References

Dark Material Substrate — Consolidated Reference List

1. The Foundation Five

These five theory groups, when combined, paved the last mile of the substrate framework. Each contributed an essential structural element; none alone is sufficient.

[R1] Bush, J.W.M. & Oza, A.U. — “Hydrodynamic Quantum Analogs.” Annual Review of Fluid Mechanics 52, 2020, pp. 235–280.

The definitive review of pilot-wave hydrodynamics. Establishes that a vibrating particle in a responsive medium reproduces quantized orbits, tunneling, and interference — the three features (self-generated pilot wave, resonance, path memory) that underpin the substrate’s treatment of the electron. Orbiting and promenading walker pairs provide the template for spin-statistics.

Supports: Hydrogen Atom, Spin-Statistics, C4 (electron mechanism)

[R1b] Dagan, Y. & Bush, J.W.M. — “Hydrodynamic quantum field theory: the free particle.” Comptes Rendus Mécanique, 2020.

Particle modeled as a 2\omega_c source in a Klein-Gordon pilot field; self-propulsion stabilizes at p = \hbar k; phase-locking as attractor. Provides the dynamical mechanism for the electron’s self-generated wave field.

Supports: C4 (electron mechanism)

[R2] Volovik, G.E. — The Universe in a Helium Droplet. Oxford University Press, 2003.

The single most important source for the framework. Key chapters:

• Ch. 4–5: Two-fluid model of superfluid helium → template for co-rotating / counter-rotating decomposition
• Ch. 7: Emergent speed of light for Weyl fermion quasiparticles; BEC quasiparticle spectrum c = \hbar/(m_1\xi) (eq. 7.51, strong-coupling limit)
• Ch. 22–25: Vortex-core bound states → gauge fields; SU(2) from doublet structure of half-quantum vortex cores
• Ch. 29–30: Cosmological constant self-tuning via thermodynamic identity \varepsilon + P = 0; emergent gravity

: Supports: C1 (c derivation), C6 (F1: Kramers doublet), C7 (\Lambda self-tuning), SC3, Emergent Speed of Light, Two Fluids, Gravity, Higgs Field, Spacetime Dynamics

[R3] Simeonov, L. — “Quantum mechanics as a two-fluid stochastic theory.” arXiv:2509.02868, 2025.

Shows that the osmotic velocity \mathbf{v}_2 = -D\nabla(\ln \rho_1) of a counter-rotating fluid can be derived from the HVBK mutual friction force in the appropriate limit. Maps the Madelung equations as a fluid form of the Schrödinger equation. Provides the formal bridge from superfluid hydrodynamics to quantum mechanics.

Supports: C2 (\hbar derivation), Two Fluids → Quantum Potential

[R4] Khoury, J. — “Dark Matter Superfluidity.” Papers include arXiv:1507.01860 (2015), arXiv:1605.08443 (2016).

Dark matter as superfluid on galactic scales; MOND-like phonon-mediated force; CDM-to-MOND transition at Landau critical velocity v_L \sim 10^{-3}c. Provides the galactic-scale connection between the substrate and observed rotation curves.

Supports: C10 (DM density), C14 (MOND transition), Galactic Dynamics

[R5] Larichev, V.D. & Reznik, G.M. — “Two-dimensional solitary Rossby waves.” Doklady Akademii Nauk SSSR 231, 1976.

The original modon paper. Derives the dispersion relation and matching conditions for dipole vortex streams that propagate against the background flow. The modon boundary matching (Bessel function j_{11}, K = j_{11}^2 + 1) is a structural pillar of the bridge equation.

Supports: C1 (modon speed = c), Emergent Speed of Light, Photon as Modon, bridge equation (K factor)

[R6] Saffman, P.G. — Vortex Dynamics. Cambridge University Press, 1992.

Ch. 3 (§3.11–3.12): vortex pair dynamics. Ch. 7: point vortex systems, Onsager negative-temperature states. Ch. 8: vortex pairs and modons, dipole propagation theory. Ch. 11: co-rotating stability. Ch. 12: 3D stability of vortex configurations. Provides the mathematical machinery for boundary layer dynamics and the five-pillar lattice stability argument (Step D of the bridge equation).

Supports: Photon as Modon, bridge equation (Step D, five-pillar argument), lattice geometry

[R7] Aftalion, A., Blanc, X. & Dalibard, J. — “Vortex patterns in a fast rotating Bose-Einstein condensate.” Physical Review A 71, 023611, 2005.

Energy functional for vortex lattice in rotating BEC. Adapted for the substrate’s constrained equilibrium (Step E of bridge equation). Key result: the Abrikosov parameter \beta_A cancels in the energy ratio.

Supports: Bridge equation (Step E, constrained optimization)

[R8] Fetter, A.L. — “Rotating trapped Bose-Einstein condensates.” Reviews of Modern Physics 81, 647, 2009. [arXiv:0801.2312]

Confirms \xi_\text{GP} = \hbar/(\sqrt{2}\,m\,c_s) — the GP healing length includes the \sqrt{2} from kinetic energy \hbar^2/(2m). This factor is the third structural pillar (1/\sqrt{2}) of the bridge equation.

Supports: Bridge equation (Step B, 1/\sqrt{2} factor)

2. Scattering Theory

Critical for the electroweak sector: Weinberg angle, fine structure constant, and the three-constant chain.

[R9] Kopnin, N.B. — Theory of Nonequilibrium Superconductivity. Oxford University Press, 2001.

Esp. Ch. 3, Ch. 14. HVBK coefficients from microscopic scattering; Breit-Wigner formula \alpha_{mf} = \tfrac{1}{2}\sin 2\delta_0; energy-dependent \alpha_{mf}(E); CdGM (Caroli–de Gennes–Matricon) bound-state spectrum; minigap \omega_0 and scattering time \tau. The convention \alpha_{mf} = \tfrac{1}{2}\sin 2\delta_0 (weak-scattering branch) is used throughout the framework.

Supports: C6 (\alpha derivation), C8 (Weinberg angle), WIP-1, WIP-5, WIP-9, Weinberg Angle

[R10] Iordanskii–Sonin–Stone scattering formalism.

Vortex scattering formalism: \alpha_{mf} = \tfrac{1}{2}\sin 2\delta_0; dissipative/reactive decomposition; weak-scattering branch selection. The substrate uses the Sonin notation and the Iordanskii force decomposition.

