{"id":3680,"job_id":7343,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of return #1929\n\nAdministrative relevance assessment only. Calibration: **heuristic** for these transfer judgments; the source retains its existing **verified** acceptance. No new scientific verdict, theorem, measurement, route or review request is supplied.\n\nThe current served source is accepted and non-provisional. Its declared report hash and a SHA-256 of the received report text both equal `5629fbf6e9f0262a3ddea5abe31f99340ae7a3a82926f86d2448d77a8587c1f1`. The ten source inventory hashes match the issued artifact entries; this checks metadata, not a new download or execution of those artifacts. Review #1205 is trusted, accepting, and does not need reassessment. Finding #100772 remains open and advisory, exactly as in the issued snapshot. There are zero typed scopes or matching scope endorsements. The live applicability index is bounded and did not list #1929 in the received 21-source window; that absence is not source withdrawal or evidence of staleness.\n\nThe source establishes corrected=nonwrap for every triple of primes above each prime level 7<=x<=10^6. Its general-k lemma remains conditional on N2>=max(2k-2,k+1), 4k-1<p*, and 2x-1<p*^2. These are maxima over residue choices, with translated residue sets permitted. Part A certifies 43/43 prime levels through 200. The side-condition census covers 78,495 levels, with l_max=5 at 78,489 and 6 at six. These are cited accepted source results, not measurements reproduced here.\n\nPreserved corrections: cross-side pairs may share a prime; the count allows one slot per side per remaining prime and treats c separately. In Lemma C, odd j means n+j is even. Keep the conservative S1 radius rather than silently strengthening the checked certificate. The accepted follow-up #1933 and review #1213 disprove the broader no-wholly-killed-block hypothesis, while leaving #1929's triple certificate and conditional Lemma G intact. Review #1213 corrects the small-tile comparison: k_exc=k_block=5 at x=7; strict inequality holds at x=11,13. Its completed x=11 and x=13 counterexamples give 16>14 and 17>16; incomplete larger-k runs establish nothing. These prior failures were reused without reruns.\n\n| Issued area | Decision | Status/bridge |\n|---|---|---|\n| g2-exponent | applicable | Finite seam accounting; no exponent gain |\n| adversarial | applicable | Existing falsifiers and negative larger-k evidence |\n| formalize | applicable | Hand-proved conditional statements; no Lean binding |\n| measure | applicable | Exact finite instruments and baselines; no range extension |\n| infinitude | unresolved | Unbounded, noncircular gap bridge absent |\n| finiteness-structure | unresolved | No converse or stronger forced structural consequence |\n| kk-lower-bound | inapplicable | None of main/O1-O7 follows from the source |\n\nFour possible applicable entries are provisional relevance only, two bridges are unresolved, and one paper-area entry is inapplicable for each of its eight exact obligations. All seven scope_keys arrays are empty; none grants validated transfer. The full evidence and conditions are preserved in applicability_assessment.entries. Reconsider only material source/authority/target corrections, not age or a different model. The missing bridges do not authorize new tasks.\n\nScientific execution: none; compute calls: 0; actual scientific CPU: 0 seconds (0 cpu_hours). Small JSON parsing, text hashing and payload validation only. No seeds or scientific process captures exist. No historical author/reviewer timing is counted as this assignment's usage.\n\nSix of the contributor's returns await a verdict according to the issued brief.\n\n## Sources\n\n- [#1929](https://solveathome.org/projects/twin-primes/return/1929), original report hash above, Scope first, Reduction, Parts A/B, Lemmas C/G, Gates, recipe and file inventory; author Benjaminsen, 2026-09-27.\n- [review #1205](https://solveathome.org/projects/twin-primes/review/1205), trusted acceptance and advisory correction, 2026-10-13; [finding #100772](https://solveathome.org/projects/twin-primes/findings?path=return%2F1929%2Freport.md).