test(ddx-core): gate the finite-difference oracle on a measured noise floor (closes #67)

[alxmrs]

Closes #67. First of four small ddx-core fixes from the soaks, stacked: #67's oracle gate (this PR) ← #87's integer casts ← the quotient rule ← the power rule. The M3/M4 stack (#70–#83) and the v2 soak PRs (#89–#93) now sit on top of them.

The false positive

The nightly ddx-core soak reported d/dy CAST(power(3, power((((y + x) + abs(2.5)) - y), 2)) AS DOUBLE) = 0 as wrong, with a finite difference of 5e-5. The derivative is right, because f doesn't depend on y. What goes wrong is rounding: (y + x) - y rounds differently for each y, and the outer 3^(b²) multiplies that ulp of jitter by ∂f/∂b ≈ 7e6. So the difference quotient reads noise above the absolute tolerance (1e-5). The Richardson gate doesn't see it, because fd(h) and fd(h/2) carry noise of the same size.

The gate

test_utils::fd_noise_floor measures the noise floor rather than modelling it. It moves the variable by a few ulps, sees how far f moves beyond its slope, and divides by h. fd_failure then skips any point where four times the floor isn't under the tolerance. noise_gate_skips_only_rounding_dominated_points checks both directions:

• Nightly fuzz: 1 property failure(s) in ddx-core simulation soak #67's expression is gated and is no longer reported at its seed;
• well-conditioned expressions keep a floor far under the tolerance;
• a wrong derivative is still caught.

The bounded suites pass. #67's DDX_SOAK_BASE=5820328895 replays clean, and a 3-minute soak (158k cases) found nothing.

🤖 Generated with Claude Code

https://claude.ai/code/session_01CvszJhH8pn8H9G69wEPMU2

[alxmrs]

LGTM, good fix.