Primary papers: Iordanskii, S.V. (1964); Sonin, E.B. — Rev. Mod. Phys. 59, 87, 1987; Stone, M. (2000).

Supports: C6, C8, SC5

[R11] Stone, M. — “Iordanskii Force and the Gravitational Aharonov-Bohm Effect for a Moving Vortex.” arXiv:cond-mat/9909313, 2000.

Berry phase for quasiparticle-vortex scattering; spectral asymmetry; independent route to g^2 = 4\sin^2\delta_0 via Berry curvature flux integral. Provides Route 2 confirmation of the fine structure constant derivation.

Supports: C6 (Route 2), SC5

[R12] Thouless, D.J., Ao, P. & Niu, Q. — “Transverse Force on a Quantized Vortex in a Superfluid.” Physical Review Letters 76, 1996.

Topological origin of transverse force coefficients; Berry phase connection. Confirms that vortex scattering coefficients have topological protection.

Supports: C6, SC5

3. Analog Gravity & General Relativity

How the substrate generates GR as its low-energy effective theory.

[R13] Barceló, C., Liberati, S. & Visser, M. — “Analogue gravity.” Living Reviews in Relativity 8, 12, 2005. Also: gr-qc/0104001, gr-qc/0106002, gr-qc/0011026.

Acoustic metric exact at kinematic level; demonstrates that dynamic equivalence requires fluid EOM to produce correct metric response. The linearized substrate satisfies this. Provides the formal framework (BLV framework) for deriving GR from fluid dynamics.

Supports: SC1, SC2, S3.7, bridge equation (Step A), Spacetime Dynamics

[R14] Zloshchastiev, K.G. — “Superfluid vacuum theory.” 2023.

Derives speed of light from superfluid vacuum properties. Complements Volovik’s quasiparticle spectrum with an alternative derivation route.

Supports: C1, Emergent Speed of Light

[R15] Unruh, W.G. — “Experimental Black-Hole Evaporation?” Physical Review Letters 46, 1351, 1981.

Original acoustic metric derivation: sound in a flowing fluid propagates on an effective curved spacetime. Foundation for the ebbing current = Schwarzschild flow identification.

Supports: Spacetime Dynamics: Ebbing Current

[R16] Painlevé, P. (1921) / Gullstrand, A. (1922).

Painlevé-Gullstrand form of the Schwarzschild metric — “rain coordinates.” The substrate’s ebbing current maps exactly to this form: ds^2 = -c^2 dt^2 + (dr - v_\text{ebb}\,dt)^2 + r^2 d\Omega^2 with v_\text{ebb} = \sqrt{2GM/r}.

Supports: SC1, Spacetime: Acoustic Metric

[R17] Hamilton, A.J.S. & Lisle, J.P. — “The river model of black holes.” American Journal of Physics 76, 519, 2008.

PG metric interpreted as literal inflow — “the river of space.” Direct physical analog of the substrate’s ebbing current.

Supports: Spacetime: Acoustic Metric

[R66] Sakharov, A.D. — “Vacuum Quantum Fluctuations in Curved Space and the Theory of Gravitation.” Doklady Akademii Nauk SSSR 177, 70–71, 1967. [Translated in Soviet Physics Doklady 12, 1040, 1968.]

The induced gravity hypothesis: the Einstein-Hilbert action is not fundamental but arises as the leading one-loop correction from quantum fields propagating on a curved background. In the substrate, the BLV acoustic metric [R13] provides the curved background, and the Seeley-DeWitt heat-kernel coefficient a_1 = R/6 generates the \int\sqrt{-g}\,R\,d^4x term in the effective action. This is Step A of the bridge equation derivation: the 4\pi in \kappa_q\Omega_v = 4\pi c^2 is the Gauss’s law factor from gravitational self-consistency via Sakharov’s mechanism.

Supports: Bridge equation (Step A, 4\pi factor), Bridge Equation

4. Quantum Foundations

The interpretive backbone: how fluid dynamics reproduces quantum mechanics.

[R18] Nelson, E. — “Derivation of the Schrödinger Equation from Newtonian Mechanics.” Physical Review 150, 1079, 1966.

Stochastic mechanics: quantum potential emerges from diffusion in a fluctuating medium. Provides the formal connection between the substrate’s counter-rotating diffusion and the quantum potential.

Supports: Two Fluids → Quantum Potential

[R19] Bohm, D. & Vigier, J.-P. — “Model of the Causal Interpretation of Quantum Theory in Terms of a Fluid with Irregular Fluctuations.” Physical Review 96, 208, 1954.

Subquantum fluctuations in a fluid medium. Establishes that a stochastic fluid can reproduce pilot-wave dynamics. Historical precursor to the substrate’s two-fluid decomposition.

Supports: Two Fluids → Quantum Potential

[R20] Hestenes, D. — Space-Time Algebra. Gordon and Breach, 1966; 2nd ed. Birkhäuser, 2015. Also: “The Zitterbewegung Interpretation of Quantum Mechanics.” Foundations of Physics 20, 1990.

Geometric algebra / spinors; Zitterbewegung interpretation of spin as physical rotation. Informs the substrate’s treatment of spin as angular momentum of the effective quantum about its axis.

Supports: Spin-Statistics (spin measurement)

[R21] de Broglie, L. — Pilot wave theory (1927).

Compton vibration → de Broglie wavelength chain. The substrate recovers this as a three-line derivation from modon phase-locking.

Supports: Three-line derivation (historical context)

[R22] Valentini, A. — Non-equilibrium quantum mechanics papers.

Explores deviations from Born-rule statistics in pilot-wave theory. Relevant to the substrate’s prediction that Born-rule violations may be detectable in extreme conditions.

Supports: Observational Predictions

[R23] ’t Hooft, G. — “The Cellular Automaton Interpretation of Quantum Mechanics.” Springer, 2016.

Deterministic underpinning of quantum mechanics via discrete substrate. Shares philosophical motivation with the substrate framework’s deterministic fluid dynamics.

Supports: Observational Predictions (context)

[R69] Bell, J.S. — “On the Einstein Podolsky Rosen Paradox.” Physics Physique Fizika 1, 195–200, 1964.

Proves that any theory satisfying realism, locality, and measurement independence must obey |S| \leq 2 for certain correlation measurements. The substrate framework is realistic and measurement-independent but violates locality at the sub-emergent level: a torsional Kelvin wave on a topologically protected half-quantum vortex channel propagates the measurement disturbance at v_\text{ch} \gg c. The geometric identity R_A(-\hat{\mathbf{s}}_0) = -\hat{\mathbf{a}} erases the hidden variable from B’s state, yielding E(\theta) = -\cos\theta exactly with no classical dilution. No-signaling is preserved by averaging over the random hidden axis \hat{\mathbf{s}}_0.

