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R0053-27058 · q-20261015-advance-20261117-r03-uniform-limit-continuity-theorem-0083
Use mode=moving_spike, positive integer scale=9, and the full sequence/domain description in the result. Give (mode, scale, sequence_description, scope_or_obstruction, theorem_application_claim).
G001 — Use mode=moving_spike, positive integer scale=9, and the full sequence/domain description in the result. Give (mode, scale, sequence_description, scope_or_obstruction, 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 = [uniform-limit-boundary]
After
derived = [[mode, scale, sequence_description, scope_or_obstruction, theorem_application_claim]]
Conditions: none
List the complete source field order and mode-specific roles without JavaScript or answer-shape inference;No,undefined and infinity retain their distinct meanings.
Rule: source_ordered_fields_without_JS · Uses: G001
Before
source roles = [moving_spike, 9]
After
derived = [moving_spike, 9, f_n(x)=max(0,1-(n+9)*abs(x-1/(n+9)))_on_[0,1], continuous_pointwise_to_zero_but_sup_norm_one, No]
Conditions: none
Powers tend to0 for x<1 but equal1 at x=1,so convergence is only pointwise.A constant step sequence is uniform but its terms are discontinuous.A finite grid can miss a unit bump between points.A moving spike is continuous,attains1 at its moving peak and eventually vanishes at each fixed x,so its sup error stays1.No rejects the theorem premises/method,not every underlying convergence claim or a performed formal proof.
Rule: Uniform_original_WHOLE_boundary_premise_obstruction · Uses: G001, S001
S002 · premise_and_result_audit — Reverse-check the complete original data,step operands and premises;finite checks,conditional named-theorem use and general formal proof remain distinct.S001 · premise_and_result_audit — Reverse-check the complete original data,step operands and premises;finite checks,conditional named-theorem use and general formal proof remain distinct.(moving_spike, 9, f_n(x)=max(0,1-(n+9)*abs(x-1/(n+9)))_on_[0,1], continuous_pointwise_to_zero_but_sup_norm_one, 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: 84f6bcf110a4bd7a51d0730e351295572c98ea56162f67eb656dc8238dbe3e6ccandidate record SHA-256: 4e20cca1944fb2dfdb3cdc9df3a84e6731a075beebf6f7117332d821be0e4608semantic review receipt SHA-256: 1b7a62514347b82518305d5feb4369a52d7d44c442a0f2b131e9eb3cd7b45f62question-first witness SHA-256: 79dc2a1077081f3ea2a03f75e32778163bf05e814cdf4c29ed86e567295f9ee1Lean: NOT_RUN · human review: NOT_PERFORMED