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Information-theoretic Limits on Programmatic Specification of Biological Systems

DOI: 10.64898/2026.07.27.740886
Published: 2026-08-01

Information-theoretic Limits on Programmatic Specification of Biological Systems

Authors: Tuomo Kiiskinen, Oscar Kivinen, Manuel A Rivas

DOI: 10.64898/2026.07.27.740886

Status: bioRxiv preprint (July 27, 2026)

Code: github.com/yuj1r0/itol (MIT license)

Executive Summary

This paper provides a rigorous information-theoretic proof that an organism genome plus environmental signals is provably insufficient to deterministically specify its own microstate trajectory. The genome acts as a generator specification (a hockey coach game plan) rather than a trajectory program (figure-skating choreography). The gap is filled by a shared physical substrate Phi (the universal compiler) that compiles the coarse spec into a functioning organism via physics at runtime.

QNFO Relevance: HIGH - Structural Consilience with Autaxys OC

This paper arrives at the same structural conclusion as Autaxys Ontological Closure from biology rather than physics:

  • Finite genomic specification (C_G <= 2n bits) = finite D/R procedure
  • Coarse-graining threshold C*(B) = computable modulus of convergence boundary
  • Universal compiler Phi = shared physical substrate
  • Generator specification (not trajectory program) = compilation (not execution)

Layer mapping: Layer 4 (Information Theory) DIRECT -> Layer 5 (Autaxys) STRONG -> Layer 6 (Physics = Computable Reals) MEDIUM

Key Technical Contributions

  • Dual Hartley/Shannon entropy faces for the coarse-graining threshold
  • Runtime-randomness lemma (bits relocated to runtime must still be consumed)
  • Initial-condition mixing lemma (Laplacian-demon loophole closed)
  • Zero-error addressability proposition (pigeonhole for deterministic spec)
  • Environmental rescue impossibility across 7 physical modalities

Empirical Validation

Five worked cases: E. coli proteome (3-24x genomic budget gap), Drosophila Bicoid morphogen (~1.5 bits/nucleus), C. elegans descriptor ladder (threshold crossed at voxel delta=0.10um), AlphaFold-2 cross-organism compression, JCVI-syn3A 4D whole-cell simulation.

Assessment

  • Rigor: Mathematical proofs complete (31-page supplementary)
  • Reproducibility: Open-source code with fixed seeds and YAML configs
  • Peer review: bioRxiv preprint, not yet peer-reviewed
  • Companion code: github.com/yuj1r0/itol (MIT, Python >= 3.10)