Upload README.md with huggingface_hub

README.md

@@ -0,0 +1,97 @@
+---
+license: mit
+tags:
+- formal-verification
+- coq
+- threshold-logic
+- neuromorphic
+- functionally-complete
+---
+
+# tiny-NOR-prover
+
+Formally verified NOR gate. Single threshold neuron computing negated disjunction with 100% accuracy.
+
+## Architecture
+
+| Component | Value |
+|-----------|-------|
+| Inputs | 2 |
+| Outputs | 1 |
+| Neurons | 1 |
+| Parameters | 3 |
+| Weights | [-1, -1] |
+| Bias | 0 |
+| Activation | Heaviside step |
+
+## Key Properties
+
+- 100% accuracy (4/4 inputs correct)
+- Coq-proven correctness
+- Single threshold neuron
+- Integer weights
+- Commutative: NOR(x,y) = NOR(y,x)
+- Functionally complete (can build any Boolean function)
+- Self-dual: NOR(x,x) = NOT(x)
+
+## Usage
+
+```python
+import torch
+from safetensors.torch import load_file
+
+weights = load_file('nor.safetensors')
+
+def nor_gate(x, y):
+    # Heaviside: weighted_sum + bias >= 0
+    inputs = torch.tensor([float(x), float(y)])
+    weighted_sum = (inputs * weights['weight']).sum() + weights['bias']
+    return int(weighted_sum >= 0)
+
+# Test
+print(nor_gate(0, 0))  # 1
+print(nor_gate(0, 1))  # 0
+print(nor_gate(1, 0))  # 0
+print(nor_gate(1, 1))  # 0
+```
+
+## Verification
+
+**Coq Theorem**:
+```coq
+Theorem nor_correct : forall x y, nor_circuit x y = negb (orb x y).
+```
+
+Proven axiom-free with properties:
+- Commutativity
+- Self-duality (NOR(x,x) = NOT(x))
+- Functional completeness
+- Identity with false gives NOT
+- Absorption with true gives false
+
+Full proof: [coq-circuits/Boolean/NOR.v](https://github.com/CharlesCNorton/coq-circuits)
+
+## Circuit Operation
+
+Input combination produces weighted sum:
+- (0,0): 0*(-1) + 0*(-1) + 0 = 0 >= 0 → 1
+- (0,1): 0*(-1) + 1*(-1) + 0 = -1 < 0 → 0
+- (1,0): 1*(-1) + 0*(-1) + 0 = -1 < 0 → 0
+- (1,1): 1*(-1) + 1*(-1) + 0 = -2 < 0 → 0
+
+Fires only when both inputs are false.
+
+## Functional Completeness
+
+NOR is functionally complete - any Boolean function can be built from NOR gates alone. This makes it particularly important for circuit composition.
+
+## Citation
+
+```bibtex
+@software{tiny_nor_prover_2025,
+  title={tiny-NOR-prover: Formally Verified NOR Gate},
+  author={Norton, Charles},
+  url={https://huggingface.co/phanerozoic/tiny-NOR-prover},
+  year={2025}
+}
+```