τ-manifold and Book III handoff

The Liouville-type obstruction analysis closes the Central-Theorem chain by removing the specific classical objection that compactness would force all holomorphic functions to be constant: because j^2=+1 gives a hyperbolic, not elliptic, operator, nonconstant bounded τ-holomorphic functions remain available. What remains is not an ambient smooth manifold imported from outside, but a τ-manifold structure: boundary-determined data, admissible ω-germ transformations, finite spectral support, and the four-atom boundary grammar assembled into a single geometric object. Book II therefore ends with a canonical geometric body, but not yet physics. Book III can now ask the next question in a disciplined way: which internally earned relational structures of this body can serve as physical localization sites?