Supports: Observational Predictions (Bell’s theorem and entanglement)

[R70] Clauser, J.F., Horne, M.A., Shimony, A. & Holt, R.A. — “Proposed Experiment to Test Local Hidden-Variable Theories.” Physical Review Letters 23, 880–884, 1969.

The CHSH inequality |S| \leq 2: the experimentally testable form of Bell’s theorem. The substrate framework reproduces the quantum-optimal violation |S| = 2\sqrt{2} (the Tsirelson bound) within the channel’s range L < L_\text{max}, and predicts degradation toward the classical bound at extreme separations.

Supports: Observational Predictions (CHSH verification)

[R44] Bohr, N. — “On the Constitution of Atoms and Molecules.” Philosophical Magazine 26, 1–25, 1913.

Original quantized orbit model of the hydrogen atom. The substrate framework recovers Bohr’s energy levels exactly as boundary-matching eigenvalues. Explicitly invoked in Hydrogen Flywheel: “Bohr’s semiclassical model gets the energy levels exactly right for circular orbits” — because the Coulomb region (Layer 3) is smooth co-rotating flow where the quantum potential Q is small.

Supports: Hydrogen Flywheel (Coulomb region, semiclassical limit)

[R45] Lamb, W.E. & Retherford, R.C. — “Fine Structure of the Hydrogen Atom by a Microwave Method.” Physical Review 72, 241, 1947.

Experimental discovery that 2s_{1/2} and 2p_{1/2} are not degenerate — the Lamb shift of \approx 1058 MHz. In the substrate picture, this splitting arises from the dc1/dag substrate exerting slightly different average pressure on a spherically symmetric (s) vs. axially symmetric (p) boundary configuration. Listed as a quantitative prediction that would distinguish the framework from QED.

Supports: Hydrogen Flywheel (predictions)

[R46] Bethe, H.A. — “The Electromagnetic Shift of Energy Levels.” Physical Review 72, 339, 1947.

First successful QED calculation of the Lamb shift via vacuum fluctuations — the standard-model explanation the substrate framework seeks to reproduce mechanically. The substrate predicts the same shift from boundary-topology-dependent substrate pressure rather than virtual photon loops.

Supports: Hydrogen Flywheel (predictions, QED contrast)

[R47] London, F. — “Zur Theorie und Systematik der Molekularkräfte.” Zeitschrift für Physik 63, 245–279, 1930.

Quantum-mechanical derivation of the 1/r^6 van der Waals dispersion interaction. In the substrate picture, the r^{-6} dependence arises because the co-rotating signal makes a round trip (r^{-3} out, r^{-3} back) and the energy scales as the square of the fluctuation amplitude. Supports the Hydrogen Flywheel discussion of chemistry emerging from overlapping exponential tails.

Supports: Hydrogen Flywheel (exterior, van der Waals, chemistry)

[R59] Pauli, W. — “Über den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren.” Zeitschrift für Physik 31, 765, 1925.

The exclusion principle: no two identical fermions can occupy the same quantum state. The substrate framework derives this from boundary topology — two same-state fermions would require two same-chirality cores to share a single counter-rotating buffer layer, creating an irreconcilable shear instability that forces one into a different state.

Supports: Spin-Statistics (Pauli exclusion from boundary conflict)

[R60] Schwinger, J. — “On Quantum-Electrodynamics and the Magnetic Moment of the Electron.” Physical Review 73, 416, 1948.

First QED calculation of the anomalous magnetic moment: (g-2)/2 = \alpha/(2\pi). In the dual-spin gyroscope model, the same result emerges from the core-boundary moment asymmetry \eta = \sqrt{\alpha/(2\pi)} \approx 0.034, meaning the co-rotating core is \sim 3.4\% more massive than the counter-rotating boundary shell. This is the target for constraint C9.

Supports: Spin-Statistics (anomalous magnetic moment, C9)

[R61] Stern, O. & Gerlach, W. — “Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld.” Zeitschrift für Physik 9, 349, 1922.

Experimental demonstration that spin angular momentum is quantized — a beam of silver atoms splits into exactly two components in an inhomogeneous magnetic field. The dual-spin gyroscope model reproduces this: boundary-matching quantization at l = 1/2 allows exactly two steady states (m = \pm 1/2), and the phase-locking timescale \tau_\text{lock} \sim 10^{-21} s explains why the transition appears instantaneous.

Supports: Spin-Statistics (measurement, discrete outcomes)

4b. Nuclear & QCD Foundations

How the substrate’s deepest inner tier maps onto QCD phenomenology.

[R49] Yang, Y.-B., Liang, J., Bi, Y.-J., et al. — “Proton Mass Decomposition from the QCD Energy Momentum Tensor.” Physical Review Letters 121, 212001, 2018.

Lattice QCD calculation decomposing the proton mass: quark condensate (\sim 9\%), quark energy (\sim 32\%), gluon energy (\sim 36\%), and trace anomaly (\sim 23\%). Confirms that \sim 99\% of the proton’s 938.3 MeV comes from field energy rather than bare quark masses (\sim 9 MeV total). In the substrate picture, all non-quark-mass contributions map to counter-rotating boundary layer energy at the three-fold junction.

Supports: Proton Core (mass budget)

[R50] Gell-Mann, M. — “Isotopic Spin and New Unstable Particles.” Physical Review 92, 833, 1953. / Nishijima, K. — “Charge Independence Theory of V Particles.” Progress of Theoretical Physics 13, 285, 1955.

The charge formula Q = T_3 + Y/2. The substrate reinterprets: T_3 → quark orbital orientation relative to the junction axis (Type A contains axis → +1/2; Type B perpendicular → -1/2); Y → junction topology (+1/3 per branch, measuring three-fold structure). Yields Q_u = +2/3, Q_d = -1/3 from pure geometry.

Supports: Proton Core (charge fractions, Gell-Mann–Nishijima mapping)

[R51] Wilson, K.G. — “Confinement of Quarks.” Physical Review D 10, 2445, 1974.

