Rename from tiny-NAND-verified

README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+- functionally-complete
+---
+
+# threshold-nand
+
+The universal gate. Any Boolean function can be constructed from NAND alone.
+
+## Circuit
+
+```
+    x   y
+    │   │
+    └─┬─┘
+      ▼
+  ┌────────┐
+  │w: -1,-1│
+  │ b: +1  │
+  └────────┘
+      │
+      ▼
+  NAND(x,y)
+```
+
+## Mechanism
+
+Negative weights mean inputs *subtract* from the sum. The positive bias starts us above threshold, and inputs pull us down:
+
+| x | y | sum | output |
+|---|---|-----|--------|
+| 0 | 0 | +1 | 1 |
+| 0 | 1 | 0 | 1 |
+| 1 | 0 | 0 | 1 |
+| 1 | 1 | -1 | 0 |
+
+Only when both inputs are active do we fall below threshold. This is AND with inverted output.
+
+## Parameters
+
+| | |
+|---|---|
+| Weights | [-1, -1] |
+| Bias | +1 |
+| Total | 3 parameters |
+
+## Functional Completeness
+
+NAND can build any Boolean function:
+
+- NOT(x) = NAND(x, x)
+- AND(x,y) = NOT(NAND(x,y)) = NAND(NAND(x,y), NAND(x,y))
+- OR(x,y) = NAND(NOT(x), NOT(y))
+
+This is why NAND gates dominate digital logic fabrication.
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+import torch
+
+w = load_file('model.safetensors')
+
+def nand_gate(x, y):
+    inputs = torch.tensor([float(x), float(y)])
+    return int((inputs * w['weight']).sum() + w['bias'] >= 0)
+```
+
+## Files
+
+```
+threshold-nand/
+├── model.safetensors
+├── model.py
+├── config.json
+└── README.md
+```
+
+## License
+
+MIT

config.json

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+{
+  "model_type": "threshold_network",
+  "task": "nand_gate",
+  "architecture": "2 -> 1",
+  "input_size": 2,
+  "output_size": 1,
+  "num_neurons": 1,
+  "num_parameters": 3,
+  "activation": "heaviside",
+  "weight_constraints": "integer",
+  "verification": {
+    "method": "coq_proof",
+    "exhaustive": true,
+    "inputs_tested": 4
+  },
+  "accuracy": {
+    "all_inputs": "4/4",
+    "percentage": 100.0
+  },
+  "properties": ["functionally_complete"],
+  "github": "https://github.com/CharlesCNorton/coq-circuits"
+}

model.py

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+"""
+Threshold Network for NAND Gate
+
+A formally verified single-neuron threshold network computing negated conjunction.
+Weights are integer-constrained and activation uses the Heaviside step function.
+NAND is functionally complete - any Boolean function can be built from NAND gates.
+"""
+
+import torch
+from safetensors.torch import load_file
+
+
+class ThresholdNAND:
+    """
+    NAND gate implemented as a threshold neuron.
+
+    Circuit: output = (w1*x1 + w2*x2 + bias >= 0)
+    With weights=[-1,-1], bias=1: fires unless both inputs are 1.
+    """
+
+    def __init__(self, weights_dict):
+        self.weight = weights_dict['weight']
+        self.bias = weights_dict['bias']
+
+    def __call__(self, x1, x2):
+        inputs = torch.tensor([float(x1), float(x2)])
+        weighted_sum = (inputs * self.weight).sum() + self.bias
+        return (weighted_sum >= 0).float()
+
+    @classmethod
+    def from_safetensors(cls, path="model.safetensors"):
+        return cls(load_file(path))
+
+
+def forward(x, weights):
+    """
+    Forward pass with Heaviside activation.
+
+    Args:
+        x: Input tensor of shape [..., 2]
+        weights: Dict with 'weight' and 'bias' tensors
+
+    Returns:
+        NAND(x[0], x[1])
+    """
+    x = torch.as_tensor(x, dtype=torch.float32)
+    weighted_sum = (x * weights['weight']).sum(dim=-1) + weights['bias']
+    return (weighted_sum >= 0).float()
+
+
+if __name__ == "__main__":
+    weights = load_file("model.safetensors")
+    model = ThresholdNAND(weights)
+
+    print("NAND Gate Truth Table:")
+    print("-" * 25)
+    for x1 in [0, 1]:
+        for x2 in [0, 1]:
+            out = int(model(x1, x2).item())
+            expected = 1 - (x1 & x2)
+            status = "OK" if out == expected else "FAIL"
+            print(f"NAND({x1}, {x2}) = {out}  [{status}]")

model.safetensors

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+size 140