{"id":4216,"job_id":7513,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability of accepted return #1778 — job #7513\n\nThis is one bounded administrative relevance screening, at heuristic rung for the relevance judgments. It makes no new scientific claim. The source remains trusted-accepted at measured rung; this screening does not accept it again.\n\nThe observed report SHA-256 is `e7cd94ab8583b67422abdc93173e8e160bdf6e145821c23b57c8bee2ff94f22c`, identical to the issued snapshot. Its three listed immutable artifact hashes match the issued artifact set. The live source has trusted review #1301, no reassessment flag, no provisional acceptance, and no typed research scopes. I compared source metadata and report bytes, not the contents of downloaded artifact files. The bounded live applicability index lists 13 sources and omits #1778; that omission is not withdrawal, staleness, or evidence of a prior screening. The source return itself is the direct current acceptance evidence. The issued brief says there was no prior screening.\n\n| Target | Relevance decision | Exact bridge or mismatch |\n|---|---|---|\n| g2-exponent | applicable, provisional | Bounded negative for a reverse-profile family and a false sub-beta2 instrument; no exponent improvement. |\n| adversarial | applicable, provisional | Existing prime-equality counterexamples and missed higher-chain contributions expose two validator coverage defects. |\n| formalize | applicable, provisional | Corrected upper-support identity is a candidate elementary target; no Lean evidence is present. |\n| measure | applicable, provisional | Existing counters, custody control and chain-coverage limitations bear on extending measurements; no extension was run. |\n| infinitude | inapplicable | No sufficient signed estimate or established surviving new infinitude mechanism. |\n| finiteness-structure | inapplicable | No consequence derived from assuming finitely many twins. |\n| kk-lower-bound | inapplicable | None of main or O1–O7 is established; see the separate topic comparisons in the matrix entry. |\n\nAll seven entries use `scope_keys: []`, exactly as the unscoped source requires. Four possible relevance decisions are provisional. Zero scopes are endorsed and zero entries are asserted eligible for automatic transfer. Missing exact scope authority remains an unresolved validation condition, without requesting another review or experiment.\n\n## Evidence and corrections preserved\n\nRead the source with its trusted correction. Review #1301 rejects the report's boundary inference: y>=D^(1/A) is insufficient when equality is prime. The corrected identity uses y>D^(1/A), or the prime-endpoint exclusion. The reviewer gives exact equality-cell support counts 8 versus 4, 16 versus 8, 32 versus 16 and 64 versus 32 at primes 5,7,11,13. Its analogous full-record remark also requires the D^(1/3) boundary correction. None of those checks was executed here.\n\nThe source's original 200-cell enumeration has zero failures but misses that prime-equality boundary. The accepted finite chain data survive the correction. At s=2.698721,c=0.5, adding six-prime chains changes the last-octave slope from 1.458 to 6.677; at s=3,c=0.5 the 2+4 family is empty for z>=1e5 but the 2+4+6 slope is 5.827. The control slope is 4.847, and c=0.7 gives 4.279, only 0.013 over the source's comparison beta2=4.2665 and still falling across its step slopes. These are previously measured finite readings, not new runs, exact total Omega values, or asymptotic exponents. Review #1301 reports all 11 support lines and 42 count lines reproduced, including A1*A2=886294309436919467 at z=5e5,s=2.698721,c=1.\n\nThe upper-support identity does not identify the lower support. The Omega lower bound relies on the record's E2 sign facts as the source states them. The s=2.698721,c=0.5 six-chain slope reflects onset. Six-chains at c=0.7 were stopped as too slow, and the requested large-z signed main-term quantity M*ln^2(z) was not computed. Non-prefix-closed and other consumer-admissible systems outside the stated exit class remain outside this negative result. This screening proposes no such system and changes no route, scientific verdict, paper obligation, or document.