# Port-to-dipole normalization audit

Audit snapshot: campaign `symmetric_dipole_mse_q1e4_v1`, update 23.

## Quantities validated directly

- The sampled Gaussian source and the analytic source expression agree with
  normalized correlation 1.00000008 and projection scale 1.00000012.
- Replaying the analytic target through the same three source-off fitting
  windows returns field Q=10018.79 and energy Q=10017.98 for the specified
  Q=10000 target. Field and energy residuals are 5.36e-6 and 7.91e-7.
- An independent nonlinear damped-cosine fit to the live field gives Q=110.639
  and wavelength 779.4734 nm. The native estimator gives Q=110.562 and
  779.4714 nm. An independent log-energy fit gives Q=110.577.
- The Purcell constant is arithmetically correct for its stated assumptions:

  \[
  F_P=\frac{3}{4\pi^2}\frac{Q}{V/(\lambda/n)^3}=666.9973
  \]

  at Q=10000, physical V=0.1 um3, wavelength 780 nm, and n=1.755121.

## Source-power convention

The mode solver normalizes the retained y/z quadrant to unit flux. Direct
evaluation gives reduced-plane flux 0.9999991 and unfolded full-cross-section
flux 3.9999971. With amplitude 1/sqrt(2), each physical x port therefore has
flux two and the x-reflected pair has total flux four in this solver
normalization, not one.

The target's central prompt coefficient does match this configured source:
`sqrt(2) * E_mode(center)` equals the coherent field from the two amplitude-
1/sqrt(2) x sources. Consequently the common source scale cancels from the
normalized waveform MSE. It does not, however, support an absolute unit-power
claim.

## Mode-volume convention

The stored-energy formula and octant factor are consistent with

\[
V=\frac{8U_{\rm reduced}}{\epsilon_d E_{y,\rm rms}^2}.
\]

The live implementation used the fixed target epsilon 3.08045. The dipole cell
is trainable, and at update 23 its density was 0.318525, epsilon 2.746699, and
n=1.657317. Using the actual local material changes physical V from 0.222584
to 0.249631 um3 and normalized V from 2.541064 to 2.399463. The dashboard
therefore labels the history explicitly as `V/(lambda/n_target)^3` and gives a
current-point local-index correction.

## What is not physically calibrated

The amplitude-derived beta is not a measured branching ratio. The scene has no
port-flux detector. It subtracts the target prompt rather than the geometry's
own nonresonant response, then assumes that multiplying the prompt port field
by sqrt(Purcell) supplies an absolute reciprocal-field calibration. That step
requires the bare guided-mode LDOS and the complex port-cavity coupling
coefficient; Q/V and beta alone do not specify it. The update-23 value was
3640.6%, which is an immediate physical impossibility and a useful diagnostic
of the missing calibration.

The target has an exact discrete carrier, pulse envelope, center frequency,
and specified pole lifetime. Its cavity-to-prompt amplitude and relative phase
are prescribed design choices, not a unique temporal coupled-mode solution.
There is no target spatial eigenfunction: only the three-component field at the
central dipole enters the loss. Late x-y and x-z field images are telemetry.

## Requirements for an absolute successor

1. Normalize the unfolded two-port source to the intended total incident
   power, or carry the reduced-domain multiplicity explicitly.
2. Fix the emitter material or use its actual local epsilon in every V and
   Purcell calculation.
3. Record modal Poynting flux at both waveguide ports and an enclosing loss
   surface so beta is a branching ratio rather than an amplitude proxy.
4. Calibrate the complex target amplitude from temporal coupled-mode theory
   using the port normalization, external decay rate, mode energy, and local
   field, or from a reciprocal dipole/port reference solve.
5. Use occasional longer forward-only ringdown audits once the 2 ps tape no
   longer resolves the fitted decay reliably.