# n128 — xi closed: the bridge has a number
# (2026-07-11; n127's "one factor wide" gap, closed at class B.
#  Script: n128_xi_closed.py. The falsifiability gap — the third
#  priority deliverable — is DONE at model level.)

## The result
The bridge constant is the two-channel ratio of the monitor, and it
is a LAW, not a number: measured on the minimal monitored mediator
by the independent route (steady-state statics + integrated dynamics,
no filter formulas):
   R = Gamma_dynamic / Omega_static = zeta * Q,   Q = kappa/|Delta|
   slope 1.0000 over four decades of Q (gate X1 PASS)
   zeta = 0.4834 +- 0.0000, kappa-independent (gate X2 PASS)
   shape: Lorentzian in omega, knee at kappa/2, max dev 11% at the
   far point (gate X3 reported — the Delta-sideband structure).
THE DYNAMIC CHANNEL IS Q TIMES THE STATIC ONE. Gravity is the
Q-suppressed static residue of the same monitor whose dynamic
channel decoheres — that is WHY the audit is loud where gravity is
weak, in one measured ratio.

## The assembled formula [class B]
Eliminating g^2 via G (the static channel IS Newton — the
framework's central claim) and taking the E10 lock with the
electron-anchor Q = alpha/alpha_G = 4.2e42:
   Gamma(P, omega) = 0.48 * Q * (G/c^5) * P^2/(hbar gamma) * gamma^2/(gamma^2+omega^2)
with gamma = alpha m_e c^2/hbar = 5.66e18 s^-1 and P = the coherent
BRANCH-DIFFERENTIAL energy-flow modulation. Every lab frequency is
below the knee (optical 1e15 << 5.7e18), so L(omega) ~ 1.

## The feasibility verdict
   P = 1 uW  -> 9.4e-8 s^-1   (out of reach)
   P = 1 mW  -> 0.094 s^-1    (MEASURABLE: ~10 s coherence suffices)
   P = 1 W   -> 9.4e4 s^-1    (saturating)
THE AUDITOMETER'S TARGET IS THE MILLIWATT. A coherent differential
modulation of ~1 mW on a matter-wave superposition, held for tens of
seconds, decides. And the kill is now TWO-SIDED [class B]: a flat
null at mW amplitudes no longer hides behind the gap — it kills the
electron-anchored framework (surviving retreats: the proton anchor
buys (m_p/m_e)~1836x in gamma, i.e. 1836x in required P^2... the
window is finite and named; beyond it, dead).

## Class-B declarations (what the formula assumes, all named)
1. The minimal single-mediator model's zeta transfers to the lattice
   monitor up to O(1) (the Q^1 law itself is filter-structural and
   should transfer exactly; zeta may move within [0.1, 10]).
2. Q via the E10 lock with the ELECTRON anchor (the registered bet).
3. The static channel = Newtonian gravity (the framework's central
   claim — if that is wrong, everything upstream died already).
4. P identified as branch-differential dE/dt (the n100 Auditometer's
   operational definition).

## One sentence
The theory now states, in SI units, how fast the vacuum's auditor
writes: half a hertz per (milliwatt)^2 of coherent disagreement
between branches — and stakes its life on it.