TORUS Ladder Dynamics IX: Predictive Gates, Topology Effects, and Rung Participation in Closure Universality

Overview TORUS Ladder Dynamics IX marks a transition in the TORUS Ladder series from replication to explanation.Earlier releases (I–VIII) established that closure universality can emerge under strict preregistration,independent ladder construction, and matched structural nulls, and that such behavior generalizes acrossmultiple ordered domains. Release IX introduces a new abstraction layer:outcome-blind domain structure as a predictive constraint on closure behavior. This release consists of three notebooks: - Notebook 31 — Generator + Domain Features - Loads frozen, auditable ordered domains - Computes preregistered outcome-blind structural features - Generates independent parent ladders per domain - Constructs matched null children per eligible parent - Writes registry-first artifacts with full provenance - Notebook 32 — Endpoints-Only Audit - Consumes only Notebook 31 artifacts - Computes per-domain primary endpoints under Fix-A contamination prevention - Produces consensus scales, universality indices, null baselines, and separation metrics - Writes audited outputs with cryptographic hashes - Notebook 33 — Exploratory Addendum (IX-E) - Evaluates topology (linear vs cyclic adjacency; TORUS-of-tori) - Computes rung participation signatures (OSQN-like behavior) - Produces feature–outcome basin maps (TORUS-brot) - Generates hypothesis-forming diagnostics without modifying preregistered IX claims Preregistered Methodological Contracts Domain IsolationNo ladder spans multiple domains. Cross-domain comparisons are side-by-side only. Contamination PreventionObserved metrics are computed exclusively from eligible parent ladders:- Observed pool: is_null == False AND eligible == True- Null pool: is_null == True AND eligible == True AND parent_ladder_id ∈ observed parentsNull children are never permitted in observed calculations. Registry-First ProvenanceEvery ladder instance (parent or null) is assigned a persistent ladder_id.All downstream analyses reference ladder_id exclusively, preventing post hoc selection. Eligibility GatesA ladder is eligible if at least one preregistered N in the analysis window produces a finite RMSunder a strict minimum-deltas constraint. Domains The following domains are evaluated identically under the IX pipeline: - PHYSICAL_CONSTANTS Frozen ordered physical constants domain derived from established CODATA-based ordering rules. - PRIME_GAPS Deterministic prime gap sequence with preregistered ordering derived from OEIS sources. - H_SPECTRA Hydrogen spectral line domain derived from NIST Atomic Spectra Database data using an outcome-blind ordering rule. Significance TORUS Ladder Dynamics IX demonstrates that closure universality is conditioned by measurable structuralproperties of ordered systems, rather than being a generic artifact of ordering itself.By introducing domain-level features, topology sensitivity, and rung participation diagnostics,this release establishes the basis for preregistered predictive tests in subsequent TORUS Ladder Dynamics work. 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. VIII Introduces outcome-blind domain feature extraction, topology-conditioned ladder dynamics, and rung participation signatures as explanatory tools for closure universality.