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- Peer review: bioRxiv preprint, not yet peer-reviewed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)