VSAG-TF – A Variable-Signature Framework for Transonic Flow Mach-Normalized Sonic Stratification, Tricomi-Type Probes, and Certified Sonic-Zone Enclosure

This paper develops a variable-signature framework for transonic flow. Given the squared
flow speed q = |v|2 and the squared local sound speed a = c2, the Mach-normalized signature
field is defined by
σTF = q − a
q + a .
Its sign encodes the subsonic, sonic, and supersonic regimes as negative, neutral, and
positive signature regions. The framework refines the sonic locus into regular and residual
components, separates stagnation as the endpoint subset {σTF = −1} ⊂ Y−, introduces a
local Tricomi-type probe for signature-controlled elliptic–rank-degenerate–hyperbolic type
change, and develops certified sonic-zone diagnostics for uncertain computed or measured
data. In particular, if a computed signature field σh satisfies the certified error bound
|σ − σh| ≤ ηh,
then the true sonic locus satisfies the one-sided enclosure
Y0(σ) ⊂ Nη,h(σh).
Thus the method gives a no-false-negative enclosure principle for sonic-zone tracking under
numerical or measurement uncertainty