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R0051-26211 · q-20261015-advance-20261116-r01-contraction-mapping-theorem-0086
Use boundary mode=noncomplete_space and positive exact scale=11. Give (mode, space_description, mapping_description, outside_fixed_point, q_as_fraction, theorem_application_claim).
G001 — Use boundary mode=noncomplete_space and positive exact scale=11. Give (mode, space_description, mapping_description, outside_fixed_point, q_as_fraction, theorem_application_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 = [contract-boundary]
After
derived = [[mode, space_description, mapping_description, outside_fixed_point, q_as_fraction, theorem_application_claim]]
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.
Rule: source_ordered_fields_without_JS · Uses: G001
Before
source roles = [noncomplete_space, 11]
After
derived = [noncomplete_space, X=(0,11), T(x)=(x+11)/2, fixed_point=11_outside_X, [1, 2], No]
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.
Rule: Contraction_original_boundary_mode_actual_scope_not_invented_witness · Uses: G001, S001
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.(noncomplete_space, X=(0,11), T(x)=(x+11)/2, fixed_point=11_outside_X, [1, 2], 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: a347d1ee99f5f9f575d4470d21dd06ba8c3fb547b5059a5a567addf45188aba7candidate record SHA-256: 0b67a40fe6fd0d68d7ed627481124e9a0a3357941269dfe841d584568d8b73easemantic review receipt SHA-256: 90df1e889242e9afdf01e068788ee8500ef366ffcfc0496e30a6800de32631c3question-first witness SHA-256: ae1e849608590ca856c9f3b6911ba58e3bf53c608eb7369606192a770f48bd5cLean: NOT_RUN · human review: NOT_PERFORMED