justintymemiller

The Resonant Theory (TRT) models the physical vacuum as a continuous, compressible Tisza-Landau two-fluid substrate (the Quantum Plenum) governed by two strictly dimensionless electro-hydrodynamic invariants derived from the fine-structure constant: the Universal Acoustic Susceptibility A_RT = alpha^-1 / e = 50.412727 and the equilibrium normal-fluid mass fraction beta_TRT = e / A_RT = 0.05392055. Conditioned on six explicitly declared constitutive postulates (P1-P6) and discrete structural indices (Table 1), and anchored to the local present-epoch wave speed c_0 = 2.99792458e8 m/s and carrier frequency f_0 = 76.4496 MHz (L_0 = 3.92144 m, tau_0 = (2*pi*f_0)^-1 = 2.0818 ns), the framework establishes: (1) a universal topological soliton rest-energy functional H_sol(p, q, D) = E_e * [(p*q)*pi^D + Delta M_visc(beta_TRT)] on T^5 under which the electron is the (1,1,0) ground state (pi^0 = 1, H_sol = E_e = m_e*c_0^2) and the proton is the knotted (2,3,5) Trefoil state whose covering degree d = 6 sweeps D = 5 half-wave phase modes (pi^5 = 306.0197) plus poloidal dipole boundary drag (2/pi)*beta_TRT = 0.034327, yielding mu_TRT = H_sol(2,3,5)/H_sol(1,1,0) = 6*pi^5 + (2/pi)*beta_TRT = 1836.152436 (0.13 ppm from CODATA m_p/m_e) with zero measure mismatch; (2) a compressible Bernoulli cavitation nucleation mass floor mu_0 = A_RT*h*f_0/c_0^2 = 2.8414e-41 kg; (3) a curl-compatible zero-mean solenoidal regularized 3D vorticity PDE admitting an a priori global L2 enstrophy bound for smooth solutions with zero spatial mean on R^3 and T^3 (Theorem 1); (4) forward line-of-sight ray propagation s in [0, d_L] in a 1D quarter-wave causal horizon resonator (k_1*R_H = pi/2) deriving a strictly positive achromatic +8.47% apparent local Hubble shift (H_late = 73.11 km/s/Mpc from H_early = 67.40 km/s/Mpc); (5) a linearized Poisson hydrostatic pressure-depletion law reproducing Newtonian gravity and an emergent galactic acoustic acceleration threshold a_gal = pi*a_0 = pi*c_0*H_early*beta_TRT = 1.11e-10 m/s^2 reproducing flat galactic rotation curves and the baryonic Tully-Fisher plateau without dark matter; and (6) a pre-registered 2028-2030 Europa Clipper outer-cruise Doppler falsification test (a_plenum = 8.47 +/- 0.34 x 10^-10 m/s^2) evaluated against a 100% mathematically exhaustive four-regime decision protocol.

The Resonant Theory (TRT) models the physical vacuum as a continuous, compressible Tisza-Landau two-fluid substrate (the Quantum Plenum) governed by two strictly dimensionless electro-hydrodynamic invariants derived from the fine-structure constant: the Universal Acoustic Susceptibility A_RT = alpha^-1 / e = 50.412727 and the equilibrium normal-fluid mass fraction beta_TRT = e / A_RT = 0.05392055. Conditioned on six explicitly declared constitutive postulates (P1-P6) and anchored to the local present-epoch wave speed c_0 = 2.99792458e8 m/s and carrier frequency f_0 = 76.4496 MHz (L_0 = 3.92144 m), the framework establishes: (1) a constitutive Trefoil (2,3) torus-soliton rest-energy ratio mu_TRT = 6*pi^5 + (2/pi)*beta_TRT = 1836.152436 (0.13 ppm from CODATA m_p/m_e); (2) a classical Bernoulli cavitation mass floor mu_0 = A_RT*h*f_0/c_0^2 = 2.8414e-41 kg; (3) a curl-compatible solenoidal Leray-Helmholtz regularized 3D vorticity PDE admitting a complete a priori global L2 enstrophy bound for smooth solutions on R^3 and T^3 (Theorem 1); (4) an exact 1D quarter-wave cosine resonator mode (k_1*R_H = pi/2) predicting a +8.47% apparent local Hubble shift (H_late = 73.11 km/s/Mpc from H_early = 67.40 km/s/Mpc); (5) a linearized Poisson hydrostatic pressure-depletion law reproducing Newtonian gravity; and (6) a pre-registered 2028-2030 Europa Clipper outer-cruise Doppler falsification test (a_plenum = 8.47 +/- 0.34 x 10^-10 m/s^2 against a 3-sigma navigation noise floor of 0.65 x 10^-10 m/s^2).

