2 The Organising Equation

2.1 The Observer as the First Principle

We take as the starting point:

Axiom (Observer Existence). There exists at least one observer.

An observer is defined operationally, following Paper I [meskanen2001]: a finite information structure whose state sequence encodes causally efficacious subjective experience. Paper I establishes from four modest axioms that such a structure must be finite, substrate independent, and that the universe containing it must be static and timeless. We take those results as working hypotheses and build on them here.

2.2 Probability of Existence via Solomonoff Induction

Given the observer axiom, which universe does the observer find herself in? By substrate independence, the observer is a finite information structure and the universe is the minimal information structure that contains her. The natural prior over universes is then determined by description length:

(1)

where Γ_O is the set of all histories compatible with the existence of O, 𝒞_O[γ] is the total description cost of γ given O, and Z_O = ∑ _γ∈ΓO exp(−𝒞_O[γ]). This is Solomonoff induction [solomonoff1964] in path-integral form.

The apparent free parameter λ (an inverse temperature in the Boltzmann analogy) has been set to unity: rescaling λ is equivalent to rescaling 𝒞_O, and only the ordering of histories by cost is physically meaningful. λ is a units choice, not a physical constant.

2.3 Physical Law as Large-Deviation Minimiser

The conjecture is that the observed regularities of physics are the histories γ^∗ that minimise 𝒞_O[γ] subject to observer compatibility:

A universe that is chaotic or structureless is not forbidden by this equation; it simply has a higher description cost and contributes negligibly to Z_O. We do not assume finiteness; we expect to derive it, because finite universes compress better than infinite ones. We do not assume order; we expect to derive it, because ordered histories are shorter to describe. Whether equation (1) alone is sufficient to force these properties in full generality, without additional structure, is an open question.