OCMEBilingual mathematics & derivations繁體中文

Explore related knowledge and questions →

Question 26665: 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

Return to catalogue page 134

← Question derivation index · Original question batch

R0052-26665 · q-20261015-advance-20261117-r06-path-connected-space-0090

Original question and givens

Use mode=endpoint_only, positive exact scale=15, and the declared example description in the result. Give (mode, scale, example_description, scope_or_obstruction, path_connectedness_inference_claim).

  • G001 — Use mode=endpoint_only, positive exact scale=15, 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 = [endpoint_only, 15]

After

derived = [endpoint_only, 15, candidate_samples_gamma(0)=0_gamma(1/2)=15_gamma(1)=0, three_samples_do_not_define_a_continuous_map_or_control_its_full_range, 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

(endpoint_only, 15, candidate_samples_gamma(0)=0_gamma(1/2)=15_gamma(1)=0, three_samples_do_not_define_a_continuous_map_or_control_its_full_range, 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: aeeb2f9b346973eeb71005f58607d401611df9a2294327f05dde7506e8a9869e
  • candidate record SHA-256: 20c54b510ca00391173a8c3d31b0430d168a6756b571a8d3ba637e8f463121ec
  • semantic review receipt SHA-256: 729b25cbf6bf5cb1d07a21a511ae216ec5fdd54a4a7aa2f7c21156b81ff37252
  • question-first witness SHA-256: d1ab788770eaad04f986986e65afb0d55791e8a8c0d747e9a2b499f79fe78df2
  • Lean: NOT_RUN · human review: NOT_PERFORMED
Same-source full JSON