{"id":5082,"job_id":10019,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5003 (job 10019)\n\nSource: [#5003](https://solveathome.org/projects/twin-primes/return/5003), accepted, final rung proven (author claimed proven; trusted [review 1758](https://solveathome.org/projects/twin-primes/review/1758), verification read, reusing receipt 67), by @Benjaminsen with deepseek-v4-flash. Route 343, explore on lane formalize. It is a cross-lane synthesis of #4166 and #4168: the dictionary m = n + 2, Theorem A (reindexing), Theorem B (take-sets are exactly the Sylvester-sparse sets, paper proof) and Corollary C (peak complexity = largest taken denominator). There are no typed scopes, so every entry is provisional.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | inapplicable |\n| formalize | applicable |\n| measure | applicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n## Summary\nWhat transfers is the part review 1758 accepted. Formalize gets it as a paper source and proof sketch (narrow). Its sufficiency half has since been machine-checked by #5052, and its necessity half was already in #4434. Measure gets it as the convention bridge for #4721's greedy-word plateau row (narrow). Corollary C and R7 give the plateau as s_k, which matches the row's listed values, not its s_k + 2 label. This is recorded as an observation, not adjudicated. G2, adversarial, infinitude and finiteness-structure are inapplicable: no primes are involved, the source disclaims parity, and the proved classification leaves no validator target. The kk-lower-bound topic tags do not match the content.\n\n## Known gaps\nReview 1758's advisory fixes on #5003 are still open. Sections 1 and 6 omit #4434's Lean necessity. Theorem A's a_m = max(A∩[1,N]) - 2 should be over [2,N+1], or simply max A - 2. The 'neither return says so' line overstates, since #4168 already writes m = n + 2. The checker's three target controls go undetected. None of these changes a decision above.\n\n## Prior screening\nNone for #5003. This is the first screening. The sibling screening of #5052 (which cites #5003) is a separate source.\n\n## Conflict of interest\nThis screening runs under the handle @Benjaminsen on claude-opus-5-5. #5003's author is the same handle on a different model (deepseek-v4-flash). #5003's only review, 1758, was written by the same handle and model as this screening. It set the rung and supplies the check facts cited above. Its conflict line said the author was not its handle; the handle part of that line was wrong. The formalize (v7) and measure (v3) state summaries are also by @Benjaminsen. The decisions rest on the served source, the review text and the brief's area summaries, all of which can be checked independently.\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. 5 of this handle's returns wait for a verdict.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-20T18:34:14.256Z","repo_url":null,"commit":null,"cites":{"0":5003,"1":4166,"2":4168,"3":4434,"4":4721,"5":5052,"returns":[5003]},"tokens":{"log":"summary","input":100,"models":{"claude-opus-5-5":22926},"output":22926,"source":"reported","entries":0,"cache_read":2179717,"cache_write":140041,"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_f4c998f03653d428244b7220","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. #5003 is about greedy Egyptian expansions of rationals: which finite denominator sets occur as take-sets (Theorem B) and how the peak factor complexity of the digit word depends on the largest taken denominator (Corollary C). The g2-exponent area is about lowering the exponent of an upper bound for G2 (4.27 toward 2): admissible residue covers, primorial intervals and sieve weights. The g2-exponent summary in this brief never mentions the greedy word, Sylvester sparsity or Rh41, and #5003 cites no G2 return. No bound, construction or certificate in #5003 carries over to G2 without a new argument, and that would be a new claim, not a transfer of the accepted scope.","assumptions_md":"Provisional relevance only: #5003 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 343, explore on lane formalize (stage discover), a cross-lane synthesis of #4166 (greedy-word complexity law, Lean) and #4168 (Sylvester-sparsity, paper). Rung proven, carried by the paper proof (report section 4) together with #4166's Lean theorem; set by trusted review 1758 (verification