Jungfraujoch/docs/RUGNUX_MODEL_AND_REFERENCE.md

# Models and reference data

What Rugnux does with outside knowledge — an atomic model, a predicted model, a reference dataset, a
cell or a space group you already know — and, decision by decision, what that knowledge is and is not
allowed to change. The first section is the short version; the tables after it are the precise one;
the rest walks through a run step by step.

```{contents} On this page
:local:
:depth: 2
```

## In short

- **Rugnux needs nothing but the images.** Indexing, the cell, the space group, the resolution cut,
  scaling, merging and the error model all come from the data. Everything on this page is optional.
- **A model (`--model`, `--mr`) does not change how your data are processed.** The images are
  indexed, integrated, scaled and merged the same way with or without it, and the space group is
  determined before the model is used. The merged intensities and their sigmas in
  `<prefix>.mtz` are the same numbers either way.
- **The model can only relabel, and only if the data accept it.** It is first tested against
  copies of itself placed in random orientations. A model that fits no better than those changes
  nothing at all: the reflection files are byte for byte what a run without a model writes. A model
  that does fit may change three *labels* in `<prefix>.mtz`: the **hand** of the space group
  (P4₁2₁2 against P4₃2₁2, which the intensities cannot tell apart), the **indexing** where the
  lattice allows two equally valid ones, and the **axes** the files are written on. No
  intensity is changed, no reflection is added or removed, and no other space group is ever taken.
- **A different space group chosen by the model goes to a separate file.** If the model prefers
  another space group, or a twinned subgroup, that merge is written *beside* the answer as
  `<prefix>_mr.mtz`/`.cif`, with the model as placed there. `<prefix>.mtz` stays the data's own
  answer.
- **A reference dataset (`-z`) and a space group or cell you give (`-S`, `-C`) are different:** they
  are taken as facts about the crystal. They fix the space group and the cell before processing,
  so with them the space group is yours, not the data's.
- **One exception to "processed the same":** on **serial stills** given `--model` together with
  `-C` and `-S`, the model is used during integration to choose, crystal by crystal, between the two
  equally valid indexings — the same job a reference dataset does there (see
  [Serial stills](#serial-stills-the-one-place-a-model-acts-before-the-merge)).

## Every option that brings in a model or reference data

| Option | What you give | What Rugnux uses it for | Can it change `<prefix>.mtz`? |
|---|---|---|---|
| *(none)* | — | Everything from the data | — |
| `--model <file>` | An atomic model, PDB or mmCIF, gzipped or not, recognised by content: an experimental structure or a prediction | Validation after the merge (R-work/R-free, CC(model, data), maps, the placed model); a rigid-body placement checked against a null, with molecular replacement where the rigid body does not place it, and straight away for a prediction | Labels only (hand, indexing, axes), and only where the model fits. Other space groups → `<prefix>_mr.*` |
| `--mr <file>` | The same kinds of model | As `--model`, but molecular replacement straight away, without the rigid body. `--mode mx` only, not together with `--model` | Hand label only. Other space groups → `<prefix>_mr.*` |
| PAE file beside a prediction | `AF-<id>-F1-predicted_aligned_error_v<n>.json` next to `AF-<id>-F1-model_v<n>.cif` (read automatically, no option) | Cuts the prediction into rigid domains for molecular replacement | No (a domain alone can only confirm the answer's group) |
| `-z, --reference <file>` (`--reference-mtz`) | Merged data of the same crystal form: an MTZ, or a PDB structure-factor mmCIF (`-sf.cif`) | Fixes the space group (in its own setting) and the cell (softly), puts the merge on its axes, resolves the indexing ambiguity, hands over its R-free set, reports CC<sub>ref</sub> on stills. Never a scale anchor | **Yes**: the space group, the axes, the indexing and the free set are the reference's |
| `--reference-column <label>` | An MTZ column label | Which column of the reference is read | Through `-z` only |
| `-S, --space-group` | A space group | Fixes it: no space-group search | **Yes**: the group is yours (a fitting model may still relabel its hand) |
| `-C, --unit-cell` | A cell | Indexing looks for this cell (within tolerance); the FFT search range is widened to cover it; on stills it turns on the shared-geometry refinement and, with `-S` and `--model`, the per-image use of the model | **Yes**: the cell, and the axis order the files are written in |
| `--force-rotation-lattice` | Nine numbers: a lattice | Skips the first-pass indexing and uses this lattice | **Yes**: the lattice |
| `--report-resolution <dmin>[,<dmax>]` | Another program's resolution range | A second statistics table at that range (`REFRES_*`) | No — report only |