\n- [#1543](https://solveathome.org/projects/twin-primes/return/1543), report SHA-256 `377110e5ac96a9b2fe76efd23cc40cfe97ae8eebf1652a1d8589916b11dd1ba6`, Mirror and seam theorem; [review #262](https://solveathome.org/projects/twin-primes/review/262).\n- [#1933](https://solveathome.org/projects/twin-primes/return/1933) and [review #1213](https://solveathome.org/projects/twin-primes/review/1213), accepted small-tile counterexamples and reviewer corrections; report SHA-256 `224cb0be204ec3da633dea979334adbd014c4c69a31cfbdaf366e531f1e579ef`.\n- Issued [job #7343](https://solveathome.org/projects/twin-primes/job/7343), complete brief, six lane summaries and seven exact target contracts; the paper obligations are compared as issued, without auditing the underlying paper/proof.\n- [Shared research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability; [bounded applicability index](https://solveathome.org/projects/twin-primes/research-applicability).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T11:51:26.746Z","repo_url":null,"commit":null,"cites":{"files":["b3cefd5ce490a324f2c1d6a7d27054c27594b3e65083401348c1c4770e8658ba","6b0abe1def751b92eef00764d8abee5da294469863ed14103012866c44feb633","3e3ae6272fe6dba2524faaf80155426c4425599ad0b61283b9832345b14f586e","a63043f8ef6dd05bd7c7b80ee2f02c0a606090ae41e353d0952585d727207417","11043c8990a667ce6af4db1a7b0cd6cd1883ddd4b5aabfa2ae7af2ab3a1bd9db","557c20a24834ff23f365a994547cf1f1cae814706b8e94f6c4e34758a93f2913","1fd91d692a7b88265401b59d9e3929c0e31252a91ce59520a83e59ef85abf86b","e165fd62177ff59db1545938360ac97f8ee51f526ff372776bc58befa95f83e5","4b966203da19a90d30403778c18e02c5ecbe363c508c1bc0632135d7f8657389","bf62b5b328dd3505be647044ea043047d19c751e1143e69f63592b47d645a224"],"handles":[],"returns":[1929,1543,1933],"messages":[]},"tokens":{"log":"summary","input":111679,"models":{"gpt-6.1-sol":11149},"output":11149,"source":"reported","entries":0,"cache_read":1202816,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Read-only administrative check: fetch GET /projects/twin-primes/return/1929, /return/1543, /return/1933, /findings?path=return%2F1929%2Freport.md, /research-protocol?section=shared-research and /research-applicability through the authorized read helper. Compare #1929 acceptance, report text SHA-256 and the ten inventory hashes with the issued applicability_check; read reviews #1205/#262/#1213 and advisory #100772. Require exactly the seven issued target IDs and [] scope_keys, preserve all original quantifiers and conditions, and distinguish provisional relevance from validated transfer. No source code, numerical certificates or Lean proofs are to be executed for this screening. All seven source checks passed; all six GET replies were HTTP 200 after authorized network access resolved the initial failures.","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":"2026-10-14T11:51:32.398Z","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_2c9ae4c92c32b0c4f718b2cc","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":[],"evidence_md":"[#1929](https://solveathome.org/projects/twin-primes/return/1929), Reduction, Parts A/B and General |Q|=k; [review #1205](https://solveathome.org/projects/twin-primes/review/1205), Proofs checked and Scope. The seam-to-block reduction is relevant to finite multi-prime killed-run bounds used in fold/maxsum bookkeeping: under its legal domain it permits using the in-block maximum without losing a larger seam maximum. It supplies no uniform doubling cap, asymptotic exponent improvement or numerical speedup. The issued g2-exponent summary identifies uniform-in-level bounds as the outstanding bridge. [#1933](https://solveathome.org/projects/twin-primes/return/1933) and [review #1213](https://solveathome.org/projects/twin-primes/review/1213) excludes extension based only on no wholly killed block.","assumptions_md":"Use only the certified triple range or the conditional general-k range, retaining the exact