Lattice gauge theory and the area-law criterion for quark confinement. The substrate maps the confining linear potential (V \propto \sigma r, with string tension \sigma \approx 0.18 GeV^2 \approx 0.9 GeV/fm) to a counter-rotating vortex sheet whose energy per unit length is constant — set by the local substrate density \rho_\text{cr} and velocity jump \Delta v at the nuclear scale, independent of tube length.

Supports: Proton Core (confinement, string tension)

5. Galactic Dynamics & Cosmological Dark Matter

[R24] McGaugh, S.S., Lelli, F. & Schombert, J.M. — “Radial Acceleration Relation in Rotationally Supported Galaxies.” Physical Review Letters 117, 201101, 2016.

Measured MOND acceleration scale g_\dagger = (1.20 \pm 0.02_\text{stat} \pm 0.24_\text{sys}) \times 10^{-10} m/s². The substrate derives a_0 = c\sqrt{G\rho_\text{DM}} = 1.20 \times 10^{-10} m/s², matching to <1\% with zero free parameters.

Supports: C14 (MOND acceleration scale), Galactic Dynamics

[R25] Milgrom, M. — “A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis.” Astrophysical Journal 270, 365, 1983.

Original MOND proposal. The substrate derives the MOND field equation \nabla \cdot [|\nabla\Phi|\nabla\Phi] \propto \rho_b from boundary parity symmetry, providing a physical mechanism for Milgrom’s empirical relation.

Supports: C14, Galactic Dynamics (historical context)

[R26] Berezhiani, L. & Khoury, J. — “Theory of Dark Matter Superfluidity.” Physical Review D 92, 103510, 2015.

Detailed superfluid DM model with phonon-mediated MOND force. Complements [R4] with the mathematical formalism for the CDM-to-MOND transition.

Supports: C10, C14

[R63] Bekenstein, J. & Milgrom, M. — “Does the Missing Mass Problem Signal the Breakdown of Newtonian Gravity?” Astrophysical Journal 286, 7–14, 1984.

The AQUAL (AQUAdratic Lagrangian) formulation of MOND: \nabla \cdot [\mu(|\nabla\Phi|/a_0)\,\nabla\Phi] = 4\pi G\rho_b. This is the covariant field-theoretic version of Milgrom’s empirical law — the target equation that the substrate’s parity-symmetric current-phase relation reproduces in the deep-MOND limit. The interpolation function \mu(x) mediates the Newtonian-to-MOND transition; in the substrate, it emerges from the competition between the Hubble-induced linear term and the parity-symmetric quadratic term in the boundary CPR.

Supports: C14 (MOND field equation), Galactic Dynamics (AQUAL formulation)

[R64] Tully, R.B. & Fisher, J.R. — “A New Method of Determining Distances to Galaxies.” Astronomy & Astrophysics 54, 661–673, 1977.

The original Tully-Fisher relation: luminosity scales as a power of rotation velocity. The baryonic version (M_b \propto v^4) follows from MOND as a zero-parameter consequence. The substrate derives the BTFR normalization from a_0 = c\sqrt{G\rho_\text{DM}}: v^4 = a_0 G M_b.

Supports: C14 (BTFR normalization), Galactic Dynamics (flat rotation curves, Tully-Fisher)

[R65] Lelli, F., McGaugh, S.S. & Schombert, J.M. — “SPARC: Mass Models for 175 Disk Galaxies with Spitzer Photometry and Accurate Rotation Curves.” Astronomical Journal 152, 157, 2016.

The SPARC (Spitzer Photometry & Accurate Rotation Curves) galaxy catalog: 175 galaxies with 3.6 μm photometry and high-quality HI/Hα rotation curves. Provides the dataset underlying the RAR [R24] and the BTFR exponent M_b \propto v^{3.98 \pm 0.06} with scatter consistent with observational error. The negligible intrinsic scatter is a key substrate prediction: universal boundary physics → universal RAR.

Supports: C14 (BTFR exponent, RAR scatter), Galactic Dynamics (observational data)

6. Vortex Lattice & Stability

Sources for the bridge equation’s five-pillar stability argument (Step D) and lattice geometry.

[R27] Tkachenko, V.K. — “On Vortex Lattices.” Soviet Physics JETP 23, 1049, 1966.

Proves that among all doubly-infinite 2D arrays of equal-strength vortices, the triangular (Abrikosov) lattice has the lowest energy. First pillar of the Step D argument.

Supports: Bridge equation (Step D, Pillar 1)

[R28] Jimenez, J. — “Stability of a pair of co-rotating vortices.” Journal of Fluid Mechanics 68, 49, 1975.

Proves co-rotating vortex pairs are stable to long-wave 3D perturbations (Saffman §12.2.3). Second pillar: parallel vortex lines don’t buckle.

Supports: Bridge equation (Step D, Pillar 2)

[R67] Crow, S.C. — “Stability Theory for a Pair of Trailing Vortices.” AIAA Journal 8, 2172–2179, 1970.

The Crow instability: counter-rotating vortex pairs are unstable to long-wavelength sinusoidal perturbations that grow exponentially, leading to reconnection and ring formation. In the bridge equation’s five-pillar argument (Step D, Pillar 3), the Crow instability is invoked as the mechanism that does not apply to the substrate’s same-sign vortex lattice — co-rotating arrays are immune because the self-induced velocity perturbation reinforces alignment rather than driving reconnection. This contrast (Crow for counter-rotating, Jimenez [R28] for co-rotating) is what ensures the lattice consists of straight parallel filaments.

Supports: Bridge equation (Step D, Pillar 3 — by exclusion), Bridge Equation

[R29] Moffatt, H.K. — “The degree of knottedness of tangled vortex lines.” Journal of Fluid Mechanics 35, 117, 1969.

Helicity conservation in inviscid flow. For parallel vortex lines, \mathbf{u} \perp \boldsymbol{\omega} everywhere, so helicity is identically zero — topologically selecting the parallel configuration. Third pillar.

Supports: Bridge equation (Step D, Pillar 3)

[R30] Onsager, L. — “Statistical Hydrodynamics.” Nuovo Cimento Supplemento 6, 279, 1949.

Negative-temperature theorem for point vortex systems: at negative temperature, same-sign vortices cluster, forming the most compact arrangement (\boldsymbol{\omega}' > 0 everywhere) at fixed vorticity magnitude. Fourth pillar.

