FREE THE MATH

// WHAT IS THIS MATH?

It predicts tipping points. When does a power grid go from stressed to blacked out? When does a heartbeat go from irregular to dangerous? When does a market correction become a crash?

Turns out these are the same question, mathematically. Different fields figured that out at different times — and mostly didn't notice each other doing it.

// THE PATTERN

Between 1935 and 2025, researchers in at least six fields developed mathematical tools for detecting when systems are about to tip — largely in parallel:

• Physics (1944) — correlation length
• Biology (1994) — heart rate scaling
• Finance (1994) — market memory
• Machine Learning (2001) — neural network stability
• Power Grids (2004) — cascade prediction
• Traffic Flow (1935/2004) — congestion tipping points

Each field published in its own journals, invented its own terminology, and cited its own literature. Cross-domain awareness was minimal until after 2010.

// WHAT DID THIS COST?

A cardiologist in 1996 could have used techniques a physicist published in 1971. But she'd have had to find a statistical mechanics journal, recognize the connection through completely different notation, and translate it to biological data. That almost never happened.

So the tools got reinvented. Multiple times. In separate journals behind separate paywalls. Meanwhile the applications waited.

// THE RESEARCH

The full analysis is documented in a paper on arXiv, endorsed by Didier Sornette (ETH Zurich).

If you're short on time, start with Appendix B — the plain-language summary. You don't need the technical sections to understand what was found and why it matters.

// THE BOTTOM LINE

The math works. It's been validated across domains for decades. And it's fundamental — derivable from first principles, not proprietary to any field.

It should be free.

// COMMON QUESTIONS

Is this actually new?
The individual discoveries are known. What's new is documenting the full convergence pattern — classifying each instance by type and providing citation network evidence that these fields remained siloed for decades.

How is this different from Sornette (2004)?
Sornette's textbook is the most important prior synthesis — we cite it extensively. Our contribution adds a discovery classification taxonomy and quantitative citation analysis showing parallel development continued even after his synthesis.

Why arXiv and not a journal?
arXiv is how physics papers reach the community. The paper is endorsed by Didier Sornette of ETH Zurich. Journal review is a separate, longer process — arXiv makes the work immediately accessible, consistent with our argument.

What's the conflict of interest?
Fully disclosed. The authors developed a framework (Appendix A) classified as "unvalidated candidate". The convergence pattern in the main paper stands on six to nine other discoveries.

What about Catastrophe Theory?
Related topic. The current paper doesn't cover it. A future revision may.

Were these really independent discoveries?
Degree of independence varies — the paper classifies each case. Some fields had zero cross-citation for decades. Others had partial awareness but still re-derived the tools from scratch.

// CONTACT