On the Limits of Flow and Transport Metrics Under Admissibility (Boundary Paper)

Abstract

Paper VI: The Constraint Geometry series establishes admissibility as a prior structural criterion governing which dynamics remain bounded, stable, and resolvable under finite constraint. Having fixed this foundation, a natural secondary impulse arises to quantify flow, transport, or directional intensity as descriptive properties of admissible systems. This paper examines that impulse as a boundary problem. We identify that most flow-like metrics violate admissibility requirements by reintroducing prediction, control affordances, or symmetry breaking under finite resolution. No numerical evaluation, simulation, or explicit construction is presented. The purpose of this paper is jurisdictional: to identify which classes of flow metrics are structurally excluded, why they fail, and under what extreme restrictions a weakened, research-only notion might exist without contaminating doctrine or registry truth.

CRL-0 · Stage-0 · observer-only · non-authoritative · no methods, thresholds, procedures, or operational guidance.

Revised V1.2 (Feb1, 2026): This revision aligns the document to CRL-0 licensing posture (observer-only, non-authoritative, non-procedural) and strengthens non-operational boundaries. Structural claims and results unchanged.

Revision v1.3 (June 2026): Title-page affiliation and series-position language updated for consistency with the Constraint Geometry Series. Structural claims, abstract, and body content unchanged.

Revision v1.4 (June 2026): Re-render to restore Figure 1 boundary diagram (page 6) and populate Table of Contents (page 2). The prior v1.3 (June 2026) shipped with these elements missing due to a single-pass render with a missing source figure file. Doctrinal content, abstract, and structural claims unchanged.

Keywords: Admissibility, empirical limits, finite observation, flow metrics, transport metrics, governance, invariants, refusal-first, identifiability, claim taxonomy, observer-only