The Resonant Theory (TRT) models the physical vacuum as a continuous, compressible Tisza-Landau two-fluid substrate (the Quantum Plenum) governed by two strictly dimensionless electro-hydrodynamic invariants derived from the fine-structure constant: the Universal Acoustic Susceptibility A_RT = alpha^-1 / e = 50.412727 and the equilibrium normal-fluid mass fraction beta_TRT = e / A_RT = 0.05392055. Conditioned on six explicitly declared constitutive postulates (P1-P6) and discrete structural indices (Table 1), and anchored to the local present-epoch wave speed c_0 = 2.99792458e8 m/s and carrier frequency f_0 = 76.4496 MHz (L_0 = 3.92144 m, tau_0 = (2*pi*f_0)^-1 = 2.0818 ns), the framework establishes: (1) a lepton-baryon ground-state topological soliton rest-energy functional H_sol(p, q, D) = E_e * [(p*q)*pi^D + Delta M_visc(p, beta_TRT)] on T^5 with pairwise poloidal strand shear Delta M_visc(p, beta_TRT) = binom(p,2)*(2/pi)*beta_TRT = (p*(p-1)/pi)*beta_TRT, under which the unknotted electron is the (1,1,0) ground state (binom(1,2)=0 => Delta M_visc = 0, H_sol = E_e = m_e*c_0^2) and the proton is the knotted (2,3,5) Trefoil state whose covering map has degree d = 6, sweeping D = 5 radian-normalized phase modes (pi^5 = 306.0197) plus single-pair strand shear (2/pi)*beta_TRT = 0.034327, evaluating the constitutive ratio mu_TRT = H_sol(2,3,5)/H_sol(1,1,0) = 6*pi^5 + (2/pi)*beta_TRT = 1836.152436 (0.13 ppm from CODATA m_p/m_e); (2) a Mach-1 sonic-horizon PDE characteristic degeneracy where steady compressible potential flow (delta_ij - u_i*u_j/c_0^2)*partial_i u_j = 0 exhibits parabolic characteristic degeneracy at the Mach-1 sonic horizon (|u| = c_0, with hyperbolic flow for |u| > c_0; rho_sonic = rho_0*e^-1/2, Delta P_sonic = 0.39347 P_0), defining the constitutive core nucleation mass floor mu_0 = A_RT*h*f_0/c_0^2 = 2.8414e-41 kg without vacuum density singularity (rho -> 0); (3) a curl-compatible zero-mean solenoidal regularized 3D vorticity PDE admitting an a priori finite-horizon Grönwall enstrophy bound on R^3 and time-uniform absorbing-ball bound on T^3 for smooth solutions (Theorem 1); (4) forward line-of-sight ray propagation s in [0, d_L] in a 1D quarter-wave causal horizon resonator (k_1*R_H = pi/2) under the Postulate P5 macro-waveguide action-transfer closure deriving an apparent local Hubble shift (H_late = 73.11 km/s/Mpc from H_early = 67.40 km/s/Mpc); (5) a weak-field static acoustic pressure-depletion law nabla^2 P = 4*pi*G*rho_0*rho_M in a static substrate (u_substrate = 0, j_0 = 0, identically satisfying mass continuity partial_t rho + nabla.j = 0 without fluid drainage) held in exact hydrostatic momentum balance by carrier radiation reaction f_rad = +nabla P, where matter solitons of mass m_i experience wave-gradient force F_grad = -(m_i/rho_0)*nabla P yielding universal free-fall acceleration a = -(1/rho_0)*nabla P = -GM/r^2 strictly independent of body composition (Weak Equivalence Principle), alongside an emergent galactic acoustic acceleration threshold a_gal = pi*a_0 = pi*c_0*H_early*beta_TRT = 1.11e-10 m/s^2 matching Milgrom's scale to within 7.6% and flat rotation curves; and (6) a pre-registered prospective 2028-2030 Europa Clipper outer-cruise Doppler falsification test (a_plenum = 8.47 +/- 0.34 x 10^-10 m/s^2) evaluated against an exhaustive four-regime decision protocol.

