# T_CC_NEUTRAL — Pre-registered analysis recipe

**Test:** Cosmic-chronometer H(z) ratio vs ΛCDM and vs a naive uniform BEC
multiplier. This is the empirical twin of the public script
`dct_eddington_ratio_per_z.py`, run inside the T-harness with frozen
recipe hashing.

## Null hypothesis A (ΛCDM)

At each redshift, H\_obs(z) / H\_ΛCDM(z) scatters about **1** with no
systematic trend beyond measurement error.

## Null hypothesis B (naive BEC / uniform multiplier)

A single multiplicative shift **H\_obs / H\_ΛCDM ≈ 1/√P₀ ≈ 1.084**
across the compilation (simple uniform rescaling). This is **not**
the corpus-canonical late-time story (cosmic chronometers reject it);
it is included as a sharp falsification target for the naive form.

## Public dataset

Moresco compilation of cosmic-chronometer H(z) measurements, as
embedded in `dct_eddington_ratio_per_z.py` (31 rows). Primary citation:
M. Moresco *et al.*, Living Rev. Relativ. **25**, 6 (2022),
[doi:10.1007/s41114-022-00040-z](https://doi.org/10.1007/s41114-022-00040-z).

ΛCDM reference expansion uses Planck PR3–style defaults
(H₀ = 67.36 km/s/Mpc, Ω\_m = 0.315, Ω\_Λ = 0.685), matching the
site verification script.

## Statistical method

1. For each point, compute H\_ΛCDM(z) and ratio r\_i = H\_obs / H\_ΛCDM.
2. Inverse-variance weighted mean ⟨r⟩ and σ\_⟨r⟩ on the ratio plane
   (uncertainties scaled by H\_ΛCDM in the denominator).
3. σ-distance to 1.000 (ΛCDM) and to 1.084 (naive BEC), using the
   audit-locked headline ⟨r⟩ = 1.0143 ± 0.0227 unless re-computed
   drift exceeds 0.001 (then report both).

## Decision rule

- **NEUTRAL\_VS\_LCDM:** |⟨r⟩ − 1| ≤ 2σ\_⟨r⟩ (consistent with ΛCDM mean).
- **NEGATIVE\_VS\_NAIVE\_BEC:** |⟨r⟩ − 1.084| > 2σ\_⟨r⟩ (reject uniform 1/√P₀).
- Headline site verdict: naive BEC form **rejected** (~3σ); ΛCDM ratio
  **not** rejected (~0.6σ).

## Falsifier signature

A future compilation giving ⟨r⟩ consistent with **1.084 ± 0.02** while
ΛCDM remains at 1.000 would revive the naive multiplier; conversely
⟨r⟩ → 1.000 at sub-percent precision with many independent points would
strengthen ΛCDM and leave DCT needing a non-uniform H(z) extension
(already acknowledged on `/empirical/` and `/observables/cc-hz/`).

## Important caveat

Temporal Avrami P(z) branches used in interim site experiments were
**reverted** (2026-05-05) as non-corpus-canonical. This harness tests
only the **ratio vs ΛCDM** and the **naive multiplier** — not an Avrami
rescaling ansatz.