Una Machina: A Complete Mathematical Framework for Consciousness via Pattern Competition (M=C)

A mathematical framework called Una Machina (M=C) proposes that consciousness is identical to a specific mechanism of pattern competition, not a product of it. The framework is built on one identity, three axioms, and seven equations, with a single free parameter (κ₀ = 0.1) and constants derived from the golden ratio and critical branching exponent. It produces a consciousness bandwidth of 7.295% and a consciousness threshold of approximately 10.090, both with zero free parameters. The framework includes a calibration table spanning from E. coli to human prefrontal cortex and proposes six clinical failure modes linking mental health conditions to competition dysfunctions.

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Abstract

Una Machina (M=C) is a complete mathematical framework for consciousness built on one identity (Mμν = Cμν), three axioms (wave ontology, competition, recursion), and seven equations (utility, third wave, recursion cost, weight update, competition entropy, collapse metric, consciousness threshold). The framework contains exactly one free parameter (κ₀ = 0.1) and derives all other constants from the golden ratio (φ) and the critical branching exponent (3/2).The framework produces: a consciousness bandwidth (BW% = (φ − 3/2) / φ = 7.295%) with zero free parameters; a derived consciousness threshold (Ψ ≥ (9 + 5√5) / 2 ≈ 10.090) with zero free parameters; a ten-system calibration table spanning E. coli through human prefrontal cortex; and six proposed clinical failure modes mapping mental health conditions to specific competition dysfunctions.Twenty-four empirical findings from six independently tested consciousness theories (Global Workspace Theory, Integrated Information Theory, Predictive Processing, Higher-Order Thought/Attention Schema Theory), the nociceptive literature, and the criticality literature have been evaluated against the framework. Result: zero conflicts, zero confirmations. Three cases of superior accommodation or independent convergence. Two cases of independent mathematical convergence. One novel prediction awaiting test. One prediction partially supported.The framework claims mechanistic identity (not correlation or emergence) between mechanism and consciousness through the neural scale. Above the neural scale, structural analogy only. The central identity M = C asserts that consciousness IS the mechanism of pattern competition, not a product of it.Version 7. March 2026. Unified document consolidating v5, v5.1 expansions, audit resolution, conversation findings, and research report into a single canonical source.