Consistency check Agrees, both ways
Test 2 — Dual GR, both ways
Solving the same problem through the 13-dimensional reduction and through standard four-dimensional General Relativity are two different calculations — and they return the same numbers, not approximately but as the same value, because the construction contains Einstein's equations exactly in the appropriate limit. The check here: a light ray grazing the limb of the Sun, worked both ways.
What was done
The frozen shape — four familiar dimensions carrying a compact internal geometry — must, reduced back down to ordinary four-dimensional spacetime, reproduce General Relativity in the regime GR has already been tested in. Not approximately mimic it: contain it. The relationship claimed is the one Einstein's gravity has to Newton's — the new frame doesn't rival GR, it derives it, and hands it back exactly in the tested limit. The specific check: take a light ray grazing the limb of the Sun, and compute how far it bends.
This was worked as two separate derivations from the same underlying shape: a reduction of the full
geometry down to the four-dimensional metric and a direct post-Newtonian expansion of that metric
(extracting the PPN parameter γ), compared against the standard general-relativistic light-bending
formula
α = (1+γ)·2GM/(c²·b)
evaluated at the solar limb (impact parameter b = R⊙).
Both ways?
Yes — this is the point of the test. The write-up explicitly describes the result as "worked two independent ways that land on the same number." The two routes start from the same frozen geometry but take different technical paths down to the observable; agreement between them is an internal consistency check (does the geometry's own machinery contradict itself when you reduce it two different ways?), not an external validation by itself. The external validation is the second half: the resulting number is then checked against Einstein's known value and the modern experimental bound.
Honest result
| Quantity | Value from the shape | Comparison value | Status |
|---|---|---|---|
| Solar-limb light deflection | 1.75 arcsec (post-Newtonian γ = 1) | Einstein's classic prediction, 1.75 arcsec; Eddington's 1919 eclipse target value 1.7505 arcsec | Agrees |
| PPN γ | γ = 1, exactly, from the reduction | Cassini bound: γ = 1 ± 2.3×10⁻⁵ (Bertotti, Iess & Tortora 2003) | Well inside bound |
Both independent derivations return the same post-Newtonian γ = 1, and the resulting deflection angle matches Einstein's textbook value comfortably inside the tightest modern experimental bound on γ (the Cassini spacecraft radio-tracking measurement). The Relativistic Optics Lab's own reproduction of this same textbook figure — an independently coded calculator, built as part of the NASA-facing calculator suite — lands at 1.7511903… arcsec against the 1.7505 arcsec Eddington target, a relative error of about 4×10⁻⁴, well inside its declared 0.05% tolerance. See Test 3 for that validation run in full, and the live suite itself at /gut/nasa/ — 64 of 64 checks, with the dual-route reductions exhibited computationally, route against route, on benchmarks anyone can re-run.
The same reduction also fixes the ripple sector, and there the record is even sharper: the linearized machinery automatically returns a spin-2 wave with exactly two polarizations, moving at the speed of light, ghost-free — none of it chosen by hand — and the resulting prediction that gravitational waves travel at light speed is confirmed by the 2017 neutron-star merger (GW170817) to ~1 part in 10¹⁵, the sharpest propagation constraint in existence. The operator and path-integral quantizations agree — the cross-check that fails when a quantization is ill-defined. Proven: the UQF-5A/5B dossier (graviton and linearized-Einstein recovery).
Data sources
- Einstein's classic prediction and Eddington's 1919 eclipse expedition target value (1.7505 arcsec) — standard textbook general relativity (e.g. Will, Theory and Experiment in Gravitational Physics, 2018 edition).
- Cassini PPN bound γ = 1 ± 2.3×10⁻⁵ — Bertotti, Iess & Tortora, Nature 425:374 (2003), from the spacecraft's radio-tracking Doppler signature during solar conjunction.
- Independent calculator cross-check — the Relativistic Optics Lab's Light Deflection
calculator and its validation suite (
ANALYTIC.deflection.solar_limb,PUBLIC.deflection.solar_limb_canonical,HORIZONS.deflection.mercury_grazinginvalidation_report.json), using IAU 2009 solar GM and IAU 2015 nominal solar radius — the live suite at /gut/nasa/. - Graviton / linearized-Einstein recovery — the UQF-5A/5B dossier, including the GW170817 speed-of-gravity comparison (~1 part in 10¹⁵).
What this does not show
This is a reproduce-known check, stated as such: it returns the same number general relativity already gives. A mismatch here would have been fatal to the whole program — it would mean the shape, reduced to ordinary spacetime, contradicts a century of solar-system tests. A match is necessary but not sufficient: it shows the machinery hasn't quietly broken General Relativity in the one regime everyone agrees on, and it is not yet a beyond-GR measurement. It does not prove the larger thirteen-dimensional shape is correct — but note what it does establish. The new theory does not ask anyone to abandon Einstein; it hands Einstein back, exactly, the way Einstein handed back Newton. Containment of the established theory in a limit is the strongest relationship a successor can have to prior physics — stronger than compatibility — and here it is demonstrated route against route, on named benchmarks anyone can re-run.