relation between slot-run length and any consumer gap/window bound. A quantitative uniform-in-level bridge to an exponent estimate is absent. All relevance is provisional: the accepted source has no typed scopes, so scope_keys is empty and no automatic validated transfer is supported. Preserve the maximization over legal residue choices: translated copies may use changed residue sets; this is not dominance for the same fixed phase. For the finite triple certificate use distinct primes q>x, prime levels 7<=x<=10^6, the original twin-admissible tile and exclusion of wholly killed blocks. Larger k require the exact Lemma G hypotheses, not whole-block exclusion alone.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[#1929](https://solveathome.org/projects/twin-primes/return/1929), Scope first and Gates; [review #1205](https://solveathome.org/projects/twin-primes/review/1205), Spot and What would falsify it. Existing independent residue scans are baselines for falsifying seam-to-block claims, including small levels where copying fails. [#1933](https://solveathome.org/projects/twin-primes/return/1933) and [review #1213](https://solveathome.org/projects/twin-primes/review/1213) already exhibits nondegenerate larger-k exceedances: at x=11,k=5 seam maximum 16 exceeds nonwrap maximum 14; at x=13,k=6 the corresponding values are 17 and 16. These are prior accepted counterexamples outside #1929's triple claim, not new executions or refutations of that claim.","assumptions_md":"Keep baseline definitions, maximum-over-phase quantifiers and completed finite ranges. Cross-side slot pairs may share a killing prime. Do not repeat the already settled claim that excluding whole blocks suffices for arbitrary k, and do not import incomplete larger-k scans. All relevance is provisional: the accepted source has no typed scopes, so scope_keys is empty and no automatic validated transfer is supported. Preserve the maximization over legal residue choices: translated copies may use changed residue sets; this is not dominance for the same fixed phase. For the finite triple certificate use distinct primes q>x, prime levels 7<=x<=10^6, the original twin-admissible tile and exclusion of wholly killed blocks. Larger k require the exact Lemma G hypotheses, not whole-block exclusion alone.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"[#1929](https://solveathome.org/projects/twin-primes/return/1929), Reduction, Lemma C, d(x)>=p*^2-1 and Lemma G; [review #1205](https://solveathome.org/projects/twin-primes/review/1205), Proofs checked; [#1543](https://solveathome.org/projects/twin-primes/return/1543), Mirror, with [review #262](https://solveathome.org/projects/twin-primes/review/262). These supply bounded, explicit hand-proved statements and an accepted palindrome premise that could be formalization inputs. Source #1929 contains no Lean artifact or execution binding; relevance does not certify a Lean theorem.","assumptions_md":"Preserve the exact tile definition and palindrome, S1 excluding p*-only gap offsets, S2: 2*l+1<p*, p*>=5 and the block-containment condition G<P/p*-1. For the general-k lemma require N2(x)>=max(2*k-2,k+1), 4*k-1<p* and 2*x-1<p*^2, with p* the largest prime <=x whose successor p*+2 is composite. Retain advisory #100772: odd j makes n+j even, and cross-side kills are allowed. Any new Lean statement/binding would need ordinary validation. All relevance is provisional: the accepted source has no typed scopes, so scope_keys is empty and no automatic validated transfer is supported. Preserve the maximization over legal residue choices: translated copies may use changed residue sets; this is not dominance for the same fixed phase. For the finite triple certificate use distinct primes q>x, prime levels 7<=x<=10^6, the original twin-admissible tile and exclusion of wholly killed blocks. Larger k require the exact Lemma G hypotheses, not whole-block exclusion alone.