# n127 — the units bridge, staked out (n122 item #1, the first analytic pass)
# (2026-07-11, end of the night. NOT the derivation — the surveyor's
#  stakes: the form, the anchor, the feasibility, and the ONE constant
#  left, with its derivation route named. Class [B] throughout.)

## The candidate form (dimensional + structural, both sectors agree)
The toy's law is Gamma ∝ (dT00/dt)^2 / (gamma^2 + omega^2). The only
dimensionally consistent completion with no new scale is:
   Gamma(P, omega) = xi * P^2 / (hbar^2 gamma (gamma^2 + omega^2))
where P = the coherent BRANCH-DIFFERENTIAL energy-flow modulation
(watts of dE/dt difference between superposition branches), gamma =
the audit bandwidth, xi = dimensionless, O(1) if natural.

## The anchor (already registered, prediction family 1-2)
   gamma = alpha * m_e c^2 / hbar = 5.66e18 s^-1   (hbar gamma = 3.73 keV)
G cancels (n93); the anchor is the declared electron-anchor bet.

## The feasibility table (why this page matters)
At omega << gamma, Gamma = xi * P^2/(hbar^2 gamma^3):
   P = 1 nW  -> Gamma = 5e-7  s^-1   (out of reach)
   P = 1 uW  -> Gamma = 0.5   s^-1   (MEASURABLE in seconds)
   P = 1 mW  -> Gamma = 5e5   s^-1   (saturating, easy)
IF xi is O(1), a microwatt of coherent differential T00 modulation
on a matter-wave superposition decoheres at ~1 Hz: the Auditometer
is not a heroic experiment — it is a hard but ordinary one. The
entire question is xi.

## The one constant left, and its derivation route (the real campaign)
xi is NOT free: the same channel's omega -> 0 limit IS Newtonian
gravity (the framework's central claim), so xi is fixed by matching
the static audit response to G. Route, staged: (i) write the audit's
mediated static energy for two masses in the Lindblad model with the
derivative coupling (the n125-selected shape); (ii) match to
-G m1 m2/r: this pins (coupling^2/gamma) in SI; (iii) insert into
the dynamic channel: xi drops out as a ratio — the SAME
coupling^2/gamma appears in both, so xi = a pure number computed
from the model's filter functions (the Lorentzian's normalization
vs the static limit's). No new physics enters: xi is an exercise in
keeping track of factors. A hard exercise — the toy's dichotomy
says the static and clock channels split, and xi rides on exactly
that split — but a bounded one.
STATUS AFTER TONIGHT: form staked, anchor in place, feasibility
computed, xi's derivation reduced to a defined calculation. The
falsifiability gap is no longer unattempted; it is one factor wide.

## Honesty box
- P is the BRANCH-DIFFERENTIAL coherent modulation — an XFEL's raw
  power is not P; the experimental P must be engineered and will be
  far below the beam power. The table's watts are targets for the
  instrument designer, not beam specs.
- If xi comes out absurdly small (the dichotomy suppressing the
  dynamic channel by Q or worse), the Auditometer dies at the
  design stage and the framework loses its flagship to a number it
  computed itself. That is the risk of finishing this calculation —
  and the reason it must be finished.