What we call gravitational redshift is not a metric effect — it is a direct reading of how deeply light sat in the spation lattice when it was emitted. And one law, v = c√z, carries that depth from the hydrogen atom to the outer solar system without a single fitted parameter.
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SDT space is a relay lattice. Matter crushes the volume it displaces, tightening the local spation closure ℓ_P. Light advances one spation per tick, so a tighter closure means locally slower light and a slower clock. Define the convergence depth:
Four things turn out to be one quantity — three readings of the same closure deficit, plus the colour shift it imprints on light:
No attraction anywhere in this. Nothing is pulled — the convergence pushes, and matter takes the path of least resistance through the gradient. A closed least-resistance path is an orbit.
This is the whole paper in one comparison. Take the convergence depth at the solar surface — the depth solar hydrogen emits from — and compare it to the measured solar gravitational redshift:
| quantity | value |
|---|---|
| SDT depth at emission, z = ϟ_⊙/R_⊙ | |
| observed solar redshift, GM/(c²R_⊙) | |
| ratio |
The shift is the displacement depth at emission. Lab hydrogen emits its line in Earth's shallow regime; solar hydrogen in the Sun's deeper one; we record the difference as z. A satellite's clock runs at √(1−z) for the depth at its altitude — which is exactly the GPS correction, already applied every day.
Displacement pressure provides the centripetal force: v²/r = c²ϟ/r². Solve it and the bound-motion law is just the square root of the depth:
One relation, validated forward — no fitting — across fifteen orders of magnitude:
| system | radius | v = c√(ϟ/r) | reference |
|---|---|---|---|
| heliocentric orbit | 292 AU | — | |
| Earth orbit | 1 AU | 29.78 km/s | |
| hydrogen ground state | a₀ | v = αc | |
| proton surface | R_p | k=0.546<1 |
At hydrogen the law returns k_H = 1/α = 137.036 and the ground-state c-boundary α²a₀ = r_e exactly — the famous constants fall out of the same equation that gives a planet's speed.
From the movement budget v_circ²+v²=c², the clock rate is dτ/dt = √(1−1/k²). As k falls toward 1 (v→c) the clock halts and bound matter dissolves at the c-boundary. The hydrogen ground state sits exactly 1/α = 137 steps from that edge. So α = v/c = 1/k is at once a speed ratio, a clock rate, and a position in a countdown.
If c tracks the local closure, then 299,792,458 m/s is just Earth's value. We sit in the Milky Way's own depth floor, z_gal ≈ 3.5×10⁻⁷, so the absolute relay ceiling is higher:
That ~105 m/s isotropic deficit, present even in empty interstellar space, is a prediction with no counterpart in metric gravity — and one of the three falsifiers below.
A calibrated emitter on a solar descent shows Δλ/λ = ϟ_⊙(1/r−1/r_obs): +2.05×10⁻⁷ at 0.046 AU. GPS-anchored; 5–6 orders above comb precision.
A constant, isotropic ~105 m/s deficit below c_∞ in field-free interstellar space. No metric counterpart.
Oort bodies suspended at the depth surface L_⊙/(4πr²)=F_CMB → , not a purely Keplerian distribution.
Slide α below — the SDT hydrogen speed walks off αc and k_H leaves 137. There is nowhere to hide; α is load-bearing.
The redshift = depth identity (0.03%). The one centripetal law v=c√z, forward-validated atom→292 AU. k_H=137, koppa=r_e from that law. ℓ_P=√(ϟ·ƛ) reproduces the Planck length, mass-independent.
ϟ ≡ GM/c², so the first-order redshift is an identity — the novelty is the interpretation + the 2nd-order predictions, not new 1st-order numbers. The absolute ℓ_P,∞ needs one scale-seed. The galactic floor carries the MW-mass ±20%. The proton/electron internal radii are measured, not yet derived.
The same depth/convergence-floor picture, with the derived acceleration scale a₀ = cH₀/2π = m/s²:
135 SPARC galaxies, baryons only: RMS 23.8%, unbiased, Tully–Fisher slope 3.58.
Galactic + atomic + stellar response on one curve, RMS 8.8%; a wrong floor degrades it 6×.
Every number on this page is recomputed live and matches the paper's reproducibility script keystone.js in one run.