threshold-atmost5outof8

At-most-5-out-of-8 detector. Fires when 5 or fewer inputs are active. The sub-supermajority bound.

Circuit

  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
   │  │  │  │  │  │  │  │
   └──┴──┴──┴──┼──┴──┴──┴──┘
               ▼
          ┌─────────┐
          │ w: -1×8 │
          │ b:  +5  │
          └─────────┘
               │
               ▼
           HW ≤ 5?

Below Supermajority

This circuit blocks supermajority (≥6):

HW	AtMost5	Interpretation
0-5	1	Below 75% threshold
6-8	0	Supermajority achieved

If you need 6/8 to pass something, AtMost5 detects when you don't have it.

Includes Bare Majority

HW	Status	AtMost5
4	Tie	1
5	Bare majority	1
6	Supermajority	0

Unlike AtMost4, this includes the minimal majority case. A 5-3 vote passes Majority but still fires AtMost5.

Coverage

HW	C(8,k)	AtMost5?
0-5	163	Yes
6	28	No
7	8	No
8	1	No

Total: 163 of 256 inputs (63.7%). Same count as AtMost4 by symmetry.

Dual of AtLeast3

Circuit	Condition	Count
AtLeast3	HW ≥ 3	219
AtMost5	HW ≤ 5	219

Under bit-flip, AtMost5 inputs map to AtLeast3 inputs.

Parameters

Component	Value
Weights	all -1
Bias	+5
Total	9 parameters

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def atmost5(bits):
    inp = torch.tensor([float(b) for b in bits])
    return int((inp * w['weight']).sum() + w['bias'] >= 0)

# Bare majority: still below supermajority
print(atmost5([1,1,1,1,1,0,0,0]))  # 1

# Supermajority: fails
print(atmost5([1,1,1,1,1,1,0,0]))  # 0

Files

threshold-atmost5outof8/
├── model.safetensors
├── model.py
├── config.json
└── README.md

License

MIT