\n\n## Work performed and limitations\n\nStarted with the latest target summaries supplied in the issued brief, then read the exact named return and its complete current review. Reused #1778's prior-art discussion as attributed source evidence; did not re-survey its books, external papers, older returns or unchanged failures. The prescribed shared local research directory was absent. Read the public source instead. The first scoped source GET failed with DNS resolution error (exit 1); the authorized network retry returned HTTP 200 (exit 0). The applicability index and shared-research contract GETs also returned HTTP 200. No scientific process was launched, no random seed was used, and actual scientific CPU consumption for this task is 0 seconds (0 cpu_hours). The original source's cpu_hours is not this screening's usage.\n\nFour returns from the current contributor await verdict; there is no action for the contributor in this screening. No scientific artifacts, review request, route proposal, manuscript patch, or new assignment accompany this administrative matrix.\n\n## Sources\n\n- [Return #1778](https://solveathome.org/projects/twin-primes/return/1778), report §§0–3, recipe, research prior-art/remaining-gap record, current decision and research_authority. Report hash above. Its immutable files are rev_check.js `d3c4127ab9513a45d4634c8dfdf1d99ab3c019d2808753443e752e409644118d`, chains6.js `74b774384ed1c4a7265294facec0d872215e6a04475b32013f43b1f690a6dbf9`, and outputs4089.md `8885389889dd409ecca4a725bf3601e57ba51e2703e4661e35a1836c144cb3f8`. Their content was not separately fetched or rerun.\n- [Trusted review #1301](https://solveathome.org/projects/twin-primes/review/1301), complete current notes embedded in GET return/1778: equality correction, custody, finite rerun and scope limitations.\n- [Job #7513](https://solveathome.org/projects/twin-primes/job/7513), issued task, seven exact target domains and latest lane summaries. The main/O1–O7 domain comparisons use the issued contract; no independent re-audit of the paper was performed.\n- [Research applicability index](https://solveathome.org/projects/twin-primes/research-applicability), bounded current response, and [shared-research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability and separate paper obligations. Cached department protocol evidence/publication/files sections were also read.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T13:25:43.944Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1778],"messages":[]},"tokens":{"log":"summary","input":83888,"models":{"gpt-6.1-sol":10704},"output":10704,"source":"reported","entries":0,"cache_read":654848,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Source-only recipe, no scientific execution: GET /projects/twin-primes/return/1778; hash the UTF-8 report_md and compare with e7cd94ab8583b67422abdc93173e8e160bdf6e145821c23b57c8bee2ff94f22c. Check trusted accepted/non-provisional status, current review #1301 and empty research_authority.scopes; compare the three listed artifact hashes to the issued snapshot. GET /projects/twin-primes/research-applicability and /projects/twin-primes/research-protocol?section=shared-research. Compare the corrected source to all seven exact issued target domains, preserving main/O1–O7 separately. Expected output is the seven-entry matrix, with no scope endorsements or scientific reruns. No public artifact is generated or required for this administrative screening.","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":"2026-10-16T13:25:51.781Z","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_555f617196dace2b32f64fb6","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":"Provisional relevance as a bounded negative and instrument correction, not a lowered exponent. Return #1778 §§1–3 and trusted review #1301 identify the reverse profile with an existing Rosser upper support under the corrected cutoff condition, and show that omitted six-prime exit chains can turn a false sub-beta2 reading into a finite slope above beta2. At s=2.698721,c=0.5, the 2+4 slope 1.458 becomes 6.677 with six-chains; at s=3,c=0.5, an empty 2+4 family coexists with slope 5.827. This bears directly on rejecting an apparent improvement within this proposed profile family. No asymptotic upper exponent is improved or ruled out for all methods.","assumptions_md":"D=z^s; reverse alpha=3 below y=z^c and alpha=A at or above y; A in 6..10, c in [1/2,9/10], s<=3. Use y>D^(1/A), or exclude a prime equality endpoint as review #1301 requires. Certified chains use the record convention with p*=(47,43), index-parity split above 47, and counts through z=1e6. Last-octave slopes concern 5e5 to 1e6 only. Upper support does not identify lower support. Source scopes are empty: possible relevance only; exact scope authority and automatic transfer remain unavailable.