`-S`, `-C`, `-z` and `--force-rotation-lattice` are *assertions*: Rugnux takes them as true and
does not test them against a null. Use them when you know; leave them out to let the data decide
(a de-novo run is the recommended default — see [Running Rugnux](RUGNUX_TUTORIAL.md#rotation-data)).
`--model` and `--mr` are *hypotheses*: Rugnux tests them, and what it lets them change is limited
and stated below. In `--mode calibration` a cell given with `-C` names the calibrant instead
([Detector calibration](RUGNUX_CALIBRATION.md)); nothing on this page applies there.

## Four kinds of influence

Every decision and every output of a run falls in one of four classes. The decision table below uses
these letters.

- **(a) Data only.** Never influenced by any model. The same with and without `--model`/`--mr`.
- **(b) Model-informed label in `<prefix>.mtz`.** A choice between alternatives the data *cannot*
  separate and that are all equally valid descriptions of the same measurement: the hand of an
  enantiomorphic pair, an indexing ambiguity, the setting (axes). The model may make it only after it
  has passed its null; the intensities do not change. Reported as `SPACE_GROUP_ENANTIOMORPH=
  ASSUMED_FROM_MODEL`, `MODEL_DECISIONS_TAKEN=`, `MODEL_ENANTIOMORPH_ADOPTED=`,
  `MODEL_INDEXING_OPERATOR=`, `SETTING_SOURCE= MODEL`, and the withdrawal of
  `INDEXING_AMBIGUITY_OPERATORS=`.
- **(c) Model-driven, separate files only.** A choice the data *could* in principle make but did not
  make the model's way: another space group with the same rotations (other screw axes), or the twin
  hypothesis' subgroup. Written only as `<prefix>_mr.mtz`/`.cif` with `<prefix>_mr_model.pdb`/`.cif`
  (and named by `MODEL_CHOICE_FILE_PREFIX=`, `MODEL_CHOICE_SPACE_GROUP=`, `MR_DECISION=`). Never in
  `<prefix>.mtz`.
- **(d) Report-only model statistics.** Numbers about the model against the data, which nothing in
  the pipeline acts on: `R_WORK`/`R_FREE`, `R_MODEL_SHELL_SCALED`, `CC_MODEL_*`, `MODEL_FIT*`,
  `MODEL_PLACEMENT`, the `MR_*` keys, the anomalous sites, the maps.

## Decision by decision

"Reference" means `-z`. A dash means the option plays no part.

| Decision | Without anything | With `-S` / `-C` | With `-z` | With `--model` / `--mr` | Class |
|---|---|---|---|---|---|
| Spot finding, beam centre, detector geometry | data | — | — | — | (a) |
| Indexing, lattice, cell | data (de novo) | your cell / lattice | the reference's cell, softly | — | (a) |
| Integration | data | — | — | — (stills: see below) | (a) |
| Scaling, error model, ISa | data | — | — (never a scale anchor) | — | (a) |
| Outlier rejection, frame disposition | data | — | — | — | (a) |
| Resolution cut | data (CC1/2 fall-off) | — | — | — (`CC_MODEL_CONFIRMED_TO_D_MIN` is reported, never used) | (a) |
| Point group, Laue class, centring | data (space-group search) | `-S` fixes it | the reference's | — | (a) |
| Screw axes (space group within the point group) | data | `-S` | the reference's | a different choice → `<prefix>_mr.*` only | (a) in `p.mtz`, (c) beside it |
| Hand (enantiomorph) | not decidable: `SPACE_GROUP_ENANTIOMORPH= UNDETERMINED` | `GIVEN` | `GIVEN` | relabelled to the model's where it fits, past the anomalous veto: `ASSUMED_FROM_MODEL` | (b) |
| Indexing ambiguity (merohedral reindex) | arbitrary on rotation (`INDEXING_AMBIGUITY_OPERATORS=`); mixed on stills (warning) | — | resolved against the reference | resolved by the rigid-body model where its lead beats its null, rotation; per image on stills with `-C`/`-S`. Never by molecular replacement | (b) |
| Setting (which axis is a, b, c) | standard setting | `-C`'s axis order; `-S`'s symbol | the reference's | the model's, where it fits and there is no `-z` (`SETTING_SOURCE= MODEL`) | (b) |
| Twinning check (L-test, twin laws) | data | — | — | — | (a) |
| Twin hypothesis `<prefix>_twin_<SG>.*` | data (when the group may have absorbed a twin law) | — | — | the model may also *ask* for this merge; written then only where the model chooses it | (a) / (c) |
| Anomalous signal, Friedel handling | data (`-A`) | — | — | — (the anomalous map is report-only, and the veto on the hand) | (a) |
| R-free test set | hash of the index | — | the reference's flags, where it matches | — (drawn again on the model's axes if the setting moved; never chosen by the model) | (a) |
| Merged intensities and sigmas in `p.mtz` | data | — | — | — | (a) |
| `p.mtz` space-group label | data | yours | the reference's | hand relabel only | (b) |
| `<prefix>_mr.mtz`/`.cif`, `<prefix>_mr_model.*` | not written | — | — | another group or the twin subgroup the model chose | (c) |
| Maps, `<prefix>_model.*`, section 5 of the report | not written | — | — | always, whatever the verdict | (d) |

