Migrated from Method backlog

This issue was created from a legacy filesystem backlog card. GitHub Issues are now the live work tracker; repository docs remain Method evidence.

Source backlog: docs/method/backlog/asap/MATH_deterministic-trig.md
Original lane: asap
Original legend: MATH

Original backlog card

Milestone: Proof Core | Priority: P1

Deterministic Trig Oracle

Pin error budget and verify the deterministic trig oracle for cross-OS audit.
Issue #177 is closed; this item now tracks the remaining release-gate evidence
gap rather than the core trig implementation.

Issues: #177

Status: mostly implemented. warp_math::trig, the 2048-vector golden
test, deterministic-math docs, and Linux/macOS G1 workflow steps exist. The
remaining work is to align the release claim with explicit Alpine/musl evidence
or adjust the claim if broad musl CI remains the only Alpine-class coverage.

T-9-3-1: Verify and integrate deterministic trig oracle into release gate

User Story: As a release engineer, I want a CI gate that verifies the deterministic trig oracle (sin/cos) produces identical results across macOS, Ubuntu, and Alpine so that cross-OS determinism is proven before every release.

Requirements:

• R1: Keep the existing 2048-vector golden suite in
  crates/warp-math/tests/trig_golden_vectors.rs.
• R2: Keep the pinned 0-ULP golden-vector budget and <=16 ULP libm reference
  budget documented in determinism claims.
• R3: Preserve the existing Linux/macOS G1 workflow coverage and add explicit
  Alpine/musl evidence if DET-004 continues to claim Alpine.
• R4: Verify that the oracle's golden-vector outputs are bit-identical on every
  platform named by DET-004.
• R5: Keep the LUT-backed algorithm documented in
  docs/determinism/SPEC_DETERMINISTIC_MATH.md.

Acceptance Criteria:

• AC1: Golden test suite covers 2048 input values across [-2*TAU, 2*TAU]
  for sin and cos.
• AC2: All 2048 values produce bit-identical results across every platform
  named by DET-004.
• AC3: CI evidence explicitly covers every platform named by DET-004.
• AC4: Error budget is documented as 0 ULP for golden-vector bit identity,
  with a separate <=16 ULP budget against the libm reference.
• AC5: Algorithm documentation exists in
  docs/determinism/SPEC_DETERMINISTIC_MATH.md.

Definition of Done:

• Code reviewed and merged
• Tests pass (CI green)
• Documentation updated (if applicable)

Scope: Golden test extraction, CI matrix job, cross-OS verification, documentation.
Out of Scope: New trig functions (atan2, tan); trig performance optimization; WASM trig verification (separate task).

Test Plan:

• Goldens: 1000-value golden vector file for sin and cos, checked into the repository.
• Failures: A platform producing a different bit pattern for any value (CI fails, release blocked).
• Edges: sin(0), sin(pi), sin(2pi), cos(0), cos(pi/2) — boundary values where naive implementations differ.
• Fuzz/Stress: Extended suite: 100,000 uniformly-spaced values in [0, 2pi], verified bit-identical (CI nightly).

Blocked By: none
Blocking: none

Est. Hours: 4h
Expected Complexity: ~300 LoC