TORUS Ladder Dynamics X: Out-of-Sample Validation of Predictive Gates for Closure Universality

Background and Motivation Earlier TORUS Ladder Dynamics releases (I–VIII) demonstrated that closure phenomena emerge robustly in certain ordered systems, survive strict null controls, and are sensitive to construction independence. TORUS Ladder Dynamics IX extended this work across multiple domains, revealing that universality is conditional, not universal in the naïve sense. The natural next scientific question is not “does closure appear?” but rather: Can closure behavior be predicted from domain structure before ladders are built? Zenodo X answers this question. Scientific Contract (unchanged from IX unless stated) All notebooks in this release enforce: Absolute domain isolationNo ladder spans multiple domains. No pooling of endpoints across domains. Contamination preventionObserved metrics are computed only from eligible parent ladders.Null children exist solely to form baseline distributions. Registry-first provenanceEvery ladder instance is tracked via ladder_id, with all downstream artifacts referencing this registry. Strict preregistered eligibilityA ladder is eligible iff at least one N in the prereg window yields a finite RMS under the minimum-deltas constraint. Overview of Notebooks in This Release Notebook 34 — Predictive Gate Freezing Inputs: IX artifacts only. Output: predictive_gates_34.json Defines X-34-v1: A minimal entropy-based gate (with locked thresholds). No retraining or parameter tuning allowed downstream. Notebook 35 — Out-of-Sample Domain Generation Inputs: domains_pack_for_notebook35.zip predictive_gates_34.json Generates new biochemical, geophysical, and synthetic control domains. Computes domain features. Applies the frozen gate before ladder generation. Produces ladder registries and audit artifacts. Notebook 36 — Endpoint Validation Inputs: Notebook 35 outputs. Computes UI, NSS, bootstrap null distributions. Produces prediction-vs-observation validation tables. Notebook 37 — Quantum Domain Add-On Inputs: domains_pack_for_notebook37_quantum_addon.zip Same frozen gate from Notebook 34. Adds: Hydrogen energy eigenvalue domain. Adjacent energy-gap domain. Synthetic harmonic oscillator control. Runs full ladder + null pipeline again. Confirms predictive performance on quantum-derived systems. Key Findings Predictive gates frozen in IX generalize to new domains without retraining. Quantum-derived domains exhibit strong null separation (NSS = 1.0) but only achieve separating classification when parent consensus (UI) is sufficiently high—demonstrating correct constraint behavior. Synthetic controls behave exactly as expected, validating the gate’s discriminative power. Failure cases remain informative rather than pathological, reinforcing falsifiability. Why This Matters TORUS Ladder Dynamics X demonstrates that closure universality is not merely observable—it is predictable under constrained conditions. This elevates TORUS from a descriptive framework to a testable structural theory of ordered constraint systems, opening the door to causal classification and forward prediction. 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. IX Introduces outcome-blind domain structure as a predictive constraint on closure behavior.