## A run with `--model`, step by step

1. **The file is read and classified.** PDB or mmCIF, by content. A **prediction** — ModelCIF's
   quality metrics, or no cell and one B value per residue between 0 and 100 (an AlphaFold file) —
   is told apart from an **experimental structure** (`MR_MODEL_KIND=`). A model that cannot be read
   does not fail the run; the report says `MODEL_VALIDATION= NOT_PERFORMED` and carries a warning.
2. **The data are processed without the model.** Indexing, integration, scaling, the space-group
   search, the resolution cut, the error model, outlier rejection: none of them reads the model
   (on serial stills with `-C`/`-S`, see the next section). The only thing the model asks for here is
   one extra merge: the merge in a subgroup (the twin hypothesis) where the indexed lattice's group
   was promoted by a metric re-ask, or where the model's own group has fewer rotations than the
   adopted one — so that the model can be scored there. That merge is written only if the model
   chooses it.
3. **Rigid-body placement** (experimental structures, not with `--mr`). The model is put into the
   data's cell and refined as one rigid body on the working reflections; the step is kept only if
   it lowers R-free. A model written in another description of the lattice (other axes, other
   centring) is first put into the data's (`MODEL_CHANGE_OF_BASIS=`).
4. **The null.** The same model is turned to nine random orientations about its own centroid and
   placed the same way. The real fit has to beat them by 4.51 of their standard deviations on
   R-work (3σ allowing for the null being nine draws): `MODEL_FIT= ACCEPTED`, `MODEL_FIT_SIGMA=`.
   Otherwise `REJECTED`, and the model decides nothing. There is no fixed threshold on R
   ([§14.5](CPU_DATA_ANALYSIS_DECISIONS.md#145-does-the-model-fit-the-null-it-is-scored-against)).
5. **What an accepted model may do** (class b), applied to the reflections before they are written:
   - **hand** — where the data's group is the enantiomorph of the model's, the files take the
     model's group as their label. No reflection moves and I(+)/I(-) stay as measured. Vetoed where
     the anomalous difference map read at the model's atoms is inverted (warning `MODEL_HAND`);
   - **indexing** — where the lattice admits alternative indexings and no `-z` already settled it,
     the candidate with the lowest R-free, *if* its lead over the runner-up beats the lead a random
     placement of the same model takes (`MODEL_INDEXING_MARGIN_SIGMA=` ≥ 3). The data are
     reindexed into the model's frame, never the model into the data's;
   - **setting** — a model written on other axes takes the files to its setting
     (`SETTING_SOURCE= MODEL`), so that reflections and coordinates can be used together.
6. **The twin hypothesis.** Where a subgroup merge exists, the model is scored against it plainly
   and as twinned by its law. The maps come from whichever merge the model fits better on R-free
   (`MAPS_FROM=`). Where the model also fits there against its null, it has chosen the subgroup,
   and that merge is written again as `<prefix>_mr.mtz`/`.cif` (class c).
7. **Molecular replacement**, for a prediction, with `--mr`, or for an experimental structure the
   rigid body did not place (in the answer's merge or in the subgroup's). As many copies as the cell
   most probably holds are searched for in every space group the merge cannot tell apart and in the
   twin hypothesis' subgroup, and the choice has its own null. `MR_DECISION=` is one of:
   `AGREES` (the answer's group — nothing changes); `ENANTIOMORPH` (the answer's files take the hand
   label, past the same anomalous veto, else `ENANTIOMORPH_VETOED`); `SPACE_GROUP` or
   `TWIN_SUBGROUP` (written as `<prefix>_mr.*` only); `UNDECIDED` or `NOT_PLACED` (nothing is
   written). Molecular replacement never reindexes and never sets `MODEL_FIT`. Not placing a model
   is a result, not a warning ([Molecular replacement](RUGNUX_REPORT.md#molecular-replacement)).
8. **Validation and files.** R-factors, CC(model, data), maps and the placed model are computed
   for the placement that was kept, against the merge it was chosen on, and written:
   `<prefix>_maps.mtz` (map coefficients), `_model.cif`/`.pdb` — or the
   `<prefix>_mr_*` equivalents where the choice was `<prefix>_mr`. A rejected model gets its maps
   too: that is the case where looking at it in the density is most useful.
9. **The reflection files** — `<prefix>.mtz`, `.cif`, `.hkl`, `_unmerged.mtz` — are written last,
   carrying only the class-(b) labels from step 5 and the hand from step 7.

