TORUS Ladder Dynamics VII: Cross-Ladder Universality Under Preregistered Eligibility Constraints

This release tests whether discrete closure scales identified in earlier TORUS Ladder studies persist as cross-ladder invariants when ladders are generated by independent construction rules, rather than by reruns or parameter tuning. Using a preregistered definition of “independent ladder,” registry-first provenance, and matched structural null controls, we measure whether a consensus closure scale (N) recurs across independent ladders and separates from null expectations under the same scoring and recurrence diagnostics used in prior releases. No interpretive or dimensional claims are made at this stage. The goal is to establish (or falsify) universality as a necessary precondition for later work on dimensional anchoring. What Zenodo 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 What TORUS Ladder Dynamics VII adds This release locks three preregistered constraints to prevent drift: 1) Independent ladder definition (contracted) Independent ladders must be generated by construction rules that change ordering or inclusion structure (not seed reruns). 2) Primary endpoints (anti–metric shopping) - Universality Index (UI): fraction of eligible parent ladders only in which a consensus N appears in the top-k list and passes a preregistered recurrence gate. - Null-Separation Score (NSS): bootstrap tail probability of observed UI against matched nulls. 3) Registry-based artifact design (anti–cherry-picking)All ladder instances (including nulls) are listed in `ladder_registry_27.csv`, and every output references `ladder_id`. Methods overview (high level) - Ladders are constructed using preregistered independent construction families (and optional outcome-blind metadata subset rules).- An eligibility gate restricts primary endpoint computation to ladders that yield at least one finite RMS score in the preregistered N window.- Matched nulls are generated per eligible parent ladder by shuffling its omega (preserving marginals while breaking adjacency), and are used exclusively as a baseline distribution for bootstrap comparison.- UI (observed, parent-only) and NSS (bootstrap comparison against matched nulls) are computed strictly from preregistered steps; other diagnostics are reported as secondary. Files Core notebooks- TORUS_Ladder_Dynamics_VII_Notebook_27.ipynb Ladder construction, registry formation, eligibility enforcement, and diagnostic summaries. - TORUS_Ladder_Dynamics_VII_Notebook_28.ipynb Parent-only universality estimation with matched-null bootstrap baselines (inference only). Primary endpoint outputs (Notebook 27)- ladder_registry_27.csv — Canonical registry of all ladder instances, including parent/child relationships.- cross_ladder_summary_27.csv — Ladder-level summaries and top-k closure lists.- primary_endpoints_27.csv — Preliminary endpoint summaries from ladder generation.- universality_spectrum_27.csv — Closure frequency spectrum across generated ladders.- null_distributions_27.csv — Null diagnostics used during construction and validation. Secondary diagnostics (Notebook 27)- rung_participation_signature_vii_27.csv — Rung participation stability signatures.- operator_probe_summary_27.csv — Operator-level probe diagnostics. Primary endpoint outputs (Notebook 28) (Computed exclusively from Notebook 27 outputs; no ladder regeneration) - primary_endpoints_28.csv — Final parent-only UI, NSS, consensus N, and bootstrap statistics.- null_distributions_28.csv — Matched-null bootstrap distribution used for NSS.- universality_spectrum_28.csv — Observed parent-ladder closure spectrum. Audit & reproducibility artifacts- notebook27_audit.json — SHA-256 hashes, byte sizes, and summary statistics for all inputs and outputs used in Notebook 27. - notebook28_audit.json — SHA-256 hashes, byte sizes, and summary statistics for all inputs and outputs used in Notebook 28. Shared reproducibility artifacts(Applies to Notebooks 27 & 28) - README.md - requirements.txt - CITATION.cff - LICENSE.txt - SHA256SUMS.txt