Checked drag and radial contact kernels

Link Ludus::FoundationMath and include <ludus/foundation/math/dynamics.hpp> from the installed SDK. Both functions return MathStatus, allocate nothing, are noexcept, and leave caller outputs unchanged on failure. A geometric miss is Success with Hit=false.

namespace math = ludus::foundation::math;
math::LinearDragStep step;
if (math::IsSuccess(math::TryComputeLinearDragStep(0.7, tickSeconds, step)))
{
    // Constant target velocity u. Position/velocity are game-owned vectors.
    position = position + u * tickSeconds + (velocity - u) * step.DistanceScale;
    velocity = u + (velocity - u) * step.VelocityScale;
}
math::RadialSweepContact contact;
if (math::IsSuccess(math::TrySweepRadialBand(start, end, center,
                                          radiusStart, radiusEnd,
                                          hullRadius + ringHalfWidth, contact)) && contact.Hit)
{
    // Fraction is in [0,1], Normal points away from center (zero at center).
    // Game decides whether/how to apply an impulse and remembers consumption.
}

Drag inputs are finite and nonnegative. Zero rate is ballistic; zero duration preserves velocity and yields zero displacement. Coefficients may be cached until rate or tick duration changes. The target velocity is constant over the interval; the caller owns unit consistency, bounded state, and speed limiting.

The sweep is a point against an annular/spherical radial band. Use Vector3d with Z=0 for a 2D ring. Endpoint radii and width must be finite/nonnegative; shrinking bands are supported. Linear motion and linear radius share the same interval. Initial overlap and tangency count as contact. Geometry is scaled before root solving; a 64-machine-epsilon tolerance in normalized coordinates accommodates roundoff, so near-boundary classifications have that relative uncertainty. Coordinate differences that overflow, or radii/width lost during normalization, return OutOfRange. This is not an arbitrary-precision geometry predicate.

An exponential drag trajectory needs a chord approximation or subdivision to use this linear sweep. Do not silently interpret its fraction as an exact time on a nonlinear path. See the simulation design and reference review.

Validation record

On October 3, 2026, native Development completed 47 CTest entries: 45 passed and two live Wayland/keyboard entries were explicitly skipped. ASan/UBSan completed 41 entries: 39 passed with the same two live-platform skips. The numerical suite passed 495 assertions across seven cases; the allocation probe passed 14 assertions. Native/browser warning-clean builds, public header/include gates, pinned clang-format 18, clang-tidy 18, SDK dependency/manifest audits and installed consumer execution passed. Existing pinned tools/dependencies were reused in an isolated checkout; the tidy runner was invoked against its configured compile database because the reused dependency bootstrap fingerprint was stale after changing the source manifest. Generated-source analysis was completed after building its module maps.

The companion Sandbox tests exercise the production SDK and an independent bounded-world reference. Browser smoke evidence uses Chromium SwiftShader and emulated touch; it does not certify physical mobile hardware or native rendering.