D-PHT-1: phasors without transcendental calls (probe + board)

[AdaWorldAPI]

This PR adds a probe and a board entry. No production primitive and no ndarray change.

The question: can two observables that need only phasors avoid every transcendental call in the hot path?

• Wankel apex coordinates: z_k(θ) = e·e^{i3θ} + R·e^{i(θ + 2πk/3)}.
• Coherent interference: I = |Σ A_i e^{iφ_i}|², over 1,000 sources and 65,536 detectors.

The phase is a u32 in turns, so 3θ is phase.wrapping_mul(3) and wraparound is free.

Files:

• Probe: crates/lance-graph-mask-risc/examples/phasor_trig_probe.rs
• Board: entries/2026-10-08-phasor-trig-probe.md, plus a STATUS_BOARD row

CARGO_PROFILE_RELEASE_DEBUG=0 cargo run --release -p lance-graph-mask-risc --example phasor_trig_probe

Inventory

• Missing: CORDIC, a phase LUT, or a SIMD sin/cos anywhere in ndarray or lance-graph.
• Not what it looks like: ndarray::hpc::vml::vscos/vssin call scalar cos/sin per lane inside an F32x16 wrapper.

Measured

Medians of 5 runs.

Wankel apex, 1M phases

arm	ns per apex	max error, R = 100
f64 sin_cos	66.8	reference
f32 sin_cos	25.4	5.1e-5
2^12 LUT, interpolated	5.6	4.6e-5
2^12 LUT, nearest	3.1	8.7e-2
CORDIC, 24 iterations	258	1.4e-5
ndarray vml	50.9	3.4e-5

Interference, 1,000 × 65,536

arm	ns per term
f64 sin_cos	45.9
f32 sin_cos	36.4
2^12 LUT	9.95
CORDIC	156.7
floor: one √	2.36

Two waves: I = A1² + A2² + 2A1A2 cos Δφ replaces two complex phasors with one cosine.

• 2.8× faster, exact to 1e-14 of peak.
• 6× faster with a LUT on Δφ.

Trajectory, 1M steps:

• an f64 recurrence drifts 4.8e-9;
• an f32 recurrence drifts 1.95 units without renormalisation;
• an integer phase accumulator has no drift by construction.

Amplitude-bounded early exit for I ≥ T, with max(0, |S| − R)² ≤ I ≤ (|S| + R)²:

• Correctness: equals the full fold on every detector.
• Uniform amplitudes: still needs 94–98 % of the terms. |S| grows like √N while R shrinks like N, so the bound only closes at the very end.
• Heavy-tailed amplitudes (i^-1.5): needs only 28–122 of 1,000 terms.
• The LUT version carries the table's own error in the bound and falls back to f64 for any detector it cannot decide.

Falsifiers

• Wankel invariants hold to 1e-11 on 100,000 angles in ±1000 rad: curve membership, constant side R√3, rotor centre at distance e, threefold symmetry, and the 3:1 law.
• Disable runs, each red then restored:
  • dropping the remaining amplitude from the bound;
  • dropping the LUT error from the bound;
  • casting a negative phase difference through u64.
• Two bugs in this probe's own first run were caught by its assertions: a saturating cast, and an R = 0 decision made through √. Both are fixed and described in the entry.

Verdicts

• ADOPT, in a separate ndarray PR: a u32-turns phase with an interpolated 2^12 LUT, exposed through ndarray::simd, plus an integer phase accumulator for trajectories.
• ADOPT: the closed form for two waves.
• PROBE: the amplitude-bounded early exit, only for heavy-tailed amplitude sets.
• REJECT:
  • CORDIC on CPU: 2.6–4.8× slower than native f64;
  • the f32 recurrence without renormalisation;
  • treating vml as SIMD.

Not done: a SIMD gather of the LUT, the rotor as a moving mask, the VSA comparison, and log buckets.

Checks

• cargo clippy -p lance-graph-mask-risc --examples -D warnings: clean.
• fmt: clean.
• Every compile used debug 0.
• The entries index is regenerated; the supersession index is unchanged.
• Expect a conflict: this branch and D-MHB-1: Mexican-hat response without a raster (probe + board) #1415 both add a STATUS_BOARD section above D-RPF and both regenerate the entries index. Whichever merges second needs a merge plus a regenerated index.

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https://claude.ai/code/session_01EFw2WdKr1oxvaKCJC2ua2R

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[chatgpt-codex-connector]

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Review	Status	Commit	Review trigger
📝 Code Review	✅ Completed 2026-10-08T19:16:42.329860Z	b44e85f	Draft marked ready

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[chatgpt-codex-connector]

Execute the advertised exact fallback

When the LUT bound remains undecided—which the recorded results say occurs for 35–2,679 detectors—this branch only increments a counter and never performs or validates the promised f64 fallback. Those detectors therefore receive no classification, so the probe cannot support its claim that the LUT path equals the full fold on every detector; its work counts also omit the additional reference evaluation. Run the reference fold here and assert or return its decision.

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