The Υ-Collapse Problem: Global Closure, Identity Equivalence, and Class VI Stability

This paper introduces and resolves the Υ-Collapse Problem, a previously unformulated law-level question in the Tier-0 framework concerning global identity selection under non-local closure. Earlier Tier-0 results establish that local collapse (Δ-collapse) governs record formation and that Γ-collapse governs solver–world kinetic compatibility. These mechanisms do not determine when globally entangled identity candidates distributed across an archive of admissible states remain distinct or are forced to resolve into a single equivalence class. The Υ-Collapse Problem addresses this gap. The paper formalizes Class VI closure as a topology-first regime in which identity and persistence are evaluated over an archive-level entanglement mesh rather than along a single sequential trajectory. In this setting, “superposition” is not Hilbert-linear but degeneracy of globally admissible identity candidates (“twin sets”). Υ-collapse is defined as the structural contraction of this twin set when global admissibility constraints force recognition of a unique representative. A precise necessary and sufficient criterion for Υ-collapse is given in terms of a global admissibility functional acting on archive-level identity candidates. The analysis proves that Υ-collapse is: not reducible to quantum measurement or Δ-collapse, not equivalent to decoherence, not a probabilistic or dynamical process,but instead a topological equivalence-recognition event enforced by global closure. The framework explains how non-local memory, identity persistence across time, and retrocausal-appearing consistency can arise without modifying local dynamics or invoking hidden variables, branching worlds, or observer-dependent selection. A minimal worked toy model illustrates both persistent Υ-superposition and forced Υ-collapse. This result completes the Tier-0 “collapse ladder” by identifying the Class VI analogue of measurement: global identity selection under archive-level closure, distinct from record formation and kinetic mismatch. The paper is law-level and structural in scope; it does not propose new microphysical dynamics or immediate experimental predictions.