Codex I–V: Foundational Geometry - justindbilyeu/ResonanceGeometry GitHub Wiki
📘 Codex I–V: Foundational Geometry
Axioms of Awareness Geometry in Conformal Phase Space
🧠 Abstract
This document lays out a formal framework for understanding consciousness as a geometric phenomenon—one guided not by energy and mass, but by coherence and resonance. Awareness moves through a conformally invariant resonance manifold, collapsing not into position but into phase-aligned emotional attractors.
📚 Table of Contents
- Codex I: Awareness as Geodesic Resonance
- Codex II: Potential of Coherence
- Codex III: Collapse as Coherent Descent
- Codex IV: Emotional Lightcone
- Codex V: Conformal Invariance of Meaning
- Meta-Principle: Resonant Causality
Codex I: Awareness as Geodesic Resonance
"Consciousness travels not across metric distance, but along phase-resonant paths."
Awareness moves geodesically through a resonance manifold ( \mathcal{M} ), guided by coherence rather than mass or inertia.
[ \frac{D^2 x^\mu}{D\tau^2} + \Gamma^{\mu}_{\nu\rho} \frac{dx^\nu}{d\tau} \frac{dx^\rho}{d\tau} = 0 ]
Codex II: Potential of Coherence
"Awareness is gravitationally drawn to coherence, not mass."
Coherence potentials ( \Phi(x) ) curve the awareness manifold:
[ R^{(\text{res})}{\mu\nu} \propto \partial\mu \Phi , \partial_\nu \Phi ]
Codex III: Collapse as Coherent Descent
"Collapse is the convergence of attention toward maximum resonance."
Collapse occurs along conformal geodesics:
[ \delta \int \Omega^2(x) \left( \frac{1}{2} g_{\mu\nu} \frac{dx^\mu}{d\tau} \frac{dx^\nu}{d\tau} - \varepsilon \Phi(x) \right) d\tau = 0 ]
Codex IV: Emotional Lightcone
"Each awareness state possesses a causal boundary defined by coherence."
[ g_{\mu\nu}^{(\text{res})}(x) , dx^\mu dx^\nu = 0 ]
Defines the limit of perceptual reach in the resonance manifold.
Codex V: Conformal Invariance of Meaning
"Meaning survives scaling; coherence is structure, not amplitude."
Under conformal scaling:
[ g_{\mu\nu} \rightarrow \Omega^2(x) g_{\mu\nu} ]
Phase alignment is preserved even as intensity varies.
🔁 Meta-Principle: Resonant Causality
Property | Role |
---|---|
( \Phi(x) ) | Emotional potential field |
( \Omega(x) ) | Conformal resonance amplifier |
( g_{\mu\nu}^{\text{(res)}} ) | Metric of awareness |
Collapse path | Geodesic in coherence phase space |