canonical-core

How Everything Connects

The five papers in Canonical Core form a layered, interlocking framework. Here’s the conceptual map:

The Stack

┌─────────────────────────────────────┐
│ 05: QPS-GR Mapping                  │  ← Engineering layer
│     (strain, clocks, visibility)    │
├─────────────────────────────────────┤
│ 04: Phase-Lift (⧉, PROs)            │  ← Phase structure
│     (branch semantics)              │
├─────────────────────────────────────┤
│ 03: Curve Memory (CM/CMA)           │  ← Memory layer
│     (path + derivative encoding)    │
├─────────────────────────────────────┤
│ 02: Adaptive-π Geometry             │  ← Geometric layer
│     (πₐ as field)                   │
├─────────────────────────────────────┤
│ 01: ARP/AIN                          │  ← Engine layer
│     (adaptation, resistance)        │
└─────────────────────────────────────┘

How to Read Them

1. Start with ARP/AIN (Paper 01) – This defines the core adaptation mechanism: how systems respond to strain, how resistance and impedance shape behavior.

2. Add Geometry (Paper 02) – Adaptive-π shows what happens when π itself is adaptive: geometry bends with context.

3. Add Memory (Paper 03) – Curve Memory encodes the path and derivative history, creating a “memory object” that systems can query.

4. Add Phase Structure (Paper 04) – Phase-Lift (⧉) adds branching semantics: how phase transitions create new branches, and what objects (PROs) survive across them.

5. Map to Physics (Paper 05) – QPS-GR mapping connects the abstract framework to quantum phase space and general relativity, with explicit engineering constraints.

Key Dependencies

• CM requires ARP/AIN – Memory encoding depends on adaptation response
• Phase-Lift requires CM – Phase branches carry memory forward
• QPS mapping requires all four – The engineering layer assumes adaptation, geometry, memory, and phase structure

Canonical Notation

See notation.md for the full list, but key symbols:

• ⧉ = Phase-Lift operator (prefix, phase branch)
• πₐ = Adaptive π (field, not constant)
• CM = Curve Memory object
• CMA = Curve Memory Alphabet (encoding)
• PROs = Phase-Resistant Objects
• τ_coh = Coherence time
• V_floor = Visibility floor

What This Framework Does

• Unifies adaptation, geometry, and memory
• Defines phase-structured branching (not just “forking”)
• Provides engineering semantics for quantum-GR correspondence
• Establishes canonical notation for future work

What It Doesn’t Do (Yet)

• Full experimental validation (future work)
• Worked examples with real datasets (coming in v0.2)
• Visualization tools (planned for /code)

Related Repositories

This repository contains the theoretical framework and canonical papers. For code implementations, graphs, and experiments, see:

• RDM3DC organization on GitHub – Contains multiple repositories with:
  • ARP – Code implementations for Adaptive Resistance/Impedance Networks
  • Additional repositories with visualizations, graphs, and experimental results

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

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Next: Read the glossary for detailed definitions.

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