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[2] ai.viXra.org:2603.0069 [pdf] submitted on 2026-03-14 18:44:16
Authors: Jorge Andrés Villaluz
Comments: 11 Pages.
We identify a universal geometric hierarchy RU/ℓP ∼1061, where RU is the radiusof the observable universe and ℓP is the Planck length, and show that this singledimensionless ratio unies ve apparently independent results in modern cosmology.This hierarchy is formalized by the master inequality:2RU·10−n ≤ℓP,which establishes the physical resolution interval n ∈[61,62): the number of dec-imal places of π needed to describe the geometry of the observable universe withsub-Planckian precision. The same scale governs the BekensteinHawking entropybound Smax ∼4π(RU/ℓP)2, the ne-tuning condition δρ/ρ∼10−60, and the discrep-ancy factor of the vacuum catastrophe ∼10122. We further propose two falsiablepredictions: (1) the resolution parameter n(t) evolves with cosmic expansion asn(t) ≈61.4 + log10(t/t0), and (2) the cosmological constant satises Λ(t) ∝t−2, arelation testable with next-generation surveys such as Euclid and LSST. The uni-fying thread throughout is spherical geometry: π appears in all these expressionsbecause the observable universe is a sphere.
Category: History and Philosophy of Physics
[1] ai.viXra.org:2603.0008 [pdf] submitted on 2026-03-02 17:05:48
Authors: Rajanikanr Panda, Moninder Singh Modgil, Dnyandeo Dattatray Patil, Krish Jhurani
Comments: 32 Pages.
We develop a unified theoretical framework integrating cortical electrophysiology, non-equilibrium thermodynamics, Morse topology, renormalization group scaling, and compact-time cosmology into a single neuro-anthropological model. Assuming a temporally compact spacetime manifold S1 with Kalpic period TK, all admissible physical observables satisfy the periodic boundary condition A(t+TK) = A(t). Embedding cortical dynamics within this topology, we show that baseline electroencephalographic (EEG) rhythms become Fourier-constrained variables whose slow modulation across cosmological epochs constitutes a civilizational order parameter rather than a merely developmental marker. We construct population-level spectral density functionals and demonstrate that mean dominant frequency ¯ f(t), spectral entropy H(t), and reticular activating system (RAS) drive R(t) form a coupled nonlinear dynamical system subject to global Kalpic compensation. Stochastic resonance analysis reveals that ultra-slow cosmological forcing can be amplified through noise-assisted phase transitions. Renormalization group treatment establishes scale-dependent flow of cortical coupling constants across Kalpa duration, while Morse-theoretic analysis proves that entropy extrema and neural phase reversals occur in even-numbered pairs on the compact temporal manifold. Extending to a spatially distributed nonlinear field theory, we formulate a Kalpaboundary effective action describing seam-localized phase interference. Within this framework, the phenomenology of dejavu is reinterpreted as inter-cycle neural phase overlap at the compact-time seam, modulated by entropy-slope reversal andRAS coupling. We prove an Entropy—Memory Duality Theorem showing that integrated entropy production over one Kalpa is globally compensated by integrated memory gradients, preserving informational closure. Finally, we define a cosmological-scale Kalpa Recurrence Operator acting on civilizational phase space, derive its discrete spectrum, and construct a statistical model predicting epoch-dependent dejavu frequency as a function of informational complexity. The resulting synthesis proposes that baseline EEG structure, civilizational dynamics, and subjective temporal anomalies are mathematically constrained consequences of compact temporal topology.
Category: History and Philosophy of Physics