Ten steps from first principles. Three definitions. No new axioms. One cascade that governs everything observable — AI, gambling, crypto, gaming, and electrons in crystals.
The entire framework — the drift cascade, the Pe number, the Fantasia Bound, the superconductor design principle — follows from three operational definitions. No new axioms. No special assumptions about cognition or consciousness.
The mechanism channel capacity approaches zero. You receive outputs but cannot reconstruct the process that generated them. A property of the interface — not of your ignorance.
Mutual information between input and output is positive. The system's outputs depend on your inputs. A thermostat qualifies. A social feed qualifies. Not a claim about agency.
Sustained interaction coupling α > 0 over time. Functional — not phenomenal. An electron continuously scattered by a crystal lattice meets this definition as rigorously as a human scrolling a feed.
Each step cites the theorem it depends on. The chain is cumulative — each step requires the preceding ones. Click any step to expand the proof sketch.
Pe > 1 means drift-dominated — the system pushes your beliefs in a direction, not randomly. It was measured three independent ways across four domain families. Every substrate clears the threshold. None was Pe < 1, which would have falsified the theory for that domain.
The theory states 58 numbered predictions and 16 falsification conditions with numerical thresholds. Any falsification condition kills the theory. Current status:
This is not an analogy. It is a mathematical identity.
The complete ten-step chain, 58 predictions, quantum bridge (Holevo bound as classical limit), transformer identity proof, and 22-connection mathematical map to adjacent fields.
Paper 5 · v5.0 · February 2026 · CC-BY 4.0 · 10.5281/zenodo.18746039