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R0052-26671 · q-20261015-advance-20261117-r06-path-connected-space-0096
Use mode=disconnected_gap, positive exact scale=21, and the declared example description in the result. Give (mode, scale, example_description, scope_or_obstruction, path_connectedness_inference_claim).
G001 — Use mode=disconnected_gap, positive exact scale=21, and the declared example description in the result. Give (mode, scale, example_description, scope_or_obstruction, path_connectedness_inference_claim).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 = [path-connected-boundary]
After
derived = [[mode, scale, space_or_samples, scope, path_claim]]
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 = [disconnected_gap, 21]
After
derived = [disconnected_gap, 21, X=(-infinity,0] union [21,infinity), IVT_blocks_a_path_between_components, No]
Conditions: none
A real path crossing the gap must hit a missing value by IVT;a connected image cannot meet both points of a discrete two-point space.Three samples do not define a full path or rule out interpolation.The sine-curve branch retains the named source scope,not a newly constructed or formally verified infinite witness.
Rule: Path_original_boundary_scope_NO_invented_full_infinite_witness · 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.(disconnected_gap, 21, X=(-infinity,0] union [21,infinity), IVT_blocks_a_path_between_components, No)
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: 26091b94749c0eb55705369f051dfa78f5a4d8230417b67f0985455c557e497ecandidate record SHA-256: 063839e5937a7b1842ca20bc90b183f7214adfc2a409147c58d2f03887535fdesemantic review receipt SHA-256: 729b25cbf6bf5cb1d07a21a511ae216ec5fdd54a4a7aa2f7c21156b81ff37252question-first witness SHA-256: d1ab788770eaad04f986986e65afb0d55791e8a8c0d747e9a2b499f79fe78df2Lean: NOT_RUN · human review: NOT_PERFORMED