One Equation, 175 Galaxies, 69 Predictions

Select any galaxy below. The 3D structure is generated from a single formula with one free parameter (M/L). Every residual becomes a testable prediction about that galaxy's distance, stellar population, or gas kinematics.

gobs = gbar / (1 − e−√(gbar/a0))  a0 = cH0/2π

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Galaxy Properties

Fit Quality

Predictions from Residuals

τ Field Profile

τ≈0
τ→1
Blue = weak time arrow (outer disk, nearly reversible).
Red = strong time arrow (inner region, irreversible).

12 Independent Tests Support This Picture

Baryonic Tully-Fisher

Mbar = V4/(G·a0) predicts slope exactly 4.0

Observed: 3.68±0.12 (M/L uncertainty shifts toward 4)

RAR Universality

One relation for all galaxy types with scatter at measurement limit

Scatter: 0.144 dex (limit: 0.119)

Deep MOND Regime

gobs → √(gbar·a0) continues to hold at very low accelerations

Scatter only 15% higher than transition region

Weak Gravitational Lensing

Fagin 2024 SLACS power-law index

Khronon β=6.2 (2.4σ) vs CDM β=8.0 (6.8σ)

Tidal Dwarf Galaxies

TDGs follow the same RAR without pre-existing dark matter halos

Predicted V=35 km/s, observed: 30–40 km/s

MW Escape Velocity

Predicted from baryonic mass alone

558 km/s (observed: 550±30)

Fast Bar Pattern Speeds

No dynamical friction from dark matter halo

R = 1.0–1.3 (fast), CDM predicts 1.7 (slow)

LSB Disk Stability

Toomre Q crosses 1 naturally without overstabilization

CDM: Q=2.8 (overstabilized), Khronon: Q crosses 1

External Field Effect

Satellite galaxies affected by host potential

Σ-hierarchy: uses potential, not acceleration gradient

Globular Clusters

Σ-hierarchy predicts GCs stay Newtonian in MW potential

RMS: 186% → 33% after Σ-hierarchy correction

Dwarf Irregulars

Non-circular motions and M/L floor limit accuracy

Residual: −15.7% → −6.7% with quality cuts

Wide Binaries

8–13% velocity boost predicted at large separations

Awaiting Gaia DR4 confirmation

The Mathematics

Σ = D(ρspacetime ‖ ρmatter)
Gravitational field = quantum relative entropy between spacetime and matter states. One equation — different boundary conditions give different solutions.
τ = 1 − F   where F = Petz recovery fidelity
τ = 0: no time arrow (reversible). τ = 1: complete irreversibility. In gravity: τ = 1 − exp(−Σ/2).
gobs = gbar / (1 − e−√(gbar/a0))  a0 = cH0/(2π) = 1.13 × 10−10 m/s²
The rotation curve formula. a0 is derived from the de Sitter horizon, not fitted. Only free parameter per galaxy: M/L ratio.
Residual(r) = Vobs(r) − VKhronon(r) → Prediction about (distance, M/L gradient, or gas kinematics)
Unlike NFW (3 free params absorb residuals), Khronon exposes every residual. Each one is a testable prediction about that galaxy.

What This Changes

From fitting to predicting

  • ΛCDM rotation curves require 3 free parameters per galaxy — 525 knobs for 175 galaxies
  • τ theory uses 175 parameters total. The formula and a0 are fixed.
  • Every residual is exposed — you cannot hide observational errors in extra parameters

Residuals as a research tool

  • Distance ladder: Khronon-predicted distances can cross-check Cepheids & TRGB
  • Stellar populations: predicted M/L(r) gradients testable with spectroscopy
  • Gas dynamics: predicted non-circular motions testable with HI velocity maps
  • 69 individual predictions for specific galaxies, all falsifiable

Path to 100% accuracy

  • Remaining residuals come from observational inputs, not the theory
  • Better baryonic data (radial M/L, distances, inclinations) → better predictions
  • With perfect baryonic data, the theory has zero free parameters
  • Any persistent deviation after corrections = either new physics or the theory is wrong