ECQC extremal correlations: full-rank rigidity and complete stabilizer classification v1

Exact scope

Complete full-Schmidt-rank equality classification without a stabilizer assumption; exact scores of every two-qudit pure stabilizer state at every odd prime; sharp global pure-state ratio p/2 for every prime p congruent to 1 modulo 4. Full-rank attainers are exactly the affine Bell states with s^2=-1: 2p^2 distinct rays when they exist. A separate theorem proves a flat nonzero Schmidt spectrum and a rank gap for general equality.

Fixed source: c0a1085e360604a1f8f274290eb1556202a315ab, directory research/ecqc-stabilizer-saturation. The attached source ZIP and eight-page PDF concern this companion paper only; the automatic GitHub source archive also contains other repository research, which is not attributed to this paper.

Complete written proofs and two exact checker implementations. Both replays were rerun in a second environment with byte-identical JSON outputs. Finite checks do not replace the all-prime proofs. Published Holevo equality is cited explicitly. No complete Lean formalization or external professional mathematical peer review is claimed.

The general rank-deficient equality classification and sharp pure ratio at p congruent to 3 modulo 4, p >= 7, are not settled. Prior mixed-state disproofs and this project's preceding pure-state paper are credited.

Author: Yongxian Zhang (张永贤), School of Computer Science and Engineering, South China University of Technology. Email: mxymmxym1@gmail.com. ORCID: 0009-0000-3864-3536. No external funding. AI-assisted research, coding, writing, and self-audit. All rights reserved for separately authored original material; inherited licenses and notices retained.

Corrections must use a new release; no replacement of frozen assets or tags. A DOI, if assigned, is archival metadata, not evidence of correctness or priority.