The Resonant Theory (TRT) models the physical vacuum as a continuous, compressible Tisza-Landau two-fluid substrate (the Quantum Plenum) governed by two strictly dimensionless electro-hydrodynamic invariants derived from the fine-structure constant: the Universal Acoustic Susceptibility A_RT = alpha^-1 / e = 50.412727 and the equilibrium normal-fluid mass fraction beta_TRT = e / A_RT = 0.05392055. Conditioned on six explicitly declared constitutive postulates (P1-P6) and discrete structural indices (Table 1), and anchored to the local present-epoch wave speed c_0 = 2.99792458e8 m/s and carrier frequency f_0 = 76.4496 MHz (L_0 = 3.92144 m, tau_0 = (2*pi*f_0)^-1 = 2.0818 ns), the framework establishes: (1) a lepton-baryon ground-state topological soliton rest-energy functional H_sol(p, q, D) = E_e * [(p*q)*pi^D + Delta M_visc(p, beta_TRT)] on T^5 with pairwise poloidal strand shear Delta M_visc(p, beta_TRT) = binom(p,2)*(2/pi)*beta_TRT = (p*(p-1)/pi)*beta_TRT, under which the unknotted electron is the (1,1,0) ground state (binom(1,2)=0 => Delta M_visc = 0, H_sol = E_e = m_e*c_0^2) and the proton is the knotted (2,3,5) Trefoil state whose covering map has degree d = 6, sweeping D = 5 radian-normalized phase modes (pi^5 = 306.0197) plus single-pair strand shear (2/pi)*beta_TRT = 0.034327, evaluating the constitutive ratio mu_TRT = H_sol(2,3,5)/H_sol(1,1,0) = 6*pi^5 + (2/pi)*beta_TRT = 1836.152436 (0.13 ppm from CODATA m_p/m_e); (2) a Mach-1 sonic-horizon PDE characteristic degeneracy where steady compressible potential flow (delta_ij - u_i*u_j/c_0^2)*partial_i u_j = 0 transitions from elliptic to hyperbolic at |u| = c_0 (rho_sonic = rho_0*e^-1/2, Delta P_sonic = 0.39347 P_0), defining the constitutive core nucleation mass floor mu_0 = A_RT*h*f_0/c_0^2 = 2.8414e-41 kg without vacuum density singularity (rho -> 0); (3) a curl-compatible zero-mean solenoidal regularized 3D vorticity PDE admitting an a priori global L2 enstrophy bound for smooth solutions with zero spatial mean on R^3 and T^3 (Theorem 1); (4) forward line-of-sight ray propagation s in [0, d_L] in a 1D quarter-wave causal horizon resonator (k_1*R_H = pi/2) under the Postulate P5 macro-waveguide action-transfer closure deriving an apparent local Hubble shift (H_late = 73.11 km/s/Mpc from H_early = 67.40 km/s/Mpc); (5) a weak-field static acoustic pressure-depletion law nabla^2 P = 4*pi*G*rho_0*rho_M in a static substrate (u_substrate = 0, j_0 = 0, identically satisfying mass continuity partial_t rho + nabla.j = 0 everywhere in the exterior vacuum) where the exterior harmonic depression nabla^2 P = 0 yields acoustic radiation buoyancy acceleration g = -(1/rho_0)*nabla P = -GM/r^2 reproducing Newtonian gravity dynamically without fluid drainage (with test-parcel kinematic free-fall speed v(r) = sqrt(2GM/r) from Bernoulli energy conservation), alongside an emergent galactic acoustic acceleration threshold a_gal = pi*a_0 = pi*c_0*H_early*beta_TRT = 1.11e-10 m/s^2 matching Milgrom's scale to within 7.6% and flat rotation curves; and (6) a pre-registered prospective 2028-2030 Europa Clipper outer-cruise Doppler falsification test (a_plenum = 8.47 +/- 0.34 x 10^-10 m/s^2) evaluated against an exhaustive four-regime decision protocol.

