Proslambenomenos

Proslambenomenos#

N. Joven — 2026 — ORCID 0009-0008-0679-0812 — CC0 1.0

Source: proslambenomenos | harmonics | 201 | intersections

A pendulum swings. A planet orbits. A galaxy rotates.

At some point, these motions become so slow — so close to the expansion rate of the universe itself — that the distinction between “orbiting” and “drifting” breaks down. That threshold has a name in astronomy: the MOND acceleration scale, \(a_0 \approx 1.2 \times 10^{-10}\) m/s\(^2\).

Below this acceleration, galaxies stop behaving the way Newton predicts. Rotation curves flatten. The missing-mass problem appears. This has been known since the 1980s. What hasn’t been settled is why that particular number.

In ancient Greek music theory, the proslambenomenos was the lowest tone in the Greater Perfect System — the reference pitch from which every interval was measured. It turns out there’s a physical analogue.

The cosmological constant \(\Lambda\) sets a frequency. The Hubble rate \(H_0\) is an overtone. And the MOND scale is the next one down:

\[\Lambda \;\xrightarrow{c\sqrt{\cdot/3}}\; \nu_\Lambda \;\xrightarrow{\div\sqrt{\Omega_\Lambda}}\; H_0 \;\xrightarrow{c/2\pi}\; a_0\]

No free parameters. The predicted value is \(1.04 \times 10^{-10}\) m/s\(^2\). The measured value is \(1.2 \times 10^{-10}\) m/s\(^2\). The ratio is 1.15 — within the range set by the shape of the galactic frequency distribution.

This site presents the derivation, the numerical evidence across 175 galaxies, and the physical mechanism — oscillators synchronizing through friction, the same dynamics that make a violin string sing or a geological fault slip.

Where to start#

  • The short version: Proslambenomenos — the derivation in one document

  • The numbers: 201 — 175 SPARC-X galaxies, predicted vs. observed rotation curves

  • The mechanism: Intersections — stick-slip dynamics, why synchronization produces flat rotation curves

  • The full framework: Harmonics — 30 derivations (D0–D29), from counting to Einstein

  • Where are we? Our Address — the universe’s computational clock on the Stern-Brocot tree

  • From scratch? First Principles — sin(ωt) to Einstein in 10 steps

  • The math? Oscillations — 47 oscillations, pure math of 1/φ

Source#

All notebooks on this site are executed during build — you can verify every number yourself.