Fourteen theorems extending the anchor identity into a complete structural algebra: closed-form Thomas–Wigner rotation, SLD saturation, Jeffreys uniqueness, the Gudermannian bridge, Möbius covariance, modular flow, holographic complexity, a γ² Page curve, and a Lawvere obstruction to self-knowledge.

The Measurement Irreversibility Criterion: a physics-based necessary condition for consciousness derived from the Fisher–Lorentz identity. Current digital AI architectures fail this minimum condition. Three testable predictions distinguish it from IIT, GNWT, and the Free Energy Principle.

A pre-registered qubit experiment crossing the PB 45° baseline at V_× ≈ 0.9102. About 45k shots at 3σ on any current superconducting, trapped-ion, or neutral-atom platform. No new instrumentation. Either outcome is publishable.

A finite-dimensional Bisognano–Wichmann analog. Modular flow on the qubit is an SL(2,ℂ) boost with imaginary spinor rapidity ζ = 2itη_M. Twelve theorems; a saturating Mandelstam–Tamm bound; Bloch precession at 2η_M. Every coefficient verified to 4 × 10⁻¹⁵.

The Fisher information of a binary classifier’s sigmoid output equals γ²(V). Amari’s natural gradient inherits the conformal geometry of the qubit Bloch ball at every binary classification node in every neural network. A relativistic speed limit on classifier convergence.

One identity traced across twenty cross-disciplinary domains — thermodynamics, population genetics, allosteric biology, ecosystem tipping points, quantum speed limits, flat-band superconductivity, embryonic development. Nine proven results, three honest tensions, thirty-three falsifiable predictions.

The open-access preprint the published Quantum Reports manuscript is based on: the conformal equivalence of the Bures and Beltrami–Klein metrics on the qubit Bloch ball, and the obstruction at N ≥ 3.

The open-access preprint companion to the peer-reviewed BioSystems article: I = n_H²/4 at the midpoint of any Hill-type curve, traced through hemoglobin, the flagellar motor, and morphogenesis.

The open-access preprint companion to the peer-reviewed Next Research article: Grover as a Fubini–Study geodesic, battery charging through the Gudermannian, the Zeno timescale as ħ/ΔE · γ(V).