threshold-exactly7outof8

Exactly-7-out-of-8 detector. Fires when precisely seven inputs are active. The lone-dissenter detector.

Circuit

  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
   │  │  │  │  │  │  │  │
   └──┴──┴──┴──┼──┴──┴──┴──┘
               │
       ┌───────┴───────┐
       ▼               ▼
  ┌─────────┐     ┌─────────┐
  │  ≥ 7    │     │  ≤ 7    │
  │ b = -7  │     │ b = +7  │
  └─────────┘     └─────────┘
       │               │
       └───────┬───────┘
               ▼
          ┌─────────┐
          │   AND   │
          └─────────┘
               │
               ▼
      one dissenter?

The Singleton Complement

This circuit detects the complement of Exactly1: instead of one voice in the wilderness, it's one holdout against consensus.

Circuit	Pattern	Interpretation
Exactly1	00000001	Pioneer, outlier
Exactly7	11111110	Holdout, veto

Both fire on exactly 8 input patterns (one for each position).

Near-Unanimity

7/8 = 87.5% - overwhelming but not complete agreement:

• Hung jury: 11-1 in a 12-person jury (scaled to 8)
• Single point of failure: All systems go except one
• Error correction: A single bit flip from all-ones

The circuit identifies the liminal state between consensus and unanimity.

Dual of Exactly1

Circuit	HW	Count	Interpretation
Exactly1	1	8	One active
Exactly7	7	8	One inactive

They are perfect duals. Bitwise NOT maps each Exactly1 input to a unique Exactly7 input.

The Holdout Problem

In consensus systems:

HW	Status	Exactly7
6	Multiple dissenters	0
7	Single holdout	1
8	Complete consensus	0

Exactly7 identifies the unique scenario: overwhelming support with precisely one objector. This is useful for:

• Identifying the blocking vote
• Detecting near-consensus states
• Finding the single bit error in a codeword

Parameters

Component	Weights	Bias
AtLeast7	all +1	-7
AtMost7	all -1	+7
AND	[+1, +1]	-2

Total: 3 neurons, 21 parameters, 2 layers

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def exactly7(bits):
    inp = torch.tensor([float(b) for b in bits])
    atleast = int((inp * w['atleast.weight']).sum() + w['atleast.bias'] >= 0)
    atmost = int((inp * w['atmost.weight']).sum() + w['atmost.bias'] >= 0)
    comb = torch.tensor([float(atleast), float(atmost)])
    return int((comb * w['and.weight']).sum() + w['and.bias'] >= 0)

# One holdout at position 3
bits = [1, 1, 1, 0, 1, 1, 1, 1]
print(exactly7(bits))  # 1

# Complete unanimity - no holdout
bits = [1, 1, 1, 1, 1, 1, 1, 1]
print(exactly7(bits))  # 0

Contrast with 7-out-of-8

Circuit	Condition	Fires on
7-out-of-8	HW ≥ 7	HW = 7, 8 (9 patterns)
Exactly7	HW = 7	HW = 7 only (8 patterns)

The difference: 7-out-of-8 includes unanimity. Exactly7 excludes it.

Files

threshold-exactly7outof8/
├── model.safetensors
├── model.py
├── config.json
└── README.md

License

MIT