Matter, source algebras, and policy T0

A finite named matter interface $\Gamma$ carries one joint state

Names specify access to declared factors. Classical registers are jointly block diagonal in their distinguished bases, including their correlations with other factors.

A surviving source boundary is an explicitly embedded unital ${}^{\ast }$-subalgebra

Its accessible state functional is

For a fixed Hermitian $B_{\mathrm{src}}\in {\mathcal{A}}_{\mathrm{src}}$ and fixed $\kappa$, a table token $m_{\mathrm{src}}$ can carry the semantic promise

The example below uses $B_{\mathrm{src}}=Z$ and $\kappa =1$.

T0. Every sourced history begins with an already supplied classical token. At each sourced command the token must satisfy its declared promise for the current surviving source state. No token-acquisition operation or operational promise test occurs in the history.

“Current token” means correct for the current source functional. It does not mean that the selected packet is already installed before source replacement.

For a fixed token, the promised state class may be convex. The union of classes for different deterministic expectation labels need not be convex. Nothing here implements a state-only deterministic source selection on the full quantum state space.