# T_H0_ENVELOPE — result

**Run:** 2026-05-05T15:42:43Z
**Recipe SHA-256:** `67c1811052f7b76f5f0c3c7fca86fd9acc365580940f36dcc5d5470c31aa537f`

## Two-method ratio test (the operative DCT prediction)

- DCT canonical ratio `1/√P₀ = 1/√0.851 = 1.0840`
- Observed ratio `H_SH0ES / H_Planck = 1.0837 ± 0.0174`
- σ-distance DCT from observed: `-0.02σ`
- **Classification: PASS**

## 17-method scatter test (post-hoc rank — see caveat)

- Constant-H best fit: `69.09` km/s/Mpc; χ² = 61.12
- Linear-in-rank fit: slope = `+0.9141 ± 0.1302` km/s/Mpc/rank, intercept `67.65`
- χ²(linear) = 11.84; Δχ² = 49.28
- Slope σ from zero: `7.02σ`
- Fit endpoints: H@rank0 = 67.65, H@rank8.5 = 75.42, ratio = 1.1149
- Jackknife slope range: [0.8521, 0.9518], std 0.0220

**Post-hoc rank caveat:**
Information-density rank assignment is post-hoc; pre-registration of the rank is required to promote this from post-dictive to pre-dictive. Result is NEUTRAL until that happens.

## BAO coupling caveat

Homogeneous conformal P(t) cancels from radial null chi(z); legacy DESI Delta-chi^2 from rescaling D_M is a retracted map, not a homogeneous prediction. Operational H_phys targets are separate from photon BAO rulers (DCT-BAO-01; /observables/bao/).

## Falsifier signature

A measured ratio outside `1.0830 ± 0.005` at >5σ falsifies DCT's conformal-frame H₀ mechanism as applied to this two-method ratio. Today's two-method ratio matches DCT at the 0.02σ level. This ratio test is logically separate from photon null BAO χ(z); see BAO caveat above.