Supports: Bridge equation (Step D, Pillar 4)

[R31] Baym, G. — “Tkachenko modes of vortex lattices.” 2003. [arXiv: cond-mat/0305294]

Stiff-limit Tkachenko wave speed c_T = \sqrt{\hbar\Omega/(4m)}. The 8\pi factor for lattice shear (vs the substrate’s 4\pi for GR coupling) provides the key distinction between Tkachenko elasticity and gravitational metric structure. Ratio \xi_\text{SC2}/\xi_\text{Baym} = 2^{1/3} (exact).

Supports: SC2 (clarification), WIP-13 (Tkachenko observables), bridge equation

[R32] Sonin, E.B. — “Vortex oscillations and hydrodynamics of rotating superfluids.” Reviews of Modern Physics 59, 87, 1987.

Comprehensive treatment of vortex dynamics in rotating superfluids. Vortex scattering formalism used in the Weinberg angle derivation.

Supports: Weinberg Angle, C6, C8

[R33] Barenghi, C.F., Skrbek, L. & Sreenivasan, K.R. — “Introduction to Quantum Turbulence.” Proceedings of the National Academy of Sciences 111 (Supplement 1), 2014. Also: review articles on HVBK equations and vortex dynamics in superfluids (2023).

Most accessible modern treatment of mutual friction and vortex dynamics in superfluids. Contains the HVBK (Hall–Vinen–Bekarevich–Khalatnikov) equations that provide the formal foundation for the two-fluid decomposition.

Supports: C2 (\hbar derivation), Two Fluids → Quantum Potential, Weinberg Angle

[R62] Vinen, W.F. — “Mutual Friction in a Heat Current in Liquid Helium II.” Proceedings of the Royal Society A 240, 114 & 128, 1957; “The Detection of Single Quanta of Circulation in Liquid Helium II.” Proceedings of the Royal Society A 260, 218, 1961.

The Vinen equation governs the evolution of quantized vortex line density L in a superfluid: dL/dt = \alpha_V |\mathbf{v}_{ns}| L^{3/2} - \beta_V \kappa L^2. In the dual-spin gyroscope model, the counter-rotating boundary’s vortex density self-regulates through the Vinen equation until the boundary-matching condition is satisfied — this is the nonlinear mechanism that drives spin measurement to one of exactly two discrete outcomes.

Supports: Spin-Statistics (measurement dynamics, vortex density regulation)

7. Experimental Analogs

[R34] Autti, S., Dmitriev, V.V., Mäkinen, J.T., et al. — “Observation of Half-Quantum Vortices in Topological Superfluid He-3.” Physical Review Letters 117, 255301, 2016.

Experimental observation of half-quantum vortices supporting Kramers-protected bound states in He-3 B-phase. Direct analog of the substrate’s half-quantum vortex cores that produce the Kramers doublet (C6, F1).

Supports: C6 (F1: Kramers doublet), Observational Predictions

[R35] He-3 A-phase (various authors).

Emergent “speed of light” for Weyl fermion quasiparticles: c_\text{eff} = v_F(\Delta/E_F)^{1/2}. Laboratory demonstration of emergent Lorentz invariance in a condensed matter system.

Supports: Spacetime Dynamics (introduction)

[R36] He-3 B-phase (various authors, including Autti et al.).

Higgs mechanism analog; chirality ordering; half-quantum vortices. The B-phase’s chirality transition is the template for the substrate’s Higgs mechanism (local chirality ordering of dc1/dag substrate).

Supports: Higgs Field

[R37] WR 140 — Wolf-Rayet + O-star binary (JWST, 2022).

Colliding stellar winds create spiral “pinwheel” shock structure. Kelvin-Helmholtz instabilities along the wind-collision interface produce vortical rolls — a vortex street at stellar scale. Visual analog of counter-rotating boundary formation.

Supports: Visual Context (astronomical analogs)

[R38] Eta Carinae — wind-wind collision zone.

X-ray-bright structures varying with orbital phase. Simulations (Parkin et al. 2011) show counter-rotating eddies along the contact discontinuity.

Supports: Visual Context (astronomical analogs)

[R39] PSR J0737-3039 — the double pulsar.

Two pulsars with measured spin orientations. Magnetosphere interaction creates standing wave patterns — electromagnetic “boundary layers” between two co-rotating systems.

Supports: Visual Context (astronomical analogs)

[R40] Type II superconductor vortex lattices.

Quantized vortex lines self-organize into Abrikosov lattice. Inter-vortex regions carry counter-rotating screening currents. Lattice spacing set by balance between vortex repulsion and external field. Visible analog of substrate boundary physics.

Supports: Conductors, bridge equation (lattice geometry)

[R68] Abo-Shaeer, J.R., Raman, C., Vogels, J.M. & Ketterle, W. — “Observation of Vortex Lattices in Bose-Einstein Condensates.” Science 292, 476–479, 2001.

First direct imaging of large, highly ordered triangular vortex lattices (\sim 100 vortices) in rotating BECs at MIT. The lattices are stable over thousands of rotation periods and adopt Tkachenko’s predicted triangular geometry, providing experimental confirmation of Pillars 1–3 and 5 of the bridge equation’s Step D argument. Complemented by ENS work (Madison et al., PRL 84, 806, 2000) on few-vortex nucleation and JILA (Engels et al., PRL 90, 170405, 2003) on lattice dynamics. These experiments demonstrate that co-rotating vortex lattices in quantum fluids spontaneously and stably adopt the same geometry the substrate requires.

Supports: Bridge equation (Step D, experimental confirmation), Bridge Equation

[R71] Michelson, A.A. & Morley, E.W. — “On the Relative Motion of the Earth and the Luminiferous Ether.” American Journal of Science 34, 333–345, 1887.

The null result that ruled out the classical luminiferous aether. The substrate framework passes this test because it is a superfluid, not a rigid elastic medium: the BLV acoustic metric [R13] is Lorentz-invariant at low energies, so all measurements by quasiparticle instruments (light, matter) see no preferred frame. The framework predicts that Lorentz invariance breaks down at the substrate granularity scale with a roton-minimum spectral signature — qualitatively different from generic quantum gravity corrections.

Supports: Observational Predictions (Michelson-Morley consistency)

[R72] Aspect, A., Dalibard, J. & Roger, G. — “Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell’s Inequalities.” Physical Review Letters 49, 1804–1807, 1982.

First Bell test with time-varying analyzers, closing the locality loophole at 12 m separation. The substrate requires only a modest channel speed (v_\text{ch}/c \sim 40, i.e., m_e/m_s \sim 1{,}100) to reproduce the observed -\cos\theta correlations at this separation.

