tiny-6OutOf8-verified

Formally verified 6-out-of-8 threshold gate. Single threshold neuron with 100% accuracy.

Architecture

Component	Value
Inputs	8
Outputs	1
Neurons	1
Parameters	9
Weights	[1, 1, 1, 1, 1, 1, 1, 1]
Bias	-6
Activation	Heaviside step

Key Properties

• 100% accuracy (256/256 inputs correct)
• Coq-proven correctness
• Single threshold neuron
• Integer weights
• Fires when at least 6 of 8 inputs are true

Usage

import torch
from safetensors.torch import load_file

weights = load_file('sixoutof8.safetensors')

def sixoutof8_gate(bits):
    # bits: list of 8 binary values
    inputs = torch.tensor([float(b) for b in bits])
    weighted_sum = (inputs * weights['weight']).sum() + weights['bias']
    return int(weighted_sum >= 0)

# Test
print({func}_gate([0,0,0,0,0,0,0,0]))  # 0 (0/6, below threshold)
print({func}_gate([1,1,1,1,1,0,0,0]))  # 0 (5/8, below threshold)
print({func}_gate([1,1,1,1,1,1,0,0]))  # 1 (6/8, at threshold)
print(sixoutof8_gate([1,1,1,1,1,1,1,1]))  # 1 (8/8, above threshold)

Verification

Coq Theorem:

Theorem sixout_eight_correct : forall x0 x1 x2 x3 x4 x5 x6 x7,
  sixout_eight_circuit [x0; x1; x2; x3; x4; x5; x6; x7] =
  sixout_eight_spec [x0; x1; x2; x3; x4; x5; x6; x7].

Proven axiom-free via:

1. Exhaustive: All 256 inputs verified
2. Universal: Quantified proof over boolean combinations
3. Algebraic: Hamming weight ≥ 6

Full proof: coq-circuits/Threshold/SixOutOfEight.v

Circuit Operation

Input with h true bits (Hamming weight h):

• Weighted sum: h - 6
• Output: 1 if h ≥ 6, else 0

Citation

@software{tiny_6outof8_prover_2025,
  title={tiny-6OutOf8-verified: Formally Verified 6-out-of-8 threshold gate},
  author={Norton, Charles},
  url={https://huggingface.co/phanerozoic/tiny-6OutOf8-verified},
  year={2025}
}