Inherited Topological Attractors in Chemical Space: Resolving the 10¹²³-Year Paradox in Prebiotic Self-Organization Through Trans-Cyclic Cosmological Priming
The origin of life’s rapid emergence (~10⁹ years) and universal biochemical features (homochirality, conserved metabolic pathways) present a fundamental puzzle: random chemical search in configuration space predicts timescales exceeding 10¹²³ years, rendering biogenesis essentially impossible within cosmic history. We present a comprehensive theoretical framework unifying Penrose’s Conformal Cyclic Cosmology (CCC) with sheaf-theoretic descriptions of prebiotic chemical organization. We suggest that biological information from extinct systems in the previous cosmic Aeon (Aeonn) can survive the conformal boundary transition (ℐ⁺n → ℐ⁻(n+1)) through squeezed quantum states with squeezing parameter r ~ 10⁸⁶, which suppress decoherence over timescales approaching 10⁹⁷ years. This information, encoded in photonic field correlations, establishes topological attractors in the chemical configuration space of the subsequent Aeon (Aeon(n+1)) via modified Casimir forces. Using formal concept analysis and sheaf theory, we show that microenvironmental integration satisfying locality and gluing conditions enables coherent assembly of inherited structural motifs, reducing effective search space by ~10⁶⁴ orders of magnitude. The framework makes seven falsifiable predictions including universal homochirality (enantiomeric excess ~0.2% from photonic bias amplified by autocatalysis), convergent metabolic network topology across independent biogenesis events, and specific cosmic microwave background non-Gaussian signatures at ℓ ~ 1000-3000. Numerical simulations of molecular dynamics in squeezed electromagnetic vacua demonstrate biogenesis timescales of τbio ~ 10⁹ years, consistent with terrestrial observations. This work provides the first physically viable mechanism for trans-Aeon biological information transfer, resolving the combinatorial impossibility problem and suggesting life is an iteratively optimized feature of cosmic evolution rather than a contingent chemical accident.
