spectral-budget

A budget primitive for bounded sequential domains: token windows, time horizons, request counts — anything where you need to refuse work that would exceed a principled ceiling, and surface a structured reason when you do.

use spectral_budget::SpectralBudget;

// 200 000-token context window; admit up to 3 ring-down periods.
let budget = SpectralBudget {
    principal_period: 200_000.0,
    ring_down_factor: 3.0,
};

assert!(budget.admits(400_000.0));
assert!(budget.try_admit(700_000.0).is_err());

Why this shape

The framing comes from the Faber–Krahn inequality on the principal eigenvalue of a bounded Laplacian: a closed domain of diameter d with propagation speed c has a slowest mode with period T_1 ≈ 2·d/c. Capping aggregate diameter at k · T_1 (default k = 3) keeps becoming finite. The same arithmetic applies whether d is photon path-length, an LLM token window, an audio duration, or an agent reasoning depth.

In practice this means:

• principal_period is your domain's natural period: context-window size for LLM calls, total path-length horizon for a renderer, max audio bar length for an audio bed.
• ring_down_factor is how many of those periods you'll tolerate before refusing. 3.0 is the well-tempered default — three rings of the slowest mode.
• try_admit returns a structured BudgetError::Exceeded carrying the diameter, the bound, T_1, and the factor — diagnosable at the call site without inspecting internals.

License

Dual MIT / Apache-2.0. © 3BSN LLC.