Minimal Causal Order in a Coupled Binary Recurrent System
Year: 2026
Type: preprint
Abstract: This preprint establishes a constructive existence result for a strict pairwise clamp-constitutive causal-order relation in a finite deterministic binary product-coordinate system. The primary witness is T(a,b) = (a XOR b, a). Under explicitly defined local actual-context causal efficacy, time-unrolled phase-wise recurrent closure, and constant-coordinate clamp interventions, the A organization is necessary for recurrence of B while B is not reciprocally necessary for recurrence of A. An analytic lemma excludes qualifying joint orbits of period one or two, and exhaustive enumeration of all 256 deterministic maps on the four-state binary product domain identifies exactly four qualifying maps. The deposit includes the main manuscript, a technical verification dossier that freezes the predicates and audit criteria, and the exact executable Python enumeration script used for the reported computational check. The result is class-relative and does not claim universal physical minimality, closure-specific necessity under replacement drive, exact trajectory identity across regimes, or endogenous generation of a new causal order.
Author: RAZUVAEV, MAKSIM
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203780187
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