OCMEBilingual mathematics & derivations繁體中文

Explore related knowledge and questions →

Question 26212: Failed Completeness, Self-Map or Global Strict-Contraction Premises Block the Theorem

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 132

← Question derivation index · Original question batch

R0051-26212 · q-20261015-advance-20261116-r01-contraction-mapping-theorem-0087

Original question and givens

Use boundary mode=sampled_pairs and positive exact scale=12. Give (mode, scale, sampled_pair_result, unchecked_pair_statement, global_contraction_claim, boundary).

  • G001 — Use boundary mode=sampled_pairs and positive exact scale=12. Give (mode, scale, sampled_pair_result, unchecked_pair_statement, global_contraction_claim, boundary).

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 = [contract-boundary]

After

derived = [[mode, scale, sampled_pair_result, unchecked_pair_statement, global_contraction_claim, boundary]]

Conditions: none

List the full source field order without JavaScript.Original modes select contract6/4/6/6 and IVT8/7/8 roles,without padding or answer-shape inference.

Step identifiers and dependencies

Rule: source_ordered_fields_without_JS · Uses: G001

S002 · implies

Before

source roles = [sampled_pairs, 12]

After

derived = [sampled_pairs, 12, checked_pairs_pass, one_unchecked_pair_violates_global_bound, No, sampled_pairs_do_not_prove_global_contraction]

Conditions: none

The two-point identity at q1 has two fixed points;nonself maps do not iterate in the same space;on(0,s),(x+s)/2 has its fixed point s outside.sampled_pairs supplies only source scope,not a complete recomputable metric/map counterexample.

Step identifiers and dependencies

Rule: Contraction_original_boundary_mode_actual_scope_not_invented_witness · Uses: G001, S001

Reverse checks

  • S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

(sampled_pairs, 12, checked_pairs_pass, one_unchecked_pair_violates_global_bound, No, sampled_pairs_do_not_prove_global_contraction)

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: 177fadd763d7fc1a2b11d99c47d8edc698facd951569ecab4983c9a8ebe8f26a
  • candidate record SHA-256: 5529c6738932d92d747f19dee0757dfb5b1e510b952ca3f640434fc32f56bf44
  • semantic review receipt SHA-256: 90df1e889242e9afdf01e068788ee8500ef366ffcfc0496e30a6800de32631c3
  • question-first witness SHA-256: ae1e849608590ca856c9f3b6911ba58e3bf53c608eb7369606192a770f48bd5c
  • Lean: NOT_RUN · human review: NOT_PERFORMED
Same-source full JSON