The Resonant Theory (TRT) models the physical vacuum as a continuous, compressible Tisza-Landau two-fluid substrate (the Quantum Plenum) governed by two strictly dimensionless electro-hydrodynamic invariants derived from the fine-structure constant: the Universal Acoustic Susceptibility A_RT = alpha^-1 / e = 50.412727 and the equilibrium normal-fluid mass fraction beta_TRT = e / A_RT = 0.05392055. Conditioned on six explicitly declared constitutive postulates (P1-P6) and discrete structural indices (Table 1), and anchored to the local present-epoch wave speed c_0 = 2.99792458e8 m/s and carrier frequency f_0 = 76.4496 MHz (L_0 = 3.92144 m, tau_0 = (2*pi*f_0)^-1 = 2.0818 ns), the framework establishes: (1) a lepton-baryon ground-state topological soliton rest-energy functional H_sol(p, q, D) = E_e * [(p*q)*pi^D + Delta M_visc(p, beta_TRT)] on T^5 with pairwise poloidal strand shear Delta M_visc(p, beta_TRT) = binom(p,2)*(2/pi)*beta_TRT = (p*(p-1)/pi)*beta_TRT, under which the unknotted electron is the (1,1,0) ground state (binom(1,2)=0 => Delta M_visc = 0, H_sol = E_e = m_e*c_0^2) and the proton is the knotted (2,3,5) Trefoil state whose covering map has degree d = 6, sweeping D = 5 radian-normalized phase modes (pi^5 = 306.0197) plus single-pair strand shear (2/pi)*beta_TRT = 0.034327, evaluating the constitutive ratio mu_TRT = H_sol(2,3,5)/H_sol(1,1,0) = 6*pi^5 + (2/pi)*beta_TRT = 1836.152436 (0.13 ppm from CODATA m_p/m_e); (2) a Mach-1 sonic-horizon PDE characteristic degeneracy where steady compressible potential flow (delta_ij - u_i*u_j/c_0^2)*partial_i u_j = 0 transitions from elliptic to hyperbolic at |u| = c_0 (rho_sonic = rho_0*e^-1/2, Delta P_sonic = 0.39347 P_0), defining the constitutive core nucleation mass floor mu_0 = A_RT*h*f_0/c_0^2 = 2.8414e-41 kg without vacuum density singularity (rho -> 0); (3) a curl-compatible zero-mean solenoidal regularized 3D vorticity PDE admitting an a priori global L2 enstrophy bound for smooth solutions with zero spatial mean on R^3 and T^3 (Theorem 1); (4) forward line-of-sight ray propagation s in [0, d_L] in a 1D quarter-wave causal horizon resonator (k_1*R_H = pi/2) under the Postulate P5 macro-waveguide action-transfer closure deriving an apparent local Hubble shift (H_late = 73.11 km/s/Mpc from H_early = 67.40 km/s/Mpc); (5) a weak-field linearized acoustic pressure-depletion law nabla^2 P = 4*pi*G*rho_0*rho_M balanced by steady convective superfluid sink flow (u_s * nabla)u_s = -(1/rho_0)*nabla P = -GM/r^2 reproducing Newtonian gravity and an emergent galactic acoustic acceleration threshold a_gal = pi*a_0 = pi*c_0*H_early*beta_TRT = 1.11e-10 m/s^2 matching Milgrom's scale to within 7.6% and flat rotation curves; and (6) a pre-registered prospective 2028-2030 Europa Clipper outer-cruise Doppler falsification test (a_plenum = 8.47 +/- 0.34 x 10^-10 m/s^2) evaluated against an exhaustive four-regime decision protocol.

