Constant CANONICAL_KEY_MIN_WIDTH 

pub const CANONICAL_KEY_MIN_WIDTH: usize = 8;

Batch WIDTH (sequences) at or above which the canonical depth→slot assignment is applied. Below it verify_batch_order / verify_batch_permutation take their canonical = false arm, which is the pre-canonical (pre-PR-#552) behaviour byte for byte: each sequence keeps its own confidence-chosen depth and the batch sorts deepest-first, ssm-slot second, ties on input index (a stable sort_by_key(|(a, k)| (Reverse(k), slot)), exactly what both call sites used before).

Default 8, from a same-binary same-session A/B on dgx2 (ladder-38 round 7, tip e0b845f11) with ONE variable — the kill switch ATLAS_NO_CANONICAL_VERIFY_KEY=1. tok/s, higher is better:

 C  | canonical ON            | canonical OFF          | verdict
----+-------------------------+------------------------+------------------
  2 | 30.09                   | 30.83                  | costs -2.4%
  4 | 64.00 (round 7: 65.56)  | 68.11 (round 6, no it) | costs ~-3.7%
  8 | 110.63                  | 106.48                 | GAINS +3.9%
 16 | 203.50                  | 203.44                 | no effect
 32 | 291.50                  | 291.52                 | no effect
 64 | 387.62                  | 386.99                 | no effect
128 | 477.55                  | 477.69                 | no effect

The shape of that table follows the key counts (module docs): the collapse pays exactly where the arrangement space is large. Above width 8 the gate is inert in either direction — D-Cut is off there (dcut_width_cap), ks is uniform, and both arms reduce to “sort by slot” (pinned by uniform_depths_are_identical_under_both_arms), which is why the C>=16 rungs move by <= 0.2% either way.

Hypothesis for the cost below 8, recorded but NOT load-bearing for this threshold (the threshold is the measurement, not the mechanism): forcing the assignment makes the two-launch batched GDN conv+WY fast path decline more often, i.e. n*(2k-1) launches per layer instead of 2 — 768 vs 96 per step at n=2, k=4 over 48 GDN layers. PR #553’s rate telemetry under ATLAS_MTP_ACCEPT_DEBUG reports that decline rate directly.