canonical-core

Canonical Core

A unified theoretical framework for adaptive systems, geometric computation, and phase-structured branching.

This repository contains the foundational white papers for:

https://rdm3dc.github.io/canonical-core/

📚 Papers (Recommended Reading Order)

  1. ARP/AIN: Adaptive Resistance and Adaptive Impedance Networks
    The core adaptation engine: how systems respond to strain and memory.

  2. Adaptive-π Geometry and Adaptive-π Calculus
    πₐ as a genuinely new adaptive phase-period field that defines the local unit of phase wrap; geometric implications and phase-theoretic applications.

  3. Curve Memory and Curve Memory Alphabet
    How paths and derivatives encode memory; the CMA encoding system.

  4. Phase-Lift, PR-Root, and PROs
    ⧉ operator, phase-structured branching, and Phase-Resistant Objects.

  5. QPS-GR: Strain, Clock Offset, Visibility, and Refresh Mapping
    Engineering layer mapping quantum phase space to general relativity.

🧭 Quick Start

New to this work? Start with Paper 01 (ARP/AIN), then follow the numbered order.

Looking for notation? See docs/notation.md for canonical symbols (⧉, πₐ, τ_coh, V_floor, etc.).

Want the big picture? Read docs/index.md for how all five papers connect.

🔑 Key Concepts

Symbol Meaning
⧉ Phase-Lift operator (prefix, phase-structured branch)
πₐ Adaptive-π field (adaptive phase-period field, genuinely new concept)
CM Curve Memory (path + derivative memory object)
CMA Curve Memory Alphabet (encoding system)
PROs Phase-Resistant Objects (survive phase transitions)
τ_coh Coherence time
V_floor Visibility floor
QPS Quantum Phase Space

See the full glossary for detailed definitions.

📖 Citation

If you use this work, please cite:

@software{canonical_core_2026,
  author = ,
  title = {Canonical Core: ARP/AIN, Adaptive-π, Curve Memory, Phase-Lift, and QPS Mapping},
  year = {2026},
  url = {https://github.com/RDM3DC/canonical-core},
  version = {0.1.0}
}

Or use GitHub’s “Cite this repository” button (top right).

📂 Repository Structure

canonical-core/
├── README.md              ← You are here
├── LICENSE                ← CC BY 4.0 (text) or MIT (code)
├── CITATION.cff           ← Enables GitHub citation button
├── CHANGELOG.md           ← Version history
├── papers/                ← The five canonical white papers
│   ├── 01-arp-ain.md
│   ├── 02-adaptive-pi-geometry.md
│   ├── 03-curve-memory-cma.md
│   ├── 04-phase-lift-pros.md
│   └── 05-qps-gr-refresh-mapping.md
├── docs/                  ← Glossary, notation, roadmap
│   ├── index.md           ← How everything connects
│   ├── glossary.md        ← All symbols and terms
│   ├── notation.md        ← Canonical notation rules
│   └── roadmap.md         ← Future extensions
├── figures/               ← Diagrams and visualizations
├── code/                  ← (Optional) Prototypes and implementations
└── experiments/           ← (Optional) Notebooks, datasets, logs

🔗 Related Repositories

This is the canonical reference repository for the theoretical papers. For code implementations, graphs, and experiments, see the RDM3DC organization on GitHub, which includes:

Visit github.com/RDM3DC to explore all related projects.

🛠️ Status

🔒 Canonical Notation Rules

  1. ⧉ is the Phase-Lift operator – prefix, phase-structured branch
  2. π remains constant (3.14159…) – πₐ is the adaptive field
  3. CM is a memory object – encodes path + derivative history
  4. QPS mapping is an engineering layer – explicit assumptions about quantum-GR correspondence

See docs/notation.md for the full canon.

🗺️ Roadmap

See CHANGELOG.md for version history.

📜 License

Papers (text): CC BY 4.0 – Free to use with attribution
Code (if any): MIT License

🤝 Contributing

This is a canonical reference repository. If you find errors or have questions:

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