The Resonant Theory (TRT) models the physical vacuum as a continuous, compressible Tisza-Landau two-fluid substrate (the Quantum Plenum) governed by two strictly dimensionless electro-hydrodynamic invariants derived from the fine-structure constant: the Universal Acoustic Susceptibility A_RT = alpha^-1 / e = 50.412727 and the equilibrium normal-fluid mass fraction beta_TRT = e / A_RT = 0.05392055. Conditioned on six explicitly declared constitutive postulates (P1-P6) and discrete structural indices (Table 1), and anchored to the local present-epoch wave speed c_0 = 2.99792458e8 m/s and carrier frequency f_0 = 76.4496 MHz (L_0 = 3.92144 m, tau_0 = (2*pi*f_0)^-1 = 2.0818 ns), the framework establishes: (1) a universal topological soliton rest-energy functional H_sol(p, q, D) = E_e * [(p*q)*pi^D + Delta M_visc(p, beta_TRT)] on T^5 with closed-form topological viscous drag Delta M_visc(p, beta_TRT) = (p*(p-1)/pi)*beta_TRT, under which the electron is the (1,1,0) ground state (Delta M_visc = 0, H_sol = E_e = m_e*c_0^2) and the proton is the knotted (2,3,5) Trefoil state whose covering degree d = 6 sweeps D = 5 half-wave phase modes (pi^5 = 306.0197) plus poloidal dipole boundary drag (2/pi)*beta_TRT = 0.034327, evaluating the constitutive ratio mu_TRT = H_sol(2,3,5)/H_sol(1,1,0) = 6*pi^5 + (2/pi)*beta_TRT = 1836.152436 (0.13 ppm from CODATA m_p/m_e) under a single uniform functional with zero measure mismatch; (2) a compressible acoustic cavitation mass floor mu_0 = A_RT*h*f_0/c_0^2 = 2.8414e-41 kg nucleating at the transonic flow velocity threshold (|u| = c_0, rho = rho_0*e^-1/2, Delta P_spinodal = 0.39347 P_0) with zero logarithmic vacuum singularity; (3) a curl-compatible zero-mean solenoidal regularized 3D vorticity PDE admitting an a priori global L2 enstrophy bound for smooth solutions with zero spatial mean on R^3 and T^3 (Theorem 1); (4) forward line-of-sight ray propagation s in [0, d_L] in a 1D quarter-wave causal horizon resonator (k_1*R_H = pi/2) under the Postulate P5 macro-waveguide action-transfer closure deriving an apparent local Hubble shift (H_late = 73.11 km/s/Mpc from H_early = 67.40 km/s/Mpc); (5) a linearized Poisson hydrostatic pressure-depletion law reproducing Newtonian gravity and an emergent galactic acoustic acceleration threshold a_gal = pi*a_0 = pi*c_0*H_early*beta_TRT = 1.11e-10 m/s^2 matching Milgrom's scale to within 7.6% and flat rotation curves; and (6) a pre-registered prospective 2028-2030 Europa Clipper outer-cruise Doppler falsification test (a_plenum = 8.47 +/- 0.34 x 10^-10 m/s^2) evaluated against an exhaustive four-regime decision protocol.

The Resonant Theory (TRT) models the physical vacuum as a continuous, compressible Tisza-Landau two-fluid substrate (the Quantum Plenum) governed by two strictly dimensionless electro-hydrodynamic invariants derived from the fine-structure constant: the Universal Acoustic Susceptibility A_RT = alpha^-1 / e = 50.412727 and the equilibrium normal-fluid mass fraction beta_TRT = e / A_RT = 0.05392055. Conditioned on six explicitly declared constitutive postulates (P1-P6) and discrete structural indices (Table 1), and anchored to the local present-epoch wave speed c_0 = 2.99792458e8 m/s and carrier frequency f_0 = 76.4496 MHz (L_0 = 3.92144 m, tau_0 = (2*pi*f_0)^-1 = 2.0818 ns), the framework establishes: (1) a universal topological soliton rest-energy functional H_sol(p, q, D) = E_e * [(p*q)*pi^D + Delta M_visc(p, beta_TRT)] on T^5 with closed-form topological viscous drag Delta M_visc(p, beta_TRT) = (p*(p-1)/pi)*beta_TRT, under which the electron is the (1,1,0) ground state (Delta M_visc = 0, H_sol = E_e = m_e*c_0^2) and the proton is the knotted (2,3,5) Trefoil state whose covering degree d = 6 sweeps D = 5 half-wave phase modes (pi^5 = 306.0197) plus poloidal dipole boundary drag (2/pi)*beta_TRT = 0.034327, yielding mu_TRT = H_sol(2,3,5)/H_sol(1,1,0) = 6*pi^5 + (2/pi)*beta_TRT = 1836.152436 (0.13 ppm from CODATA m_p/m_e) under a single uniform functional with zero measure mismatch; (2) a compressible spinodal acoustic cavitation nucleation mass floor mu_0 = A_RT*h*f_0/c_0^2 = 2.8414e-41 kg nucleating at the transonic spinodal limit (|u| = c_0, rho = rho_0*e^-1/2, Delta P_spinodal = (1 - e^-1/2)*P_0 = 0.39347 P_0) with zero logarithmic vacuum singularity; (3) a curl-compatible zero-mean solenoidal regularized 3D vorticity PDE admitting an a priori global L2 enstrophy bound for smooth solutions under Navier-Stokes with cubic Hall-Vinen damping (Theorem 1); (4) forward line-of-sight ray propagation s in [0, d_L] in a 1D quarter-wave causal horizon resonator (k_1*R_H = pi/2) deriving a strictly positive achromatic +8.47% apparent local Hubble shift (H_late = 73.11 km/s/Mpc from H_early = 67.40 km/s/Mpc) and midpoint geometric-mean BAO scale lambda_BAO = 152.53 Mpc with zero coordinate ambiguity; (5) a linearized Poisson hydrostatic pressure-depletion law reproducing Newtonian gravity and an emergent galactic acoustic acceleration threshold a_gal = pi*a_0 = pi*c_0*H_early*beta_TRT = 1.11e-10 m/s^2 matching Milgrom's scale to within 7.6% and reproducing the baryonic Tully-Fisher flat rotation plateau without dark matter; and (6) a pre-registered 2028-2030 Europa Clipper outer-cruise Doppler falsification test (a_plenum = 8.47 +/- 0.34 x 10^-10 m/s^2) evaluated against a 100% mathematically exhaustive four-regime decision protocol.

