📘 PHDM Nomenclature Reference - Canonical Definitions

last-synced: 2026-02-16T07:29:14.387Z

PHDM Nomenclature Reference

Version: 1.0.0

Date: February 10, 2026

Status: Authoritative

Purpose: Single source of truth for PHDM naming conventions across the entire SCBE-AETHERMOORE codebase and documentation.

Canonical Definition

PHDM = Polyhedral Hamiltonian Defense Manifold

This is the only acceptable expansion for the PHDM acronym across all documentation, code comments, presentations, and patent filings.

What It Actually Does

The implementation in src/harmonic/phdm.ts performs:

Polyhedral: Traverses 16 canonical polyhedra (5 Platonic, 3 Archimedean, 2 Kepler-Poinsot, 6 others)
Hamiltonian: Follows Hamiltonian paths through the polyhedral graph
Defense: Generates HMAC key chains from topological invariants for intrusion detection
Manifold: Monitors state deviations against a 6D geodesic spline in hyperbolic space

Geometry Model: Poincaré ball model (NOT half-plane)

Retired Names (DO NOT USE)

❌ Poincare Half-plane Drift Monitor

Where it appeared: CLAUDE.md:74, CLAUDE.md:217, STRUCTURE.md:72

Why retired: Wrong geometry model—the implementation uses the Poincaré ball model, not the half-plane model. The geometry is polyhedral, not half-plane.

Status: REMOVE from all documentation

❌ Piecewise Hamiltonian Distance Metric

Where it appeared: SCBE_PATENT_PORTFOLIO.md:121

Why retired: This describes a sub-operation (distance calculation), not the full module. Too narrow in scope.

Status: REMOVE from all documentation

❌ Polynomial Hamiltonian Detection Module

Where it appeared: SCBE-AETHERMOORE-v3.0.0/tests/harmonic/phdm.test.ts:2 (legacy)

Why retired: Wrong word entirely—should be “Polyhedral” not “Polynomial”

Status: REMOVE from all legacy references

❌ Polyhedral Hamiltonian Dynamic Mesh

Where it appeared: python/scbe/brain.py:4, multiple Notion pages

Why retired: “Dynamic Mesh” describes the cognitive architecture specialization (brain tissue), not the core security function. This caused confusion between the security layer and the cognitive layer.

Status: Deprecated—use context-specific alias below instead

❌ Polyhedra-Based Geometric Defense Manifold

Where it appeared: Patent documentation

Why retired: Redundant phrasing—”Polyhedral” already means “based on polyhedra”

Status: REMOVE from patent docs

❌ Polyhedral Coherence Verification

Where it appeared: Layer descriptions

Why retired: Too vague—doesn’t capture the Hamiltonian path structure

Status: REMOVE from layer documentation

❌ Polyhedral Hamiltonian Density Matrix

Where it appeared: Technical Appendix C

Why retired: “Density Matrix” is quantum mechanics terminology that doesn’t apply here. Causes confusion with actual quantum computing concepts.

Status: REMOVE from technical appendices

Context-Specific Aliases (ALLOWED)

When PHDM is used in specialized contexts, you may clarify the role with an alias, but always include the full canonical name first.

✅ PHDM Cognitive Lattice

Context: When discussing the brain architecture implementation in python/scbe/brain.py

Usage: “The PHDM (Polyhedral Hamiltonian Defense Manifold) serves as a cognitive lattice in the AetherBrain architecture…”

Purpose: Clarifies that PHDM is being used as the substrate for AI reasoning, not just security

✅ PHDM Brain Substrate

Context: AI cognitive architecture discussions

Usage: “The PHDM brain substrate organizes reasoning into 16 polyhedral nodes…”

Purpose: Emphasizes the cognitive function without changing the acronym

✅ PHDM Security Container

Context: When contrasting cognitive vs. security roles

Usage: “PHDM functions as both a cognitive lattice (internal reasoning) and a security container (boundary enforcement)…”

Purpose: Clarifies the dual-role nature

Migration Guide

Code Files to Update

Notion Pages to Update

🧠 PHDM as AI Brain Architecture - The Geometric Skull — Update all references to “Dynamic Mesh”
SCBE-AETHERMOORE + PHDM: Complete Mathematical & Security Specification — Update Chapter 6 title
Technical Appendix C: PHDM Consciousness Encoding — Remove “Density Matrix” terminology
Patent documentation pages — Standardize all PHDM references

Standard Code Comment Template

Use this header for all PHDM-related files:

/**
 * PHDM: Polyhedral Hamiltonian Defense Manifold
 * 
 * Traverses 16 canonical polyhedra in Hamiltonian paths to generate
 * HMAC key chains from topological invariants (Euler characteristic, genus)
 * and monitors state deviations against a 6D geodesic spline for intrusion detection.
 * 
 * Geometry: Poincaré ball model (hyperbolic space)
 * Security: Quantum-resistant cryptographic containment
 * 
 * @see https://notion.so/phdm-spec for full specification
 */

FAQ

Q: Why not keep “Dynamic Mesh” since it’s more descriptive for the brain architecture?

A: “Dynamic Mesh” describes how PHDM is used in one context (cognitive architecture), not what PHDM is. The module’s primary function is defense/security. Use “PHDM Cognitive Lattice” as a clarifying phrase when needed.

Q: Can I use “PHDM” alone without expanding it?

A: Yes, but the first occurrence in any document should expand it as “PHDM (Polyhedral Hamiltonian Defense Manifold)” for clarity.

Q: What about presentations and marketing materials?

A: Always use the canonical expansion. If you need a simplified explanation, say: “PHDM creates a geometric cage that makes dangerous AI behaviors mathematically impossible.”

🧠 PHDM as AI Brain Architecture - The Geometric Skull
SCBE-AETHERMOORE + PHDM: Complete Mathematical & Security Specification
📐 Hamiltonian Braid Specification - Formal Mathematical Definition

Status: This document is the authoritative source for PHDM naming. Any conflicts between this page and other documentation should be resolved in favor of this specification.

Last Updated: February 10, 2026

Maintained By: Issac Davis