Theorem 1.1 (Empirical Equivalence). LET and SR yield identical predictions. Section 1.2, (1.6).

Theorem 3.1 (Unruh–Visser). Sound in a moving fluid propagates on an effective curved spacetime. Section 3.1, (3.16).

Theorem 3.2 (Gravity–Ether Identity). The PG metric is exactly the acoustic metric for ether flowing at free-fall velocity. Section 3.3, (3.21).

Theorem 3.3 (Emergent Lorentz Invariance). Lorentz symmetry is exact at $\lambda \gg \ell_e$, violated at $O(\ell_e/\lambda)^2$. Section 3.8.

Theorem 3.4 (Kerr–Ether Identity). Kerr metric in Doran coordinates is the ether metric with spiralling flow; decomposes into gravitoelectric + gravitomagnetic sectors. Section 3.10.10, (3.90).

Theorem 3.5 (Nonlinear Ether Field Equation). The ether's complete field equation is the Einstein equation $G_{\mu\nu} = (8\pi G/c^4)T_{\mu\nu}$, derived via Weinberg–Deser–Lovelock uniqueness. Section 3.11.8, (3.151).

Theorem 3.6 (Post-Newtonian Parameters). $\beta = \gamma = 1$; all ten PPN parameters match GR. Section 3.12.5–3.12.8, Eqs. 3.181, 3.186.

Theorem 3.7 (Hawking Radiation). Ether horizon at $v = c$ produces thermal radiation at $T_H = \hbar c^3/(8\pi k_B GM)$. Section 3.13.6, (3.220).

Theorem 3.8 (Gravitational Wave Polarisations). Exactly two tensor modes ($+$ and $\times$); scalar breathing mode is non-radiative. Section 3.14.9.

Theorem 3.9 (Unruh Radiation). Uniformly accelerating observer detects thermal radiation at $T_U = \hbar a/(2\pi k_B c)$. Section 3.15.4, (3.258).

Theorem 3.10 (Einstein Equation from Ether Thermodynamics). $G_{\mu\nu} + \Lambda g_{\mu\nu} = (8\pi G/c^4)T_{\mu\nu}$ derived from ZPF entanglement entropy, Unruh temperature, and the Clausius relation. $G$ determined by ZPF mode counting. Section 3.17.8, (3.324).

Theorem 4.1 (Gravitational Dielectric). Superfluid ether EOS yields MOND: $\nabla\!\cdot\![\mu_e\,\mathbf{g}] = -4\pi G\rho_m$. Section 4.2, (4.17).

Theorem 4.2 (ZPF Lorentz Invariance). $\rho(\omega) \propto \omega^3$ is uniquely Lorentz-invariant; gives $w = -1$. Section 4.3, (4.143).

Theorem 4.3 (Cosmological Perturbation Reduction). Ether perturbation equations reduce to $\Lambda$CDM for $k \ll k_J$; corrections $(k/k_J)^2 < 4 \times 10^{-7}$ at CMB scales. CMB compatibility follows as corollary. Section 4.5.5.

Proposition 4.4 (MOND Acceleration from Cosmology). $a_0 = \Omega_{\text{DM}} c H_0/\sqrt{2}$; agrees with observation to 0.5%; evolves with redshift as $(1+z)^{3/2}$ during matter domination. Section 4.7.12, (4.236).

Definition 5.1 (Plasma as Perturbed Ether). Three criteria: quasi-neutrality, collective response, statistical validity. Section 5.2.

Theorem 5.1 (EM Dielectric). Stix tensor derived from ether SED dynamics. Section 5.4, (5.46)–(5.47).

Theorem 5.2 (Alfvén–Ether Equivalence). $v_A = \sqrt{G_{\text{eff}}/\rho_{\text{eff}}}$ with $G_{\text{eff}} = B_0^2/\mu_0$. Section 5.5, (5.79).

Theorem 6.1 (Boyer). SED oscillator reaches $\langle E\rangle = \hbar\omega_0/2$. Section 6.2, (6.25).

Theorem 6.3 (Hydrogen Ground State). SED equilibrium radius $= a_B = 0.529$ Å (Bohr radius; not to be confused with the MOND acceleration $a_0$ of §4). Section 6.3.

Theorem 7.1 (Nelson). Stochastic diffusion with $D = \hbar/(2m)$ yields Schrödinger equation. Section 7.2, (7.25).

Theorem 8.1 (Bell–CHSH). Local hidden variables: $|S| \leq 2$. Section 8.1.

Theorem 8.3 (SED Entanglement). Parametric coupling + ZPF → entangled Gaussian state. Section 8.3.

Theorem 8.5 (Bell Violation, $T = 0$). $|S| = 2\sqrt{2}$ via Nelson osmotic velocity. Section 8.5.

Proposition 8.3 (No-Signalling). Alice's marginals independent of Bob's setting. Section 8.5.

Proposition 3.1 (Sourced Ether Wave Equation). $\Box\Phi = -4\pi G\rho_m$ gives GW generation; Peters formula follows. Section 3.7.2, (3.42a).

Proposition 3.2 (Spatial Non-Flatness). Kerr–Doran spatial sections have intrinsic curvature $O(r_sa^2/r^3)$; vanishes for $a = 0$ or $M = 0$. Section 3.10.7.

Proposition 6.1 (Transverse Microstructure Constraint). Single-parameter model $\ell_e = \hbar/(m_ec)$ fails; ether must be multi-component. Section 6.6.4, (6.50).

Proposition 7.2 (Spin Emergence Pathway). Multi-component ether with nodal spectrum → spin-½ via Volovik's theorem. Section 7.7.

Proposition 7.3 (Bohmian Mechanics from Ether Dynamics). The Madelung velocity $\nabla S/m$ is the de Broglie–Bohm guidance velocity; the quantum potential is the ether's diffusion pressure; the guidance equation is the superfluid velocity equation. Section 7.6.5, (7.48).

Theorem 8.8 (Thermal Bell). $|S(T)| = 2\sqrt{2}/(1 + 2n_{\text{th}})^2$ — falsifiable prediction. Section 8.7, (8.81).

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PART I: FOUNDATIONS