`MODEL_PLACEMENT=` summarises steps 3–7: `RIGID_BODY`, `MR` or `NOT_PLACED`.

In `--mode scale`, `--model` is steps 3–5 only: the rigid body, its null, and the hand and indexing
it may settle. There is no molecular replacement, no setting change and no twin hypothesis, and
`--mr` is refused.

### Serial stills: the one place a model acts before the merge

On serial stills each crystal is indexed on its own, so where the lattice admits two indexings, each
crystal lands in one of them at random and a merge averages reflections that are not equivalent.
That has to be settled per crystal, at integration time — by the time there is a merge, the hands
are already mixed. A reference dataset (`-z`) is the tool for it. Without one, `--model` given
together with `-C` and `-S` supplies the reference intensities instead: structure factors computed
from the model, against which each crystal's intensities are correlated to choose its indexing.

This is the only point at which a model affects which observations are merged together, and it is
not gated by the null — there is no merge yet to test the model on. It chooses only between
indexings that are equally valid for each crystal; a model that does not belong to the crystal
carries no information to choose with, so the crystals stay mixed, as they would without a model.
After the merge, the model is validated as in the steps above. Without `-C` and `-S`, or on rotation
data, the model is not used before the merge at all.

## Where a model can touch the space group

Spelled out, because this is the question that matters most:

1. **The space group in `<prefix>.mtz` is decided without the model** — by the space-group search,
   or by you (`-S`, `-z`). The model is read after that decision.
2. **The model can change one thing about that group: its hand,** between the two members of an
   enantiomorphic pair (P3₁/P3₂, P4₁2₁2/P4₃2₁2, P6₁22/P6₅22, …). The intensities are identical for
   both, so this is the one group choice no data can make; a model that fits carries chemical
   knowledge (the hand of its amino acids) the intensities do not. It is a label: no reflection
   moves. It applies to a group you gave with `-S` or `-z` too. The report says
   `SPACE_GROUP_ENANTIOMORPH= ASSUMED_FROM_MODEL` — *assumed*, not determined — also where the model
   simply agrees with the hand the run wrote.
3. **Everything else the model prefers goes beside the answer.** Other screw axes with the same
   rotations (e.g. P2 against P2₁ where the absences did not decide), or the twin hypothesis'
   subgroup: `<prefix>_mr.mtz`/`.cif`. The model never changes the point group, the lattice or the
   centring of `<prefix>.mtz`.

The safeguards behind 2 and 3:

- **The null.** The model must beat its own random placements by 4.51 sd, rigid body and molecular
  replacement alike, before it may relabel anything or have a `<prefix>_mr` file written.
- **The anomalous veto.** The hand is taken only where the anomalous difference map, read at the
  model's atoms, is not inverted. The veto can act only where the merge kept the Bijvoet split —
  every rotation merge does; serial stills only with `-A`. R-free cannot see the hand at all.
- **The indexing margin.** An indexing is taken only where the model's preference beats what a
  randomly placed copy of it would show.
- **Molecular replacement's own rules.** Its choice of group has its own null (`NULL_SIGMA`); a
  placement must pack (`CLASH`, `MATTHEWS`); a choice that translational NCS could explain, or one
  where the merge's own group was searched to fewer copies, is left `UNDECIDED`; a single domain of
  a prediction cut by its PAE can only confirm the answer's group, never change it; in P1 the first
  copy's origin is fixed and it counts only on its rotation function. The details are in
  [Molecular replacement](RUGNUX_REPORT.md#molecular-replacement).
- **The wrong-model test.** Rugnux's validation battery runs a set of datasets once without a model
  and once with each of five models of *unrelated* proteins (similar size, unrelated sequence and
  fold, and for the enantiomorphic sets a model in the other hand), and requires the reflection data
  and every report key outside section 5 to be identical, `MODEL_FIT` not accepted, molecular
  replacement not placing the model and no model decision taken
  ("The wrong-model null" in `tools/battery/README.md`; see also [Tests](TESTS.md)).

