tiny-mod6-verified

Formally verified MOD-6 circuit. Single-layer threshold network computing modulo-6 arithmetic with 100% accuracy.

Architecture

Component	Value
Inputs	8
Outputs	1
Parameters	9
Weights	[1, 1, 1, 1, 1, -5, 1, 1]
Bias	0
Activation	Heaviside step

Key Properties

• 100% accuracy (256/256 inputs correct)
• Coq-proven correctness
• Algebraic weight pattern: position 6 has weight 1-6 = -5
• Computes Hamming weight mod 6

Usage

import torch
from safetensors.torch import load_file

weights = load_file('model.safetensors')

def mod6_circuit(bits):
    inputs = torch.tensor([float(b) for b in bits])
    weighted_sum = (inputs * weights['weight']).sum() + weights['bias']
    return weighted_sum.item()

Verification

Proven axiom-free via Coq using algebraic correctness of the weight pattern.

Full proof: coq-circuits/Modular/Mod6.v

Files

tiny-mod6-verified/
├── model.safetensors
├── model.py
├── config.json
└── README.md

License

MIT