# T_PPN_GAMMA — Pre-registered analysis recipe

**Test:** Cassini Saturn-conjunction Shapiro-delay PPN γ measurement
vs DCT canonical prediction.

## Null hypothesis

GR predicts `γ = 1` exactly. Brans-Dicke at `ω_BD = ∞` reduces to GR.
Standard physics null: `γ − 1 = 0`.

## Alternative hypothesis

DCT canonical PPN γ at the post-Newtonian level (DCT-PPN-01 §III):
`γ − 1 = − 1 / (2ω₀ + 3) = − 1 / (c_BD · P₀²) = − 1 / 100,077`
Derivation from `2ω₀ + 3 = c_BD · P₀² = 100,077` (master identity;
cluster DCT-PPN-01 and Foundation deposit).

## Public dataset

Bertotti, Iess & Tortora 2003, *Nature* 425 374, doi 10.1038/nature01997
— Cassini Saturn-conjunction radio-tracking measurement of Shapiro
delay. Reported value: `γ − 1 = (2.1 ± 2.3) × 10⁻⁵`.

## Statistical method

One-sided σ-distance test:
- DCT predicted value `γ_DCT − 1 = − 9.992 × 10⁻⁶`
- Cassini measurement `γ_meas − 1 = (2.1 ± 2.3) × 10⁻⁵`
- σ-distance `(γ_DCT − γ_meas) / σ_meas = (−9.992e-6 − 2.1e-5) / 2.3e-5
  = − 1.35σ`
- Null (GR) σ-distance `(0 − 2.1e-5) / 2.3e-5 = − 0.91σ`

## Decision rule

- DCT consistent with Cassini at <1σ → **NEUTRAL** (data does not
  discriminate DCT from GR)
- DCT consistent at 1–3σ → **NEUTRAL** with mild residual
- DCT excluded at >5σ → **MISS**
- DCT distinct from GR at the Cassini sensitivity but within bounds →
  **NEUTRAL**

## Falsifier signature

Decisive test awaits BepiColombo MORE 2028 (forecast σ_γ ~ 1.4 × 10⁻⁶);
under that sensitivity DCT's −9.99 × 10⁻⁶ is a clean 7σ separation
from GR's 0. Until then, T_PPN_GAMMA is a **consistency check**: DCT
must lie within Cassini's 1σ band, which it does.

## Cross-validation

Mercury MESSENGER (Park et al. 2017) also constrains `|γ − 1| < 4 × 10⁻⁵`,
consistent with DCT.

## What could go wrong

- Cassini's reported uncertainty is 1σ; the systematic budget includes
  solar plasma and tropospheric noise that may bias the central value.
- DCT canonical `2ω₀ + 3 = 100,077` is a topological identity at 4 ppm
  rounding; the DCT prediction is robust to this.