Commutation-Discriminant Quaternionic Spacetime (CDQS) | A Developing, 4D-Conserved, Algebraic Reconception of General Relativity; and Potentially Comprehensive Cosmological Description—Absent of Cosmological Constants and Dark Matter

Commutation-Discriminant Quaternionic Spacetime (CDQS) is an actively-developing theory that reworks and subsumes General Relativity as a non-commutative quaternion algebra construct, positing energy conservation in four dimensions, scalar–vector energy exchange, and algebraic curvature as fundamental. If the containing concepts and derivations hold up to objective and unbiased scrutiny, then the implications are beyond profound. The theory is highly ambitious but succinct and mathematically supported, increasingly reinforced by external data with each passing day. It posits a single, quaternionic algebra construct and coinciding spectral operator to describe: energy curvature spacetime momentum field strength Quantum Field Theory Quantum Chromodynamics intrinsic coherent matter rotation without the need for a separate metric tensor, stress-energy tensor, or weak-field gauge. It algebraically addresses phenomenologies that are pathological to ΛCDM, such as: missing mass naked singularities galactic rotation curves baryonic scaling relations early structure formation dark energy coincidence Einstein is fully recovered. Observable symmetries are dynamic but also fully recovered. Shell-closure of a quaternion-native QCD analog is explicit. Galactic rotation has been algebraically modeled against SPARC without dark matter, showing a mean residual comparable to coreNFW-LCDM. CMB likelihood CAMB testing against 2018 unbinned Planck high-ℓ plus lensing and ACT DR.6 multi-frequency plus lensing has shown that not only does CDQS contend in the early-time context with a same-stack Standard Model reference, it actually improves raw fit to a statistically significant degree (p≈0.0036). This distribution should be considered relatively informal and under active development, but the author also wishes it to serve as a beacon to rekindle tangible interest in quaternionic physics. When time is reclassified as an active, energetic degree of freedom which participates in cosmic evolution, by all appearances thus far and subject to the scrutiny of all, the figurative dark clouds which once descended upon quaternions evaporate and give way to atmospheric clarity. Minimum files, .yamls, and modified CAMB source are all provided for complete transparency and external validation. Galactic rotation modeling is also provided to enable full reproducibility against the same SPARC dataset. v2 contains an updated CAMB source and paper sections for black holes and universal origin. 7A40782AED1FD354C5738EAB1E7096B010BA0ED4E65D55DAA16DC11029D34AB3BADBA5C268C8F7672A7CEF19DC1A91E7D00AB400605E3E2F613C85F794A86700 The author wishes to acknowledge these conceptually similar or peripherally adjacent works that they were not aware of until the present moment, shortly following this submission, even though they were in no way referenced or utilized in the construction of CDQS: https://repo-archives.ihes.fr/FONDS_IHES/I_Prepublications/CONNES/1994-1998/M_96_37/M_96_37.pdfhttps://arxiv.org/abs/1702.03817https://link.springer.com/article/10.1007/s00006-026-01436-8https://web.ma.utexas.edu/users/dafr/detsur.pdfhttps://www.sciencedirect.com/science/article/pii/S0393044020302357