## Free set and model bias

**How the free set is made.** Rugnux draws its own test set (5 %, raised towards about 500 reflections on small data but never above 10 %):
each reflection's flag is a hash of its index, taken over its orbit under the lattice's metric
symmetry, so symmetry mates, Friedel mates and twin-law mates share a flag, every dataset of one
crystal form written on the same axes gets the same set, and the set does not depend on the space
group a file is merged in
([R-free test-set flags](CPU_DATA_ANALYSIS_INTEGRATION.md#107-r-free-test-set-flags)). The model
plays no part in it. Where a fitting model moves the files to its setting, the set is drawn again on
the new axes by the same rule; an indexing-ambiguity reindex leaves it unchanged, since twin-law
mates share a flag. With `-z`, the reference's flags are inherited where the merge matches it
(`REFERENCE_FREE_FLAGS_INHERITED=`).

**What is fitted on which reflections.** Everything fitted to place and scale the model — the
overall scale, the anisotropic *B*, the bulk solvent, the rigid body — is fitted on the working
reflections only. The free set is then used for a few discrete *selections*: whether the rigid-body
step is kept, which indexing wins, and in molecular replacement which placement and which group.
Each of those leaves R-free very slightly optimistic where it fires. The coordinates, B-factors and
occupancies of the model are never refined.

**What `R_FREE` means here — and what it does not.** It is the model as placed, scored on Rugnux's
free set: a check that the model fits these data, and a trend number between datasets of one
campaign. It is **not** a refinement R-free, and it is not cross-validated against the model's own
history:

- A **deposited model** was refined by its depositor against *their* working set. Rugnux's free set
  is a different 5 %, so about 95 % of Rugnux's free reflections were in the working set the model
  was refined on. R-free here therefore reads close to R-work (the two differ by a median 0.001
  over our corpus), and it is optimistic in the usual model-bias sense.
- To score a deposited model on its own test set, give its structure factors as the reference
  (`-z 1abc-sf.cif`): the depositor's free flags are then inherited. But `-z` is an assertion — it
  also fixes the space group and the cell — so that is no longer a de-novo run.
- A **predicted model** has not been refined against any diffraction data, so it carries no such
  memory; what remains is the selection effect above.
- For comparing two runs against one model, read `R_MODEL_SHELL_SCALED`, not `R_FREE`
  ([Comparing two runs](RUGNUX_REPORT.md#comparing-two-runs-r_model_shell_scaled)).

**What cannot leak, and what can.** The model never enters the merged intensities, their sigmas, the
choice of reflections, the resolution cut or the weights, so `<prefix>.mtz` carries no model bias in
its numbers — only the class-(b) labels. The **maps** are model-phased, and carry the model bias any
model-phased map carries: read the mFo−DFc map, and treat density that only the 2mFo−DFc map shows
with the usual care. CC(model, data) is read in one direction only: a confirmed shell is evidence for
the data, a weak shell says nothing about them, and nothing acts on it.

## Practical guidance

**When to give a model.**

- **You have a structure of this crystal form** (a fragment campaign, a ligand soak, a reference
  structure): give it with `--model`. You get maps and a placed model ready for refinement, the
  indexing of every dataset brought into the model's, and the hand fixed — the things that make a
  campaign's files directly comparable. A wrong or rejected model costs a few seconds and changes
  nothing.
- **You have a structure of the same protein in another crystal form**: `--model` too. The rigid
  body will not place it, and molecular replacement is tried automatically.
- **You have only a prediction** (AlphaFold, ModelCIF): `--model` (or `--mr`). Download the PAE JSON
  with it and keep its AlphaFold DB file name, so it is cut into domains when the whole model does
  not place. A prediction is good for: confirming the space group, naming the hand where the data
  cannot, offering a twinned or lower-symmetry alternative where the data are ambiguous, and a
  first set of maps. It is not a refined model, and its R-factors read accordingly.
- **You have a previous dataset of the same crystal form** and want the same indexing and free set:
  `-z`, not `--model`. It is the stronger tool for the indexing ambiguity and the only one that
  carries a free set over, but it pins the space group and cell.
- **You want to compare with another program's statistics**: `--report-resolution`, which changes
  nothing else.

