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Question 26672: A Disconnected Gap, Discrete Pair and Endpoint Samples Have Different Obstructions

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0052-26672 · q-20261015-advance-20261117-r06-path-connected-space-0097

Original question and givens

Use mode=discrete_two_point, positive exact scale=22, and the declared example description in the result. Give (mode, scale, example_description, scope_or_obstruction, path_connectedness_inference_claim).

  • G001 — Use mode=discrete_two_point, positive exact scale=22, and the declared example description in the result. Give (mode, scale, example_description, scope_or_obstruction, path_connectedness_inference_claim).

Definition and scope

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.

Step-by-step derivation

S001 · implies

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.

Step identifiers and dependencies

Rule: source_ordered_fields_without_JS · Uses: G001

S002 · implies

Before

source roles = [discrete_two_point, 22]

After

derived = [discrete_two_point, 22, X={0,22}_with_discrete_topology, continuous_image_of_connected_[0,1]_cannot_meet_both_points, 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.

Step identifiers and dependencies

Rule: Path_original_boundary_scope_NO_invented_full_infinite_witness · Uses: G001, S001

Reverse checks

  • 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.

Result

(discrete_two_point, 22, X={0,22}_with_discrete_topology, continuous_image_of_connected_[0,1]_cannot_meet_both_points, No)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

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.

Source hashes and review receipts
  • input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
  • original question SHA-256: 8d6556ce71337b0cc5a67d79bad87304665984f6b8003bb842acc837fabd196c
  • candidate record SHA-256: d253a566d3bf6b8bdf73fb11c52479f9c93274709ecb698bfe31f5351c55080e
  • semantic review receipt SHA-256: 729b25cbf6bf5cb1d07a21a511ae216ec5fdd54a4a7aa2f7c21156b81ff37252
  • question-first witness SHA-256: d1ab788770eaad04f986986e65afb0d55791e8a8c0d747e9a2b499f79fe78df2
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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