hpc: HDR rolling floor — integer σ-lattice thresholds on demand

[AdaWorldAPI]

What this adds

hpc::rolling_floor, harvested from lance-graph's graph/blasgraph/hdr.rs and built on #327's exact MomentsU32.

The design rule is: the accumulator owns the facts, and each query derives its own view.

Stored state:

• exact moments (n, Σx, Σx²), folded on every observation;
• a deterministic Algorithm-R reservoir;
• the shape belief, which is either Gaussian or Empirical(sorted sample, μ_s, σ_s);
• the drift anchor (μ, σ).

Derived per call, never stored: every threshold. A threshold is a SigmaLevel(k), a point k quarter-σ below the noise floor.

• Gaussian shape: μ_t − k·σ_t/4, using the running coordinates.
• Empirical shape: take the sample value x at k's Gaussian-equivalent tail rank, Φ(−k/4)·len, and move it into the current frame: μ_t + ⌊(x − μ_s)·σ_t/σ_s⌋, computed in i128.
• shade(x, levels) counts how many lattice points a response survives.
• Everything is integer; the old f32 quantile path is gone.

Parameter drift vs shape drift

	parameter (μ, σ)	shape (Gaussian vs empirical)
When it updates	every observation (the running coordinates)	only at a drift-free checkpoint (every 1000 observations after the first 1000, with a reservoir of at least 100)
What drift does	a checkpoint with |Δμ| > σ/2 or |Δσ| > σ/4 raises a FloorShift; recalibrate moves the anchor and forgets the moments and the reservoir	the shape is kept. A drift checkpoint does not judge the shape from evidence that spans two regimes

• The coordinates are valid from the first observation: they are (x, 0) after one sample. Only at n = 0 do thresholds fall back to the anchor, which is the prior.
• When σ = 0, every Gaussian level collapses onto μ.

Behavioural deltas

Exact moments vs the legacy integer Welford: at every checkpoint the drift rule sees the same (μ, σ) on the five oracle streams (95 checkpoints).

Rank unification uses the rule min(⌊p·len/10000⌋, len−1), checked against the reference f32 rule ⌊q·len⌋ for every reservoir length from 1 to 1000:

level	old q	new p/10000	lengths whose rank changed	first change	at len 1000
cascade 1σ … 3σ	0.1587 … 0.0013	same	0	—	—
median	0.5	5000	0	—	—
band 1σ	0.159	1587	150	L=63: 10→9	159→158
band 2σ	0.023	228	98	L=87: 2→1	23→22
band 3σ	0.001	13	230	L=770: 0→1	1→1

The band cuts moved from coarse approximations onto the exact Gaussian tail of their σ level, so band and cascade now read one table.

Half-σ levels 12/10/8/6 reproduce the integer SigmaGate::custom tiers exactly: discovery, strong, evidence, hint.

Tests

• 23 unit tests plus 7 doctests. They pass on x86-64-v3, x86-64-v4 and aarch64 (qemu). Clippy -D warnings, fmt and --no-default-features are all clean.
• Disable runs: I broke each guard in turn and confirmed it fails at least one test (12/12). The guards covered:
  • running vs anchor frame;
  • the n = 0 fallback;
  • drift checked before shape;
  • shape kept through recalibration;
  • moments forgotten on recalibration;
  • the tail table;
  • rank rounding;
  • empirical floor division;
  • the σ_s = 0 branch;
  • strict < in shade;
  • the k·σ/4 order of operations;
  • the empirical frame projection.

Benchmark

examples/hdr_rolling_floor_bench.rs, release build, x86-64-v4.

Hot path, per observation:

step	ns
popcount of 2048 B	58.1
MomentsU32::observe	1.16
reservoir	3.39
RollingFloor::observe, checkpoints included	11.8

Periodic path, per checkpoint:

step	ns
shape: sort, median, kurtosis	7336
empirical, locating 8 levels	63

Query path, on demand:

step	ns
Gaussian thresholds of 8 levels	25
shade over 8 levels	31

Callers

• lance-graph hdr.rs Cascade (#1278): the band and cascade APIs are unchanged, and both now derive from SigmaLevel.
• Raumgewinn / infight: the future Go-board / Gobang evaluators have no code yet (the tic-tac-toe probe was ruled F0-degenerate). Today's Raumgewinn uses an f64 floor in perturbation-sim. No production caller is claimed.

Scope fence

git diff origin/master...HEAD contains 0 matches for ZGamma, zspace, Fisher, hyperbolic, Palette256, FisherZTable, bgz or Mexican.

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Summary by CodeRabbit

• New Features
  • Added rolling-floor analysis with variance-based thresholds, kurtosis estimates, and shading calculations.
  • Added single-value observation support for moment statistics.
  • Added a benchmark example covering distance calculations, statistics, rolling-floor updates, and related operations.
• Bug Fixes
  • Improved accuracy for calculations involving large values, including variance roots, threshold subtraction, and kurtosis estimates.

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📝 Walkthrough

Walkthrough

The PR exposes the rolling_floor module, adds MomentsU32::observe, updates rolling-floor spread, threshold, and kurtosis arithmetic, and registers a std-gated benchmark example.

Changes

Rolling-Floor Statistics

Layer / File(s)	Summary
Wide-integer statistics and shape calculations src/hpc/mod.rs, src/hpc/statistics.rs, src/hpc/rolling_floor.rs	Adds MomentsU32::observe and wide-integer square-root and kurtosis calculations. Empirical shape calculations use full-width variance.
Rolling-floor spread and threshold arithmetic src/hpc/rolling_floor.rs	Preserves full-width variance in spread calculations and uses wide arithmetic for Gaussian thresholds. Adds tests for full-range arithmetic, kurtosis fallback, and square roots.
Benchmark workload and registration Cargo.toml, examples/hdr_rolling_floor_bench.rs	Registers a std-gated benchmark for distance, moments, reservoir and rolling-floor updates, empirical-shape calculations, and threshold queries.

Estimated code review effort: 3 (Moderate) | ~25 minutes

Change: Feature

Merge Risk: ⚪ Minimal · up to aeda1

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Inline comments:
In `@src/hpc/rolling_floor.rs`:
- Around line 231-242: Update ReservoirU32::kurtosis to use saturating addition
when accumulating the fourth-power deviations and saturating multiplication for
the ×100 scaling before division, so extreme values yield a large kurtosis
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