Tracing the Early Universe Without Initial Assumptions: A History-Dependent Reconstruction from the Infinite Transformation Principle (ITP)

This paper investigates whether the present large-scale structure of the universe contains sufficient fossil information to reconstruct a consistent early state without imposing any initial conditions such as a singularity, inflation, or Gaussianity. Using the Infinite Transformation Principle (ITP), we treat cosmic evolution as a history-dependent, non-Markovian process that retains weak memory on long-wavelength modes. We formulate the inverse cosmological problem as a stability analysis of the backward flow operator T−1. The ITP introduces a memory functional M(z), creating a correction ∆J(z) to the forward Jacobian. We show that ∆J(z) ≈ −D Plong acts as a dissipative, contractive filter on superhorizon modes. Using low-ℓ CMB structure, supervoid topology, and curvature drift Ωk(z) as preserved sufficient statistics, we reconstruct the early-state manifold E. A supporting mathematical appendix demonstrates backward stability on the relevant subspace. The reconstruction yields finite-density, phase-coherent, geometrically regulated early states without requiring a classical singularity or inflationary smoothing. Long-wavelength modes remain contractive under backward evolution due to the thermodynamic role of the memory field. The three large-scale observables enforce a unique, self-consistent solution for the memory kernel K(z, z′), eliminating the degeneracy inherent in the standard Markovian ΛCDM framework. Within its domain of validity, the ITP reconstruction converts the early universe from an assumed beginning into a mathematically recoverable state. The framework makes four falsifiable predictions: persistent low-ℓ CMB coherence, CMB–void alignment, slow curvature drift (|dΩk/ dz| ∼ 10−4), and a non-zero equilateral/orthogonal non-Gaussianity. Failure of any single prediction falsifies the entire approach.