# Proslambenomenos

[N. Joven](https://github.com/nickjoven) — 2026 — [ORCID 0009-0008-0679-0812](https://orcid.org/0009-0008-0679-0812) — CC0 1.0

Source: [proslambenomenos](https://github.com/nickjoven/proslambenomenos) | [harmonics](https://github.com/nickjoven/harmonics) | [201](https://github.com/nickjoven/201) | [intersections](https://github.com/nickjoven/intersections)

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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](proslambenomenos/proslambenomenos.html) —
  the derivation in one document
- **The numbers**: [201](201/joven_unifying_framework.html) —
  175 SPARC-X galaxies, predicted vs. observed rotation curves
- **The mechanism**: [Intersections](intersections/joven_stick_slip_dark_matter.html) —
  stick-slip dynamics, why synchronization produces flat rotation curves
- **The full framework**: [Harmonics](harmonics/sync_cost/FRAMEWORK.html) —
  30 derivations (D0–D29), from counting to Einstein
- **Where are we?** [Our Address](https://nickjoven.github.io/submediant-site/our_address.html) —
  the universe's computational clock on the Stern-Brocot tree
- **From scratch?** [First Principles](https://nickjoven.github.io/submediant-site/first-principles.html) —
  sin(ωt) to Einstein in 10 steps
- **The math?** [Oscillations](https://nickjoven.github.io/submediant-site/oscillations.html) —
  47 oscillations, pure math of 1/φ

## Source

- [proslambenomenos](https://github.com/nickjoven/proslambenomenos) — the self-contained preprint
- [201](https://github.com/nickjoven/201) — the numerical framework
- [intersections](https://github.com/nickjoven/intersections) — the physical substrate
- [harmonics](https://github.com/nickjoven/harmonics) — the synchronization cost derivations

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