The Geometric Description of Physics at the Cosmic Scale:Mass, Information, Causality, Force, and the Quantum Relations from Geometry

Abstract

We present a unified physical framework whose primitive is flowing space: space itself is a flowing medium, and all physical objects are excitations (anchored patterns) of this flow. From a small set of postulates — vector light speed (direction-changeable), three anchored directions, and the counting of space-displacement “strands” — the framework derives, in a single chain of exact identities: mass as symplectic entanglement volume, information as symplectic volume conserved under unitary transport, and the four forces as the four channels of the Leibniz decomposition of the flow momentum p = m(C −v). The quantum relations E = ℏω, the de Broglie relation p = h/λ, the Planck–Einstein relation E = hf , and the uncertainty product ∆x ∆p = ℏ emerge from helix geometry, with the geometric choice r = λ/2π (reduced wavelength as helix radius); Pauli exclusion is the geometric rank criterion for identical strands. All identities are verified numerically with physical constants at machine precision (relative errors ≲ 10−10), and the derivation chain is fully formalized in Lean 4 with zero sorry. The honest status is stated: the derivation chains are closed (geometry ⇒ quantum relations), while first-principle derivations of the geometric choice r = λ/2π and of the remaining input constants (e, M0) are not yet achieved.

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