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R0052-26909 · q-20261015-advance-20261117-r01-series-comparison-test-0084
Boundary mode=finite_sample, positive scale=9. Give (mode, scale, sample_scope, eventual_comparison_claim, boundary).
G001 — Boundary mode=finite_sample, positive scale=9. Give (mode, scale, sample_scope, eventual_comparison_claim, boundary).Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Before
source roles = [series-comparison-boundary]
After
derived = [[mode, scale, scope, eventual_forall, certificate]]
Conditions: none
List this operation/mode exact source field order without JavaScript.Keep Boolean,string and null roles distinct;do not pad fields or infer the interface from answer shape.
Rule: source_ordered_fields_without_JS · Uses: G001
Before
source roles = [finite_sample, 9]
After
derived = [finite_sample, 9, first_N_terms_compare_next_term_fails, No, finite_samples_do_not_establish_eventual_forall]
Conditions: none
finite_sample is a scope statement,not a complete infinite witness.A divergent upper series cannot force a smaller one to diverge,e.g.1/n²<=1/n.Signed terms fail nonnegativity and unknown_reference lacks the reference status.No rejects this inference,not every underlying convergence claim.
Rule: Series_original_comparison_boundary_scope_and_direction · Uses: G001, S001
S002 · premise_and_result_audit — Reverse-check the complete original data,types,field order and premises;finite audits are not formal proofs of infinite theorems.S001 · premise_and_result_audit — Reverse-check the complete original data,types,field order and premises;finite audits are not formal proofs of infinite theorems.(finite_sample, 9, first_N_terms_compare_next_term_fails, No, finite_samples_do_not_establish_eventual_forall)
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: b6491feea48bed964f6efe97ef7e4b6912db8589216f0383feb4de06460ee3ffcandidate record SHA-256: fdbe51fe4ef17e2bda704eb85c4ed29488829a1f65294620474a2c125017fb95semantic review receipt SHA-256: 729b25cbf6bf5cb1d07a21a511ae216ec5fdd54a4a7aa2f7c21156b81ff37252question-first witness SHA-256: d1ab788770eaad04f986986e65afb0d55791e8a8c0d747e9a2b499f79fe78df2Lean: NOT_RUN · human review: NOT_PERFORMED