Fungible Computation Between Paradigms

Demonstrating Equivalence Between Neural and Classical Computation Through Exact Digital Emulation

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Why This Exists

This repository contains the paper arguing that neural and classical computation are fungible—interchangeable representations of the same underlying computational primitives.

Who is it for: Researchers interested in the theoretical foundations of neural computation, the neural-symbolic divide, and verified AI systems.

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Abstract

We present empirical evidence that neural and classical computation are fungible under bounded digital semantics. This claim is supported by three systems that achieve exact (not approximate) bidirectional translation between paradigms:

1. FLYNNCONCEIVABLE — A neural network implementation of the MOS 6502 CPU achieving 100% accuracy across 460,928 verified input combinations.

2. Spline-6502 — A lookup-spline representation that compresses 3.7MB of neural parameters to 3,088 bytes while maintaining 100% accuracy.

3. TriX — A sparse ternary neural architecture where routing emerges from weight structure, demonstrating mathematical equivalence between content-addressable routing and spline interval selection.

The composition yields a constructive proof: a spline-based neural network executes correctly on a neural network emulating a 6502 processor.

Thesis: The perceived boundary between "neural" and "classical" computation is an artifact of implementation, not a fundamental distinction.

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Repository Structure

fungible-computation/
├── README.md           # This file
├── paper/
│   ├── main.tex        # Paper source
│   ├── figures/        # Generated figures
│   └── references.bib  # Bibliography
├── REPRODUCIBILITY.md  # How to reproduce all claims
└── LICENSE

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Key Claims

Claim	Evidence	Verification
Neural → Classical (exact)	FLYNNCONCEIVABLE	460,928 combinations, 0 errors
Classical → Neural (compressed)	Spline-6502	591,500+ combinations, 0 errors, 1198× compression
Routing = Lookup	TriX	Mathematical equivalence demonstrated

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Reproducibility

See REPRODUCIBILITY.md for:

• Pinned commits for all code repositories
• Commands to reproduce every claim
• Expected outputs

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Code Repositories

This paper draws evidence from three independent implementations:

Repository	Description	Link
trix	2-bit sparse ternary neural networks	github.com/anjaustin/trix
flynnconceivable	Neural 6502 CPU	github.com/anjaustin/flynnconceivable
hollywood-squares-os	Coordination OS (related work)	github.com/anjaustin/hollywood-squares-os

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Citation

@article{fungible2025,
  title={Fungible Computation Between Paradigms: Demonstrating Equivalence 
         Between Neural and Classical Computation Through Exact Digital Emulation},
  author={Josserand-Austin, Tripp},
  year={2025}
}

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License

MIT License. See LICENSE.