Automorph Inc. Introduces Six Birds (preprint)

One Calculus of Emergence for Life, Physics, and Mathematics

Wilmington, DE, Jan. 26, 2026 (GLOBE NEWSWIRE) -- A new preprint, Six Birds: Foundations of Emergence Calculus, introduces a compact mathematical framework for a question that appears across science and engineering: how do stable “things” and stable “laws” arise when we only ever see the world through limited interfaces?

The paper proposes Six Birds (P1–P6): six closure operations that recur whenever a system builds a coherent theory from partial observation. The central claim is expansive but concrete: the same emergence mechanics that we usually associate with life also govern the birth and evolution of theories themselves. In this view, a “theory” is not just a description; it is a repeatable completion of observations into stable objects and rules. When a theory is genuinely stable, applying the same completion again shouldn’t change what you get.

One of the paper’s most striking results is that nothing stays constant once you extend a theory. The work proves a “Nothing Stays Constant” lemma: when you add a new yes/no distinction to a coarse description of a finite world, the new distinction is almost never redundant. With overwhelmingly high probability, it splits at least one previously indistinguishable category—meaning the refined theory is a strict extension of the old one. Put simply: once you start adding new predicates, you don’t merely rename the world—you create new stable distinctions that force the theory’s vocabulary (and its effective “laws”) to evolve.

This gives a precise, operational way to talk about novelty in theory-building: new variables aren’t decorations. Under mild assumptions, new distinctions almost surely change what can be said, what counts as an object, and which regularities can be compressed into law-like statements.

Quote (author):
“Plato imagined reality written in timeless Forms. Six Birds says reality keeps building new theories: new objects appear, new variables become meaningful, and new laws emerge as the layer stabilizes. That’s true for life—and just as true for physics and mathematics.” — Ioannis Tsiokos

This work is a research preprint and has not yet been peer reviewed. An immutable copy of the preprint is archived on Arweave.

Press Inquiries

IOANNIS TSIOKOS
ioannis [at] automorph.io
+306936576875
https://www.automorph.io
1207 Delaware Ave #4131

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