Boundary Invariance from Projective Phase Structure: Heisenberg Fixed Points, No-Signaling, and Symmetry-Selection Channels

This paper gives a finite-dimensional, first-principles derivation of boundary invariance from completion-locked projective phase and channel data. No-signaling and conserved boundary structure are derived from fixed carrier and channel structure, rather than imposed as external constraints. The central invariant is the Heisenberg fixed-point condition Φ*(X) = X for every boundary observable X in the locked boundary algebra. Equivalently, boundary expectations and boundary POVM laws are preserved uniformly over input states exactly when the admissible complement channel fixes the boundary algebra in the Heisenberg picture. Inside a completion-locked datum, a label encoded only through an admissible complement channel has zero statistical channel into fixed boundary outcomes. Here completion-locked means that the projective phase carrier, boundary algebra, admissible boundary-observable charts, state and normalization data, admissible channel class, and channel-extraction maps are fixed before Bell tables, tensor-factor partitions, random-unitary selections, or quotient channels are compared. The primitive carrier is the projective phase bundle U(1) → S(H) → P(H). Tensor factorizations, Bell partitions, product tests, and local boundary observable algebras enter downstream as locked charts. The theorem sequence is: projective phase carrier → locked boundary algebra → admissible complement channel → Heisenberg fixed point → invariant boundary law. The theorem is realized in three explicit boundary-channel settings: projective quantum no-signaling; Gibbs-weighted random-unitary symmetry-selection channels, whose invariant algebra is the active commutant; and finite equilibrium-combinatorial quotient realizations, whose barycentric extraction is a boundary channel with diamond-norm control of the selected equilibrium limit. Taken together, these results place projective no-signaling, random-unitary active-commutant conservation, and equilibrium-quotient channel convergence under one exact finite-dimensional fixed-point law: admissible complement dynamics preserve boundary data exactly when their Heisenberg dual fixes the locked boundary algebra. The result is a finite-dimensional boundary framework for exact no-signaling, steering without unconditioned boundary signaling, conserved commutants, zero label-to-boundary information, and quotient-selected channel convergence. License note: Distributed under CC BY-NC-ND 4.0.