docs: state the q convention at every numeric q and on the q flags

Every q in the pipeline is 2*pi/d (Definitions.h, the azint bin mapping), but
the numbers in 3.3, 7.6 and 10.10 and the --azim-* flags never said so, and a
reader taking q = 1/d would set --azim-q-spacing or --azim-max-q wrong by
2*pi. The 7.6 ice triplet is spelled out so 'within 0.06 of one another' reads
as the adjacent-ring spacing it is.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EFEJG6WBQv8th4UJFNe53N

docs/CPU_DATA_ANALYSIS.md

@@ -403,7 +403,7 @@ Because detection reads the pixel's ring, a pixel that falls outside the azimuth
 
 Spot finding can be restricted to a resolution range $[d_\mathrm{high}, d_\mathrm{low}]$ by masking pixels outside the range. Optionally, spots in identified ice-ring regions can be tagged so that subsequent indexing/refinement may include or exclude them (see §4 and §6).
 
-A single per-image **ice-ring score** is derived from a radial profile: for each hexagonal-ice powder ring (see *Where the ring positions come from* below), the profile intensity at the ring is divided by a smooth background estimated from the *whole* profile — a running median of the non-ice bins, interpolated under each ring — and the strongest ring's ratio is reported (1 = no ice, $>1$ = ice above background). A whole-profile background is used rather than a couple of adjacent shoulder bins so the estimate is robust to the radial binning: at a coarse Q-spacing a local shoulder can be only ~1 bin and would double-count the ring's own edge (offline processing defaults to a fine 0.01 1/Å spacing, `--azim-q-spacing`, so the rings are well resolved). The reported quantity is the ice *magnitude* rather than a significance: with many photons any real ice ring is statistically significant, so significance does not discriminate.
+A single per-image **ice-ring score** is derived from a radial profile: for each hexagonal-ice powder ring (see *Where the ring positions come from* below), the profile intensity at the ring is divided by a smooth background estimated from the *whole* profile — a running median of the non-ice bins, interpolated under each ring — and the strongest ring's ratio is reported (1 = no ice, $>1$ = ice above background). A whole-profile background is used rather than a couple of adjacent shoulder bins so the estimate is robust to the radial binning: at a coarse Q-spacing a local shoulder can be only ~1 bin and would double-count the ring's own edge (offline processing defaults to a fine 0.01 Å⁻¹ spacing — in $q = 2\pi/d$, like every $q$ in this document (§1.2) — `--azim-q-spacing`, so the rings are well resolved). The reported quantity is the ice *magnitude* rather than a significance: with many photons any real ice ring is statistically significant, so significance does not discriminate.
 
 The profile the score is read off is the **peak-excluded** one, not the plain azimuthal integration: where adaptive spot finding runs (§3.2 — the offline and viewer default), the score uses the sigma-clipped per-resolution-ring background that finder already computes for its threshold. This matters more than it sounds. A plain azimuthal profile is a per-ring *mean*, so a few strong low-resolution reflections landing in a ring's bin raise it exactly as ice would; measured over a rotation battery, that alone ranked ice-free crystals above crystals that really are iced. An ice ring is azimuthally smooth and survives the sigma clip, while Bragg peaks do not, so on the clipped profile ice-free crystals sit near 1 and crystals with confirmed ice above 2. Only where no adaptive finder ran (the FPGA workflow) does the score fall back to the plain profile.
 
@@ -671,7 +671,7 @@ The **distance** is different: it follows from $r=F\tan2\theta$ with $\sin\theta
 
 A plain radial profile — one azimuthal sector — has averaged the ring over every direction and carries no centre at all, so the profile route requires at least four sectors and uses 32 by default. Sixteen to thirty-two are enough; beyond that the limit is the ring's own texture, not counting statistics.
 
-The extraction window around a ring is capped at half the gap to its neighbour, because the background under a peak is taken from the ends of that window: hexagonal ice has three rings within 0.06 Å⁻¹ of one another, which a fixed window merges into a single peak. Where only one ring is in reach the two tilts are held at their input values rather than fitted, since on a single ring they are degenerate with the centre (above) and the fit would otherwise trade the centre away for them.
+The extraction window around a ring is capped at half the gap to its neighbour, because the background under a peak is taken from the ends of that window: hexagonal ice has a triplet of rings (1.947, 1.916 and 1.882 Å) whose neighbours sit only 0.05–0.06 Å⁻¹ apart in $q = 2\pi/d$, which a fixed window merges into a single peak. Where only one ring is in reach the two tilts are held at their input values rather than fitted, since on a single ring they are degenerate with the centre (above) and the fit would otherwise trade the centre away for them.
 
 ---
 
@@ -1015,7 +1015,7 @@ A reference dataset (`--reference-mtz`) supplies known intensities for the same
 
 ### 10.10 Ice rings at the scale and merge stages
 
-Where the gate of §3.3 has found ice, reflections falling within $\pm w$ in $q$ of a hexagonal-ice band ($w=0.03$ Å$^{-1}$ offline, about the measured ring half-width) are marked. Marked reflections are **excluded where a model is fitted** — the per-frame scale $G$, the per-image correlation, and the $P1$ merge the space-group search runs on — because ice contamination is a *positive bias*, not extra scatter, and a least-squares scale absorbs it into $G$ and into the error-model $b$, where it damages every other reflection on the same frame. They are **kept in the final merge**, which is also what the established scaling programs do by default, so the affected shells keep their completeness.
+Where the gate of §3.3 has found ice, reflections falling within $\pm w$ in $q = 2\pi/d$ (§1.2) of a hexagonal-ice band ($w=0.03$ Å$^{-1}$ offline, about the measured ring half-width) are marked. Marked reflections are **excluded where a model is fitted** — the per-frame scale $G$, the per-image correlation, and the $P1$ merge the space-group search runs on — because ice contamination is a *positive bias*, not extra scatter, and a least-squares scale absorbs it into $G$ and into the error-model $b$, where it damages every other reflection on the same frame. They are **kept in the final merge**, which is also what the established scaling programs do by default, so the affected shells keep their completeness.
 
 Nothing on an ice band is deleted from the merged output. Deleting the bands was implemented, measured against an external arbiter rather than against the merge's own statistics, and removed: on the one rotation-battery crystal where a band was both dead by its own merged $\mathrm{CC}_{1/2}$ and scorable by anomalous peak height, dropping it changed the mean anomalous density at the known sites by $-0.001\pm0.018\,\sigma$ — about 2 % of the site height — while removing 1149 unique reflections whose mean $I/\sigma$ was 3.62 against the dataset's own 3.05, i.e. better-than-average data, and costing 6 to 8 points of completeness in the affected shell.
 

docs/RUGNUX.md

@@ -1038,7 +1038,8 @@ Spot finding:
 | `--max-spots <num>` | Maximum spots kept per image (the strongest ones) and handed to indexing. **If omitted, the budget is measured** on rotation data: the first pass reads how deep into an image's spot list its spots still lie on the lattice it found, and the run keeps that many (never more than 1000). Give a value to pin it. Stills always use the fixed 1000. |
 | `--detect-ice-rings[=on\|off]` | Flag ice-ring spots (de-prioritised in indexing) and exclude ice-ring reflections from scaling. Default: the master file's `detect_ice_rings`, or — where the file carries no such key — **on for rotation and off for stills** |
 
-Azimuthal integration (the radial profile behind the per-image ice-ring score):
+Azimuthal integration (the radial profile behind the per-image ice-ring score). Every *q* here is
+*q* = 2π/*d*, in Å⁻¹:
 
 | Option | Description |
 | --- | --- |