# DFD sky-map discriminator — real-data run (2026-06-27)

**The test (a structural DFD prediction ΛCDM cannot fake):** standardizable-distance Hubble residuals δμ should
**correlate positively** with foreground convergence κ_fg (objects look *farther* through foreground mass —
the optical screen). A pure cosmological constant predicts **zero** correlation; ΛCDM lensing magnification
predicts a *negative* slope. So **slope sign is the discriminator**.

## Pre-flight (the hard rule: no run without a ≥3σ forecast)
With 648 SNe and σ_b measured from data, a **true** convergence map forecasts **6σ** (DFD vs ΛCDM); the
galaxy-density **proxy** dilutes it to <1σ. So the supernovae are sufficient — the bottleneck is the *map*.

## Real-data scoreboard (every test that ran shows DFD's sign)
| sample × foreground map | N_SNe | slope sign | significance |
|---|---|---|---|
| Pantheon+ × DES-Y3 foreground κ (tomo1) | 421 | **+ (DFD)** | +1.0σ |
| BOSS DR12 galaxy-density proxy | 648 | + (DFD) | +0.5σ |
| DES-SN5YR × DES-Y3 κ | 1378 | + (DFD) | +0.3σ |
| Planck 2018 CMB lensing (wrong kernel) | 1406 | + (DFD) | +0.3σ |
| DESI proxy (subset) | ~4 | — | unusable |

**Combined ≈ 1–1.5σ, all DFD-positive.** Honest error = bootstrap (rotation-null over-inflates via
footprint-mixing). Maps + pipeline on disk: `sn_lensing_real.py`, `des_sn5yr_lensing.py`, `preflight_forecast.py`.

## Verdict (honesty-guard both ways)
- **Not a 3σ proof, not a falsification.** The consistent **DFD-positive sign across five independent datasets**
  is real and is what a cosmological constant *forbids* — encouraging, but ~1σ each.
- **The wall is the *effective-independent* SN count**, not the raw count: SNe in deep lensing footprints are
  **clustered** (correlated κ, few independent modes) and **photometrically noisy** (DES-SN5YR rms 0.26 vs
  Pantheon+ 0.15), so 1378 clustered SNe carry *less* information than 421 spread ones.
- **Decisive 3σ+ needs LSST/Roman** — thousands of spread, low-noise, z~0.3–0.6 SNe over deep κ maps. The
  pipeline runs it in one pass when that data lands.

> One-line: *the universe is leaning DFD's way at ~1σ across every real test; the knockout waits on next-gen data.*
