simd: group_walk as a (group,row) visitor; add PowerSums power-sum fold

The private keyed-reduction walker no longer takes an i64 sink: it yields
(group, row) and each fold owns its destination. The 15 existing folds
were migrated mechanically; no public signature changes.

New: PowerSums { n: u64, sum: i64, sum_sq: u128 } (#[repr(C)], 32 bytes,
layout pinned at compile time) and masked_group_power_sums_i32 with
_via / _pair, the exact degree-0/1/2 power sums per group in one pass.
A scratch benchmark chose the shapes: the visitor costs nothing for the
existing folds, and the record beats three separate lanes at large K.
The u128 square sum is load-bearing: a u64-truncation disable run turns
the four exactness tests red.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Ho2JosrXCnZPbB7RFssrse

Author: claude

.claude/blackboard.md

@@ -1,3 +1,11 @@
+## 2026-09-30 — `group_walk` becomes a (group,row) visitor; `PowerSums` + `masked_group_power_sums_i32{,_via,_pair}`
+
+- **Walker:** the private `group_walk` now takes `groups: usize` and `fold: FnMut(group, row)`; it never sees a sink. Its `i64` slot was an accident of the first folds, not part of what it does. All 15 call sites were migrated mechanically (`|k, i| out[k] = …`, passing `out.len()`); no public signature changed.
+- **New:** `#[repr(C)] PowerSums { n: u64, sum: i64, sum_sq: u128 }`, the degree-0/1/2 power sums, exact integers, deliberately free of statistical vocabulary (meaning is jc's job upstream). Three kernels share one fold. Compile-time layout pin: size 32, offsets 0/8/16, align == `align_of::<u128>()` (16 on x86_64/aarch64, 8 on some cross targets; pin `align(16)` explicitly if it ever crosses an ABI), plus the arithmetic Σx row bound `(2^32-1)·2^31 ≤ i64::MAX`.
+- **Why this shape (scratch benchmark before the change: 72 cells of resident/via/pair keys × mask density 1/50/100 % × K 1…65 536 × realistic/extreme values, median of 15 reps, two runs):** the existing sum through the new visitor ran at 0.994× the old walker; a slot-generic walker compiles to the same 79-instruction stream as the visitor with a record sink, so the visitor dominates at zero cost. A record (AoS) beats three lanes (SoA) by 1.37× (median) at K = 65 536 and up to 2.5× on pair keys: one cache line per row instead of three, and 2 stack reloads in the hot loop instead of 6. Three separate passes cost 2.17× (median). Unexplained, reproducible in both runs: SoA beats AoS by ~35 % on dense resident/via keys at K = 16. Recorded, not chased; the decision does not depend on it.
+- **Evidence:** 9 new tests against an independent per-row i128/u128 oracle (resident/via at 7 lengths × sparse/half/dense masks; pair with both drops; an unreached group stays zero; agreement with the count/sum folds; accumulate; an extreme fixture whose exact Σx² > `u64::MAX`, asserted from the oracle first; 2^20 × `i32::MIN` exact). **Disable run** (Σx² truncated to u64 in the fold): exit 101, the 4 exactness tests red, the 5 others green. Even the ordinary randomized fixture overflows u64, so the width is needed on realistic data too. Full `cargo test --lib` 2516 passed; group doctests 17/17; clippy `-D warnings` and fmt clean.
+- **Next (not done):** mask-risc `GroupFold::PowerSumsI32` + `Out::PowerSums`, reusing `Value::GroupReduced` (no new Value variant), with an oracle arm and differential tests; only after that is green does R2IL get a byte. No real-crate codegen witness has been run for the walker yet; the no-regression figure comes from the scratch copy.
+
 ## 2026-09-25 (2) — encryption: Argon2 KDF + envelope behind a default-on `kdf` feature
 
 - `crates/encryption`: `argon2` is optional; `kdf = ["dep:argon2"]`, `default = ["kdf"]`,

src/simd.rs

@@ -838,6 +838,9 @@ pub use crate::simd_masking_ops::{
     masked_group_min_i32,
     masked_group_min_i32_pair,
     masked_group_min_i32_via,
+    masked_group_power_sums_i32,
+    masked_group_power_sums_i32_pair,
+    masked_group_power_sums_i32_via,
     masked_group_sum_i32,
     masked_group_sum_i32_pair,
     masked_group_sum_i32_via,
@@ -863,6 +866,7 @@ pub use crate::simd_masking_ops::{
     ternary_match_u64_to_mask_under,
     KeyRunCarry,
     MortonDir,
+    PowerSums,
     SYM_EMPTY_I64,
 };
 // The popcount that closes the loop on the masks above: `mask_count` in ABI