Supports: Observational Predictions (Bell test constraints on v_\text{ch})

[R73] Handsteiner, J. et al. — “Cosmic Bell Test: Measurement Settings from Milky Way Stars.” Physical Review Letters 118, 060401, 2017.

Cosmic Bell test using quasar photons to set detector choices, closing the freedom-of-choice loophole at 600 m separation. In the substrate framework, this test constrains the measurement-independence assumption: detector settings chosen by cosmic sources billions of light-years away cannot be correlated with the local hidden variable \hat{\mathbf{s}}_0.

Supports: Observational Predictions (Bell test, measurement independence)

[R74] Yin, J. et al. — “Satellite-Based Entanglement Distribution over 1200 Kilometers.” Science 356, 1140–1144, 2017.

Micius satellite Bell test at 1,200 km separation — the longest-distance Bell test to date. Observed correlations consistent with E(\theta) = -\cos\theta with no degradation. In the substrate framework, this constrains v_\text{ch} > 4 \times 10^6\,c and m_e/m_s > \sim 10^8. Future tests at lunar (3.8 \times 10^5 km) or interplanetary (\sim 10^8 km) distances would probe deeper into the channel speed parameter space. Degradation of Bell correlations at extreme distance is the framework’s most distinctive testable prediction.

Supports: Observational Predictions (Bell test constraints, testable prediction)

[R75] Tonomura, A., Osakabe, N., Matsuda, T., et al. — “Evidence for Aharonov-Bohm Effect with Magnetic Field Completely Shielded from Electron Wave.” Physical Review Letters 56, 792–795, 1986.

Definitive demonstration of the Aharonov-Bohm effect using electron holography with superconducting-shielded toroidal magnets, eliminating all stray-field loopholes. In the substrate framework, the AB phase arises because the vector potential \mathbf{A} is the chirality phase gradient of the dc1/dag substrate — a topological wind with zero curl but nonzero circulation, analogous to the velocity field around a point vortex in a superfluid. The electron’s counter-rotating boundary precesses in this chirality wind, accumulating the geometric phase \Delta\varphi = e\Phi/\hbar.

Supports: Observational Predictions (Aharonov-Bohm interpretation)

7b. Condensed Matter & Superconductivity

The theoretical foundations that the Conductors chapter maps to substrate mechanics.

[R52] Bardeen, J., Cooper, L.N. & Schrieffer, J.R. — “Theory of Superconductivity.” Physical Review 108, 1175, 1957.

The BCS theory of superconductivity. Key results mapped to substrate equivalents: energy gap \Delta = 2\hbar\omega_D\exp(-1/N(0)V) → vortex binding energy of the shared counter-rotating seam; coherence length \xi_\text{BCS} = \hbar v_F/(\pi\Delta) → spatial extent of the pair vortex; critical temperature T_c = \Delta/(1.76\,k_B) → thermal destruction threshold for the shared vortex; isotope effect T_c \propto M^{-1/2} → phonon frequency scaling of channel distortion rate. The substrate framework treats BCS as the correct effective theory and seeks to derive its parameters from \alpha_\text{mf}.

Supports: Conductors (superconductivity, BCS mapping, open derivations)

[R53] Cooper, L.N. — “Bound Electron Pairs in a Degenerate Fermi Gas.” Physical Review 104, 1189, 1956.

Demonstrates that an arbitrarily weak attractive interaction binds electron pairs at the Fermi surface. In the substrate picture, the Cooper pair is a promenading pair (cf. Bush & Oza [R1]): two same-chirality electrons in anti-phase Compton breathing, bound by a shared counter-rotating vortex. The BCS singlet (↑↓) maps to opposite Compton phase rather than opposite circulation chirality.

Supports: Conductors (Cooper pair mechanism)

[R54] London, F. & London, H. — “The Electromagnetic Equations of the Supraconductor.” Proceedings of the Royal Society A 149, 71, 1935.

The two London equations: \partial\mathbf{J}/\partial t = (n_s e^2/m)\mathbf{E} (frictionless acceleration) and \nabla\times\mathbf{J} = -(n_s e^2/m)\mathbf{B} (Meissner screening). The substrate targets their derivation from HVBK mutual friction with the pair condensate as superfluid component (open derivation #1). The London penetration depth \lambda_L = \sqrt{m/(\mu_0 n_s e^2)} uses m_e (not m_\text{eff}) because it couples via charge, not circulation.

Supports: Conductors (Meissner effect, London equations, open derivation #1)

[R55] Ginzburg, V.L. & Landau, L.D. — “On the Theory of Superconductivity.” Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki 20, 1064, 1950.

Ginzburg-Landau theory and the order parameter \psi = \sqrt{\rho}\,e^{i\theta}. The GL parameter \kappa = \lambda_L/\xi distinguishes Type I (\kappa < 1/\sqrt{2}) from Type II (\kappa > 1/\sqrt{2}). In the substrate picture, \kappa is the ratio of cooperative screening depth to pair vortex extent — determining whether flux insertion disrupts the nearest pairs.

Supports: Conductors (Type I/II distinction, GL parameter)

[R56] Abrikosov, A.A. — “On the Magnetic Properties of Superconductors of the Second Group.” Soviet Physics JETP 5, 1174, 1957.

Prediction of the vortex lattice in Type II superconductors — quantized flux tubes in a triangular array. The substrate framework identifies this as substrate boundary physics made directly visible: the triangular geometry is the same Tkachenko-optimal packing [R27] that the bridge equation requires at the substrate scale. Each flux vortex is a channel where external co-rotating flow punches through the pair condensate, surrounded by counter-rotating screening eddies.

Supports: Conductors (Abrikosov lattice, Type II), bridge equation (lattice geometry analog)

[R57] Meissner, W. & Ochsenfeld, R. — “Ein neuer Effekt bei Eintritt der Supraleitfähigkeit.” Naturwissenschaften 21, 787, 1933.

Discovery of complete magnetic flux expulsion below T_c. In the substrate picture, the Cooper pairs collectively generate screening currents (cooperative co-rotating flows) that cancel external magnetic field within the bulk, protecting their shared counter-rotating vortex seams. The screening penetrates to depth \lambda_L before full cancellation.

Supports: Conductors (Meissner effect)

[R58] McMillan, W.L. — “Transition Temperature of Strong-Coupled Superconductors.” Physical Review 167, 331, 1968.

