# n48 — pre-registration: motion-gated decoherence (before code)

**The model's flagship divergent prediction.** GR (any quantization):
no intrinsic decoherence of mass superpositions. Collapse models (DP):
a STATIC decoherence floor, present at rest. Drainage: decoherence only
when matter OUTRUNS the vacuum's rearrangement — zero at rest, rate
growing as (dT00/dt)^2 / gamma_drain, with a knee at the drainage rate.

## Minimal dynamical toy (declared)
- Drainage field relaxes toward the instantaneous minimum-cost solution:
  d(dk)/dt = -gamma * (dk - dk*(c(t))), gamma = gamma_drain.
- The vacuum reads ONLY sum-rule violations v(t) = A dk(t) + c(t)
  (n39's principle), continuously, into a record register.
- Mass superposition: two branches with consumption patterns c_L(t),
  c_R(t) = patterns at sites 60/61 (opposite parity displacement),
  amplitude-modulated c(t) = F*(1 + eps*sin(2 pi nu t)), eps = 0.5.
- Branch distinguishability accumulates from the difference of violation
  histories: Gamma_dec = kappa_read * |Delta v(t)|^2 time-averaged
  (Gaussian-record overlap; kappa_read fixed at 1, units absorbed).

## Registered predictions and gates
- P1 NO STATIC FLOOR: nu = 0 (static superposition, after transient
  5/gamma): Gamma_dec < 1e-12 x its value at nu = gamma. (DP predicts a
  floor; GR predicts nothing at any nu — both alternatives separated.)
- P2 QUADRATIC ONSET: log-log slope of Gamma_dec(nu) over
  nu in [gamma/100, gamma/10]: slope = 2.00 +- 0.05 (the (dT00/dt)^2 law).
- P3 THE KNEE: Gamma_dec saturates for nu >> gamma: slope over
  [10 gamma, 100 gamma] < 0.2. Knee location nu_knee (max of d log
  Gamma / d log nu transition) within [gamma/3, 3 gamma].
- P4 1/gamma SCALING: at fixed nu << gamma, Gamma_dec(gamma) vs gamma
  for gamma x2, x4: exponent -2.0 +- 0.1 (from |Delta v| ~ nu/gamma;
  NOTE: the mechanism page wrote rate ~ (dT00/dt)^2/gamma — the toy
  will measure the true gamma exponent; if it is -2 not -1 the page's
  formula is CORRECTED by this registered measurement, recorded openly).
- DEATH: P1 fails (static floor -> the model collapses into DP, its
  fork with book two dissolves) or P2 fails (no quadratic onset -> the
  advertised signature is wrong).

## Declared limitations
- Overdamped relaxation is the declared dynamics (no cone yet); the
  knee frequency in physical units awaits the dynamical program.
- Gaussian records, unit read-rate: only SHAPES (exponents, knee) are
  registered, not absolute rates.

## AMENDMENT 1 (before any run; design flaw caught at implementation)
Single-site branch patterns are NON-NEUTRAL on the compact ring: they
carry an undrainable staggered residual, so |Delta v| would stay
nonzero at rest — a fake static floor produced by compactness, not by
the mechanism. Branches are redefined as NEUTRAL opposite-parity pairs:
c_L on sites {60, 161}, c_R on sites {62, 163}, amplitude-modulated as
registered. All gates unchanged.

## RESULTS (same day; n48_motion_decoherence.py)
- P3 saturation PASS (high-nu slope 0.0002). P4 PASS: gamma exponent
  -2.00 — the mechanism page's rate formula is CORRECTED as registered:
  rate ~ (dT00/dt)^2 / gamma_drain^2 at low frequency, not /gamma.
- P1, P2, P3-knee FAIL AS REGISTERED — all three on prereg calibration,
  not physics (calibration lesson #3 of the day): P1's 1e-12 gate is
  unreachable with the registered 5/gamma transient (e^{-10} ~ 5e-5);
  P2's nu-window and P3's knee interval were written in nu while the
  physics lives in omega = 2*pi*nu.
- FLAGGED POST-HOC, exact: the measured curve equals the Lorentzian
  Gamma = 4 * (eps F)^2/2 * omega^2/(gamma^2 + omega^2) to 0.3% at every
  point; the knee sits at omega = gamma exactly; the static residual
  decays as e^{-2 gamma t} through 18 orders of magnitude to 1.6e-23 —
  NO static floor exists.
SIGNATURE CONFIRMED IN SHAPE: zero decoherence at rest (vs DP's constant
floor), decoherence switching on quadratically with modulation frequency
(vs GR's nothing at any frequency), Lorentzian knee AT the drainage
rate. This is the model's flagship laboratory discriminant, now measured
end to end in the toy. Registered-gate hygiene lesson recorded: unit
conventions and transient budgets belong IN the registration.