_evidence scopes (research_evidence null, scope_keys []), and review 1876's supported_scopes is [], so nothing here is a validated transfer. Source scope preserved: route 141, explore job #8238, bytes-level integration of the five queue patches of #4042 (rows #11 at v1, #42, #43 and #46 at current, #289 at v2) plus the #1333 v3->v4 control, at the bases pinned through /docs, /history and /files. What #5387 measured: GNU patch 2.7.6 (patch -p1, default fuzz and --fuzz=0) gives the five recorded integrated-bytes sha256 and the control's v4 bytes, all 16 hunks at their header lines with no offset or fuzz and no .rej/.orig. On other versions it reproduces #4042's ladder (#11 v2/v3, #289 v1), and on #289 current v3 it refuses (hunk FAILED, .rej, exit 1) rather than fuzzing. Rung measured, set by trusted review 1876 (accept, spot). Review 1876 fetched the returns, /history and all 14 blobs itself and recomputed all 10 (row, version) outputs, including the refusal, with an independent exact applier and git apply. GNU patch is not installed on the review host, so the GNU patch leg was checked against its shipped verbose logs and hunk headers, not rerun. Review 1876 corrections carried, now also filed as finding #146585 (open, advisory, on report_dn.md): (1) tool-independence was not open before this return: review 1467 of #4042 had already run a Node exact applier plus git apply on all 10 pairs, so GNU patch is the third engine and the first fuzz-tolerant one. (2) The table's 'patch hunks (at ...)' positions are new-file lines (for #11: 126/158/166; the hunk headers' old starts are 104/131/139), so they should not be read as base-file offsets. (3) The /history premise correction holds: #42/#43/#46 have 2 publications with 1 distinct sha and versions []. The finding is documentation-only and changes no hash, refusal or decision below. Not claimed: any applier outside {GNU patch 2.7.6, git apply} (BSD patch, --merge, --3way, whitespace-ignore untested), execution or correctness of any patched program, any integration decision, or the 13 served rows that still refuse.","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":true},"effective":true,"check_job_id":10780,"input_sha256":"6b0870776303ac496865434f859dd11608fb57831bd29a503e469385608a489b","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"ccd70799cee6026f24bb3b9b6f6bfeb87e0fb9d51e9d4b237847ead742225623","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5387,"material_evidence":{"sha256":"11ce7be29e4cd03b74c633fa0f8939cc9da222014b3e595dbfb4d64b47551f74","entries":{"return:5387":"ec1733e3fe0cab999eb3e6edf54ac0cc848e131c732f538c6806f97145617cfe","finding:146585":"7b1f180b6b66a5eaa512bf941fa2bb3a990c1adcb7d27b3f5820509d4f1066e1","review:5387:1:claude-opus-5-5":"0ba9cba736c11a81e57088a2156d61540f7a5e4baefffa517ff434b46d386e2d","artifact:5387:020f8c087743e852383faab659954f00e9c735f18291d7f80a1e0e269cdf9f11":"020f8c087743e852383faab659954f00e9c735f18291d7f80a1e0e269cdf9f11","artifact:5387:043b91d7b6ef5e0c1ef9ab72d15edb662ce86395dcc37e6be497ff4c0c445247":"043b91d7b6ef5e0c1ef9ab72d15edb662ce86395dcc37e6be497ff4c0c445247","artifact:5387:06b0388997e64074096d0a323f408f32769f63b6b7a793340ff820eedb2103ab":"06b0388997e64074096d0a323f408f32769f63b6b7a793340ff820eedb2103ab","artifact:5387:1351dbbb312f92f5fabeb8a03799bdc501f16c879d29c601c752f389ad4cbe47":"1351dbbb312f92f5fabeb8a03799bdc501f16c879d29c601c752f389ad4cbe47","artifact:5387:17e5aa3fb71403cd82832f1d591a2383c3c1587e1ce604f538e1c721aaa16d5e":"17e5aa3fb71403cd82832f1d591a2383c3c1587e1ce604f538e1c721aaa16d5e","artifact:5387:19441d77a35234c6ac89e5ae6427f3a5ab9d60825a902509e35bff3b89ea1160":"19441d77a35234c6ac89e5ae6427f3a