From a Reference Curve to the Wave Mass
A programme: turn the empirical rotation law into a geometric target, then tie it to BeeTheory
We have an empirical reference curve that captures the shape of rotation curves: a saturating law, anchored at each visible component, that flattens far out. The programme is threefold — make it bend down at large radius as the data show, define it as a geometric target with no per-galaxy fitting, and connect it to the BeeTheory wave mass. This note lays out that path.
The starting point: the reference curves on the Milky Way
For each galaxy, the visible matter is reduced to two reference objects — a ring (disk+gas) and a sphere (bulge) — each with its own radius and circular velocity. Normalizing the data by these gives a curve anchored at (1, 1). Below, the Milky Way’s Gaia points are placed on the R/R_ring axis, with the ring curve across the full range and the bulge curve over its inner domain.
The two reference curves shown share the same saturating form, V/V_ref = 1 + A·(x−1)/(x+B) with x = R/R_ref, each anchored at (1, 1):
The coefficients are not assumed — they come from fitting the pooled, normalized rotation points of the SPARC sample: the ring law (A = 0.60, B = 0.74, flat asymptote 1.60) on the 143 bulgeless disk+gas galaxies, and the bulge law (A = 0.51, B = 1.46, asymptote 1.51) on the 32 bulged galaxies. They are fixed once on those samples and then read off — including for the Milky Way above, which was not part of the fit.
This is the empirical description we start from. The three steps below turn it into something physical.
1. The plateau must become a gentle decline
The reference curve rises and then flattens to a constant — a permanent plateau. The real data say otherwise: the Milky Way’s Gaia curve does not stay flat, it declines slightly at the edge — visible above, where the outer points fall below the reference curve. A flat asymptote cannot reproduce that decline. The first task is therefore a curve that bends downward at large radius.
2. A reference defined by geometry, not by fitting
The second goal is to fix the curve’s coefficients from measurable quantities alone — never tuned galaxy by galaxy. The inputs are purely structural:
- the shape and mass of each galaxy — its components reduced to a ring (disk+gas) and a sphere (bulge), each with a mass and a radius;
- the proper rotation velocity of each element — V_ring and V_bulge, the circular velocities of the visible components at their reference radii.
With these, the reference curve becomes a target a galaxy should meet given only its geometry and its visible kinematics — not a curve fitted after the fact. The blind tests already shown (disk+gas, and the Milky Way in its normalized frame above) are the first evidence that such geometry-only coefficients carry real predictive power.
3. The link to the BeeTheory wave mass
The third and deepest step is to show that the empirical reference curve is the observable signature of the BeeTheory wave mass — an additional mass, generated by the visible matter, that adds to the visible velocity. Its key property is that it is finite: it saturates at a fixed fraction of the visible mass rather than growing without bound. A finite added mass means the velocity it supports must eventually decline in Keplerian fashion. That property is exactly what step 1 asks for: a curve that rises, holds, then bends down at large radius. The aim is to connect the reference curve’s coefficients (A, B above) to the wave-mass parameters, so the empirical law and the wave mass become two readings of the same physics.
The reference curve is the observable signature; the wave mass is the proposed cause. The programme is to align them: a curve that declines at large radius (step 1), built from geometry alone (step 2), and identified with the finite BeeTheory wave mass (step 3). Each step is testable, and the outer decline of the Milky Way already points toward a finite mass rather than a permanent plateau.
This is a programme, not a finished derivation. The reference curves are empirical, with coefficients fitted on the SPARC sample. Gaia data from Ou et al. 2024; the Milky Way’s reference quantities were built from its known baryonic components with the SPARC recipe. What remains to be done: make the reference curve decline at large radius, fix its coefficients from geometry alone, and derive the connection to λ and ℓ from the wave function rather than by fitting.
BeeTheory.com — From a reference curve to the wave mass · Data: SPARC / Lelli et al. 2016; Gaia / Ou et al. 2024 · Initial generation: 21 May 2026 with Claude.ai · © Technoplane S.A.S. 2026