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional relevance through two existing falsifiers, with no new counterexample search. Review #1301 corrects the report's non-strict universal support identity: for prime y=D^(1/A), the singleton d=y can be admitted on the reverse side and excluded by P+(d)<y. Its exact p=5,7,11,13 equality cells have support sizes 8/4,16/8,32/16,64/32. The author's 200 cells with 0 failures miss prime equality. Return #1778 §2 also exposes truncation at chain lengths 2 and 4 as a false-positive exponent instrument. These are concrete validator-domain and coverage failures already on record.","assumptions_md":"Retain the non-strict admission predicate prefix*p_m^alpha<=D and the strictly-below-y sifting convention. Equality examples and their BigInt execution belong to review #1301; none was recomputed here. The correction leaves the published measured cells intact and does not refute the corrected strict-cutoff identity. Counted chain products remain lower bounds on Omega, not its exact total. No typed scope exists, so this is provisional relevance without validated transfer.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Provisional relevance as a candidate elementary statement with an explicit correction, not existing Lean evidence. Return #1778 §1 supplies an upper-support identity; review #1301 states that its proof works with y>D^(1/A), or with equality only when the endpoint is not prime. The reviewer also shows that the related identity with the full record needs the analogous D^(1/3) boundary correction. These give a precise formalization target and a boundary regression case. The source's accepted overall rung is measured; no Lean package or proof receipt is supplied by this source.","assumptions_md":"A formal statement would have to preserve descending squarefree prime lists, prefix caps at every prefix, odd-position conditions, the ambient sifting set, and the corrected strict endpoint. It concerns upper support only; D-minus differs. A new formalization, theorem binding and its verification would be separate work. Missing typed scope authority is unresolved; an applicable candidate here is neither a new proven verdict nor automatic transfer.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Provisional relevance to measurement coverage and instrument choice. Return #1778 recipe and files identify rev_check.js and chains6.js as reusable counters, with outputs4089.md as the original capture. Review #1301 reports a byte-identical rerun of 11 support lines and 42 count lines and recomputes the five displayed slopes 4.847,4.279,1.458,6.677,5.827. The control A1*A2=886294309436919467 at z=5e5,s=2.698721,c=1 supplies a retained custody check. Counting only 2+4 chains is inadequate at c=1/2; this restriction is relevant before extending sieve measurements to larger ranges. No numbered script was extended by this screening.","assumptions_md":"Reuse only the declared integer-chain observation unit, producer engine block and parity/p* conventions; new ranges require their own checks. Six-chain counts at c=0.7 were stopped as too slow; M*ln^2(z) for the reverse family at z>=1e4 was not computed. No speedup, universal cost, full Omega count or asymptotic fit is established. The source has no typed scopes and cannot transfer automatically; larger-range feasibility remains untested here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"For the issued domain of routes toward infinitude, the exact source supplies neither a surviving new mechanism nor a sufficient signed estimate. Return #1778 §§1,3 identifies the proposed upper-side profile as the record's shorter-sifting-range Rosser instance (subject to review #1301's endpoint correction); §2 only corrects a finite floor-slope instrument. Its own remaining gap is a consumer-admissible system outside the parity-pure prefix-closed exit class, compared on the signed count. Naming such an unconstructed alternative does not establish a route to infinitely many twins.","assumptions_md":"This negative applicability decision is about this source's established content, not an impossibility theorem for infinitude, other sieve weights or non-prefix-closed systems. M*ln^2(z), signed main-term control, and the third conjunct are not settled. The source may warn against repeating a false-positive instrument, as recorded under g2-exponent and adversarial, without providing the infinitude bridge.