The McMillan equation relating T_c to Debye temperature, electron-phonon coupling \lambda_\text{ep}, and Coulomb pseudopotential \mu^*. Referenced as the benchmark for the substrate’s open derivation #4: predicting T_c across transition metals from d-shell filling fraction (boundary roughness proxy).

Supports: Conductors (open derivation #4, T_c prediction)

8. Data Sources

[R41] Particle Data Group (PDG). — Review of Particle Physics. Updated annually.

Measured values used as inputs or cross-checks: m_e = 0.511 MeV/c^2, m_p = 938.3 MeV/c^2, \alpha = 1/137.036, \sin^2\theta_W = 0.2312, (g-2)/2 = 0.001160, m_W = 80.4 GeV, m_Z = 91.2 GeV.

Supports: C4–C6, C8–C9, SC5

[R42] Planck Collaboration. — “Planck 2018 results. VI. Cosmological parameters.” Astronomy & Astrophysics 641, A6, 2020.

\rho_\text{DM} = 2.4 \times 10^{-27} kg/m³, \Omega_\text{DM} = 0.265, A_s = 2.1 \times 10^{-9}, n_s = 0.965, r_s = 147.09 Mpc, H_0 = 67.4 km/s/Mpc, \Lambda = 1.1 \times 10^{-52} m^{-2}.

Supports: C7, C10–C13, C14, bridge equation (0.18% precision check)

[R43] LIGO/Virgo Collaboration. — GW170817 multi-messenger observation, 2017.

Confirms |c_\text{GW}/c - 1| < 6 \times 10^{-15}. The substrate predicts exact equality (all low-energy excitations inherit c from BEC spectrum).

Supports: SC2 (observational validation)

[R48] NIST Atomic Spectra Database (ASD). — National Institute of Standards and Technology, Gaithersburg, MD. https://physics.nist.gov/asd

Source for hydrogen transition rates and spectroscopic data. Einstein A-coefficient for Lyman-alpha (n=2 \to 1): A_{21} = 6.27 \times 10^8 s^{-1}. Also: H_2 bond dissociation energy D_0 = 4.478 eV, equilibrium bond length r_e = 0.741 Å. The substrate framework must reproduce A_{21} from the modon formation timescale at the n=2 boundary — a constraint on f_\text{cross} and the substrate parameters.

Supports: Hydrogen Flywheel (transition rates, predictions, chemistry)

9. Textbook & Background Reading

Topic	Source	Used in
Madelung equations	Griffiths, Introduction to Quantum Mechanics + Simeonov [R3]	Two Fluids
Kinetic theory of gases	Reif, Fundamentals of Statistical and Thermal Physics	C2 (kinetic form of \hbar)
Vortex dynamics	Saffman [R6]; Lamb-Chaplygin dipole	Photon as Modon
Superfluid hydrodynamics	Volovik [R2] Ch. 4–5; Barenghi [R33] reviews	Two Fluids, Weinberg Angle
Geometric algebra / spinors	Hestenes [R20]	Spin-Statistics
Nonequilibrium superconductivity	Kopnin [R9] (HVBK coefficients, scattering phase shift)	Weinberg Angle
Gross-Pitaevskii equation	Fetter [R8]; Aftalion [R7]	Bridge equation, coherence length
Hydrogen energy levels & Bohr model	Bohr [R44]; Griffiths, Introduction to Quantum Mechanics	Hydrogen Flywheel
Lamb shift & QED corrections	Lamb & Retherford [R45]; Bethe [R46]	Hydrogen Flywheel (predictions)
Van der Waals / dispersion forces	London [R47]	Hydrogen Flywheel (exterior, chemistry)
Atomic spectral data	NIST ASD [R48]	Hydrogen Flywheel (transition rates)
Proton mass decomposition (lattice QCD)	Yang et al. [R49]	Proton Core (mass budget)
Gell-Mann–Nishijima charge formula	Gell-Mann [R50]; Nishijima [R50]	Proton Core (charge fractions)
Quark confinement & string tension	Wilson [R51]; lattice QCD	Proton Core (confinement)
Drude/Sommerfeld conduction model	Drude (1900); Sommerfeld (1928); Ashcroft & Mermin, Solid State Physics	Conductors (Drude parameters)
Bloch theorem & Bloch-Grüneisen T^5 law	Bloch (1929); Ashcroft & Mermin	Conductors (temperature regimes)
BCS theory & Cooper pairing	BCS [R52]; Cooper [R53]	Conductors (superconductivity)
London equations & Meissner effect	London & London [R54]; Meissner & Ochsenfeld [R57]	Conductors (Meissner, screening)
Ginzburg-Landau theory & Abrikosov lattice	Ginzburg-Landau [R55]; Abrikosov [R56]	Conductors (Type I/II, vortex lattice)
Josephson effect	Josephson, Physics Letters 1, 251, 1962	Conductors (mapping table)
Pauli exclusion principle	Pauli [R59]	Spin-Statistics (boundary conflict)
Anomalous magnetic moment (QED)	Schwinger [R60]	Spin-Statistics (C9, g-2)
Stern-Gerlach experiment	Stern & Gerlach [R61]	Spin-Statistics (measurement)
Vinen equation (vortex line density)	Vinen [R62]	Spin-Statistics (measurement dynamics)
Induced gravity (Sakharov mechanism)	Sakharov [R66]; Seeley-DeWitt heat kernel	Bridge Equation (Step A, 4\pi factor)
Vortex pair stability (co- vs counter-rotating)	Crow [R67]; Jimenez [R28]; Saffman [R6]	Bridge Equation (Step D, Pillars 2–3)
Rotating BEC vortex lattices	Abo-Shaeer et al. [R68]; Madison et al. (2000); Engels et al. (2003)	Bridge Equation (Step D, experimental)
Bell’s theorem & CHSH inequality	Bell [R69]; CHSH [R70]	Observational Predictions (entanglement)
Bell test experiments	Aspect et al. [R72]; Handsteiner et al. [R73]; Yin et al./Micius [R74]	Observational Predictions (channel speed constraints)
Michelson-Morley null result	Michelson & Morley [R71]	Observational Predictions (Lorentz invariance)
Aharonov-Bohm effect	Tonomura et al. [R75]; Aharonov & Bohm (1959)	Observational Predictions (chirality wind)
Kelvin wave dispersion	Thomson/Lord Kelvin (1880); Saffman [R6]	Observational Predictions (channel speed)