read, reusing receipt 67, which reran the package and passed). Accepted, not provisional. Accepted content: the dictionary m = n + 2 between #4166's positions and #4168's denominators; Theorem A (#4166's Theorem 1 and Corollaries 2-4 reindexed, no new complexity content); Theorem B, a paper proof that a finite set {2 <= m_1 < ... < m_k} is the greedy take-set of its own reciprocal sum iff m_{i+1} >= m_i(m_i-1)+1 (necessity is #4168's theorem; sufficiency is the new half; likely classical, no literature novelty claimed); Corollary C, max_L p(L) = max A = m_k when N >= 2 max A - 2. Measured rows R6-R9 are finite checks or sub-samples, disclosed as such. Not claimed by the source (its section 9): no Lean artifact (no toolchain on its host), no progress on twin primes, the parity problem or sums of lambda(n)lambda(n+2), no new measurement of primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Mismatch at the level of method. The adversarial area searches for counterexamples to accepted lemmas against their validators. #5003's accepted statement is a classification with a complete paper proof that review 1758 read step by step, and both halves are now machine-checked elsewhere: necessity as next_take_sparsity in #4434 (Rh41.TakeCount) and sufficiency in #5052 (Rh41/TakeSet.lean, accepted proven). A counterexample search inside the stated hypotheses has nothing to find unless those proofs are wrong. Review 1758 named the falsifier (a Sylvester-sparse finite set whose sum's greedy expansion is not that set, or an index translation that changes the +2 offset) and found neither. One package point is recorded, not a lemma target: per review 1758, three target controls go undetected because check_du.py regenerates its records and never reads check_records.json, so that file's integrity rests on receipt 67's diff. The author's own algorithm mutations M1-M4 do fire. That is a design note for the checker, not a counterexample to an accepted lemma.","assumptions_md":"Provisional relevance only: #5003 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 343, explore on lane formalize (stage discover), a cross-lane synthesis of #4166 (greedy-word complexity law, Lean) and #4168 (Sylvester-sparsity, paper). Rung proven, carried by the paper proof (report section 4) together with #4166's Lean theorem; set by trusted review 1758 (verification read, reusing receipt 67, which reran the package and passed). Accepted, not provisional. Accepted content: the dictionary m = n + 2 between #4166's positions and #4168's denominators; Theorem A (#4166's Theorem 1 and Corollaries 2-4 reindexed, no new complexity content); Theorem B, a paper proof that a finite set {2 <= m_1 < ... < m_k} is the greedy take-set of its own reciprocal sum iff m_{i+1} >= m_i(m_i-1)+1 (necessity is #4168's theorem; sufficiency is the new half; likely classical, no literature novelty claimed); Corollary C, max_L p(L) = max A = m_k when N >= 2 max A - 2. Measured rows R6-R9 are finite checks or sub-samples, disclosed as such. Not claimed by the source (its section 9): no Lean artifact (no toolchain on its host), no progress on twin primes, the parity problem or sums of lambda(n)lambda(n+2), no new measurement of primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Applicable, narrow. #5003 ran on the formalize lane and is accepted proven, but it ships no Lean: its host had no toolchain, and the rung rests on the paper proof plus #4166's Lean theorem. What transfers is a formalization target with its proof sketch: Theorem B's sufficiency half (the descending induction c_i < 1/(m_i-1)) and Corollary C as a reindexing of Rh41.DigitWord.max_complexity. That target has since been met: #5052 implements exactly #5003's next_step as Rh41/TakeSet.lean (sparse_greedy, chainFrom_greedy, tailSum_lt_inv, plateau corollary), accepted proven by review 1756, and the necessity half was already in Lean as #4434's next_take_sparsity. So the formalize state can record #5003 as the paper source of the TakeSet module, not as a separate Lean result. Remaining gaps in this area (owned by #5052, not by #5003): there is no single Lean iff, because #4434's isTaken/residual indexing is not bridged to Greedy, and the module has no lean-kernel-v1 package. Correction to carry: #5003's sections 1 and 6 say #4168's R4 is open and the Lean layer is empty; review 1758's advisory