Information-theoretic Limits on Programmatic Specification of Biological Systems

In the paper's words

Shows via information theory that an organism does not contain enough organism-specific information to specify its own microscopic organization. The genome is a generator specification (not trajectory program). Establishes coarse-graining threshold with dual Hartley/Shannon entropy faces.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. 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.

   from Empirical Validation

How it is done

1. 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.

   from Executive Summary

2. 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

   from QNFO Relevance: HIGH - Structural Consilience with Autaxys OC

3. 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

   from Key Technical Contributions

What would falsify it

The paper's text states no explicit falsification criterion; the limits below are what it says about where the claim stops.

Where the claim stops

1. 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supplementary) Reproducibility: Open-source code with fixed seeds and YAML configs Peer review: bioRxiv preprint, not yet peer-reviewed Companion code: github.com/yuj1r0/itol (MIT, Python 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)

   from Assessment

Where to read

1. Executive Summary69 words · 1 min
2. QNFO Relevance: HIGH - Structural Consilience with Autaxys OC73 words · 1 min
3. Key Technical Contributions38 words · 1 min
4. Empirical Validation31 words · 1 min
5. Assessment29 words · 1 min