Establish numerical accuracy for truncation and codesigned modulus sets

Prove or experimentally validate the FP64-equivalent accuracy of the truncation-toward-zero Ozaki-II variant and of the codesigned A, E, and D modulus sets under their specified digit, endpoint, scaling, and escalation rules.

Background

The cited Ozaki-II accuracy theorem applies to the round-to-nearest variant, whereas the implementation and the paper’s projections use truncation toward zero. The paper explicitly declines to transfer the round-to-nearest error guarantee automatically to truncation.

The proposed all-byte, hybrid, and 7-bit modulus systems also change the residue representation and therefore require per-set verification of range, digit representability, accumulation, signed equivalence, scaling, truncation, escalation, and reconstruction conditions. Until the accuracy suite and source analysis are re-run, these systems carry obligations rather than established accuracy contracts.

References

The round-to-nearest theorem is not claimed for the truncation rule: TZ does not automatically inherit the RN bound, and TZ-grade accuracy remains an explicit validation obligation rather than an established result.

— Ozaki 2.5: Engineering the Deconstruction Path of fp64-Emulated Dense Matrix Multiplication on FP8 Tensor Cores  (2609.09095 - Matsuoka, 8 Sep 2026) in Appendix A, “Proof Obligations per Candidate Modulus Set”; Section 2, paragraph “The scheme in equations”