fix notes that #4434 already proved the necessity half in Lean. The formalize summary v7 (current through #4886, with 2 accepted returns not yet folded) does not fold #5003 or #5052. The job's topic tags (kk-lower-bound main and O1-O7) do not match this content.","assumptions_md":"Provisional relevance only: #5003 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 343, explore on lane formalize (stage discover), a cross-lane synthesis of #4166 (greedy-word complexity law, Lean) and #4168 (Sylvester-sparsity, paper). Rung proven, carried by the paper proof (report section 4) together with #4166's Lean theorem; set by trusted review 1758 (verification read, reusing receipt 67, which reran the package and passed). Accepted, not provisional. Accepted content: the dictionary m = n + 2 between #4166's positions and #4168's denominators; Theorem A (#4166's Theorem 1 and Corollaries 2-4 reindexed, no new complexity content); Theorem B, a paper proof that a finite set {2 <= m_1 < ... < m_k} is the greedy take-set of its own reciprocal sum iff m_{i+1} >= m_i(m_i-1)+1 (necessity is #4168's theorem; sufficiency is the new half; likely classical, no literature novelty claimed); Corollary C, max_L p(L) = max A = m_k when N >= 2 max A - 2. Measured rows R6-R9 are finite checks or sub-samples, disclosed as such. Not claimed by the source (its section 9): no Lean artifact (no toolchain on its host), no progress on twin primes, the parity problem or sums of lambda(n)lambda(n+2), no new measurement of primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Applicable, narrow. The measure summary v3 (current through #4721) carries greedy-word rows from #4721: the support count A(N) = O(log log N), attained at Sylvester counts, and a plateau row for x_k = (s_{k+1}-2)/(s_{k+1}-1) labelled max_L p(L) = s_k + 2 for N >= 2 s_k + 2, with values 2, 3, 7, 43, 1807 for k = 1..5. Bridge: #5003 supplies the dictionary m = n + 2 that the measure summary says to apply before comparing (#4166 positions vs #4168 denominators), and its Corollary C states the plateau as max A = m_k in denominator indexing. Its R7 row reads max_L p(L) = 2, 3, 7, 43 = s_k for k = 1..4. On reading the two served texts side by side: the listed values in the measure row equal s_k (s_1 = 2, and s_1 + 2 would be 4), so the label s_k + 2 agrees with its own numbers only in #4166's position indexing (a_m + 2 with a_m = s_k - 2). The numbers agree with Corollary C, and the label looks like the convention slip the summary warns about. The hypothesis N >= 2 s_k + 2 is stronger than Corollary C's N >= 2 s_k - 2, so the measured range lies inside it. This is a relevance observation for the next measure summary, not an adjudication. Also transferable: R8's spread of max A at fixed take count (k = 4: 52 to 4.44e14 over 5811 targets with b <= 200), which says the plateau statistic is not a proxy for the take count or density. It is a disclosed sub-sample. Not transferred: #4168's density-row reproducibility gap and the Omega_x row (it needs an upper bound on take indices, which #5003 does not give).","assumptions_md":"Provisional relevance only: #5003 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 343, explore on lane formalize (stage discover), a cross-lane synthesis of #4166 (greedy-word complexity law, Lean) and #4168 (Sylvester-sparsity, paper). Rung proven, carried by the paper proof (report section 4) together with #4166's Lean theorem; set by trusted review 1758 (verification read, reusing receipt 67, which reran the package and passed). Accepted, not provisional. Accepted content: the dictionary m = n + 2 between #4166's positions and #4168's denominators; Theorem A (#4166's Theorem 1 and Corollaries 2-4 reindexed, no new complexity content); Theorem B, a paper proof that a finite set {2 <= m_1 < ... < m_k} is the greedy take-set of its own reciprocal sum iff m_{i+1} >= m_i(m_i-1)+1 (necessity is #4168's theorem; sufficiency is the new half; likely classical, no literature novelty claimed); Corollary C, max_L p(L) = max A = m_k when N >= 2 max A - 2. Measured rows R6-R9 are finite checks or sub-samples, disclosed as such. Not claimed by the source (its section 9): no Lean artifact (no toolchain on its host), no progress on twin primes, the parity problem or sums of lambda(n)lambda(n+2), no new measurement of primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Mismatch. The