The Satyalogos Program
Formal, open-access preprints developing the mathematical core of the Satyalogos program — results in quantum foundations and quantum information. Each paper is archived with a permanent DOI on Zenodo and ships with self-contained, machine-checkable verification code. They stand on their own as peer-facing mathematical physics, and together they form one connected, cross-cited arc: a characterization of which Bell-type correlations can and cannot be the quantum singlet, the axiom that singles the singlet out, the mathematical surroundings of that axiom, and an exactly reducible, independently verifiable covariant-compression problem built on the same structure.
Characterizes a family of depth-coordinate correlation constructions for CHSH/Bell experiments and determines precisely how it relates to the quantum singlet. The family is Bell-violating and non-signalling but not rotationally invariant: its average-angle contamination is present before the probability map and survives every internal repair route short of hardcoding the relative angle. A characterization-and-exclusion result that delimits where the orientation-independent singlet can, and cannot, arise. Includes a reproducibility suite.
Proves that any U(1)-covariant, perfectly anticorrelated quantum correlation is automatically a positive-definite function, and that adding one axiom — Primitive Modal Simplicity — singles out the singlet cosine −cosΔ that saturates the Tsirelson bound |S| = 2√2. Establishes an equivalence between spectral extremality and irreducibility of the real cyclic (GNS) representation, with an explicit spin-3/2 counterexample separating the axiom from purity, covariance, and minimality. Verification suite included.
Maps the mathematical structure around the Primitive Modal Simplicity axiom and reports a dedicated attempt to derive it. Proves a sharp classification of observable uniformity and separates it from state homogeneity, with a computed USp(4) witness; the axiom remains adopted rather than derived, but now with a precisely delimited conditional bridge and an explicit open problem. The foundational note underpinning the compression paper.
Reduces a fifteen-dimensional USp(4)-covariant quantum compression problem to an exact bilinear program and produces machine-checkable two-sided bounds on the optimal entanglement fidelity — certificates verified in exact rational arithmetic with no optimizer in the loop. A methodological demonstration that a covariant capacity problem can be made exactly reducible and independently verifiable. Ships with the full verification package.
Open access & reproducibility. Every manuscript is licensed CC BY 4.0; the accompanying verification code is MIT-licensed. Each Zenodo record includes the paper, its source, and a self-contained suite that reproduces the paper's numerical and machine-checked claims from a clean checkout.
Author: Dustin Ogle, Satyalogos Inc. · ORCID 0009-0000-0372-6227.