docs(flomni): document that PandA stdev needs the analog cap-sensor term

Cross-checked PandA's raw within-point sample stdev against RT's own
per-point control-loop stdev on S06313. Confirmed the capacitive-sensor
subtraction from the position conversion formula isn't optional for a
noise estimate either: dropping it (interferometer counts alone) gives a
noise estimate ~10x too large and nearly uncorrelated with RT's (r~0.2),
because interf and cap are anti-correlated at r~-0.96 within a point. With
the full formula, PandA and RT's independent stdev estimates agree to
~8-14% and correlate at r~0.98-0.99. Also flags
average_stdeviations_x_st_fzp/_y as a cumulative-mean field, not a
per-point stdev, to avoid it being used by mistake in a future session.

csaxs_bec/bec_ipython_client/plugins/flomni/AI_docs/PANDA_POSITION_VALIDATION.md

@@ -47,7 +47,11 @@ and known-good (used successfully in reconstruction):
   not against `target_x`/`_y`.
 - `rt_positions_data_stdev_x_st_fzp`/`_y` — RT's own per-point stdev, useful
   as a sanity scale for how much residual noise to expect (order 0.005 µm in
-  the validated scan).
+  the validated scan). See §9 for a raw-PandA cross-check against this value.
+  Don't confuse this with `rt_positions_data_average_stdeviations_x_st_fzp`/
+  `_y`, which is a running/cumulative mean of `stdev_x_st_fzp` up to that
+  point in the scan (confirmed by direct comparison, 2026-09-23), not a
+  per-point noise value — it's the wrong field for a per-point comparison.
 
 One row per scan point (472 points in the validated scan, `S06313`).
 
@@ -351,3 +355,65 @@ never overlaps a gated exposure.
 **Reduced data mode** (`S00399`) validated cleanly at full accuracy — see
 §6 for the row-count/gate-fraction characterization. No contamination, no
 missing points, same R² bar as the other burst scans.
+
+## 9. Per-point stdev cross-check against RT's control-loop stdev (`S06313`, 2026-09-23)
+
+Besides the per-point mean position (§4), PandA's raw samples let you
+cross-check RT's own per-point noise estimate
+(`rt_positions_data_stdev_x_st_fzp`/`_y`, §2) against an independent
+measurement — a single-frame scan has ~998 raw PandA samples landing within
+each point's gate window (`CLOCK1`'s free-running rate over one exposure),
+so each point's within-group sample scatter is itself a noise estimate.
+
+### 9.1 Method
+
+For each grouped point (§3.2, after applying §3.3's stale-prefix drop where
+needed), compute `pos_x_um`/`pos_y_um` (§3.4's full formula) **per
+individual raw sample**, not just on the group mean, then take the
+within-group sample stdev (`ddof=1`). Compare against
+`rt_positions_data_stdev_x_st_fzp`/`_y` (not
+`average_stdeviations_x_st_fzp`/`_y` — see the note in §2).
+
+### 9.2 The analog `cap_voltage_fzp_x`/`_y` term is required, not optional
+
+Naively computing per-sample stdev from `interf_st_fzp_x`/`_y` alone
+(skipping the `CapX_FZP_microns`/`CapY_FZP_microns` subtraction in §3.4)
+gives a wildly wrong noise estimate:
+
+| | X stdev (µm) | Y stdev (µm) | corr. with RT stdev (472 points) |
+|---|---|---|---|
+| Interferometer only, no cap term | 0.072 | 0.049 | 0.22 / 0.24 |
+| Full formula (interf − cap, §3.4) | 0.0074 | 0.0063 | 0.98 / 0.99 |
+| RT's own stdev | 0.0065 | 0.0058 | — |
+
+Within a single point, `interf_st_fzp_x` and `cap_voltage_fzp_x` are
+anti-correlated at **r ≈ −0.96** (checked on point index 5, n=998 raw
+samples). The raw interferometer counts carry a large common-mode
+noise/drift component roughly 10x bigger than the true positional noise; the
+capacitive-sensor subtraction in §3.4 is what cancels it — the same
+combination that's already required for the mean position (§4) turns out to
+be even more load-bearing for the noise estimate. Both `FMC_IN.VAL1/VAL2`
+(the capacitive analog inputs) and `INENC1`-`4.VAL` (the encoder position
+inputs) are captured with `CAPTURE=Value` off the same `CLOCK1` tick (see
+`docs/developer/panda_box_free_running_setup.md`), so this isn't a
+sampling-rate mismatch between the two channels — the interferometer signal
+genuinely is that much noisier on its own.
+
+**Practical implication:** any future per-sample noise/variance analysis of
+Mode B data must use the full interf+cap combination (§3.4), never the raw
+interferometer signal alone — skipping the cap term breaks the noise
+estimate far more severely than it breaks the mean position.
+
+### 9.3 Result (`S06313`, all 472 points)
+
+PandA's within-point stdev (full formula) runs ~8–14% higher than RT's own
+stdev (X: 0.0074 vs 0.0065 µm; Y: 0.0063 vs 0.0058 µm), and the two
+independent noise estimates correlate at r ≈ 0.98 (X) / 0.99 (Y)
+point-by-point. The small systematic excess is expected, not a discrepancy:
+RT's stdev comes from its own already-averaged control-loop samples, while
+PandA's ~998 raw samples per point pick up additional high-rate noise RT's
+loop doesn't report, plus whatever small residual noise the interf/cap
+combination itself adds. This doesn't affect the mean-position validation in
+§4 (a noise-floor cross-check, not a bias check) — it's a useful additional
+confirmation that PandA's raw stream and RT's control loop are seeing
+consistent underlying physics, not just consistent means.