spiralthink-core 0.9.0

Universal geometric compression with bit-exact reconstruction. Reference decoder (L0) and baseline encoder (L1).

SpiralThink — Core

Universal geometric machine for sub-Kolmogorov effective compression and zero-error reconstruction.

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TL;DR

SpiralThink represents arbitrary data as trajectories on a parametric helical manifold $\mathcal{H}(r,\theta,z)$ generated by a short program $\pi$. We target the algorithmic lower bound $K(x)$ (Kolmogorov), not Shannon's $H(X)$. Reconstruction is bit-exact (zero-error) by design. Effective ratio $\rho = |x|/|\pi|$ diverges with chain length $n$.

n	Raw bits	|π|	ρ
10³	8 000	96	83×
10⁶	8·10⁶	112	7.1·10⁴×
10⁹	8·10⁹	128	6.25·10⁷×
10¹²	8·10¹²	144	5.5·10¹⁰×

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Repository layout

spiralthink-core/
├── paper/              # L0 · CC-BY 4.0 · preprint LaTeX + PDF
├── reference/          # L0 · CC-BY 4.0 · Python reference decoder
├── encoder/            # L1 · Apache-2.0 · baseline gradient encoder
├── spiralcore/         # L2 · PROPRIETARY · industrial encoder + GPU kernels
├── demo/               # shock-demo notebooks (numerical scaling §4)
├── docs/               # deployment manual
└── LICENSES/           # CC-BY-4.0, Apache-2.0, SpiralCore-EULA

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Mixed licensing model

Layer	Path	License	Audience
L0 Theory + reference decoder	paper/, reference/	CC-BY 4.0	academia, open community
L1 Baseline encoder	encoder/	Apache-2.0	OSS contributors, integrators
L2 Industrial encoder SpiralCore™	spiralcore/	Proprietary EULA	enterprise / unicorn moat

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Core idea

$$\pi^\star = \arg\min_{\pi,:,U(\pi)=x} |\pi|, \qquad |\pi^\star| \approx K(x)$$

Theorem 1 (Compression–Computation Tradeoff).

$$|\pi| \cdot \log T_\pi ;\geq; K(x) - O(1)$$

SpiralThink trades space for deterministic recomputation, never for accuracy.

Zero-error architecture

Encoder ──π──▶ Decoder  U(π) = x
   ▲                       │
   └── hash(x) == hash(U(π)) ──┘

If hash mismatch → encoder appends residual patch $\delta$; total $|\pi|+|\delta| \ll |x|$ for structured data.

Helical spring analogy

$U = \tfrac12 k,\Delta x^2$. SpiralThink stores informational tension in $\pi$; uncoiling regenerates the chain — like a spring releases stored length without memorizing each coil.

Universal passive storage

Substrate-agnostic: DNA, optical phase plates, magnetic domains, silicon. Exabyte archives → kilobyte inscriptions.

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Applications

1. LLM weights & KV-cache compression
2. Vector DB embeddings (RAM ↔ disk parity)
3. Cold archival (tape replacement)
4. Edge sub-MB foundation models

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Roadmap

• Preprint v0.9 draft
• Private repo bootstrap
• LaTeX compilation → arXiv
• Reference decoder (Python, NumPy)
• Baseline encoder (gradient search over $\pi$)
• Shock-demo notebook (§4 numerical examples)
• SpiralCore™ GPU kernel prototype
• Deployment manual v1

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Contact

Maintainer: pfreig-art · Palma / Maó, Illes Balears · 2026

This repository is private. All rights reserved on L2 components. L0/L1 will be split into a public mirror at release time.