Operational Accessibility Manifolds for Pointer Information: General-N Support Projection and Distributed Realizations

Environmental fragments provide indirect access to pointer information, but fragment-averaged accessibility need not determine where microscopic branch dependence resides. For an environment of N subsystems, we quantify fragment pointer information by the Holevo quantity, which upper-bounds accessible classical information, and average it over fragments of equal size. Assuming two pure pointer-conditioned environmental branches share an identical, branch-independent rest outside a carrier, we establish an exact support-projection identity and a hypergeometric formula for the complete averaged accessibility curve. A carrier of size at most two is sufficient for a finite-N order-2 constraint; for N = 4, this yields A2 = A4/6 + 4A1/3 and A3 = A4/2 + A1. The converse fails in general: an interval-certified, computer-assisted N = 4 state-space construction satisfies these relations while having minimal carrier size four. We distinguish this distributed state-space witness from realizations in the tested five-qubit controlled-gate circuits. Using the pre-operation conditional branch state and the known gate, a prospectively frozen mechanism catalog correctly classified 417/417 protocol-defined, outcome-conditioned scored events at theta = pi/2; 28 post-R0 events among 445 eligible instances were handled separately. Paired sampled-parameter tests classified 320/320 scored events at each of theta = pi/3 and 2pi/3; these paired evaluations are not independent circuit replications. A separate retrospective numerical census classified 70/70 near-zero-residual R0 events as low-carrier within the sampled circuit population. Finally, an exact product-local preservation lemma supplies a sufficient condition for invariance of fragment accessibility, not a complete characterization. Together, these results separate exact operational constraints, nonunique microscopic realizations, and circuit-specific dynamical selection.