The Law of Existence: Coherence as the Condition of Reality

This monograph argues that coherence is the foundational condition for the possibility of any observer-containing universe. It develops three interlocking results: (1) the Law of Existence, showing that incoherent worlds cannot instantiate observers, memory, or lawful dynamics; (2) the Syntactic–Ontic Separation Principle, demonstrating that no formal description or bitstring can constitute a running universe without an underlying coherent substrate; and (3) the Coherence Cluster and the Law–Ontology Equivalence Theorem, proving that real local law implies global ontic coherence. The work synthesizes metaphysics, philosophy of physics, and structural realism, and includes a documented adversarial stress-test where multiple counter-models are attempted (randomness, brute enumeration, Humean mosaics, finite combinatorics). All fail either by reintroducing global law or by collapsing into uninstantiated syntactic objects. The conclusion is that coherence is not contingent but necessary for existence.