The TDZero Cosmic Theory - Part II The fundamental Constants

TDZero Cosmic Theory - Part II: The Fundamental Constants Author: Mauro Yacote Caldas Date: March 3rd, 2026 License: Creative Commons Attribution Share Alike 4.0 International (CC BY-SA 4.0) _______________________________________ This book completes the derivation programme opened by the TDZero Cosmic Theory (2026). Starting from a single geometric object — a four-field Halbach interference pattern initiated by a spin at the temporal zero point T₀ — it derives, without free parameters, the exact values of Newton's gravitational constant G, the speed of light c, and the reduced Planck constant ℏ. It then derives the total number of temporal-dimensional frames in the cosmos (N_total ≈ 276), the observed dark energy density, and the 30/70 matter-to-dark-energy ratio. Every result follows from a single master geometric factor α = (1/4)[ln(√3 + 1) + π] = 1.03666..., itself derived from the geometry of the four-field structure. The book resolves three long-standing problems in physics: the cosmological constant problem (why dark energy is 10¹²³ times smaller than the Planck density), the cosmic coincidence problem (why matter and dark energy are comparable today), and the hierarchy problem (why gravity is so much weaker than electromagnetism). All three share the same answer: exponential dilution through temporal-dimensional depth. The Born rule of quantum mechanics — the squared-amplitude probability law assumed as a postulate in every standard formulation — is derived here as a theorem of temporal frame selection geometry. Wave function collapse is identified precisely as T₀ selecting one frame from the superposition of all 276, with probability |aₙ|² following from the equal distance of all frames from the geometric origin. The framework makes five falsifiable predictions testable within this decade: α = 1.03666...; G and c varying together near frame boundaries by the factor e^α ≈ 2.819; dark energy decreasing over cosmic time (wₐ > 0); N_total = 276 confirmed by three independent cosmological observables; and the Born rule holding exactly with no corrections. The dark energy prediction is directly comparable to current and near-future survey results from DESI, Euclid, Vera Rubin, and Nancy Grace Roman. ____________________________________ This is the fith work in a theoretical programme comprising: • The Temporal-Dimensional Zero Theory (Yacote Caldas, 2025) - https://doi.org/10.5281/zenodo.16852964 • The TDZero Zero Integration Theory (Yacote Caldas, 2025) - https://doi.org/10.5281/zenodo.18343075 • The Rotational Structure of Reality (Yacote Caldas, 2026a) - https://doi.org/10.5281/zenodo.18805466 • The TDZero Cosmic Tehory - The Fundamental Structure of Cosmnic Reality (Yacote Caldas, 2026b) - https://doi.org/10.5281/zenodo.18826151 The work is published under Creative Commons Attribution Share Alike CC BY-SA 4.0. Note on Independent Research This work was produced outside any academic institution, without departmental affiliation or grant funding. This book invites critical examination and empirical testing by the scientific community.__________________________________ Version 2: On Version 1, c_n was described as the propagation rate of the electric field of the spatial fields. That is correct but secondary. The primary statement — now made explicit in version 2 throughout — is that c_n is the velocity of B_Tₙ, the temporal magnetic field as expressed within frame TD_n. This is not B_T₀ (the full undiluted field at the Zero Temporal Point) but its expression at frame depth n, carrying amplitude A_T × e^(−αn). The electric propagation rate is a consequence of B_Tₙ’s velocity, not its origin. The scaling c_n = c₃ × e^(α(n−3)) is now physically obvious: deeper frames have stronger B_Tₙ amplitudes, and a stronger temporal field moves faster through the spatial structure of that frame.