10. Section ↔︎ Reference Quick Map

Paper Section	Key References
Substrate Particles	Volovik [R2] Ch. 7; Fetter [R8]
Emergent Speed of Light	Zloshchastiev [R14]; Barceló/Liberati/Visser [R13]; Volovik [R2] Ch. 7; Larichev & Reznik [R5]
Mass as Orbital Energy	Bush & Oza [R1]; Dagan & Bush [R1b]
Two Fluids → Quantum Potential	Simeonov [R3]; Nelson [R18]; Bohm & Vigier [R19]; Barenghi [R33]
Gravity	Volovik [R2] Ch. 29–30; Unruh [R15]; Barceló/Liberati/Visser [R13]
Photon as Modon	Saffman [R6] Ch. 8; Larichev & Reznik [R5]
Hydrogen Atom	Bush & Oza [R1]; Larichev & Reznik [R5]
Electron	Dagan & Bush [R1b]; Hestenes [R20]
Hydrogen Flywheel	Bush & Oza [R1] (promenading pairs); Larichev & Reznik [R5] (modon matching); Bohr [R44]; Lamb & Retherford [R45]; Bethe [R46]; London [R47]; NIST ASD [R48]
Proton Core	Kopnin [R9] (CdGM bound states); Yang et al. [R49] (lattice mass); Gell-Mann & Nishijima [R50]; Wilson [R51] (confinement); Saffman [R6] (junction stability); Volovik [R2] (Fermi points)
Conductors	Type II superconductor literature [R40]; Abrikosov [R56]; BCS [R52]; Cooper [R53]; London & London [R54]; Ginzburg-Landau [R55]; Meissner & Ochsenfeld [R57]; McMillan [R58]; Bush & Oza [R1] (promenading pairs); Tkachenko [R27] (lattice geometry)
Spin-Statistics	Hestenes [R20]; Bush & Oza [R1] (promenading pairs); Pauli [R59]; Schwinger [R60]; Stern & Gerlach [R61]; Vinen [R62]; Kopnin [R9] (HVBK coupling); Barenghi [R33]
Higgs Field	Volovik [R2] Ch. 29–30; He-3 B-phase [R36]
Weinberg Angle	Kopnin [R9]; Iordanskii-Sonin-Stone [R10, R11]; Barenghi [R33]
Fine Structure Constant	Kopnin [R9]; Stone [R11]; Thouless/Ao/Niu [R12]
Spacetime Dynamics	Volovik [R2]; Unruh [R15]; Painlevé/Gullstrand [R16]; Hamilton & Lisle [R17]; Barceló/Liberati/Visser [R13]
Galactic Dynamics	McGaugh/Lelli/Schombert [R24]; Milgrom [R25]; Khoury [R4]; Berezhiani & Khoury [R26]; Bekenstein & Milgrom [R63]; Tully & Fisher [R64]; Lelli/McGaugh/Schombert SPARC [R65]
Bridge Equation	Saffman [R6]; Tkachenko [R27]; Jimenez [R28]; Crow [R67]; Moffatt [R29]; Onsager [R30]; Baym [R31]; Fetter [R8]; Aftalion [R7]; Barceló/Liberati/Visser [R13]; Sakharov [R66]; Abo-Shaeer et al. [R68]
Constraint Summary	PDG [R41]; Planck 2018 [R42]
Observational Predictions	Barceló/Liberati/Visser [R13]; Volovik [R2] Ch. 7; Valentini [R22]; ’t Hooft [R23]; Autti et al. [R34]; GW170817 [R43]; Bell [R69]; CHSH [R70]; Michelson & Morley [R71]; Aspect et al. [R72]; Handsteiner et al. [R73]; Yin et al./Micius [R74]; Tonomura et al. [R75]

11. Agent Constraint Map

Which references support which constraints — for agent context loading.

Constraint	Input/Output	Key References
C1 (speed of light)	Volovik c = \hbar/(m_1\xi) + L-R modon	[R2] Volovik Ch. 7, [R5] Larichev-Reznik, [R14] Zloshchastiev
C2 (Planck’s constant)	\hbar = 2mD from HVBK	[R3] Simeonov, [R33] Barenghi
C3 (gravitational constant)	Boundary crossing fraction	[R13] BLV, [R2] Volovik Ch. 29–30
C4 (electron mass)	Effective quantum orbital energy	[R1] Bush & Oza, [R1b] Dagan & Bush
C5 (proton mass)	Effective quantum confinement	[R9] Kopnin (CdGM states)
C6 (fine structure constant)	\alpha = g^2\sin^2\theta_W/(4\pi) — derived from C8	[R9] Kopnin, [R11] Stone, [R12] Thouless
C7 (cosmological constant)	\Lambda from disequilibrium	[R2] Volovik Ch. 29–30
C8 (Weinberg angle)	\sin^2\theta_W = \alpha_{mf}/(1+\alpha_{mf}) — measured input	[R9] Kopnin, [R10] ISS, [R32] Sonin
C9 (anomalous magnetic moment)	(g-2)/2 = \alpha/(2\pi) — derived from C6	[R9] Kopnin (via C6 chain), [R60] Schwinger (QED target), [R62] Vinen (measurement dynamics)
C10 (DM density)	n_1 m_1 = \rho_\text{DM}	[R42] Planck 2018
C11–C13 (CMB parameters)	Phase transition thermodynamics	[R42] Planck 2018
C14 (MOND scale)	a_0 = c\sqrt{G\rho_\text{DM}} — zero new parameters	[R24] McGaugh, [R4] Khoury, [R25] Milgrom, [R63] Bekenstein-Milgrom AQUAL, [R64] Tully-Fisher, [R65] SPARC
SC1 (ebbing current)	Acoustic metric = PG Schwarzschild	[R15] Unruh, [R16] Painlevé-Gullstrand, [R17] Hamilton-Lisle
SC2 (vortex lattice metric)	\kappa_q \Omega_v = 4\pi c^2	[R13] BLV, [R31] Baym, [R8] Fetter, [R66] Sakharov (induced gravity)
SC5 (three-constant relation)	Zero-parameter electroweak chain	[R9] Kopnin, [R11] Stone, [R12] Thouless
Bridge equation	n_1\xi^3 = 4\pi/(K\sqrt{2}) — Steps A–E	[R13] (4\pi), [R66] Sakharov (Step A), [R5] (K), [R8] (1/\sqrt{2}), [R27–R30] + [R67] Crow (Step D), [R68] Abo-Shaeer (Step D experimental), [R7] (Step E)