Abstract
<title>Abstract</title> <p>Physical law is normally treated as a starting point: symmetries, conservation laws, and the valuesof the fundamental constants are assumed, not derived. This paper inverts that order. Tegmark’s Mathematical Universe Hypothesis proposes that physical reality is a mathematical structure, and resolves the question of which structure is realised by treating all consistent structures as equally real, distinguished only anthropically. This paper explores the complementary possibility that onestructure is privileged: the Principle of Maximum Informational Complexity (PMIC) asserts that physical reality is the unique mathematical structure that maximises a net information score, F[M] = K(O|M) − λK(M) — the algorithmic complexity of its observer-state repertoire minusthe cost of describing its own laws. A global maximiser is proved to exist and to be generically unique over the holographically admissible structure space. From this single variational principle, three structural propositions derive — rather than postulate — why the realised laws of physics exhibit gauge symmetry, conserved Noether charges, and spontaneous symmetry breaking, eachraising the score through a distinct information-theoretic mechanism. PMIC is strictly strongerthan anthropic reasoning: it requires the six fine-tuned constants of nature (ΩΛ ≃ 0.689, α ≃ 1/137,Q ≃ 2 × 10−5, ε ≃ 0.007, η ≃ 6 × 10−10, d = 3) to sit near the peak of the observer-state landscape, not merely inside a life-permitting window — a prediction falsifiable by any measurement that lies inside the anthropic window but far from the PMIC peak. Two fully computable demonstrationstest the framework. In a law-selection mode, a family of symbolic directed graphs is ranked by exact closed-form scores, yielding explicit phase boundaries. In a constant-selection mode, the cosmological constant is predicted as Ω∗Λ ≃ 0.749 directly from the Friedmann equation, with no free parameters— a genuine a priori prediction that agrees with Planck 2018 and DESI DR1 to within 99% of theproxy maximum. The same analysis shows that the fine-structure constant α ≃ 1/137 also sits near the peak of the joint two-dimensional observer-state landscape. If correct, PMIC reframes the laws of physics not as brute facts but as the necessary signature of an informationally maximal universe.</p>