TORUS Ladder Dynamics VIII: Cross-Domain Tests of Closure Universality in Ordered Constraint Systems

Overview TORUS Ladder Dynamics VIII represents a methodological pivot in the TORUS Ladder Dynamics series. Whereas prior releases (I–VII) established closure behavior and construction-rule invariance within a single ordered domain (physical constants), this release tests whether similar behavior generalizes across distinct ordered domains. Methodology We introduce a domain-pack abstraction in which each domain is defined by a frozen ordered numeric sequence with explicit provenance. Independent parent ladders are constructed within each domain using preregistered, adjacency- and inclusion-altering rules. For each eligible parent ladder, matched null ladders are generated via marginal-preserving permutations. All ladder instances are recorded in a registry, and all downstream analysis references ladders exclusively by identifier to prevent post hoc selection. Domains PHYSICAL_CONSTANTS: an ordered constants domain derived from established TORUS targets. PRIME_GAPS: a deterministic mathematical sequence with irregular adjacency structure. H_SPECTRA: an empirical resonance-based domain derived from hydrogen spectral lines. Endpoints Primary endpoints (Universality Index and Null-Separation Score) are computed in a downstream audit-only notebook that consumes only generator artifacts. Observed metrics are calculated exclusively from eligible parent ladders; null ladders serve only as matched baselines and never enter observed pools. Findings Closure universality is found to be domain-conditional. Strong null-separated consensus emerges in the spectral domain, conditional structure appears in prime gaps, and physical constants exhibit consensus without null separation under cross-domain abstraction. These results rule out both indiscriminate universality and constants-only explanations. Significance TORUS Ladder Dynamics VIII constrains TORUS into a predictive framework: closure behavior depends on the structural properties of ordered systems. This sets the stage for subsequent releases focused on constraint classification and predictive gates for universality. What TORUS Ladder Dynamics I–V already proved (cumulatively) Release What it actually locked in I Ladder closure exists and is detectable II Closure has structural mechanisms and failure modes III Closure is invariant under many deformations but brittle under specific ones IV Recurrence emerges from order mutation, not tuning V Closure can be discriminated from nulls via calibrated recurrence gates VI Closure in composite ladders persists under cyclic topology and exhibits emergent relational modes VII Constants show a dominant, non-null-explainable consensus scale under independent constructions.