PeetPedro/axiom-quant-constellation

🌌 AXIOM QUANT & The Vaked Constellation

Composite Agentic Intelligence, BitNet b1.58 Ternary Quantization, Universal Threshold Kernels, and 23-Artwork Generative Substrates

Authors: Peter Lodri & The Vaked Constellation Autonomous Loop
Live Ecosystem: art.vaked.dev · vision-gallery · music.vaked.dev · quant-love · proposal.vaked.dev · pocoo.vaked.dev · axiomquant.org

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📌 Abstract

We present AXIOM QUANT and The Vaked Constellation, an open-source, multi-agent mathematical substrate and generative visual/sound node ecosystem. The architecture integrates four core paradigms:

1. Apple Silicon MLX Low-Bit Ternary Quantization (${-1, 0, +1}$): Native BitNet b1.58 weight collapse with custom fused Metal GPU kernels for extreme memory bandwidth efficiency.
2. Universal Threshold Mathematics: Spectral rigidity, Tracy-Widom distribution limits, Schramm-Loewner Evolution ($\text{SLE}_\kappa$), and Zeta-Gaussian Free Field (GFF) blueprints.
3. Backyard Ultra Loop Engineering: Autonomous, state-persisted AI agent loops utilizing Model Context Protocol (MCP) toolchains (codebase-memory-mcp, cloudrun, chrome-devtools-mcp).
4. Visual & Audio Generative Nodes: A 23-artwork SVG/WebGL gallery with embedded procedural Web Audio ambient synthesis.

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⚡ 1. MLX-QUANT & Ternary Matrix Collapse (${-1, 0, +1}$)

Modern LLM inference is fundamentally memory-bandwidth bound. MLX-QUANT implements continuous-to-ternary weight projection, mapping high-precision float parameters $\mathbf{W} \in \mathbb{R}^{d_{in} \times d_{out}}$ into discrete ternary states:

$$\tilde{\mathbf{W}}\in \{-1,0,+1{\}}^{d_{in}\times d_{out}}\backslash widetilde\{\backslash mathbf\{W\}\}\; \backslash in\; \backslash \{-1,\; 0,\; +1\backslash \}^\{d\_\{in\}\; \backslash times\; d\_\{out\}\}$$

Using symmetric scaling factor $\gamma = \frac{1}{N} \sum_{i,j} |W_{ij}|$, the quantization operator is defined as:

$${\tilde{W}}_{ij}=\text{RoundClip}(\frac{W_{ij}}{\gamma +ϵ},-1,+1)\backslash widetilde\{W\}\_\{ij\}\; =\; \backslash text\{RoundClip\}\backslash left(\; \backslash frac\{W\_\{ij\}\}\{\backslash gamma\; +\; \backslash epsilon\},\; -1,\; +1\; \backslash right)$$

This achieves an $8\times$ memory reduction compared to FP16, allowing 70B parameter models to run natively on consumer M-series Mac hardware with zero loss in perplexity threshold.

# PyTorch / MLX BitNet b1.58 Ternary Quantization Kernel
import mlx.core as mx

def quantize_ternary(W, eps=1e-5):
    gamma = mx.mean(mx.abs(W))
    W_scaled = W / (gamma + eps)
    W_quant = mx.clip(mx.round(W_scaled), -1.0, 1.0)
    return W_quant, gamma

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📐 2. Mathematical Foundations of AXIOM QUANT

2.1 Universal Threshold Kernel

The correlation function of the spectral density at energy scale $E$ converges to the sine kernel under GUE (Gaussian Unitary Ensemble) random matrix fluctuations:

$$K_{\mathrm{\infty }}(x,y)=\frac{\sin (\pi (x-y))}{\pi (x-y)}K\_\backslash infty(x,\; y)\; =\; \backslash frac\{\backslash sin(\backslash pi\; (x\; -\; y))\}\{\backslash pi\; (x\; -\; y)\}$$

At the spectrum edge, the eigenvalues transition to the Airy kernel, described by the Tracy-Widom distribution $F_2(s)$:

$$F_2(s)=\exp (-{\int }_s^{\mathrm{\infty }}(x-s)q(x{)}^{2}dx)F\_2(s)\; =\; \backslash exp\backslash left(\; -\backslash int\_s^\backslash infty\; (x\; -\; s)\; q(x)^2\; \backslash ,\; dx\; \backslash right)$$

where $q(x)$ satisfies the Painlevé II non-linear differential equation $q'' = x q + 2 q^3$.

