THREE ROADS TO PLANCK TIME THE NON-VIOLATORY CLASSICAL UNIFICATION OF GENERAL RELATIVITY, QUANTUM MECHANICS AND INFORMATION THEORY WITH ZERO FREE PARAMETERS When pushed to critical limits, the fluid-continuum model predictably breaks down, generating unphysical mathematical infinities like the Vacuum Catastrophe and zero-volume cosmic singularities. In material reality, infinity is simply a mathematical alarm bell signaling that an abstract model has been extended far beyond its domain of validity. When the equations fracture, it often leads to increasingly complex, exotic hypotheses designed to patch a broken system—moving further away from the physical realm and classical architecture. CONCORDIA (Hyde 2026q), the natural conclusion of PK THEORY, resolves these anomalies by executing a structural shift from an infinite continuum to a discrete, finite, and bounded solid-state processing medium. This architecture is defined by The Triple Convergence—the seamless mathematical alignment of three independent operational pathways. Rather than relying on semi-classical hybrids or exotic proposals, this framework adheres strictly to proven, established physics: General Relativity, Information Theory, and Quantum Mechanics, without a single violation. It honors the foundational insights of a complete classical lineage, fully recognizing the contributions of giants from Newton and Einstein to Pauli and Boltzmann. THE THREE ROADS The Geometric Road permanently resolves the mathematical singularity using the Einstein–Hilbert action validated by de Broglie's matter-wave postulates. General relativity asserts that gravitational collapse inevitably crushes a star's mass into zero volume and infinite density. However, Albert Einstein demonstrated in 1939 that matter cannot be concentrated arbitrarily because the physical requirements for structural stability prevent a system from ever reaching its own Schwarzschild radius. PK THEORY replaces the singularity with a finite, structured endpoint: The Fifth State. At the quantum scale, space organizes into a rigid, Planck-scale tetrahedral lattice. Governed by the Kepler-Hales theorem for maximum sphere packing and quantum zero-point volume expansion, collapse stops abruptly at exactly forty percent of the Planck density, where the Pauli exclusion principle takes over and freezes the interior into a rigid, timeless phase boundary. The Informational Road treats the universe as a physical information-processing system. Topologically equivalent to a Eulerian graph, the lattice allows for a perfectly ordered, continuous flow of data via the MIMO protocol. Information entering the system is never lost; it is translated directly into geometry as immutable topological defects locked within lattice voids. By deploying the Bremermann limit and the Bekenstein bound, the macroscopic mass cancels identically, revealing the Planck time as the ultimate parallel-processing clock cycle of a system holding a total thermal entropy of zero. The Quantum Road derives this exact same timescale from the rigorous constraints of the Mandelstam–Tamm energy–time uncertainty principle. Because the Fifth State exists in a strict ground state, its energy variance is zero, locking the system in total temporal stasis. To break this stasis and initiate the expanding universe, a quantum fluctuation supplies a seed energy equal to the rest-energy of a single Planck-mass quantum. The minimum time required for this fluctuation to manifest yields the exact duration of the Planck Pivot—the deterministic clock cycle where the frozen potential energy of the geometric condensate uncoils into the kinetic phase of the universe. Three separate domains of physical law, sharing no common assumptions beyond the fundamental constants, converge parameter-free on the exact same expression. As examined in FIRE-EATER (Hyde 2026o), this discrete floor introduces a natural frequency cutoff that eliminates the infinite mode sums of quantum field theory, rendering semiclassical mechanisms like Hawking radiation entirely inapplicable to real black holes. There is no evaporation and no information loss. CONCORDIA delivers a self-consistent, classical verdict: The cosmos is a permanent record held in geometric tension, balanced perfectly by the unyielding hardware of the spatial template.
DENCER HYDE (Mon,) studied this question.