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Structural Isomorphism

Do systems from radically different scientific domains share the same underlying mathematical structure?

A pre-registered, cross-domain validation pipeline for universality classes in complex systems. One shared Python module (v4/lib/soc_pipeline.py, frozen at commit 7ee228c) is applied unchanged to thirteen independent datasets spanning geology, finance, neuroscience, ecology, banking history, software communities, power grids, and highway traffic — and a growing set of adversarial pre-registrations that have produced PASS, INCONCLUSIVE, and FAIL verdicts without per-system tuning.

Live demos

Product URL What it does
Structural Search beta.structural.bytedance.city Perplexity-style natural-language search over the cross-domain knowledge base. Streamed answer, citation cards, similar phenomena across domains.
Phase Detector phase.bytedance.city 100 tagged companies + 500-ticker S&P 500 walk-forward backtest. Research preview — not investment advice.

Get started in 30 seconds

git clone https://github.com/dada8899/structural-isomorphism.git
cd structural-isomorphism
python -m venv .venv && source .venv/bin/activate
pip install -e .
v4 status                  # show pass/fail across 13 systems + 4 nulls

Or run the pipeline programmatically:

from v4.lib.soc_pipeline import fit_clauset_powerlaw

result = fit_clauset_powerlaw(observations=my_event_sizes)
print(f"alpha = {result.alpha:.3f}, xmin = {result.xmin}")
print(f"vs lognormal LR = {result.lr_lognormal:.3f}")

See Getting Started for the full walkthrough.

Three artifacts

  • SOC pipeline

    A single shared Clauset MLE module (v4/lib/soc_pipeline.py, 339 LOC). Runs unchanged across 13 empirical systems and 4 null controls. Reports power-law vs lognormal vs exponential, with pre-registered exponent bands.

    Pipeline docs

  • SIBD-63 dataset

    63 A-level cross-domain candidate pairs, each with shared equations, variable mappings, and provenance. Curated by a multi-model LLM critic ensemble (Claude · DeepSeek · Kimi · GLM-5).

    Zenodo DOI

  • Phase Detector

    A research-preview consumer product. Tags 100 public companies with their current dynamical phase (stable / accumulating / near-critical / reversed / recovering) against nine universality patterns.

    phase.bytedance.city

What this project is

  • A reproducible pipeline. Clauset–Shalizi–Newman 2009 MLE power-law fits with KS-optimal \(x_{\mathrm{min}}\), bootstrap confidence intervals, Vuong likelihood ratios against lognormal and exponential, Omori–Utsu temporal stacking, matched-\(n\) synthetic null controls, log-binned density estimation, and Bayesian Information Criterion model comparison — all in one frozen module.
  • A pre-registration discipline. Predicted exponent bands are committed to git before data acquisition. Once pushed, bands cannot be silently widened post hoc.
  • A cross-judge ensemble. Multi-model taxonomy review (B3) and cross-judge calibration (B4) catch over-claiming on individual systems.
  • A live phase detector. D1 ships the pipeline as a queryable service with a 7-event SSE orchestrator for streaming verdicts.

Citation

If you reference this work, please cite the unified pipeline preprint:

@unpublished{structural_isomorphism_2026,
  author = {dada8899},
  title  = {Unified pre-registered validation of self-organized criticality
            across thirteen complex systems},
  year   = {2026},
  note   = {Preprint at \url{https://github.com/dada8899/structural-isomorphism}}
}

Status

This is a research repository under active development. The pipeline library is frozen at commit 7ee228c; phase papers and pre-registrations continue to accrete. See Papers for the current preprint set.