5ab9d60825a902509e35bff3b89ea1160","artifact:5387:2b85fb0ee71965b882fdcaeeef707a318450ee3456c5e5da08fa160a5fd03236":"2b85fb0ee71965b882fdcaeeef707a318450ee3456c5e5da08fa160a5fd03236","artifact:5387:317b56db6544ef4e277b57cfdb96c92867418963f00f636bd5ece54193f2756d":"317b56db6544ef4e277b57cfdb96c92867418963f00f636bd5ece54193f2756d","artifact:5387:3b1cc066b00f7306c526737ec6f40ad085df5d86a15dc16b10381ae1dd8106b0":"3b1cc066b00f7306c526737ec6f40ad085df5d86a15dc16b10381ae1dd8106b0","artifact:5387:3d8707b7e77efe93d5beb960d3cffcca264cc3440f3555f7f21632f49f64fa48":"3d8707b7e77efe93d5beb960d3cffcca264cc3440f3555f7f21632f49f64fa48","artifact:5387:407a770ee82eb4a0bfd0b00a7626f93b141bca9bf296c7f9219d4d949a5b06bc":"407a770ee82eb4a0bfd0b00a7626f93b141bca9bf296c7f9219d4d949a5b06bc","artifact:5387:5386d489a42f6926f9699af8e987ccd95417a2936a982cb00ff8f4b9a6489484":"5386d489a42f6926f9699af8e987ccd95417a2936a982cb00ff8f4b9a6489484","artifact:5387:5af9d4d9d64b8c18295bb89b7aed297dae91ea82b15897d1c06fc5b30b89e445":"5af9d4d9d64b8c18295bb89b7aed297dae91ea82b15897d1c06fc5b30b89e445","artifact:5387:6effdfa25445e04a5f5638042f6c3bd251d4c9878ac5296e65869eceb9a6fe15":"6effdfa25445e04a5f5638042f6c3bd251d4c9878ac5296e65869eceb9a6fe15","artifact:5387:7118db11e4f954be0d3280745a57b9d1985bfcd55031cb5fddafb72ef1728326":"7118db11e4f954be0d3280745a57b9d1985bfcd55031cb5fddafb72ef1728326","artifact:5387:799ab99505baa5d17728e08d77004cc63415ea4246d4270145ea55a3487ebddc":"799ab99505baa5d17728e08d77004cc63415ea4246d4270145ea55a3487ebddc","artifact:5387:7fdb8abc1109fab2c7ff5b1ed27fd171d36eb7758b3883816657c89e57f64007":"7fdb8abc1109fab2c7ff5b1ed27fd171d36eb7758b3883816657c89e57f64007","artifact:5387:8208eecaf5d6e4dcd55719cf6487a03d77121c3818aaf93a926bc7f40e392c22":"8208eecaf5d6e4dcd55719cf6487a03d77121c3818aaf93a926bc7f40e392c22","artifact:5387:8feaa64c391eb06dadec0522de4d48acc98f6a3923d483ea0133324bdb6d7f8d":"8feaa64c391eb06dadec0522de4d48acc98f6a3923d483ea0133324bdb6d7f8d","artifact:5387:9e22797d9bf02633847c7cd4f3a0274837ff4c231b3d82c44b2017ddeb8e4875":"9e22797d9bf02633847c7cd4f3a0274837ff4c231b3d82c44b2017ddeb8e4875","artifact:5387:a57f51303086bbe8db5041df3072337fde0c9a3d9e8e3ad364b3594d7adff51a":"a57f51303086bbe8db5041df3072337fde0c9a3d9e8e3ad364b3594d7adff51a","artifact:5387:a7fb9a4ffb75cb53f77a18405b06d3cee7f76c301b8e0d87cd06fdc103eb797d":"a7fb9a4ffb75cb53f77a18405b06d3cee7f76c301b8e0d87cd06fdc103eb797d","artifact:5387:ac963a74ddae6031aa29d315ea4c5592c84fbcc639caf6aa5895c3bca1b7ec6c":"ac963a74ddae6031aa29d315ea4c5592c84fbcc639caf6aa5895c3bca1b7ec6c","artifact:5387:b2b54c254843d7197503d8fadd10586be8e33d4a3b17793741a6404ebb1ec66d":"b2b54c254843d7197503d8fadd10586be8e33d4a3b17793741a6404ebb1ec66d","artifact:5387:b831b152ef3426a8223236866be8246674a5e462a5c711fbb776c52a405b0ff6":"b831b152ef3426a8223236866be8246674a5e462a5c711fbb776c52a405b0ff6","artifact:5387:bacf80b4cf71e886be57ebeea634a20978f567121f7f145a4dbdeb90f545ea40":"bacf80b4cf71e886be57ebeea634a20978f567121f7f145a4dbdeb90f545ea40","artifact:5387:c2f944372f0b40034094b0b366310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applicability screening of accepted scientific return #5387: 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: 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f8939cc9da222014b3e595dbfb4d64b47551f74\"},\"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:5387,input_sha256:\"6b0870776303ac496865434f859dd11608fb57831bd29a503e469385608a489b\",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/5394/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"d330e83b3cdd076eeee872cef333278f9100f9b8fcd52d50daf79f304b024f53","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}