What does this research mean for the field?

Numerical experiments validate the Theta-correspondence framework for biological motifs, demonstrating that BMIC violation exhibits local quadratic scaling in coupling strength consistent with standard information-geometric asymptotics. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.SUPPORTS_CONSENSUS.

What question did this study set out to answer?

This work aims to validate and extend the Theta-correspondence framework through numerical experiments.

April 13, 2026Open Access

Numerical Companion to 'Formal Correspondences in Consciousness Science': Validation and Extensions of the Theta / BMIC Framework

Key Points

This work aims to validate and extend the Theta-correspondence framework through numerical experiments.
Implemented seven numerical experiments using binary Markov kernels and biological Boolean motifs.
Conducted analysis in both Boolean synchronous and continuous-time ODE formulations.
Examined codim-46 non-genericity and BMIC violation via local quadratic scaling.
Compared conditional-independence measures on tested circuits.
Validated the Theta-correspondence framework across various biological motifs.
Identified an active-dynamics regime for agent-like behavior in Boolean circuits.
Demonstrated consistency in scaling results with established information-geometric asymptotics.

Abstract

Numerical companion material to Paper B ('Formal Correspondences in Consciousness Science: From Theta Mapping to Phi-Assembly', Austermann 2026). Paper B and its philosophical companion are at 10.5281/zenodo.18521824. Contents: Seven numerical experiments implementing and exploring the Theta-correspondence framework on minimal (2,2,2) binary Markov kernels and four canonical biological Boolean motifs (p53-Mdm2-damage, repressilator, toggle switch, coherent feedforward loop) in both Boolean synchronous and continuous-time ODE formulations. Topics covered: Empirical validation of the codim-46 non-genericity result for the P.D.A factored submanifold, with uniform random and Kauffman random-Boolean-network baselines. Local quadratic scaling of BMIC violation in coupling strength, consistent with standard information-geometric asymptotics for KL divergence on a statistical manifold. Comparison of Boolean synchronous analysis with continuous-time ODE formulations of the same biological circuits, with a rate-sweep identifying the active-dynamics regime where each motif is most agent-like. Side-by-side computation of two related but distinct conditional-independence measures: the full-kernel 'g-dependence' necessary condition and the paper's Definition 2.2 Markov blanket condition I(X'; W | X, G) = 0, with a discussion of how the two relate in practice on the circuits tested. Materials included: 10 Python scripts reproducing every experiment (self-contained; numpy + matplotlib); 2 figures; the full experimental session log; and a summary companion document in PDF and markdown. This material is deposited to make the numerical work citable and reproducible alongside Paper B. It is not itself a paper and should be cited as a dataset / code supplement.

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