Projects

An overview of all ShunyaBar Labs projects, unified by the Arithmetic Manifold framework.

---

Project Map#

THE ARITHMETIC MANIFOLD
│
├── Core Algorithms
│   ├── BAHA ──────────────────────── Lambert W branch enumeration
│   ├── NitroSAT ──────────────────── Physics-informed MaxSAT
│   └── Navokoj ───────────────────── Geometric flow SAT
│
├── Multiplicative Framework
│   ├── Multiplicative PINN ────────── PyTorch physics neural networks
│   └── Spectral-Multiplicative ────── Crystal heat kernel optimizer
│
├── Theory & Applications
│   ├── Geometry of Conditional Logic ─ CRT incremental solver
│   ├── Casimir SAT Solver ─────────── Quantum vacuum dynamics blog
│   └── Factor Agent ───────────────── Multi-agent architecture
│       └── Agentic AI Runtime ─────── Distributed systems architecture
│
├── Compression & Quotients
│   ├── Behavioral Quotients ───────── Quotient design principle
│   ├── FUTCache ───────────────────── Metric visited-set / sufficient state
│   └── Novelty Geometry ───────────── Ordered-novelty completion
│
├── Foundational
│   ├── Thermodynamic Number Line ──── Primes + Riemann zeta theory
│   └── Authorization Lattice ──────── Capability permissions
│
└── Unified
    └── shunyabar.lua ─────────────── All algorithms in one Lua module

---

Summary Table#

Project	Language	Domain	Key Innovation
BAHA	C++/Python	Optimization	Lambert W phase transition detection
NitroSAT	C99	MaxSAT	Physics-informed dynamical system
Navokoj	Python	SAT	Prime-weighted geometric flow
Multiplicative PINN	Python/PyTorch	Neural Networks	Multiplicative constraint enforcement
Spectral-Multiplicative	Crystal	Graph Optimization	Heat kernel + Casimir forces
Geometry of Conditional Logic	Python	Incremental SAT	CRT “safe corridor” repair
Casimir SAT Solver	Python	Theory/Blog	Quantum vacuum dynamics
Factor Agent	Elixir/OTP	Multi-Agent	Prime factorization architecture
Thermodynamic Number Line	R/Mathematica	Number Theory	Primes as thermodynamic fuel
Authorization Lattice	—	Capabilities	p-adic permission composition
Behavioral Quotients	—	Theory	State reduction as a behavioural quotient
FUTCache	C	Compression	Bounded-memory metric visited-set
Novelty Geometry	—	Theory	Resolution-depth ordered-discovery completion

---

Cross-Cutting Themes#

Prime Weighting#

All projects use prime weights for constraint identity:

• BAHA, NitroSAT, Navokoj: Clause/constraint weighting
• Multiplicative PINN: Physics law weighting
• Prime Euler Activations: Activation and channel gating
• Spectral-Multiplicative: Graph constraint weighting
• Factor Agent: Agent/capability weighting

Partition Function#

All projects use $Z(\beta) = \sum e^{-\beta E(s)}$:

• BAHA: Fracture detection via $\rho(\beta)$
• Navokoj: Energy definition for geometric flow
• Multiplicative PINN: Local partition function per constraint
• Casimir SAT: Equilibrium sampling distribution

Phase Transitions#

• BAHA: Direct detection via Lambert W
• NitroSAT: Critical $\beta$ scaling
• Navokoj: Adiabatic quench schedule
• Spectral-Multiplicative: Heat kernel smoothing

---

Papers & DOIs#

Year	Project	DOI
2025	Casimir SAT	10.5281/zenodo.17394165
2025	Spectral-Multiplicative	10.5281/zenodo.17596089
2025	ShunyaBar	10.5281/zenodo.18096758
2026	BAHA	10.5281/zenodo.18373732
2026	NitroSAT	10.5281/zenodo.18753235
2025	Multiplicative PINN	10.5281/zenodo.18214172
2026	Novelty Geometry	10.5281/zenodo.22058736

---

See Also#

• The Arithmetic Manifold — the unified theory connecting all projects
• Prime Weighting — how all projects use prime weights
• Agentic AI as a Distributed System — Factor Agent runtime architecture
• Partition Function — the universal mathematical object
• Phase Transitions — landscape fracture across projects
• Getting Started — run the projects yourself
• Benchmarks — performance comparison across all projects