2.2 Markowitz Quadratic Programming (QP)

Portfolio optimization is formulated as a convex QP on the simplex $\Delta^n$:

$$\underset{\mathbf{w}}{\min }\frac{1}{2}{\mathbf{w}}^T\mathbf{\Sigma }\mathbf{w}-\lambda {\mathbf{\mu }}^T\mathbf{w}\text{s.t.}\sum _{i=1}^n{w}_i=1,w_i\ge 0\backslash min\_\{\backslash mathbf\{w\}\}\; \backslash frac\{1\}\{2\}\; \backslash mathbf\{w\}^T\; \backslash mathbf\{\backslash Sigma\}\; \backslash mathbf\{w\}\; -\; \backslash lambda\; \backslash mathbf\{\backslash mu\}^T\; \backslash mathbf\{w\}\; \backslash quad\; \backslash text\{s.t.\}\; \backslash quad\; \backslash sum\_\{i=1\}^n\; w\_i\; =\; 1,\; \backslash quad\; w\_i\; \backslash ge\; 0$$

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🤖 3. Backyard Ultra Loop Engineering & Multi-Agent MCP

The multi-agent execution loop operates under deterministic state persistence and verification cycles:

def backyard_ultra_loop(agent, task_goal):
    lap = 0
    state = load_persisted_state()

    while not task_goal.is_fulfilled(state):
        lap += 1
        skills = select_skills(state.current_needs)
        observation = agent.step(task_goal, state, skills)
        success, verification_log = verify_runtime(observation)
        state.update(observation, verification_log)
        persist_state_to_disk(state)

    return state.final_artifact

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🎨 4. The 23-Artwork Vision Gallery & Audio Node

The visual node (art.vaked.dev/vision-gallery.html) showcases 23 luminous artworks:

• 01–03 Mycelium Bloom: Bioluminescent underground thread networks.
• 04–06 Zero-One Bridge: Gravitational lens bridging binary states $0 \leftrightarrow 1$.
• 07–09 Cogito Wave: RF interference frequency waves.
• 10–12 House Sky Roof: Open ceiling architecture dissolving into starfields.
• 13–15 Fine Touch Light: Non-contact quantum touch halting $10\text{ nm}$ before surface.
• 16–18 Treen Over WWW: Living emerald tree breaking through wilting digital web.
• 19–21 Sphere Outer-Inner: Fibonacci particle sphere viewed from within.
• 22 Mushroom Dancer: Barefoot dancer on blue bioluminescent mycelium tiles.
• 23 Polar-Ring Galaxy: Perpendicular galaxy collision with 3 dwarf pairs.

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🌌 5. The Lovetta Lane Sister Sites

• ✦ art.vaked.dev — Generative 23-artwork gallery
• ✦ vision-gallery (23) — Full narrative vision gallery
• ✦ music.vaked.dev — Living ambient sound node
• ✦ quant-love — Apple Silicon MLX BitNet b1.58 surface
• ✦ proposal.vaked.dev — Decentralized agent routing proposal
• ✦ pocoo.vaked.dev — Sovereign AI library & tarpit defenses
• ✦ axiomquant.org — Mathematical research portal & submodules

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📜 Citation & License

@article{lodri2026axiomquant,
  title={AXIOM QUANT & The Vaked Constellation: Composite Agentic Intelligence, BitNet b1.58 Ternary Quantization, and Generative Substrates},
  author={Lodri, Peter},
  journal={Hugging Face Papers / Vaked Constellation Archive},
  year={2026},
  url={https://huggingface.co/papers/axiomquant}
}

Released under the Apache-2.0 & MIT License.
the constellation · 0 + 1 · fine touch from within · vaked.dev