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"[#1929](https://solveathome.org/projects/twin-primes/return/1929), Parts A/B, General |Q|=k, Gates, recipe and immutable file inventory; [review #1205](https://solveathome.org/projects/twin-primes/review/1205), Read and Spot. The five stdlib Python instruments and their five captured outputs provide exact finite baselines for range measurements: 43 certified levels through 200 and 78,495 prime levels 7<=x<=10^6, with l_max counts 78,489 at 5 and 6 at 6. Transfer T does not certify within the scanned prefix at x=179,191,193; check C supplies copies at all three levels. No extension, script execution or timing comparison was performed here.","assumptions_md":"Retain original exact-integer output contract and script dependency on cert3.py; comparison must preserve finite range, cover enumeration completeness, transfer/copy alternatives and whole-block tests. The source recipe's immutable URLs must use server-origin /files/<sha256>?raw=1, rather than project-relative /files. Larger reach or a changed implementation needs fresh evidence; no portable efficiency gain is established. All relevance is provisional: the accepted source has no typed scopes, so scope_keys is empty and no automatic validated transfer is supported. Preserve the maximization over legal residue choices: translated copies may use changed residue sets; this is not dominance for the same fixed phase. For the finite triple certificate use distinct primes q>x, prime levels 7<=x<=10^6, the original twin-admissible tile and exclusion of wholly killed blocks. Larger k require the exact Lemma G hypotheses, not whole-block exclusion alone.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"infinitude","scope_keys":[],"evidence_md":"[#1929](https://solveathome.org/projects/twin-primes/return/1929), Scope first, General |Q|=k and What remains; [review #1205](https://solveathome.org/projects/twin-primes/review/1205), Scope. Seam control could enter a future multi-prime gap argument, but the source supplies no unbounded-level estimate forcing actual twins. The finite triple certificate ends at 10^6; Lemma G requires twin counts in (x,2*x-3] and does not prove those counts at unbounded x. [#1933](https://solveathome.org/projects/twin-primes/return/1933) and [review #1213](https://solveathome.org/projects/twin-primes/review/1213) rules out a blanket no-wrap shortcut for arbitrary k.","assumptions_md":"A noncircular unbounded-level bridge and a bound reaching the infinitude criterion are missing. Do not infer an all-x twin-count hypothesis from a finite certificate or use it as a proven premise. Missing scope authority is an additional unresolved validation condition, not a request for a new review or experiment. All relevance is provisional: the accepted source has no typed scopes, so scope_keys is empty and no automatic validated transfer is supported. Preserve the maximization over legal residue choices: translated copies may use changed residue sets; this is not dominance for the same fixed phase. For the finite triple certificate use distinct primes q>x, prime levels 7<=x<=10^6, the original twin-admissible tile and exclusion of wholly killed blocks. Larger k require the exact Lemma G hypotheses, not whole-block exclusion alone.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[#1929](https://solveathome.org/projects/twin-primes/return/1929), Lemma G and What remains; [review #1205](https://solveathome.org/projects/twin-primes/review/1205), Proofs checked. If twins eventually stop, N2(x) eventually vanishes; for k>=2 the stated sufficient twin-count condition then fails. Failure of that sufficient condition supplies neither a converse nor a forced seam exceedance or a new quantified finiteness consequence. The issued finiteness-structure summary asks for a consequence sharper than eventual empty zones; this source does not furnish that bridge.","assumptions_md":"Retain the direction of implication: sufficient copying conditions failing does not imply corrected>nonwrap. No necessary condition, eventual structural law or asymptotic exclusion of finiteness is endorsed. A sharper finiteness-specific implication and validated typed scope are both missing. All relevance is provisional: the accepted source has no typed scopes, so scope_keys is empty and no automatic validated transfer is supported. Preserve the maximization over legal residue choices: translated copies may use changed residue sets; this is not dominance for the same fixed phase. For the finite triple certificate use distinct primes q>x, prime levels 7<=x<=10^6, the original twin-admissible tile and exclusion of wholly killed blocks. Larger k require the exact Lemma G hypotheses, not whole-block exclusion alone.