The Resonant Theory (TRT) models the physical vacuum as a continuous, compressible Tisza-Landau two-fluid substrate (the Quantum Plenum) governed by two strictly dimensionless electro-hydrodynamic invariants derived from the fine-structure constant: the Universal Acoustic Susceptibility A_RT = alpha^-1 / e = 50.412727 and the equilibrium normal-fluid mass fraction beta_TRT = e / A_RT = 0.05392055. Conditioned on six explicitly declared constitutive postulates (P1-P6) and discrete structural indices (Table 1), and anchored to the local present-epoch wave speed c_0 = 2.99792458e8 m/s and carrier frequency f_0 = 76.4496 MHz (L_0 = 3.92144 m, tau_0 = (2*pi*f_0)^-1 = 2.0818 ns), the framework establishes: (1) a constitutive Trefoil (2,3) torus-soliton rest-energy ratio mu_TRT = H_sol(2,3)/H_sol(1,1) = 6*pi^5 + (2/pi)*beta_TRT = 1836.152436 (0.13 ppm from CODATA m_p/m_e) defined on normalized cycle coordinates xi in [0,1]^5 on T^5 with unit core Vol_5(Omega_core) = 1, where the proton's 6 covering sheets oscillate in physical half-wave phase theta_k = pi*xi_k with metric Jacobian J_5 = det(d(theta)/d(xi)) = pi^5, sweeping total phase volume d * J_5 = 6*pi^5; (2) a classical Bernoulli cavitation mass floor mu_0 = A_RT*h*f_0/c_0^2 = 2.8414e-41 kg; (3) a curl-compatible solenoidal Leray-Helmholtz regularized 3D vorticity PDE admitting an a priori global L2 enstrophy bound for smooth solutions with zero spatial mean on R^3 and T^3 (Theorem 1); (4) an exact 1D quarter-wave cosine resonator mode (k_1*R_H = pi/2) with spatially uniform total acoustic energy density and constant spatial attenuation rate gamma_cav = k_1*beta_TRT predicting an achromatic +8.47% apparent local Hubble shift (H_late = 73.11 km/s/Mpc from H_early = 67.40 km/s/Mpc); (5) a linearized Poisson hydrostatic pressure-depletion law reproducing Newtonian gravity and an emergent galactic acoustic acceleration threshold a_gal = pi*a_0 = pi*c_0*H_early*beta_TRT = 1.11e-10 m/s^2 reproducing flat galactic rotation curves and the baryonic Tully-Fisher plateau without dark matter; and (6) a pre-registered 2028-2030 Europa Clipper outer-cruise Doppler falsification test (a_plenum = 8.47 +/- 0.34 x 10^-10 m/s^2 against a 3-sigma navigation noise floor of 0.65 x 10^-10 m/s^2).

