# n43 — pre-registration: lopsidedness × absolute motion (written before any data)

**Prediction under test** (n42, on the mechanism page): the m=1 kinematic
asymmetry axis of disk galaxies aligns with the in-disk projection of the
peculiar velocity (CMB frame); fast side = leading side; amplitude grows
with v_pec.

## Pipeline
1. Catalog of per-galaxy m=1 kinematic asymmetry with PHASE (kinemetry
   phi_1) + RA, Dec, cz, photometric PA, inclination.
2. Reconstructed 3D peculiar-velocity field (CF4/CF3/2M++): interpolate
   v_pec vector at each galaxy position.
3. Project v_pec onto the disk plane using (PA, inc); compute its
   position angle phi_v in the sky/disk frame; Delta = wrap(phi_1 - phi_v).

## Pre-registered statistic and gates
- Primary: Rayleigh test on Delta (full angle, NOT doubled: the
  prediction is signed — fast side leading, Delta concentrates at 0).
- Estimator: R = |<exp(i Delta)>|, p-value from N R^2 asymptotics;
  report also the mean angle <Delta>.
- DETECTION gate: p < 0.01 AND |<Delta>| < 45 deg (concentration at 0,
  not at 180: 180 would mean fast side TRAILING — wrong sign = kill too).
- NULL gate: p > 0.1 with N >= 150 usable galaxies -> prediction refuted
  at pilot level; headstone 18 drafted (taking the Bullet-lag reading
  with it), subject to the caveats below.
- Secondary (only if detection): amplitude correlation
  Spearman(v_asym, |v_pec,plane|) > 0 at p < 0.05.

## Selection cuts (fixed now)
- inclination between 25 and 70 deg (phase measurable, projection sane);
- kinemetry quality flag good / v_asym S/N > 3 where available;
- cz < 12000 km/s (reconstruction reliable zone);
- |v_pec| interpolated > 150 km/s (signal exists to align with).

## Declared limitations (before the run)
- The 180-deg sign convention of published phi_1 may be ambiguous
  (receding vs approaching side): if so, fall back to AXIAL statistic
  (Rayleigh on 2*Delta) and the sign clause remains untested.
- Reconstructed v_pec has ~150-250 km/s errors: attenuates R, does not
  bias the mean angle; a null at small N is weak evidence.
- Disk-plane projection uses photometric PA/inc: noise, no bias expected.
- This is a PILOT: any detection demands the full-survey redo before a
  word appears outside the site.

## AMENDMENT 1 (before any real map was opened — synthetic tests only)
The m=1-phase extractor was redesigned after failing synthetic recovery
(an amplitude-modulated rotation injects only even harmonics; free-angle
phase is not the right observable). New primary observable, validated on
displaced-well physical mocks (sign recovered in all cases, null clean,
linear in displacement):
- D = (|V_rec| - |V_app|) / mean, sector fit on outer annuli (R > 0.4 Rmax);
- fast side = receding if D > 0.
- Sign chain (n42 wake + mock): v_pec projected toward the RECEDING major
  axis => well trails toward approaching side => D > 0.
NEW PRIMARY STATISTIC: binomial sign test — fraction of galaxies where
sign(D) = sign(v_pec . receding-axis direction).
- DETECTION gate: one-sided binomial p < 0.01 with the predicted sign.
- NULL gate: p > 0.1 at N >= 100 usable galaxies.
- Secondary: Spearman(|D|, |v_pec,major|) > 0, p < 0.05.
- Quality cuts unchanged; additionally require |v_pec,major| > 100 km/s
  and |D| S/N: at least 3 valid annuli.

## AMENDMENT 2 (theory revision after the n43 null; written before this test)
Revised hypothesis (drainage EFE): lopsidedness is driven by the LOCAL
drainage gradient (catchment competition), not absolute motion.
Retrodiction: cluster samples are more lopsided (measured sigma_D=0.31
vs ~0.1 field literature). New test on the SAME 111 galaxies:
- e_grad = direction of increasing 2M++ density at the galaxy;
- predicted sign: fast side = AWAY from higher density
  => sign(D) = -sign(e_grad . e_receding).
- POWER (computed before running): with sigma_D=0.31 and center-direction
  errors <~ 20 deg, N=111 detects the effect at p<0.01 if it contributes
  >= ~25% of the lopsidedness variance. If it contributes less, this test
  is UNDERPOWERED and a null is NOT a burial — only the >=25% regime dies.
- DETECTION: one-sided binomial p<0.01 with the predicted sign.
- Exploratory (flagged): the opposite sign; the |D| vs |grad| Spearman.

## RESULT OF AMENDMENT 2 (same day)
N=106 (weakest-gradient quintile cut, as implied by the power note):
- PRIMARY (fast side away from density): 43.4%, one-sided p=0.93 — FAILED.
- Exploratory opposite sign: 56.6%, p=0.10 — not significant, flagged
  exploratory; together with Spearman(|D|,|grad|)=+0.17 (p=0.088) it
  points, weakly, toward CONVENTIONAL tidal lopsidedness (near side
  pulled toward the neighbor), not drainage truncation.
Verdict: the drainage-EFE reinterpretation is disfavored at the >=25%-of-
variance level with the predicted sign; the cluster-lopsidedness
retrodiction remains only as an unproven consistency. The theory does
not keep this claim.