Tier-1 and Tier-2 Reproduction

Not every correct calculation is bit-for-bit repeatable. Kronos states, per result, which standard applies.

Deterministic, integer-and-float-stable calculations are graded Tier 1: on a matching software environment they reproduce byte-for-byte. Calculations that involve legitimate sources of numerical variation — iterative solvers, sampling, platform math differences — are graded Tier 2 and reproduce within a declared tolerance.

Grading each result this way is itself an honesty mechanism: it prevents a within-tolerance match from being over-sold as exact, and it tells a reviewer immediately whether a byte difference is a real discrepancy or expected noise.