The Resonant Theory (TRT) models the physical vacuum as a continuous, compressible Tisza-Landau two-fluid substrate (the Quantum Plenum) governed by two strictly dimensionless electro-hydrodynamic invariants derived from the fine-structure constant: the Universal Acoustic Susceptibility A_RT = alpha^-1 / e = 50.412727 and the equilibrium normal-fluid mass fraction beta_TRT = e / A_RT = 0.05392055. Conditioned on six explicitly declared constitutive postulates (P1-P6) and discrete structural indices (Table 1), and anchored to the local present-epoch wave speed c_0 = 2.99792458e8 m/s and carrier frequency f_0 = 76.4496 MHz (L_0 = 3.92144 m, tau_0 = (2*pi*f_0)^-1 = 2.0818 ns), the framework establishes: (1) a constitutive Trefoil (2,3) torus-soliton rest-energy ratio mu_TRT = H_sol(2,3)/H_sol(1,1) = 6*pi^5 + (2/pi)*beta_TRT = 1836.152436 (0.13 ppm from CODATA m_p/m_e) defined on a 6-sheeted branched covering torus T^5 -> T^5 of covering degree d = p*q = 6 normalized to the unknotted unit core Vol_5(Omega_core) = 1; (2) a classical Bernoulli cavitation mass floor mu_0 = A_RT*h*f_0/c_0^2 = 2.8414e-41 kg; (3) a curl-compatible solenoidal Leray-Helmholtz regularized 3D vorticity PDE admitting an a priori global L2 enstrophy bound for smooth solutions with zero spatial mean on R^3 and T^3 (Theorem 1); (4) an exact 1D quarter-wave cosine resonator mode (k_1*R_H = pi/2) and Hamiltonian action-transfer lemma predicting an achromatic +8.47% apparent local Hubble shift (H_late = 73.11 km/s/Mpc from H_early = 67.40 km/s/Mpc); (5) a linearized Poisson hydrostatic pressure-depletion law reproducing Newtonian gravity and an emergent acoustic acceleration floor a_gal = pi*c_0*H_early*beta_TRT = 1.11e-10 m/s^2 reproducing flat galactic rotation curves and the baryonic Tully-Fisher plateau without dark matter; and (6) a pre-registered 2028-2030 Europa Clipper outer-cruise Doppler falsification test (a_plenum = 8.47 +/- 0.34 x 10^-10 m/s^2 against a 3-sigma navigation noise floor of 0.65 x 10^-10 m/s^2).

The Resonant Theory (TRT) models the physical vacuum as a continuous, compressible Tisza-Landau two-fluid substrate (the Quantum Plenum) governed by two strictly dimensionless electro-hydrodynamic invariants derived from the fine-structure constant: the Universal Acoustic Susceptibility A_RT = alpha^-1 / e = 50.412727 and the equilibrium normal-fluid mass fraction beta_TRT = e / A_RT = 0.05392055. Conditioned on six explicitly declared constitutive postulates (P1-P6) and anchored to the local present-epoch wave speed c_0 = 2.99792458e8 m/s and carrier frequency f_0 = 76.4496 MHz (L_0 = 3.92144 m, tau_0 = (2*pi*f_0)^-1 = 2.0818 ns), the framework establishes: (1) a constitutive Trefoil (2,3) torus-soliton rest-energy ratio mu_TRT = H_sol(2,3)/H_sol(1,1) = 6*pi^5 + (2/pi)*beta_TRT = 1836.152436 (0.13 ppm from CODATA m_p/m_e) defined under a relative phase-volume winding functional on T^5 normalized to the unknotted unit core Vol_5(Omega_core) = 1; (2) a classical Bernoulli cavitation mass floor mu_0 = A_RT*h*f_0/c_0^2 = 2.8414e-41 kg; (3) a curl-compatible solenoidal Leray-Helmholtz regularized 3D vorticity PDE admitting a complete a priori global L2 enstrophy bound for smooth solutions with zero spatial mean on R^3 and T^3 (Theorem 1); (4) an exact 1D quarter-wave cosine resonator mode (k_1*R_H = pi/2) and achromatic cavity action-transfer bridge predicting a +8.47% apparent local Hubble shift (H_late = 73.11 km/s/Mpc from H_early = 67.40 km/s/Mpc); (5) a linearized Poisson hydrostatic pressure-depletion law reproducing Newtonian gravity; and (6) a pre-registered 2028-2030 Europa Clipper outer-cruise Doppler falsification test (a_plenum = 8.47 +/- 0.34 x 10^-10 m/s^2 against a 3-sigma navigation noise floor of 0.65 x 10^-10 m/s^2).