infinitude area collects routes toward infinitely many twin primes that are not in the refuted registry. #5003 is a finite combinatorial statement about greedy Egyptian expansions and the word they generate. Its section 6 says it does not touch the parity problem: #4168's lambda-value verdicts and budgets are untouched, and Corollary C constrains factor-based statistics only and implies nothing about sums of lambda(n)lambda(n+2). Section 9 claims no progress on twin primes. The infinitude summary in this brief never mentions the greedy word, and #5003 offers no route, obstruction or lemma that an infinitude argument consumes.","assumptions_md":"Provisional relevance only: #5003 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 343, explore on lane formalize (stage discover), a cross-lane synthesis of #4166 (greedy-word complexity law, Lean) and #4168 (Sylvester-sparsity, paper). Rung proven, carried by the paper proof (report section 4) together with #4166's Lean theorem; set by trusted review 1758 (verification read, reusing receipt 67, which reran the package and passed). Accepted, not provisional. Accepted content: the dictionary m = n + 2 between #4166's positions and #4168's denominators; Theorem A (#4166's Theorem 1 and Corollaries 2-4 reindexed, no new complexity content); Theorem B, a paper proof that a finite set {2 <= m_1 < ... < m_k} is the greedy take-set of its own reciprocal sum iff m_{i+1} >= m_i(m_i-1)+1 (necessity is #4168's theorem; sufficiency is the new half; likely classical, no literature novelty claimed); Corollary C, max_L p(L) = max A = m_k when N >= 2 max A - 2. Measured rows R6-R9 are finite checks or sub-samples, disclosed as such. Not claimed by the source (its section 9): no Lean artifact (no toolchain on its host), no progress on twin primes, the parity problem or sums of lambda(n)lambda(n+2), no new measurement of primes.","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-prime count would force (a disproof-shaped lane). #5003 says nothing about twin primes or their count: its objects are finite denominator sets, rational targets and digit words, and its section 9 excludes any statement about primes. The finiteness-structure summary in this brief never mentions the greedy word, and nothing in #5003's accepted scope constrains a hypothetical last twin pair.","assumptions_md":"Provisional relevance only: #5003 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 343, explore on lane formalize (stage discover), a cross-lane synthesis of #4166 (greedy-word complexity law, Lean) and #4168 (Sylvester-sparsity, paper). Rung proven, carried by the paper proof (report section 4) together with #4166's Lean theorem; set by trusted review 1758 (verification read, reusing receipt 67, which reran the package and passed). Accepted, not provisional. Accepted content: the dictionary m = n + 2 between #4166's positions and #4168's denominators; Theorem A (#4166's Theorem 1 and Corollaries 2-4 reindexed, no new complexity content); Theorem B, a paper proof that a finite set {2 <= m_1 < ... < m_k} is the greedy take-set of its own reciprocal sum iff m_{i+1} >= m_i(m_i-1)+1 (necessity is #4168's theorem; sufficiency is the new half; likely classical, no literature novelty claimed); Corollary C, max_L p(L) = max A = m_k when N >= 2 max A - 2. Measured rows R6-R9 are finite checks or sub-samples, disclosed as such. Not claimed by the source (its section 9): no Lean artifact (no toolchain on its host), no progress on twin primes, the parity problem or sums of lambda(n)lambda(n+2), no new measurement of primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Mismatch. The kk-lower-bound paper target (#2597) is a survivor-gap lower bound at A = 12, explicitly not twin-prime infinitude. Its open obligations O1-O7 are a prime harmonic asymptotic, a uniform smooth-number asymptotic, any fixed A > 4, a dyadic prime count with coefficient 1/2, a quoted sieve input, two-sided density/Euler estimates and the exact constant in eq. (28). #5003 proves facts about greedy Egyptian expansions (Theorems A and B, Corollary C). It has no primes, sieve weights, smooth-number counts or analytic constants, so it supplies none of main or O1-O7. This job's kk-lower-bound topic tags are scheduling labels. They do not bridge the content.","assumptions_md":"Provisional relevance only: #5003 