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, exactly reducible, independently verifiable covariant-compression problems built on the same structure — carried through the first nontrivial step of the symplectic tower, USp(6) = Sp(3) — and, at the top, a covariant, completely positive channel from an exact Sp(3) relational construction, the formal companion to the philosophy paper Relation Before Relata.
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.
Extends the USp(4) result to the first nontrivial rank step of the symplectic tower, USp(6) = Sp(3). Reduces the effective-channel positivity cones to seven Hermitian isotypic blocks by exact Gram-dual congruence, certifies a coherent lower witness and an outer-PPT upper bound by an exact rational sum-of-Hermitian-squares dual whose defining identity holds with zero residual, and proves a strict coherent-versus-entanglement-breaking separation that survives the first rank extension. Two standalone verifiers return ALL PASS; ships with the full reproducibility bundle.
Derives a covariant, completely positive channel from an explicit Sp(3) relational object — exact over the Gaussian rationals and verified by machine: trace-preserving and, under a stated convention premise, action-determined. An existence result that a fully relational construction, with no substance anywhere in it, can be made exact and do genuine work: compressing, transforming, and inducing a determinate action. This is the formal companion to the philosophy paper Relation Before Relata. Ships with a self-contained reproducibility bundle.
A short, non-technical way into the relational reading. The double-slit experiment is usually sold as proof that conscious observation collapses reality; this essay gives a plainer — and, in the end, stranger — account. What destroys the interference pattern is neither a mind nor a physical jolt but the forming of a relationship: the existence of which-path information anywhere in the surroundings. Drawing on which-path marking, the quantum eraser, and interaction-free measurement, it argues that being definite is a matter of being in relation — the same idea the philosophy paper Relation Before Relata works out carefully. No new physics; a reading of what the standard results mean.
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.