Multiscale Structural Regime Benchmark

This repository documents an empirical phenomenon observed in coupled dynamical systems:
the emergence of a multiscale structural regime that persists under strong null models.

No method or model is proposed here.

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Problem

When two systems appear to overlap, it is unclear whether the overlap reflects:

• genuine structural coupling, or
• coincidental effects such as shared marginals, density, or spatial support.

Existing tools typically analyze individual systems, signals, or causal influence,
but do not directly address whether a joint structure truly exists across scales.

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Benchmark Question

Is there a parameter regime in which the intersection between two systems exhibits multiscale structural persistence that cannot be explained by strong null models?

This benchmark exists to document that regime empirically.

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What Is Included

This repository contains aggregated empirical results only, organized under results/:

• Gap analysis between the real system and null controls
• Robustness checks across:
  • multiple random seeds
  • multiple spatial resolutions
  • bootstrap confidence intervals
• Parameter sweep identifying the regime where separation emerges

The key outputs are:

• copitolo_prego.png / copitolo_prego.json
  Empirical separation between REAL and NULL systems across a parameter sweep.

• copitolo_report.json
  Summary statistics including confidence intervals and robustness metrics.

• copitolo_runs.csv
  Per-run diagnostics (index estimates, fit quality, proxies).

• copitolo_sweep.json
  Regime-level behavior as the control parameter varies.

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Null Models Used

Two strong null models are used to rule out trivial explanations:

1. Marginal-preserving null (Y-permutation)
   Preserves marginal distributions while destroying correlation.

2. Support-preserving null (occupancy-preserving)
   Preserves coarse spatial support while destroying micro-geometry.

The observed regime separates from both nulls consistently.

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Interpretation Guide

• Values above zero in the reported gap plots indicate that the real system exhibits stronger multiscale structure than the corresponding null model.

• Persistence across scales, seeds, and confidence intervals indicates a regime-level phenomenon rather than noise or artifact.

This repository intentionally avoids proposing a specific metric or algorithm. It documents the phenomenon itself.

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What This Is Not

• This is not a classifier.
• This is not a predictive model.
• This is not a learning-based system.
• This repository does not include the mechanism used to detect the regime.

The focus is on existence and robustness, not implementation.

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Data Availability

Raw point clouds (Φ⁺, Φ⁻) and internal detection mechanisms are not included at this stage.

The reported results are aggregated, regime-level, and do not depend on any specific realization of the underlying systems.

Future releases may include reference datasets.

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Status

This benchmark is intended to:

• establish the existence of a multiscale structural regime,
• provide a neutral testbed for independent interpretation,
• and invite alternative explanations or detection approaches.

The phenomenon documented here remains regardless of the method used to analyze it.