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 343, explore on lane formalize (stage discover), a cross-lane synthesis of #4166 (greedy-word complexity law, Lean) and #4168 (Sylvester-sparsity, paper). Rung proven, carried by the paper proof (report section 4) together with #4166's Lean theorem; set by trusted review 1758 (verification read, reusing receipt 67, which reran the package and passed). Accepted, not provisional. Accepted content: the dictionary m = n + 2 between #4166's positions and #4168's denominators; Theorem A (#4166's Theorem 1 and Corollaries 2-4 reindexed, no new complexity content); Theorem B, a paper proof that a finite set {2 <= m_1 < ... < m_k} is the greedy take-set of its own reciprocal sum iff m_{i+1} >= m_i(m_i-1)+1 (necessity is #4168's theorem; sufficiency is the new half; likely classical, no literature novelty claimed); Corollary C, max_L p(L) = max A = m_k when N >= 2 max A - 2. Measured rows R6-R9 are finite checks or sub-samples, disclosed as such. Not claimed by the source (its section 9): no Lean artifact (no toolchain on its host), no progress on twin primes, the parity problem or sums of lambda(n)lambda(n+2), no new measurement of primes.","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":false,"check_job_id":10019,"input_sha256":"c71f81cd95510d7fdc6e4b8057ca59a4e38626c062a1e89f4aa76f67b91fc9f2","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"985c8559c30528a477c2ee7a30f6dc4e53cfd28af5c67d308c77714ebbfab798","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5003,"material_evidence":{"sha256":"101015fa771b77ca3b2913bc513bbb076b5589a11aa336017f27f359c4d2a5da","entries":{"return:5003":"b507a01aaf971ec42857098305f1cb5b09597fef2bff34390d249b19fc5592e0","artifact:5003:046e4092c1084ce2c4a06eee6e9cd93756ee4ec39a0cf7294e55f2b3336f9015":"046e4092c1084ce2c4a06eee6e9cd93756ee4ec39a0cf7294e55f2b3336f9015","artifact:5003:30db16f8e2062ffb7ccbfd11184b311d58da1a57ebeb4bb577ffcaa3f8cce9a1":"30db16f8e2062ffb7ccbfd11184b311d58da1a57ebeb4bb577ffcaa3f8cce9a1","artifact:5003:58694e53883dfce6aa902e61d4abfe3994740b97924dc6d4daaa9c4a202d0fa3":"58694e53883dfce6aa902e61d4abfe3994740b97924dc6d4daaa9c4a202d0fa3","artifact:5003:663231a0d90ef0b87625df14dbda583e7795ca2fb713d273cc403c021681e47a":"663231a0d90ef0b87625df14dbda583e7795ca2fb713d273cc403c021681e47a","artifact:5003:86a44cd8e4945fc93ed755ec0f32ed82ba493479f772aa04a6ea49047bc2cc3c":"86a44cd8e4945fc93ed755ec0f32ed82ba493479f772aa04a6ea49047bc2cc3c","artifact:5003:985c8559c30528a477c2ee7a30f6dc4e53cfd28af5c67d308c77714ebbfab798":"985c8559c30528a477c2ee7a30f6dc4e53cfd28af5c67d308c77714ebbfab798"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5003,"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 #5003: 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\":5003,\"report_sha256\":\"985c8559c30528a477c2ee7a30f6dc4e53cfd28af5c67d308c77714ebbfab798\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5003\":\"b507a01aaf971ec42857098305f1cb5b09597fef2bff34390d249b19fc5592e0\",\"artifact:5003:046e4092c1084ce2c4a06eee6e9cd93756ee4ec39a0cf7294e55f2b3336f9015\":\"046e4092c1084ce2c4a06eee6e9cd93756ee4ec39a0cf7294e55f2b3336f9015\",\"artifact:5003:30db16f8e2062ffb7ccbfd11184b311d58da1a57ebeb4bb577ffcaa3f8cce9a1\":\"30db16f8e2062ffb7ccbfd11184b311d58da1a57ebeb4bb577ffcaa3f8cce9a1\",\"artifact:5003:58694e53883dfce6aa902e61d4abfe3994740b97924dc6d4daaa9c4a202d0fa3\":\"58694e53883dfce6aa902e61d4abfe3994740b97924dc6d4daaa9c4a202d0fa3\",\"artifact:5003:663231a0d90ef0b87625df14dbda583e7795ca2fb713d273cc403c021681e47a\":\"663231a0d90ef0b87625df14dbda583e7795ca2fb713d273cc403c021681e47a\",\"artifact:5003:86a44cd8e4945fc93ed755ec0f32ed82ba493479f772aa04a6ea49047bc2cc3c\":\"86a44cd8e4945fc93ed755ec0f32ed82ba493479f772aa04a6ea49047bc2cc3c\",\"artifact:5003:985c8559c30528a477c2ee7a30f6dc4e53cfd28af5c67d308c77714ebbfab798\":\"985c8559c30528a477c2ee7a30f6dc4e53cfd28af5c67d308c77714ebbfab798\"},\"sha256\":\"101015fa771b77ca3b2913bc513bbb076b5589a11aa336017f27f359c4d2a5da\"},\"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:5003,input_sha256:\"c71f81cd95510d7fdc6e4b8057ca59a4e38626c062a1e89f4aa76f67b91fc9f2\",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/5082/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"7ac46569bfa4962a4994709623cf2c35cb6260d789d2010ef1b0df5b1ec71538","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}