Dark matter is heavier, denser, curved spacetime

Galaxies weigh more than the matter they show. Rubin and Ford found it in the rotation of Andromeda, and the rotation curves of disk galaxies measured since say the same. For the Milky Way, three kinds of tracer carry the weighing outward: the disk’s red-giant stars out to 25 kpc, globular clusters out to 39.5 kpc and satellite galaxies out to 273 kpc. Lensing weighs galaxies with no orbit at all and returns the same excess.

Against the weight stands the census of what the Galaxy holds as matter: stars, 5.43 × 10¹⁰ M☉; cold gas, 0.80 × 10¹⁰ M☉, raised by 1.36 for its helium; and hot gas at the upper end of its measured range, 5.2 × 10¹⁰ M☉ × (r/250 kpc)^3/2. Each part is counted as if wholly inside the radius wherever that raises the count, so the census is generous by construction.

Every weighing becomes one exterior reading of the weight inside the field radius:

At one radius the ratio of two readings is the ratio of the two weights, so the weight over the census is read straight off the sky.

The record also holds the local dark density at the Sun, 0.38 ± 0.04 GeV/cm³, 68,000 to 79,000 times the critical density, and the null results of direct detection to date (LZ, 2025).

The core identifies dark matter as heavier, denser omnium: the mass shadow, the compressed spacetime phase that every mass holds around it (0.7). The paper derives that identification from the chain, the two phases, the exterior density profile and the braid reading of matter, in three lemmas and a census.

Curvature is weight

At a fixed radius, curvature and weight are one quantity. Invert the reading and the weight inside is 𝓜(r_f) = c²r_fα_ext/(2G); double α_ext at r_f and the weight inside doubles. Differentiate it and the local density appears:

A source alone reads α_ext = R_s/r_f, so r_fα_ext is constant and its exterior carries no local weight. Weight sits wherever α_ext falls more slowly than 1/r_f. The Milky Way’s reading stays near 10⁻⁶ from the Sun’s circle out to 64 kpc: its exterior is full of weight.

The phase census

There is only the omnium and its patterns. The strokes of the one carrier run open, as radiation, or close into braids, the matter phase; the rest is substrate, the spacetime phase. The content of any region is exhausted by these three, so the excess must be one of them.

• Open strokes. The microwave background carries 6.9 × 10⁻¹⁰ of the local dark density, and starlight near the Sun is of the same order.
• Closed braids. Gas is in the census. The two-strand closures, neutrinos, fail on phase space: holding the local dark density at the envelope’s dispersion needs at least 19.3 eV per closure, or 14.7 eV with three species sharing the load, against a laboratory ceiling of 0.45 eV. Microlensing excludes compact matter-phase bodies as the bulk of the halo from 10⁻¹¹ to 860 M☉.
• Substrate. The Galaxy’s magnetic field, a helical gradient of the substrate (P-⁠5), weighs about 10⁻⁹ of the local dark density. Outside the two compact-body windows, what remains of the excess is substrate.

That remainder is substrate above its relaxed density. It is heavier than relaxed substrate, as a compressed spring outweighs a relaxed one: stored work enters the weight once, and compression raises the density of the one substance (I-⁠7). It is denser, carrying local weight where relaxed substrate carries none. It is curved by its own weight, which sets α_ext at every larger radius.

The reading does not know what made it

At monopole order α_ext(r_f) depends on the weight inside r_f and on nothing else: not on the support, the composition, the phase or the place in the universe. Any two configurations that hold equal weight inside a radius read alike there. A black hole and a sphere of Sgr A*’s weight with a radius of three kiloparsecs have compressions thirty orders of magnitude apart on their supports, and at 10 kpc they read the same.

Transparent, not dark

Each reading of the chain sees the envelope in its own way. The (d/t)² reading weighs it: orbits answer to its weight. The 1/(ε₀μ₀) reading sees it as refraction: a ray bends by 4G𝓜/(bc²), the envelope inside 𝓜. The E/m reading registers nothing. A line is a transition between confinement eigenvalues of a closed pattern, and the spacetime phase has no confinement problem and no mode to relax. Every detection of the envelope is a gradient detection: a rotation curve, a lensed arc.

The galaxy’s atmosphere

On Earth the envelope’s counterpart is the atmosphere. The air is weighed by a barometer, seen only through its refraction, which lifts the setting Sun by about 34′, and carried by the planet. A flat rotation curve says the same of a galaxy’s envelope: held in hydrostatic balance it is an isothermal atmosphere, with

An isothermal envelope carrying all of v₀² at the Sun reads 0.57 GeV/cm³ there; the measured local dark density is 0.67 of that, and the disk and bulge carry the rest. The analogy stops at the phase. The air is matter phase, closed braids of nitrogen and oxygen, which is why it has lines and scatters sunlight. The envelope is substrate in the spacetime phase: it has no line, and it bends light.

Held and released

The compression held around mass is the dark matter the record weighs. The compression let go is dark energy: the stored potential released as bodies lose mass, entering the field equation as Λ_eff = 8πGρ_rel/c² (0.7). They are one reservoir in two conditions, moving in opposite directions along the α axis. Held compression squeezes a ball of free test patterns; released potential is a tension equal to its energy density and swells it. At the radii of the table the released share of the Galaxy’s pull runs from 3.3 × 10⁻⁵ at 21.1 kpc to 1.0 × 10⁻² at 273 kpc, inside every error bar: the table weighs the held reservoir.

The reading carries its own exits. Each item below is a result that ends it, or a quantity the programme derives or measures next.

1. Zero
   No species to detect. The direct-detection rate of a dark-matter species is zero, because there is no species. A confirmed direct detection of the standard account’s species ends this reading.
2. Λ
   Dark energy grows. As bodies unwind, the held share falls and the released share grows, so Λ_eff grows with cumulative unwinding. A dark-energy history measured constant, or shrinking, ends this reading.
3. Lines
   No line from the envelope. The envelope emits and absorbs nothing. Every detection of it is a gradient detection, by orbits, rotation curves or lensing.
4. D-⁠01
   The two windows. The census of compact matter-phase bodies below 10⁻¹¹ M☉ and above 860 M☉, where the microlensing record ends, is to be measured.
5. O-⁠14
   The response function. How much compression each mass holds, how it is distributed, how the shadows of a population combine and the envelope’s temperature are to be derived (O-⁠14). The result must return the weighings of the table, the ephemeris bound around the Sun and the local dark density, and with it the release function that sets the size of Λ_eff.

For the same sources and data, FDT returns the consensus weighings. The enclosed weights from rotation curves and tracers are the I-⁠4 face of the one law at leading order, v_c² = c²α_ext/2 = G𝓜(r_f)/r_f. The lensing weights are the optical statement of I-⁠3 with the envelope inside 𝓜: θ = 4G𝓜/(bc²) outside the configuration and 4G𝓜_2D(<b)/(bc²) across it. The Keplerian Sun of the ephemerides and the weighed atmosphere of the Earth are returned unchanged.

The law is untouched: F = F_maxα₁α₂ holds at the Oort cloud and at 273 kpc alike (I-⁠1). What the record corrects is the input, since the 𝓜 of a galaxy includes its envelope (0.5). No divergence is claimed from α, a chart or a branch tag. The observable commitments are the zero direct-detection rate and a Λ_eff that grows with cumulative unwinding.