# n47b — pre-registration: the linear clock channel (before code)

n47 found: clocks slow near mass (real effect), dominant response
QUADRATIC in the drainage field (parity-blind), a subdominant channel in
spectral clocks with F-exponent ~1.65 hinting at a linear component.
GR demands redshift LINEAR in the source and universal across clock
constructions. This experiment isolates the linear channel or kills the
metric reading.

## Model
n47 setup (ring N=200, info-metric drainage, pair at d=99), F scan
(0.075, 0.15, 0.3) for channel separation by scaling.

## Registered decomposition
Cell-averaged shift of clock i at cell R:
  s_i(R) = a_i * E(R) + b_i * Q(R),
E = cell-averaged |dk| envelope (linear regressor), Q = cell-averaged
dk^2 (quadratic regressor). Joint least squares over cells > 2 from
consumers, all three F values simultaneously (E scales as F, Q as F^2 —
the scan is what separates the channels).

## Gates
- L1 (existence): for spectral clocks C1 and C3, the linear coefficient
  a_i is nonzero beyond fit noise: |a_i| > 10x its residual-based
  standard error. If a_i consistent with 0 for both: NO linear channel —
  the metric reading of drainage gravity DIES (GR redshift is linear;
  recorded as such, no amnesty).
- L2 (universality of the linear channel): |a_C1/a_C3 - 1| < 10% -> the
  linear channel is construction-independent: PASS. > 50% -> clock-
  dependent: the metric reading dies even with a channel present.
- L3 (control): the bond clock C2 must have a_C2 consistent with 0 and
  b_C2 = -1/8 within 2% (the analytic result) — validates the
  decomposition machinery.
- L4 (parity clocks — the anti-GR probe): intra-cell asymmetry
  delta_i(R) = shift(even site) - shift(odd site) for C1: if delta
  scales as F^1 and flips sign under consumer parity swap -> clocks ARE
  parity-sensitive at lattice scale: a sharp anti-GR signature (a real
  clock would tick FASTER near the opposite-parity mass). If delta
  scales as F^2 or vanishes: parity-blindness is exact and the metric
  reading survives L4. Either result is recorded as a prediction.

## Declared limitations
- E as regressor is one declared choice of linear functional; if L1
  fails, one registered fallback is allowed and declared NOW: replace E
  by the smooth (non-staggered) component of the local coupling shift,
  cell-averaged. No further post-hoc regressors.
- Static, 1D, envelope-level; continuum extrapolation not claimed.

## RESULTS (same day; n47b_linear_channel.py) — HEADSTONE 20
- L1 FAIL: |a|/se = 5.7 (C1) and 4.2 (C3), below the 10x gate — and the
  L3 control makes the failure robust: the bond clock, analytically
  a = 0, measures a = +7.9e-5 at 44 sigma. The fit's "significance" has
  a systematic floor ~1e-4 from higher-order (quartic) leakage; C1 and
  C3's linear coefficients sit AT that floor, with OPPOSITE SIGNS
  (+4.4e-5 vs -4.3e-4). There is no linear channel.
- L2 DEAD: spread 110%, opposite signs.
- L3: b_C2 = -0.1264, within 1.1% of the analytic -1/8 (machinery
  validated); the a-clause fired, which is the informative part (the
  systematic floor measurement).
- L4: an intra-cell parity-linear component exists (F-exponent 0.92) but
  is 0.4% of the signal and does NOT flip under consumer parity swap
  (correlation +0.84, not -1): no anti-GR parity-clock signature, and
  no rescue channel.
- The registered fallback regressor is void by structure: the drainage
  field is PURELY staggered (the Gauss sector lives at q = pi); it has
  no smooth component for clocks to couple to linearly.
VERDICT — HEADSTONE 20: drainage gravity has NO linear redshift channel.
Clock shifts are quadratic in the source; GR's redshift is linear in the
source and is measured (Pound-Rebka, GPS, optical clocks). The METRIC
READING of the static drainage mechanism is dead, structurally: a purely
staggered field offers parity-blind clocks only its square. What
survives: the force sector (n46, sign owned) and the time-dilation SIGN
(clocks do slow near mass). What is needed for resurrection, named
plainly: a mechanism generating a SMOOTH (q ~ 0) component of the
drainage field coupled linearly to consumption — nothing in the current
model provides it.