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README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+- functionally-complete
+---
+
+# threshold-nand3
+
+3-input NAND gate. Fires unless all three inputs are active. The universal gate extended.
+
+## Circuit
+
+```
+    a   b   c
+    │   │   │
+    └───┼───┘
+        │
+        ▼
+   ┌──────────┐
+   │w: -1,-1,-1│
+   │ b:  +2   │
+   └──────────┘
+        │
+        ▼
+  NAND(a,b,c)
+```
+
+## The Veto Detector
+
+3-input NAND fires when at least one input is 0:
+
+| Inputs | Sum | Output |
+|--------|-----|--------|
+| 000 | +2 | 1 |
+| 001 | +1 | 1 |
+| 010 | +1 | 1 |
+| 011 | 0 | 1 |
+| 100 | +1 | 1 |
+| 101 | 0 | 1 |
+| 110 | 0 | 1 |
+| **111** | **-1** | **0** |
+
+Only unanimous activation silences the gate.
+
+## Negative Weights
+
+Each input *subtracts* from the sum. The positive bias provides headroom:
+
+```
+sum = -a - b - c + 2 = 2 - HW
+fires when 2 - HW >= 0
+fires when HW <= 2
+```
+
+This is AtMost2 for 3 inputs.
+
+## Functional Completeness
+
+NAND is universal - any Boolean function can be built from NAND:
+
+- NOT(x) = NAND(x, x, x)
+- AND(x,y,z) = NAND(NAND(x,y,z), NAND(x,y,z), NAND(x,y,z))
+- OR(x,y,z) = NAND(NAND(x,x,x), NAND(y,y,y), NAND(z,z,z))
+
+## Dual of 3-input NOR
+
+| Gate | Weights | Bias | Fires when |
+|------|---------|------|------------|
+| **NAND3** | all -1 | +2 | HW ≤ 2 |
+| NOR3 | all -1 | 0 | HW = 0 |
+
+NAND is permissive (7 of 8 pass). NOR is restrictive (1 of 8 passes).
+
+## Parameters
+
+| Component | Value |
+|-----------|-------|
+| Weights | [-1, -1, -1] |
+| Bias | +2 |
+| **Total** | **4 parameters** |
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+import torch
+
+w = load_file('model.safetensors')
+
+def nand3(a, b, c):
+    inp = torch.tensor([float(a), float(b), float(c)])
+    return int((inp * w['weight']).sum() + w['bias'] >= 0)
+
+print(nand3(1, 1, 0))  # 1
+print(nand3(1, 1, 1))  # 0
+```
+
+## Files
+
+```
+threshold-nand3/
+├── model.safetensors
+├── model.py
+├── config.json
+└── README.md
+```
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-nand3",
+  "description": "3-input NAND gate as threshold circuit",
+  "inputs": 3,
+  "outputs": 1,
+  "neurons": 1,
+  "layers": 1,
+  "parameters": 4
+}

model.py

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+import torch
+from safetensors.torch import load_file
+
+def load_model(path='model.safetensors'):
+    return load_file(path)
+
+def nand3(a, b, c, weights):
+    """3-input NAND gate."""
+    inp = torch.tensor([float(a), float(b), float(c)])
+    return int((inp * weights['weight']).sum() + weights['bias'] >= 0)
+
+if __name__ == '__main__':
+    w = load_model()
+    print('3-input NAND truth table:')
+    for a in [0, 1]:
+        for b in [0, 1]:
+            for c in [0, 1]:
+                print(f'NAND({a},{b},{c}) = {nand3(a, b, c, w)}')

model.safetensors

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+version https://git-lfs.github.com/spec/v1
+oid sha256:9f4b18d4677acf48bb022a38bcf0fc5db72c5019c72ccba08f7d02d803e86f43
+size 144