a universal recipe for phase transitions, in twelve worlds

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Most books begin with a promise. This one begins with an observation: systems tip. Stocks tip, magnets tip, patients tip, quantum computers tip — the examples differ, the process does not. There is a mathematics for it. It is surprisingly simple. It fits in three lines of Python. This book explains how to find the moment of tipping **before** it happens. Four steps, three lines of code. The same three lines locate the Curie point of an iron magnet near 1043 Kelvin, the regime shift of the S&P 500 in the week Lehman Brothers fell in August 2008, the noise level at which a quantum computer stops being one, and the onset age of a hereditary protein disease. Several worlds, one recipe. I am aware this sounds suspicious. The first half of the book is therefore written for the suspicious — those readers tend to stay with you longer in the end.

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What is in it

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A method. An explanation of why it works. Twelve worked examples from twelve worlds. Four open conjectures, which the reader is hereby cordially invited to disprove. A companion library called `sigma-c-framework` that has all of this in code.

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What is not in it

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A theory of everything. The promise that you will, after reading it, make money on the stock market. A plan for how to get back from the unpleasant side of a tipping point to the pleasant one. I have not found the second part. Perhaps you have.

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Who it is for

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Anybody who has ever turned a knob and measured something while doing so. Anybody who can add, subtract, and remain occasionally suspicious. No degree is required; Greek letters are introduced one at a time.

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Practical

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197 pages. First edition, May 2026. Buckenhof, Bavaria.

Licence: AGPL-3.0-or-later (free) or commercial (on request).

Companion library on PyPI: `pip install sigma-c-framework`.

Empirical anchor: *AVS Quantum Science* **8**, 013804 (2026).

 

[PDF English] · [PDF Deutsch] · [PDF Français] · [PDF Español] · [PDF 日本語] 

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