Sharp Fluctuation Bounds and the Unique Optimal Code in a Spin-3/2 Quantum Tetrahedron

Linked discovery record only. The manuscript and supplement are hosted on OSF under CC BY-NC 4.0. The Figshare record contains no copy of those PDFs. Primary preprint and supplement: 10.17605/OSF.IO/34BDM (OSF public record). Rights distinction: Figshare's CC BY 4.0 selection applies only to the original text and metadata of this linked discovery listing. It does not license or relicense the separately hosted manuscript or supplement. Both OSF PDFs remain Copyright 2026 Kent Nimmo, Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0): licence terms. Abstract A binary measurement can hide logical-state dependence on its first read and reveal it when repeated. We study rank-two logical codes in singlet sectors of four equal positive spins, requiring all three opposite-pair correlations to have state-independent means. Spin 3/2 is the smallest spin supporting such a code. In its four-dimensional singlet sector, every fixed-pair-mean code obeys sum_O g_O >= 64/75 and max_O g_O >= 64/225, where g_O is the width of the compressed second moment. Both bounds are attained by a unique code plane. The optimizer is the span of the unique totally antisymmetric and totally symmetric singlets and, equivalently, the maximal-absolute-eigenvalue subspace of the oriented triple product Q = J_1 dot (J_2 cross J_3). Its two sharp-Q states have opposite handedness while sharing all individual pair-measurement distributions. Under sequential binary readout with classical records, inaccessible measurement environments, and no quantum bypass memory, a self-contained Bell-recovery bound yields an explicit response inequality. Exact recovery at detector strength eta > 0 forces each conditional-response width to satisfy d_i = eta g_i/2, and known-code conditional restoration attains this requirement. Uniform pair selection therefore has the attained minimum D = 32 eta/225. Accessible word privacy alone remains insufficient when unread noise can erase the logical state. Publication status Author-submitted preprint, version 2.5, submitted to Journal of Mathematical Physics on 22 October 2026 (JMP26-AR-03103). This is not an accepted manuscript or the publisher's version of record. No acceptance or peer-review approval is claimed. The 19-page manuscript and 3-page supplement are available at the primary OSF record. Reproducibility Private verification scripts, certificates, source archives and research code are not included in either public deposit. They remain available from the corresponding author upon reasonable request. Author Kent Nimmo; Independent Researcher, Vancouver, British Columbia, Canada; ORCID 0009-0003-8503-8891. Contact: kentnimmo@gmail.com. No external funding received.