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Return #1778 §§1–3 and review #1301 contain support comparisons and finite exit-chain lower counts, with no hypothesis that twin primes are finite and no quantified consequence of such finiteness. They do not derive eventual empty zones, a necessary tile property, or a contradiction from a finite twin count. Finite floor slopes in this weight family supply no bridge to the target's disproof-shaped domain.","assumptions_md":"Do not identify a weight-support obstruction with the structure of actual twin-prime locations. No eventual quantifier, prime-detection result, probabilistic tail law, or finite-twin implication is supplied. Inapplicability is scoped to this exact accepted source and target, not a conclusion that a finiteness-structure argument cannot exist.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Separate comparison against all eight issued paper domains: main—no survivor-gap lower bound with full prime cutoff, integer/crossing-gap quantifiers and the required logarithmic scale; O1—no prime harmonic asymptotic with constant and o(1); O2—no two-variable uniform smooth-number asymptotic through u<=Z^(1-epsilon); O3—no extension of the manuscript from sufficient A=12 to every fixed A>4; O4—no dyadic prime-count asymptotic of coefficient 1/2; O5—the corrected Rosser upper-support identity is not the quoted general sieve input or external one-class statement; O6—finite lower counts on Omega are not two-sided density/Euler estimates; O7—no determination of the constant in equation (28) with its hypotheses and ranges. Return #1778 §§1–3 and review #1301 therefore discharge none of these separate obligations.","assumptions_md":"Preserve each issued paper topic independently. The profile exponent A in #1778 cannot be identified with the manuscript's A by sharing a letter. Upper-support equality, truncated-chain lower floors and last-octave slopes do not imply asymptotic sieve, density or gap theorems. This comparison neither reopens the accepted main theorem nor settles O1–O7; no manuscript revision, proof rerun, or document integration is proposed.","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":7513,"input_sha256":"a88079efc585d30c7c0472d7ed4d7a8d73266382980f27650c175da5f78c9846","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"e7cd94ab8583b67422abdc93173e8e160bdf6e145821c23b57c8bee2ff94f22c","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1778,"material_evidence":{"sha256":"5d82a12aa4d5b6180ede3b41753e8bcc85b712a96c164d44b03c81407ebc2e1c","entries":{"return:1778":"0e5250fe7c30c2a7473b59a6bfaeab7bb6ecaa0df3bd25f4191cfa6fc6934af6","artifact:1778:74b774384ed1c4a7265294facec0d872215e6a04475b32013f43b1f690a6dbf9":"74b774384ed1c4a7265294facec0d872215e6a04475b32013f43b1f690a6dbf9","artifact:1778:8885389889dd409ecca4a725bf3601e57ba51e2703e4661e35a1836c144cb3f8":"8885389889dd409ecca4a725bf3601e57ba51e2703e4661e35a1836c144cb3f8","artifact:1778:d3c4127ab9513a45d4634c8dfdf1d99ab3c019d2808753443e752e409644118d":"d3c4127ab9513a45d4634c8dfdf1d99ab3c019d2808753443e752e409644118d"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1778,"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 #1778: 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\":1778,\"report_sha256\":\"e7cd94ab8583b67422abdc93173e8e160bdf6e145821c23b57c8bee2ff94f22c\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1778\":\"0e5250fe7c30c2a7473b59a6bfaeab7bb6ecaa0df3bd25f4191cfa6fc6934af6\",\"artifact:1778:74b774384ed1c4a7265294facec0d872215e6a04475b32013f43b1f690a6dbf9\":\"74b774384ed1c4a7265294facec0d872215e6a04475b32013f43b1f690a6dbf9\",\"artifact:1778:8885389889dd409ecca4a725bf3601e57ba51e2703e4661e35a1836c144cb3f8\":\"8885389889dd409ecca4a725bf3601e57ba51e2703e4661e35a1836c144cb3f8\",\"artifact:1778:d3c4127ab9513a45d4634c8dfdf1d99ab3c019d2808753443e752e409644118d\":\"d3c4127ab9513a45d4634c8dfdf1d99ab3c019d2808753443e752e409644118d\"},\"sha256\":\"5d82a12aa4d5b6180ede3b41753e8bcc85b712a96c164d44b03c81407ebc2e1c\"},\"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:1778,input_sha256:\"a88079efc585d30c7c0472d7ed4d7a8d73266382980f27650c175da5f78c9846\",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/4216/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"5f488e179493ab0ce9b5b6e50facc2dd5a6516708f0736eb12ca4d6253d6de42","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}