NashEmbedding tests: ContDiff encoding patch (smooth vs analytic) #
Diagnostic tests for the SmoothPeriodic.smooth field encoding.
Background. In Mathlib v4.28's WithTop ℕ∞ encoding a bare ⊤ means
analytic (ω), not C^∞ (∞). SmoothPeriodic.smooth was once typed
ContDiff ℝ ⊤ f by mistake and is now ContDiff ℝ ∞ f; these tests
guard against the encoding regressing.
Test X is the discriminating test:
- With
smooth = ContDiff ℝ ⊤(analytic), X fails to elaborate because the witnessexpNegInvGlue ∘ sinis not analytic. - With
smooth = ContDiff ℝ ∞(C^∞, the current state), X elaborates.
Tests A1, W, Y, Z elaborate in either state — they exercise concrete
witnesses (zero, flatTorusEmb, flatMetric) all of which happen to
be analytic.