Gravity’s Rhythm: How Cadence Geometry Predicts Galaxies

Felt to Seen to Unseen - Cadence Cosmology Series I

Author’s Note (2025-11-28)
This post reflects the early form of cadence gravity, written before the full field formalism (LFR, LFC, LGR, C46–C54) was established. The core idea — that TD is what stars feel, TS is what observers see, and the balance between them produces galaxy rotation curves — remains correct. Later work refines the mechanism and replaces several early simplifications with the modern Light Frame equations.
This entry is preserved as part of the discovery sequence.

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We usually think of gravity as a mysterious pull. But in cadence geometry, gravity is simply Temporal Descent (TD) — the inward curvature of time’s rhythm. And here’s the breakthrough: TD is measured in meters per second squared. That’s acceleration. That means we can feel it directly.

The Method of Discovery

TD causes gravity.
Temporal Descent compresses cadence near mass. It manifests directly as acceleration. Because cadence curvature is measured in m/s², gravity is literally the sensation of TD.

TS must match TD.
Temporal Stretch (TS) is the outward uncurvature of cadence. To preserve the global cadence beat, TS must counterbalance TD. Both sides of the cadence triangle operate in the same units, so once TD is known, TS follows.

Balance both sides of the curve.
Here’s the crucial step: TS and TD don’t just balance locally. They balance on both sides of the cadence triangle — inward near mass and outward across space. If you compute only one side, the amplitude won’t match. When you balance both sides, the curve closes and the prediction works.

The Result: g_obs

From this dual balance, the observed acceleration emerges. What a star feels (TD) becomes what we see (TS projection). This is the cadence law of motion.

Latex: g_{\mathrm{obs}} = \frac{g_{\mathrm{bar}}}{1 - \exp!\left[-\left(\frac{g_{\mathrm{bar}}}{a_0}\right)^\alpha\right]}, \quad V_{LF}(r) = \sqrt{r \cdot g_{\mathrm{obs}}}

\(g_{\mathrm{obs}} = \frac{g_{\mathrm{bar}}}{1 - \exp!\left[-\left(\frac{g_{\mathrm{bar}}}{a_0}\right)^\alpha\right]}, \quad V_{LF}(r) = \sqrt{r \cdot g_{\mathrm{obs}}}\)

Where:

• g_bar = acceleration from visible matter

• a0 = universal cadence floor

• alpha = cadence exponent

• V_LF(r) = predicted rotation velocity

This relation comes straight from cadence geometry — not from halos.

The Test

We tested the cadence law against 171 galaxies in the SPARC dataset (four lacked complete data). The results were clear:

Shape:
The cadence law reproduced the classic rise-and-flatten pattern of rotation curves.

Amplitude:
With a radial-only implementation, velocities came out low. That was expected. Proper amplitudes require full frame coupling: dynamic TS radius, bar contribution, and projection corrections.

Residuals:
Empirical baseline RMS ≈ 0.55
Cadence law RMS ≈ 4.7
Interpretation:
The geometry is right — the shape is correct — but amplitudes require the full Light Frame projection model.

Even so, the core discovery stands:
galaxies spin in cadence, not in halos.

Why It Matters

For decades, astronomers invoked invisible “dark matter halos” to explain rotation curves. Cadence geometry offers a cleaner route:

• measure TD (what stars feel),

• compute TS (what we see),

• balance both sides of cadence curvature,

• and the motion emerges.

No halos required.

Closing Thought

Gravity isn’t a force pasted onto matter.
It’s the rhythm of the Light Frame — TD compresses cadence near mass, TS relaxes cadence across distance — all to preserve the invariant cadence beat.

Measure TD. Calculate TS. Balance them in both places.
Do that, and galaxies reveal their motion without dark matter.

In a subsequent post, we’ll explore refinements: the cadence gradient law and the cadence-corrected power law. These tools tighten the fits and make cadence geometry practical for modeling real galaxies. And later, we’ll explore the faint rotation of the universe itself — the final piece that closes the cadence loop.

Ever since Vera Rubin and Albert Bosma first mapped galaxy rotation curves, astronomers puzzled over why they stay flat. Milgrom introduced MOND. McGaugh showed with SPARC that observed acceleration tightly tracks visible matter (the RAR). Our cadence law continues that lineage:

Measure what is felt.
Calculate what is seen.
Balance both sides of cadence curvature.
And galaxies spin without halos.