**Which file to use for what.**

| File | What it is | Use it for |
|---|---|---|
| `<prefix>.mtz` / `.cif` / `.hkl` | The answer: the data's space group, with only the class-(b) labels from the model | Refinement, deposition, everything by default |
| `<prefix>_model.cif` / `.pdb`, `<prefix>_maps.mtz` | The model as placed, in the frame of `<prefix>.mtz`, and its map coefficients (Coot/PyMOL open them as maps) | Starting refinement (REFMAC5, phenix.refine), PanDDA, Coot |
| `<prefix>_twin_<SG>.mtz` / `.cif` | The same data merged in a subgroup with a twin law — written from the data, model or not | Twin refinement, where you suspect the higher group absorbed a twin law |
| `<prefix>_mr.mtz` / `.cif`, `<prefix>_mr_model.pdb` / `.cif`, `<prefix>_mr_*` maps | The merge in the space group the model chose (`MODEL_CHOICE_SPACE_GROUP=`), and the model placed there | Refinement *if* you accept the model's choice; compare R-free against the answer's |

`<prefix>_mr` and `<prefix>_twin_<SG>` can describe the same subgroup; the `_mr` file then also
carries the model placed in it.

**Reading section 5 of the report**, in order:

1. `MODEL_VALIDATION=` — did it run? If `NOT_PERFORMED`, `MODEL_VALIDATION_REASON=` says why.
2. `MODEL_PLACEMENT=` — how the model was placed: `RIGID_BODY`, `MR` or `NOT_PLACED`.
3. `MODEL_FIT=`, `MODEL_FIT_SIGMA=` — the rigid body's verdict against its null. Absent where the
   rigid body was not tried (a prediction, `--mr`).
4. `MODEL_DECISIONS_TAKEN=` — `NONE` means the reflection files are what a run without a model
   writes. Otherwise `ENANTIOMORPH`, `INDEXING`, both, or `MR_ENANTIOMORPH`, with
   `MODEL_ENANTIOMORPH_ADOPTED=` and `MODEL_INDEXING_OPERATOR=`.
5. `MODEL_CHOICE_FILE_PREFIX=`, `MODEL_CHOICE_SPACE_GROUP=`, `MR_DECISION=` — whether a
   `<prefix>_mr` file was written, and in which group.
6. `R_WORK=`, `R_FREE=`, `CC_MODEL_CONFIRMED_TO_D_MIN=`, the anomalous sites — how well the placed
   model describes the data (class d).

Outside section 5, `SPACE_GROUP_ENANTIOMORPH=` (`UNDETERMINED`, `GIVEN` or `ASSUMED_FROM_MODEL`),
`SETTING_SOURCE=` and the presence or absence of `INDEXING_AMBIGUITY_OPERATORS=` say what the model
did to the answer's labels. Every key is described in [The results report](RUGNUX_REPORT.md#model-validation).

## Related pages

- [Advanced Rugnux](RUGNUX_ADVANCED.md#reference-data-and-the-indexing-ambiguity) — what `-z` does,
  the indexing ambiguity, the setting the files are written in, and
  [validating against a model](RUGNUX_ADVANCED.md#validating-against-a-model-rugnux---model).
- [The results report](RUGNUX_REPORT.md) — [model validation](RUGNUX_REPORT.md#model-validation),
  [molecular replacement](RUGNUX_REPORT.md#molecular-replacement), the
  [twin hypothesis](RUGNUX_REPORT.md#the-twin-hypothesis-twin_subgroup_) and the
  [reference-range table](RUGNUX_REPORT.md#the-reference-range-table).
- [Data analysis: space group and validation](CPU_DATA_ANALYSIS_DECISIONS.md) — the space-group
  search (§13) and the model-validation algorithms (§14).
- [Reference data](CPU_DATA_ANALYSIS_INTEGRATION.md#109-reference-data-fixing-the-space-group-and-resolving-the-indexing-ambiguity)
  and [R-free test-set flags](CPU_DATA_ANALYSIS_INTEGRATION.md#107-r-free-test-set-flags).