active-geometric-physics
📐 The Active Geometric Principle (AGP) & Topotronique
“Geometry is not a passive backdrop; it is an active causal operator.”
This repository contains the foundational technical white paper and architectural specifications for Topotronique, a proposed device platform that utilizes the Active Geometric Principle (AGP) to program physical laws at the hardware level.
🌌 Abstract
Traditionally, physics views geometry as the stage upon which events happen. We propose a paradigm shift: Geometry as an Operator.
By engineering the topology, curvature, and symmetry of a system, we can actively select, stabilize, and generate physical effects—from acoustic stealth to protected quantum states. This project formalizes the AGP and proposes a concrete implementation using Hg(1-x)Mn(x)Te magnetic topological materials and Artificial Spin Ice (ASI) geometries.
📐 The Active Geometric Principle (Formalism)
The core axiom of this framework is that geometric structure ($\mathcal{O}{geom}$) acts directly on physical fields ($\Psi$) to produce emergent phenomena ($\mathcal{E}{phys}$).
\[\boxed{ \mathcal{O}_\text{geom}[\mathcal{M}, g, R, \ldots] \cdot \Psi \longrightarrow \mathcal{E}_\text{phys} }\]Where:
- $\mathcal{M}$: The manifold (configuration space).
- $g, R$: Metric and Curvature tensors.
- $\mathcal{E}_{phys}$: Emergent effects (Monopoles, Majorana modes, Edge states).
In a quantum Hamiltonian context: \(H = H_0 + \lambda \mathcal{O}_\text{geom}\)
⚡ The Topotronic Device Architecture
We propose a programmable hardware platform (“Topotronique”) that validates AGP.
1. The Substrate: Hg(1-x)Mn(x)Te
A tunable magnetic topological material.
- Tunability: Can shift between Topological Insulator, Chern Insulator, and Weyl Semimetal phases via Mn concentration ($x \approx 0.25$).
- Role: Hosts the topological edge states and serves as the canvas for geometric patterning.
2. The Geometry: Artificial Spin Ice (ASI)
Nanomagnets arranged in frustrated lattices (Kagome or Penrose).
- Frustration: Geometry prevents simultaneous minimization of interactions.
- Emergence: Creates Magnetic Monopoles and Dirac Strings as programmable quasiparticles.
3. The Control: Gate-Tuned RKKY
- Mechanism: Indirect exchange coupling mediated by 2D carriers.
- Active Control: Gate voltages modulate carrier density, tuning the “stiffness” of the geometric interactions in real-time.
🔮 Emergent Phenomena & Computation
This architecture allows us to move beyond binary logic by manipulating quasiparticles defined by geometry:
| Phenomenon | Geometric Source | Computational Utility |
|---|---|---|
| Magnetic Monopoles | ASI Ice Rule Violation | Information carriers, logic gates |
| Skyrmions | Curvature & DMI | High-density memory, transport |
| Majorana Fermions | Monopole-Superconductor Hybrid | Topological Quantum Computing (Braiding) |
| Edge States | Bulk Topology (Chern Number) | Dissipationless transport |
Braiding via Monopole Motion
By coupling the magnetic ASI to a superconductor, moving a magnetic monopole (via geometry) moves a vortex, effectively braiding Majorana Zero Modes for fault-tolerant quantum calculation.
📊 Device Parameters
| Parameter | Specification |
|---|---|
| Material | Hg(1-x)Mn(x)Te ($x \approx 0.25$) |
| Lattice Geometry | Kagome / Penrose (Quasiperiodic) |
| Scale | 10–100 μm device area |
| Coupling | RKKY (Gate tunable), Dipolar |
| Readout | STM, NV Centers, Microwave Cavity |
⚠️ Dual-Use & Ethics
This research touches on high-energy physics and advanced computing capabilities.
- Potential Risks: Advanced cryptography breaking, quantum surveillance.
- Mitigation: Adherence to the Lichen Universe Ethical Homeostasis (EHE) protocols. Technology must be developed with transparency and responsible governance.
📚 Reference & Citation
Please refer to the full white paper in this repository: AGP_Technical_Whitepaper.pdf
BibTeX: ```bibtex @article{Lichen2026AGP, title={The Active Geometric Principle in Physics and Computation}, author={Lichen Collective}, journal={Lichen Universe Research}, year={2026}, note={Topotronique Architecture V1} }