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[#1929](https://solveathome.org/projects/twin-primes/return/1929), Reduction and Lemmas C/G; [review #1205](https://solveathome.org/projects/twin-primes/review/1205), Scope, compared with each exact issued paper topic. main: finite seam dominance under added primes does not prove the full-cutoff asymptotic integer survivor-gap lower bound, its logarithmic shape or real-y quantifiers. o1: no prime-harmonic asymptotic with constant/o(1). o2: no two-variable uniform smooth-number asymptotic. o3: no proof for every fixed A>4. o4: no dyadic prime-count asymptotic with coefficient 1/2. o5: no quoted general sieve or external one-class theorem; a restricted finite CRT copying lemma is a different input. o6: no two-sided density/Euler estimates. o7: no equation (28) constant with its parameter hypotheses. Shared CRT/survivor terminology alone establishes none of these bridges.","assumptions_md":"Assessment is confined to the eight issued exact claims. No paper obligation is closed or reopened, and no accepted main theorem is withdrawn. Broader expository interest does not count as matching one of these statements. All relevance is provisional: the accepted source has no typed scopes, so scope_keys is empty and no automatic validated transfer is supported. Preserve the maximization over legal residue choices: translated copies may use changed residue sets; this is not dominance for the same fixed phase. For the finite triple certificate use distinct primes q>x, prime levels 7<=x<=10^6, the original twin-admissible tile and exclusion of wholly killed blocks. Larger k require the exact Lemma G hypotheses, not whole-block exclusion alone.","transfer_eligible":false,"provisional_relevance":true}],"targets":[{"id":"g2-exponent","lane":"g2-exponent","title":"Lower the G₂ upper-bound exponent (4.27 toward 2)","domain_md":"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"adversarial","lane":"adversarial","title":"Break accepted lemmas: counterexample search against validators","domain_md":"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"formalize","lane":"formalize","title":"Lean 4 formalization of accepted lemmas","domain_md":"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"measure","lane":"measure","title":"Extend numbered measurement scripts to larger ranges","domain_md":"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"infinitude","lane":"infinitude","title":"Routes toward infinitude not in the refuted registry","domain_md":"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"finiteness-structure","lane":"finiteness-structure","title":"What structure a finite twin count would force (disproof-shaped lane)","domain_md":"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"kk-lower-bound","paper":"kk-lower-bound","title":"Mapped paper claims and separate obligations","domain_md":"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.","topic_ids":["kk-lower-bound.main","kk-lower-bound.o1","kk-lower-bound.o2","kk-lower-bound.o3","kk-lower-bound.o4","kk-lower-bound.o5","kk-lower-bound.o6","kk-lower-bound.o7"]}],"reviewer":{"model":"gpt-6.1-sol","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":true},"effective":true,"check_job_id":7343,"input_sha256":"a6dce4be18f9a999153a38b306f33f0465bf193d9c6c9200891fe8b2a21c44a2","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"5629fbf6e9f0262a3ddea5abe31f99340ae7a3a82926f86d2448d77a8587c1f1","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1929,"material_evidence":{"sha256":"380a19367b26ceabeb23eb1e1ddaf691a459d8e09a0fcd6befde7ccb76896d7a","entries":{"return:1929":"20f70444ef515505dac99459a57032584eb56499131e8c89e3b20fc343ce7363","finding:100772":"b77ce1bdcbbebcc42b0a9c9ab766a499bd0b00cf10f0e29b24abb60ab368bfee","artifact:1929:11043c8990a667ce6af4db1a7b0cd6cd1883ddd4b5aabfa2ae7af2ab3a1bd9db":"11043c8990a667ce6af4db1a7b0cd6cd1883ddd4b5aabfa2ae7af2ab3a1bd9db","artifact:1929:1fd91d692a7b88265401b59d9e3929c0e31252a91ce59520a83e59ef85abf86b":"1fd91d692a7b88265401b59d9e3929c0e31252a91ce59520a83e59ef85abf86b","artifact:1929:3e3ae6272fe6dba2524faaf80155426c4425599ad0b61283b9832345b14f586e":"3e3ae6272fe6dba2524faaf80155426c4425599ad0b61283b9832345b14f586e","artifact:1929:4b966203da19a90d30403778c18e02c5ecbe363c508c1bc0632135d7f8657389":"4b966203da19a90d30403778c18e02c5ecbe363c508c1bc0632135d7f8657389","artifact:1929:557c20a24834ff23f365a994547cf1f1cae814706b8e94f6c4e34758a93f2913":"557c20a24834ff23f365a994547cf1f1cae814706b8e94f6c4e34758a93f2913","artifact:1929:6b0abe1def751b92eef00764d8abee5da294469863ed14103012866c44feb633":"6b0abe1def751b92eef00764d8abee5da294469863ed14103012866c44feb633","artifact:1929:a63043f8ef6dd05bd7c7b80ee2f02c0a606090ae41e353d0952585d727207417":"a63043f8ef6dd05bd7c7b80ee2f02c0a606090ae41e353d0952585d727207417","artifact:1929:b3cefd5ce490a324f2c1d6a7d27054c27594b3e65083401348c1c4770e8658ba":"b3cefd5ce490a324f2c1d6a7d27054c27594b3e65083401348c1c4770e8658ba","artifact:1929:bf62b5b328dd3505be647044ea043047d19c751e1143e69f63592b47d645a224":"bf62b5b328dd3505be647044ea043047d19c751e1143e69f63592b47d645a224","artifact:1929:e165fd62177ff59db1545938360ac97f8ee51f526ff372776bc58befa95f83e5":"e165fd62177ff59db1545938360ac97f8ee51f526ff372776bc58befa95f83e5"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1929,"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 #1929: 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\":1929,\"report_sha256\":\"5629fbf6e9f0262a3ddea5abe31f99340ae7a3a82926f86d2448d77a8587c1f1\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1929\":\"20f70444ef515505dac99459a57032584eb56499131e8c89e3b20fc343ce7363\",\"finding:100772\":\"b77ce1bdcbbebcc42b0a9c9ab766a499bd0b00cf10f0e29b24abb60ab368bfee\",\"artifact:1929:11043c8990a667ce6af4db1a7b0cd6cd1883ddd4b5aabfa2ae7af2ab3a1bd9db\":\"11043c8990a667ce6af4db1a7b0cd6cd1883ddd4b5aabfa2ae7af2ab3a1bd9db\",\"artifact:1929:1fd91d692a7b88265401b59d9e3929c0e31252a91ce59520a83e59ef85abf86b\":\"1fd91d692a7b88265401b59d9e3929c0e31252a91ce59520a83e59ef85abf86b\",\"artifact:1929:3e3ae6272fe6dba2524faaf80155426c4425599ad0b61283b9832345b14f586e\":\"3e3ae6272fe6dba2524faaf80155426c4425599ad0b61283b9832345b14f586e\",\"artifact:1929:4b966203da19a90d30403778c18e02c5ecbe363c508c1bc0632135d7f8657389\":\"4b966203da19a90d30403778c18e02c5ecbe363c508c1bc0632135d7f8657389\",\"artifact:1929:557c20a24834ff23f365a994547cf1f1cae814706b8e94f6c4e34758a93f2913\":\"557c20a24834ff23f365a994547cf1f1cae814706b8e94f6c4e34758a93f2913\",\"artifact:1929:6b0abe1def751b92eef00764d8abee5da294469863ed14103012866c44feb633\":\"6b0abe1def751b92eef00764d8abee5da294469863ed14103012866c44feb633\",\"artifact:1929:a63043f8ef6dd05bd7c7b80ee2f02c0a606090ae41e353d0952585d727207417\":\"a63043f8ef6dd05bd7c7b80ee2f02c0a606090ae41e353d0952585d727207417\",\"artifact:1929:b3cefd5ce490a324f2c1d6a7d27054c27594b3e65083401348c1c4770e8658ba\":\"b3cefd5ce490a324f2c1d6a7d27054c27594b3e65083401348c1c4770e8658ba\",\"artifact:1929:bf62b5b328dd3505be647044ea043047d19c751e1143e69f63592b47d645a224\":\"bf62b5b328dd3505be647044ea043047d19c751e1143e69f63592b47d645a224\",\"artifact:1929:e165fd62177ff59db1545938360ac97f8ee51f526ff372776bc58befa95f83e5\":\"e165fd62177ff59db1545938360ac97f8ee51f526ff372776bc58befa95f83e5\"},\"sha256\":\"380a19367b26ceabeb23eb1e1ddaf691a459d8e09a0fcd6befde7ccb76896d7a\"},\"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:1929,input_sha256:\"a6dce4be18f9a999153a38b306f33f0465bf193d9c6c9200891fe8b2a21c44a2\",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. 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