feat: add Mash distance metric and rolling entropy support

Implement the Mash distance metric across the CLI, index, and compact vector traits. This includes adding a `Mash` variant to the `DistanceMetric` enum and `MetricArg` CLI argument, implementing the conversion from Jaccard distances using the standard mutation-rate estimator formula, and updating documentation with supported metrics and algorithmic references. Additionally, add an `entropy` method to rolling statistics for computing order-specific entropy.

docmd/implementation/obicompactvec.md

@@ -347,11 +347,24 @@ Provided finalisations:
 | `relfreq_euclidean_dist_matrix()` | `√partial_relfreq_euclidean[i,j]` |
 | `hellinger_dist_matrix()` | `√partial_hellinger[i,j] / √2` |
 | `hellinger_euclidean_dist_matrix()` | `√partial_hellinger[i,j]` |
+| `threshold_mash_dist_matrix(k, t)` | Mash distance, derived from `threshold_jaccard_dist_matrix(t)` — no separate partial |
 
 ### BitPartials
 
 Required: `partial_jaccard() -> (Array2<u64>, Array2<u64>)`, `partial_hamming() -> Array2<u64>`. Both additive across layers and partitions.
 
+Provided finalisations also include `jaccard_dist_matrix()`, `hamming_dist_matrix()`, and `mash_dist_matrix(k)`.
+
+### Mash distance
+
+`mash_dist_matrix`/`threshold_mash_dist_matrix` add no new additive primitive: both are a pointwise transform of the existing Jaccard distance matrix, per the Mash mutation-rate estimator [@Mash-distances-doc; @Fan2015-mash-formula]:
+
+```
+D = -1/k · ln(2J / (1+J)),  J = 1 - d_jaccard
+```
+
+`J ≤ 0` (i.e. `d_jaccard ≥ 1`, no shared k-mers) maps to `D = 1` (maximal distance) rather than the `ln` singularity at `J = 0`.
+
 ---
 
 ## Temp-file-backed types

docmd/index.md

@@ -13,7 +13,7 @@
 | `query`     | Query an index with sequences and annotate matches |
 | `dump`      | Dump all indexed k-mers as CSV (kmer + per-genome counts or presence); supports the shared [kmer filtering](implementation/filtering.md) system; `--head N` limits output to the first N k-mers |
 | `annotate`  | Add or update genome metadata from a CSV file; or dump metadata as CSV |
-| `distance`  | Compute pairwise distance matrix between genomes; optionally build NJ/UPGMA trees; `--presence-threshold N` sets the minimum count to consider a k-mer present when computing Jaccard on count indexes (default 1) |
+| `distance`  | Compute pairwise distance matrix between genomes (`--metric jaccard\|mash\|hamming\|bray-curtis\|relfreq-bray-curtis\|euclidean\|relfreq-euclidean\|hellinger\|hellinger-euclidean`); optionally build NJ/UPGMA trees; `--presence-threshold N` sets the minimum count to consider a k-mer present when computing Jaccard/Mash on count indexes (default 1) |
 | `unitig`    | Build a global de Bruijn graph across all partitions and enumerate its unitigs as FASTA; supports the shared [kmer filtering](implementation/filtering.md) system |
 | `select`    | Project and/or aggregate genome columns into a new or in-place index; the column-axis counterpart of `filter` (see [select](implementation/select.md)) |
 | `estimate`  | Estimate approximate-index parameters (z, evidence bits, FP rates) before indexing |

docmd/references.bib

@@ -241,3 +241,21 @@
 	volume = 33,
 	year = 2017,
 	bdsk-url-1 = {http://dx.doi.org/10.1093/bioinformatics/btw832}}
+
+@misc{Mash-distances-doc,
+	author = {{Marbl Lab}},
+	howpublished = {Mash documentation},
+	title = {Mash Distance},
+	url = {https://mash.readthedocs.io/en/latest/distances.html},
+	urldate = {2026-07-09},
+	year = 2026}
+
+@article{Fan2015-mash-formula,
+	author = {Fan, Huan and Ives, Anthony R and Surget-Groba, Yann and Cannon, Charles H},
+	doi = {10.1186/s12864-015-1647-5},
+	journal = {BMC Genomics},
+	number = 1,
+	title = {An assembly and alignment-free method of phylogeny reconstruction from next-generation sequencing data},
+	url = {https://doi.org/10.1186/s12864-015-1647-5},
+	volume = 16,
+	year = 2015}