Spacetime Cannot Be Fundamental - A No-Go Theorem for Quantum Gravity, Unitarity, and Classical Identity

We prove that spacetime cannot occupy the fundamental persistence role in any complete physical theory. The argument proceeds from the Frame/Module Exclusion Theorem (Theorem 0.2): no structure can simultaneously serve as the stable identity reference required by quantum state evolution (Frame role) and as the dynamical variable governed by field equations (Module role). The conjunction of quantum mechanics and general relativity assigns spacetime both roles simultaneously. This generates recursive persistence indeterminacy at the fundamental level — a no-go result independent of any specific dynamical details. The no-go theorem forces the existence of a pre-geometric persistence layer F₀, from which spacetime necessarily emerges. Three structural conditions for F₀ are derived from minimal persistence conditions M1–M3: the F-Condition (spacetime emergence non-contingent), the M-Condition (information preservation as structural necessity), and the K-Condition (information bound recovering the Bekenstein-Hawking result). F₀ admissibility further derives pre-geometric temporal ordering as a directed acyclic graph, pre-geometric information structure, and causal structure — establishing LP as the derivational foundation for Causal Set Theory. The M-Condition yields a previously unrecognized result: unitarity in quantum mechanics is not an independent postulate. Via the GNS construction, the admissibility algebra of F₀ generates a Hilbert space in which information-preserving evolution corresponds to unitary operators. Unitarity is M3 — the minimal persistence condition — expressed in the Hilbert space representation. A Planck-scale violation of unitarity would constitute a violation of the minimal persistence architecture itself. In the second part, the paper applies the Q1/Q2 distinction to quantum theory. Superposition is identified as the structural regime Q1 ∧ Q2_F₀ ∧ ¬Q2_classical: the system exists and persists at the pre-geometric level while classical identity is not yet evaluable. The measurement problem is reframed as a persistence problem: how does Q2_classical become evaluable from a Q2_F₀ regime? The paper provides a structural account of classical Frame stabilization, decoherence, the classical world condition, and the observer problem — without collapse axioms, many-worlds branching, or hidden variables. A heuristic Q2_classical operationalization (scale 0–4) and explicit falsification conditions with concrete examples are provided. Note on notation: The three minimal conditions M1–M3 (distinguishability, real transformation, and determinate persistence relation) are derived from D-STATE and Axiom A in Foundation Series Paper P006. All results in this paper can be equivalently stated using D-STATE + Axiom A; M1–M3 is retained for compatibility with the Foundation Series conventions. CORE CLAIMSTheorem 0.2 — Persistence Reference Non-Collapse:If Frame = Module: reference transforms. Verdict recursively indeterminate. Coupling degenerates.Theorem 1.1 — Frame/Module Conflict:QM needs stable admissibility structure (Frame). GR needs spacetime as dynamical variable (Module). Spacetime cannot be fundamental.Theorem 2.0 — Necessary Structural Layer:M3 requires a pre-spatiotemporal layer F₀.Theorems 3.1–3.3 — Pre-Geometric Dynamics:F₀ admissibility derives time (DAG), information, and causality. CST assumes this structure. LP derives it.Theorem 5.0 — Mathematical Unification Insufficiency:The QM/GR conflict is architectural. Only spacetime emergence resolves it.Theorem 6.2 — Q2_F₀ – Q2_quantum Correspondence:Q2_quantum is Q2_F₀ realized in emergent spacetime. Unitarity is not a postulate — it is the M-Condition in the continuous regime.Theorem 6.5 — Classical World Condition:A measurement outcome is not yet a world. A world requires recursively persistent Q2_classical.