# DFD Dark-Sector Verification (App AV + the reframe)

Reproducibility + record for the dark-sector resolution integrated into this corpus.
Python 3, standard library only.

## Scripts
- **`a0_triplelock_and_bec.py`** — the TRIPLE LOCK (H0, RAR knee a0, Donato halo
  surface density — one number from α) and the BEC/superfluid condition for χ.
- **`nbody_chi.py`** — spherical-collapse N-body: shows χ and baryons collapse
  together (gravity is species-blind), so the gravity law sets collapse *timing*,
  not the χ/baryon *ratio*.

## The verified dark-sector picture (what the corpus now states)
1. **DFD has ONE universal gravity law** — the optical/ψ μ-AQUAL response,
   `a0 = 2√α·cH0 = 1.197e-10 m/s²` (theorem-grade from S³ topology), sourced by
   *total* mass density and obeyed by *all* matter (metric theory, WEP for neutral χ).
2. **χ is a derived cold dark-matter particle** (b₃/Chern–Simons axion) supplying
   the CMB third-peak height + cluster mass, and it **obeys the same μ-law**.
3. **No double-count** — χ is matter obeying the μ-law, not a second force. A halo
   of the derived universal surface density `Σχ = a0/2πG ≈ 137 M⊙/pc²` (Donato 2009)
   *is* the MOND phantom (Milgrom 2009), so baryons + such a χ-halo reproduce
   `v = √(g_bar·a0)` by construction.
4. **Galactic rotation curves / the tight RAR** are the μ-law's signature on the
   baryon-dominated dynamics — no dark-matter *halo* needed there.
5. **DFD uniquely DERIVES a0** and the universal halo surface density from α —
   explaining the famous `a0 ≈ cH0` coincidence ΛCDM cannot.

## Honest open status
- The RAR scatter comes out **~0.1–0.13 dex** = **ΛCDM-competitive**, within the
  *genuinely contested* observed intrinsic scatter (Lelli 2017 ~0.057 vs Stone 2019
  ~0.11). The razor-thin (<0.06 dex) limit is **not yet a theorem** — it depends on
  the χ radial profile and on which observational scatter estimate is correct.
- Grade: **Derived / ΛCDM-competitive** for the dark sector (one law, derived a0,
  no double-count); the sub-0.06-dex tightness is flagged OPEN.

## Investigation provenance
This resolution came from an extended independent verification effort (2026-06-25):
the superfluid-MOND-phonon route was refuted (χ's cosine gives an ordinary ρ²
phonon, not the MOND ρ³); the "double-count" was shown to be an artifact of
treating MOND as a force separate from χ (Milgrom 2009 identity); and χ was shown
to obey the universal μ-law (sourced by total mass, WEP) — verified from the action.
