Introduction

A geometric extension of a quantum programming language must specify what geometry can observe. This requirement is independent of the choice of gravitational dynamics or a continuum limit. Linear ownership of quantum names does not determine a mass; a measurement record is not a coarse-graining map; and a circuit dependency region is not automatically a physical light cone.

We use a finite circuit interface with destructive readout

Its semantics is the Born destructive computational-basis measurement used by Cheung's Enter calculus Cheung2026Enter,CheungI. Measured quantum names are consumed, and their tensor factors are not returned. We do not reprove a language-wide type-safety theorem or derive the Born rule. Our mixed-state channel presentation is a finite-dimensional semantic interface for that measurement operation.

Four additional structures are declared:

1. an external classical geometric configuration;

2. a location map for active matter names;

3. coupling algebras specifying accessible matter observables;

4. a complete control and resource interface specifying update selection, applicability, support, and retained storage.

Geometry is primitive metadata, not a quantity inferred from name cardinality, measurement count, or workspace size.

Two distinctions organize the paper: