Physical realization boundary for braid compilation

A physical realization record for a mathematical braid-compilation instance contains, in addition to its finite fusion input and braid word, all of: a specified physical state space and low-energy-sector identification; a $C^2$ Hermitian path and constant-rank uniformly gapped projection; an initial preparation isometry and its cost; a slow-time schedule; an endpoint frame; a separately justified identification of band transport with the logical-frame Fibonacci $F\mathrm{/}R$ target of Finite adiabatic braid compilation input, including its phase; and a locality model for exchanges. A local-Hamiltonian model specifies a finite lattice $\mathrm{\Lambda }$ with its metric, an interaction range $R$, and a uniform per-site interaction bound $J$ for a decomposition $H(s)={\sum }_{X\subseteq \mathrm{\Lambda }}{h}_X(s)$: every $h_X(s)$ is Hermitian and supported on $X$, $\mathrm{diam}(X)\le R$, and ${\sup }_{s\in [0,1],x\in \mathrm{\Lambda }}{\sum }_{X\ni x}\mathrm{\parallel }{h}_X(s)\mathrm{\parallel }\le J\mathrm{.}$ The record separately states the local-indistinguishability and stability criteria, including their region scales, norms, tolerances, and the evidence used to establish them. It also supplies explicit preparation, excitation, measurement, and control-error terms. The first spectral-path clauses are the finite interface in Physical braid implementation interface and Finite adiabatic braid compilation input. The error ledger is Finite braid compilation and adiabatic error budget. A successful SK compilation, projective density theorem, or JRS leakage estimate supplies none of the material, locality, preparation, or band-holonomy evidence by itself; those are independent record fields, not consequences of the mathematical compiler. Only terms appearing as hypotheses in the stated error ledger contribute to its measured-output bound; a separately recorded preparation, excitation, or control error requires an additional bound before it can be included in a total physical error claim.