Axiomatic Information Topology: The G.E.M.S. Matrix Engine and the Parameter-Free Origin of Particle Generations, Invariant Mass Scales, and Cosmic Acceleration

I am looking to have this frameworks math and logic checked, feel free to contact me at adrianneillpivetta@hotmail.com

 

This paper presents the G.E.M.S. paradigm, a parameter-free, non-parametric model of foundational information physics that replaces the continuous spacetime backdrop with an integer-bound, discrete lattice manifold. Rather than treating quantum mechanics and general relativity as conflicting rulesets, the framework derives both as multi-scale perspectives of a single closed-loop accounting protocol.

First, universal cosmic invariants—including the information velocity ceiling (\(c\)), the metric floor (\(r = 10^{-15}\text{ m}\)), and the chronological clock cycle (\(dT\))—are shown to emerge as non-arbitrary geometric requirements forced by self-evident logical axioms of causal and spatial distinction.

Second, utilize the symmetries of the Clifford algebra \(C\ell_{6,1}\) alongside a localized Handshake Accounting Protocol to elegantly map the combinatorial interaction between nested base-7 horizons (\(7^{1}\) linear, \(7^{2}\) planar, and \(7^{3}\) volumetric states) and a global base-2 capacity envelope. This configuration natively drives a dynamic loop oscillation between a \(+303\) sub-saturation remainder and a \(-40\) super-saturation overflow, locking the system's dynamic hysteresis attractor precisely at the laboratory micro-remainder target of \(\Delta\alpha^{-1} = +0.000747\).

Third, the framework re-frames macroscopic phenomena as the inevitable, cascading downstream friction effects of the network archiving its own history. Under this monolithic ledger, invariant rest mass emerges as an internal spinor maintenance tax, electric charge as an axis-counting metric, gravity as instantaneous local metric friction, dark matter as localized chronological anisotropy drag, and cosmic expansion as a mandatory thermodynamic cooling radiator generating new coordinate addresses to prevent global network collapse.

Finally, we outline explicit runtime parameters for a discrete network simulator alongside four standalone, laboratory-falsifiable predictions—including a discontinuous high-velocity lepton charge spike and metronomic coordinate phase-jitter—providing a concrete experimental criteria to verify the theory against continuum field models.