The Ultrametric Sieve

A Consilience of Number, Nature, Mind, and Form

About

This publication proposes a foundational shift in the representation of integers: from decimal digit-strings to valuation vectors recording prime exponents. The "ultrametric sieve" reveals that integers form an infinite-dimensional lattice whose geometry is the product of p-adic Bruhat-Tits trees.

Contents

• ULTRAMETRIC-SIEVE.md — Complete source (Markdown, 32 sections)
• ULTRAMETRIC-SIEVE-v1.0.0.pdf — Publication-quality PDF (13 pages)
• ARTIFACT-MANIFEST.json — Checksums and metadata for all artifacts

Sections

1. The Copernican Move: From Digits to Factors
2. Why "Ultrametric"
3. The Integers as an Infinite-Dimensional Lattice
4. p-adic Geometry and the Bruhat-Tits Trees
5. The Adele Ring and the Chinese Remainder Theorem
6. The Riemann Zeta Function and the Explicit Formula
7. The abc Conjecture as an Uncertainty Principle
8. Ratios and Cross-Ratios
9. Spin Glasses and Ultrametricity
10. Holographic Duality and p-adic AdS/CFT
11. Quantum Chaos and the Riemann Spectrometer
12. Signal Processing and Photonic Devices
13. Cryptography and Data Integrity
14. Machine Learning and Representation
15. The Ultrametric Mind (Cognitive Science)
16. Sacred Numbers as Cognitive Attractors 17-20. Monetary Economics 21-23. Music and Harmonics
17. Laws of Form: The Primitive of Primitives 25-26. Embryology and Ecology 27-28. Consciousness: The Sieve Perceiving Itself 29-32. Eschatology, Praxis, and Synthesis

Citation

Rowan Quni-Gudzinas (QNFO/QWAV). "The Ultrametric Sieve: A Consilience of Number, Nature, Mind, and Form." 2026. DOI: 10.5281/zenodo.20756216

License

QNFO Unified License Agreement (QNFO-ULA)

Repository

https://github.com/rwnq8/ultrametric-sieve