Order as the Default Outcome Under Constraint

Prime 0 is the foundational paper of the Primes series and the positive ground the other four refine. It corrects a recurring misread: treating coherence as something that must be added — by intelligence, teleology, or luck — rather than something that typically falls out of constraint. The claim is that coherence is persistent or recurrent order made visible by constraint. When constraints — symmetries, conservation laws, couplings, boundary conditions, energy and entropy flows — restrict the admissible states and trajectories of a system, it often lands in stable structure: invariants, attractors, invariant measures, or stationary distributions. Coherence in this sense requires no internal model, no goal, and no learning.

The paper draws one line in particular: coherence is not intelligence. Intelligence is the special case in which constraints become learnable. Coherence is also not complexity — a crystal is highly coherent and highly compressible, while a turbulent flow can be complex yet coherent at the level of its invariant statistics. To make that operational, the paper gives a data-facing definition of coherence and a short, reproducible checklist for detecting it, worked through on the Lorenz system: point-unpredictable, yet living on a low-dimensional attractor with stable statistics that compress far better than any noise baseline. The structure is in the ensemble, not the point. As with every Prime, the paper asks no commitment to Universal Collapse Theory — coherence is a term the reader already holds and can judge on its own ground.

What this paper does not claim. "Default" marks an explanatory orientation — where to look first — not a guarantee that every constrained system becomes simple or ordered. The paper does not hold that randomness is unreal or that chaos is merely apparent disorder. It holds only that when stable structure appears, the first move is to audit the constraints that produce it before reaching for agency, purpose, or primitive chance. It authorizes no law-level claims; it is a reader lens, held as provisional and open to revision.

Keywords: coherence; constraint; attractors; conceptual hygiene; Lorenz system.