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README.md

@@ -1,92 +1,92 @@
----
-license: mit
-tags:
-- formal-verification
-- coq
-- threshold-logic
-- neuromorphic
----
-
-# tiny-OR-verified
-
-Formally verified OR gate. Single threshold neuron computing disjunction with 100% accuracy.
-
-## Architecture
-
-| Component | Value |
-|-----------|-------|
-| Inputs | 2 |
-| Outputs | 1 |
-| Neurons | 1 |
-| Parameters | 3 |
-| Weights | [1, 1] |
-| Bias | -1 |
-| Activation | Heaviside step |
-
-## Key Properties
-
-- 100% accuracy (4/4 inputs correct)
-- Coq-proven correctness
-- Single threshold neuron
-- Integer weights
-- Commutative: OR(x,y) = OR(y,x)
-- Associative: OR(x,OR(y,z)) = OR(OR(x,y),z)
-- Idempotent: OR(x,x) = x
-
-## Usage
-
-```python
-import torch
-from safetensors.torch import load_file
-
-weights = load_file('or.safetensors')
-
-def or_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(or_gate(0, 0))  # 0
-print(or_gate(0, 1))  # 1
-print(or_gate(1, 0))  # 1
-print(or_gate(1, 1))  # 1
-```
-
-## Verification
-
-**Coq Theorem**:
-```coq
-Theorem or_correct : forall x y, or_circuit x y = orb x y.
-```
-
-Proven axiom-free with properties:
-- Commutativity
-- Associativity
-- Identity (OR with false)
-- Absorption (OR with true)
-- Idempotence
-
-Full proof: [coq-circuits/Boolean/OR.v](https://github.com/CharlesCNorton/coq-circuits)
-
-## Circuit Operation
-
-Input combination produces weighted sum:
-- (0,0): 0*1 + 0*1 - 1 = -1 < 0 → 0
-- (0,1): 0*1 + 1*1 - 1 = 0 >= 0 → 1
-- (1,0): 1*1 + 0*1 - 1 = 0 >= 0 → 1
-- (1,1): 1*1 + 1*1 - 1 = 1 >= 0 → 1
-
-Requires at least one input to reach threshold.
-
-## Citation
-
-```bibtex
-@software{tiny_or_prover_2025,
-  title={tiny-OR-verified: Formally Verified OR Gate},
-  author={Norton, Charles},
-  url={https://huggingface.co/phanerozoic/tiny-OR-verified},
-  year={2025}
-}
-```
+---
+license: mit
+tags:
+- formal-verification
+- coq
+- threshold-logic
+- neuromorphic
+---
+
+# tiny-OR-verified
+
+Formally verified OR gate. Single threshold neuron computing disjunction with 100% accuracy.
+
+## Architecture
+
+| Component | Value |
+|-----------|-------|
+| Inputs | 2 |
+| Outputs | 1 |
+| Neurons | 1 |
+| Parameters | 3 |
+| Weights | [1, 1] |
+| Bias | -1 |
+| Activation | Heaviside step |
+
+## Key Properties
+
+- 100% accuracy (4/4 inputs correct)
+- Coq-proven correctness
+- Single threshold neuron
+- Integer weights
+- Commutative: OR(x,y) = OR(y,x)
+- Associative: OR(x,OR(y,z)) = OR(OR(x,y),z)
+- Idempotent: OR(x,x) = x
+
+## Usage
+
+```python
+import torch
+from safetensors.torch import load_file
+
+weights = load_file('or.safetensors')
+
+def or_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(or_gate(0, 0))  # 0
+print(or_gate(0, 1))  # 1
+print(or_gate(1, 0))  # 1
+print(or_gate(1, 1))  # 1
+```
+
+## Verification
+
+**Coq Theorem**:
+```coq
+Theorem or_correct : forall x y, or_circuit x y = orb x y.
+```
+
+Proven axiom-free with properties:
+- Commutativity
+- Associativity
+- Identity (OR with false)
+- Absorption (OR with true)
+- Idempotence
+
+Full proof: [coq-circuits/Boolean/OR.v](https://github.com/CharlesCNorton/coq-circuits/blob/main/coq/Boolean/OR.v)
+
+## Circuit Operation
+
+Input combination produces weighted sum:
+- (0,0): 0*1 + 0*1 - 1 = -1 < 0 → 0
+- (0,1): 0*1 + 1*1 - 1 = 0 >= 0 → 1
+- (1,0): 1*1 + 0*1 - 1 = 0 >= 0 → 1
+- (1,1): 1*1 + 1*1 - 1 = 1 >= 0 → 1
+
+Requires at least one input to reach threshold.
+
+## Citation
+
+```bibtex
+@software{tiny_or_prover_2025,
+  title={tiny-OR-verified: Formally Verified OR Gate},
+  author={Norton, Charles},
+  url={https://huggingface.co/phanerozoic/tiny-OR-verified},
+  year={2025}
+}
+```