From Persistent Filamentary Phases to Full Renormalization-Group Universality in Universal Modular Dynamics

Oleg Ivanovich Nesen

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From Persistent Filamentary Phases to Full Renormalization-Group Universality in Universal Modular Dynamics

O. I. Nesen

2026-10-02

https://doi.org/10.24108/preprints-3116540

Persistent infinite-volume filamentary structure is a geometric statement and, by itself, does not determine a complete dynamical universality class. We make this distinction precise for Universal Modular Dynamics (UMD) and resolve the associated T5 proof-orcounterexample problem. First, we show that the unrestricted implication from persistence of an asymptotic UMD filamentary phase to full renormalization-group (RG) universalityclass equivalence is false: conservation laws, equilibrium structure, long-range interactions, absorbing-state data, nonunique RG limits, or nondecoupling spectator sectors can preserve the carrier while changing the critical theory. We then prove a restricted positive theorem for admissible UMD thermodynamic sequences whose active critical field is scalar, Z2-odd, nonconserved, short-ranged, equilibrium and fluctuation–dissipation compatible, with codimension-one critical tuning in spatial dimension d > 4, unique full-sequence RG attraction, and either no spectator sector or a spectator satisfying the stated canonical quotient conditions. For this class, a common outcome-blind coarse-graining map, equality of the normalized linear and nonlinear RG data, control of the dangerously irrelevant quartic field, and bidirectional scaling-field and observable dictionaries yield M/∼sp ≃RG Aref (d), d > 4, where Aref (d) is the external scalar Gaussian Model-A reference. In particular, the quotient theories share the Gaussian Ornstein–Uhlenbeck fixed point, the normalized relevant and irrelevant spectrum, the nonlinear scaling-field normal form, and the quotient observable algebra with scale-decaying reconstruction error. The resulting exponents are η = 0, ν = 1/2, and z = 2, while the quartic eigenvalue yu = 4 − d < 0 is retained with its dangerousirrelevance qualification for zero-mode and finite-size thermodynamic observables. This establishes the restricted theorem T5+AG,d>4 without promoting filamentary persistence into a universal class selector. The accompanying failure alternatives and spectator-indexed classification supply the first certified entry and the strict interface for a future UMD Universality Atlas.

Ссылка для цитирования:

Nesen O. I. 2026. From Persistent Filamentary Phases to Full Renormalization-Group Universality in Universal Modular Dynamics. PREPRINTS.RU. https://doi.org/10.24108/preprints-3116540

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