Volume I: Exact Geometry and Symbolic Foundations

This lead companion rewrites the earlier "Scalar Emergence and Symbolic Foundations" volume into the part that survives independent checking: exact geometry and exact address structure.  The original project treated $\pi/\sqrt{2}$ as a broad physical scalar.  This revision deliberately narrows the claim.  It keeps the self-contained mathematics: a $45^\circ$ cone with two independent sphere-packing operators, a Pell curvature ladder in $\Z[\sqrt{2}]$, and a divisor-band address rule for rational messages.  It removes or quarantines physical, acoustic, market, and constant-governing interpretations that the exact mathematics does not support.

The governing theme is layer discipline.  Geometry may recover a volume ratio.  Number theory may recover an address.  A public convention may recover a letter.  Meaning and physical interpretation require additional evidence.  The result is not a unified scalar physics.  It is a cleaner monograph: exact identities, stated provenance, symbolic verification, and a firewall between structure and interpretation.

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