The Coralia Sequence

What is this?

A mathematically defined set of integers with unusual structural properties, plus code to reproduce and test those properties.

C = {0, 1, 2, 3, 5, 7, 9, 12, 15, 23, 30, 35}

Why does it exist?

It began as a pure math question: Is there a unique 12-element subset of {0,...,35} satisfying certain structural constraints?

Yes. Paper 1 proves it.

Paper 2 shows the axioms have predictive content: they predict where certain mathematical constants land when rounded to integers.

What can I do with it in 5 minutes?

git clone https://github.com/coralia-io/coralia-sequence.git
cd coralia-sequence
python examples/landing_demo.py

Output:

Where do these land?

  e² = 7.39 → lands on 7 ∈ C
  e^π = 23.14 → lands on 23 ∈ C
  φ⁵ = 11.09 → lands on 11 ∈ not C

Where do I go next?

I want...	Go to...
The math	core/papers/
Simple experiments	examples/
Domain applications	sandbox/
Reusable code	interfaces/
To know if this is for me	WHO_THIS_IS_FOR.md

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Structure

Directory	Status	Contents
core/	Authoritative	Library, papers, proofs, tests
interfaces/	Reusable	Grammars, classifiers, exports
sandbox/	Exploratory	Domain applications
examples/	Entry point	Simple demos

See SCOPE.md

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Papers

1. Paper 1: Existence and Uniqueness — DOI
2. Paper 2: Empirical Content of the Axioms — DOI

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Author

Emma Cecile · ORCID

License

MIT