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README.md

@@ -1,87 +1,87 @@
----
-license: mit
-tags:
-- formal-verification
-- coq
-- threshold-logic
-- neuromorphic
----
-
-# tiny-5OutOf8-verified
-
-Formally verified 5-out-of-8 threshold gate (majority). Single threshold neuron with 100% accuracy.
-
-## Architecture
-
-| Component | Value |
-|-----------|-------|
-| Inputs | 8 |
-| Outputs | 1 |
-| Neurons | 1 |
-| Parameters | 9 |
-| Weights | [1, 1, 1, 1, 1, 1, 1, 1] |
-| Bias | -5 |
-| Activation | Heaviside step |
-
-## Key Properties
-
-- 100% accuracy (256/256 inputs correct)
-- Coq-proven correctness
-- Single threshold neuron
-- Integer weights
-- Fires when at least 5 of 8 inputs are true
-- **Note**: Equivalent to Majority gate.
-
-## Usage
-
-```python
-import torch
-from safetensors.torch import load_file
-
-weights = load_file('fiveoutof8.safetensors')
-
-def fiveoutof8_gate(bits):
-    # bits: list of 8 binary values
-    inputs = torch.tensor([float(b) for b in bits])
-    weighted_sum = (inputs * weights['weight']).sum() + weights['bias']
-    return int(weighted_sum >= 0)
-
-# Test
-print({func}_gate([0,0,0,0,0,0,0,0]))  # 0 (0/5, below threshold)
-print({func}_gate([1,1,1,1,0,0,0,0]))  # 0 (4/8, below threshold)
-print({func}_gate([1,1,1,1,1,0,0,0]))  # 1 (5/8, at threshold)
-print(fiveoutof8_gate([1,1,1,1,1,1,1,1]))  # 1 (8/8, above threshold)
-```
-
-## Verification
-
-**Coq Theorem**:
-```coq
-Theorem fiveout_eight_correct : forall x0 x1 x2 x3 x4 x5 x6 x7,
-  fiveout_eight_circuit [x0; x1; x2; x3; x4; x5; x6; x7] =
-  fiveout_eight_spec [x0; x1; x2; x3; x4; x5; x6; x7].
-```
-
-Proven axiom-free via:
-1. **Exhaustive**: All 256 inputs verified
-2. **Universal**: Quantified proof over boolean combinations
-3. **Algebraic**: Hamming weight ≥ 5
-
-Full proof: [coq-circuits/Threshold/FiveOutOfEight.v](https://github.com/CharlesCNorton/coq-circuits)
-
-## Circuit Operation
-
-Input with h true bits (Hamming weight h):
-- Weighted sum: h - 5
-- Output: 1 if h ≥ 5, else 0
-
-## Citation
-
-```bibtex
-@software{tiny_5outof8_prover_2025,
-  title={tiny-5OutOf8-verified: Formally Verified 5-out-of-8 threshold gate (majority)},
-  author={Norton, Charles},
-  url={https://huggingface.co/phanerozoic/tiny-5OutOf8-verified},
-  year={2025}
-}
-```
+---
+license: mit
+tags:
+- formal-verification
+- coq
+- threshold-logic
+- neuromorphic
+---
+
+# tiny-5OutOf8-verified
+
+Formally verified 5-out-of-8 threshold gate (majority). Single threshold neuron with 100% accuracy.
+
+## Architecture
+
+| Component | Value |
+|-----------|-------|
+| Inputs | 8 |
+| Outputs | 1 |
+| Neurons | 1 |
+| Parameters | 9 |
+| Weights | [1, 1, 1, 1, 1, 1, 1, 1] |
+| Bias | -5 |
+| Activation | Heaviside step |
+
+## Key Properties
+
+- 100% accuracy (256/256 inputs correct)
+- Coq-proven correctness
+- Single threshold neuron
+- Integer weights
+- Fires when at least 5 of 8 inputs are true
+- **Note**: Equivalent to Majority gate.
+
+## Usage
+
+```python
+import torch
+from safetensors.torch import load_file
+
+weights = load_file('fiveoutof8.safetensors')
+
+def fiveoutof8_gate(bits):
+    # bits: list of 8 binary values
+    inputs = torch.tensor([float(b) for b in bits])
+    weighted_sum = (inputs * weights['weight']).sum() + weights['bias']
+    return int(weighted_sum >= 0)
+
+# Test
+print({func}_gate([0,0,0,0,0,0,0,0]))  # 0 (0/5, below threshold)
+print({func}_gate([1,1,1,1,0,0,0,0]))  # 0 (4/8, below threshold)
+print({func}_gate([1,1,1,1,1,0,0,0]))  # 1 (5/8, at threshold)
+print(fiveoutof8_gate([1,1,1,1,1,1,1,1]))  # 1 (8/8, above threshold)
+```
+
+## Verification
+
+**Coq Theorem**:
+```coq
+Theorem fiveout_eight_correct : forall x0 x1 x2 x3 x4 x5 x6 x7,
+  fiveout_eight_circuit [x0; x1; x2; x3; x4; x5; x6; x7] =
+  fiveout_eight_spec [x0; x1; x2; x3; x4; x5; x6; x7].
+```
+
+Proven axiom-free via:
+1. **Exhaustive**: All 256 inputs verified
+2. **Universal**: Quantified proof over boolean combinations
+3. **Algebraic**: Hamming weight ≥ 5
+
+Full proof: [coq-circuits/Threshold/FiveOutOfEight.v](https://github.com/CharlesCNorton/coq-circuits/blob/main/coq/Threshold/FiveOutOfEight.v)
+
+## Circuit Operation
+
+Input with h true bits (Hamming weight h):
+- Weighted sum: h - 5
+- Output: 1 if h ≥ 5, else 0
+
+## Citation
+
+```bibtex
+@software{tiny_5outof8_prover_2025,
+  title={tiny-5OutOf8-verified: Formally Verified 5-out-of-8 threshold gate (majority)},
+  author={Norton, Charles},
+  url={https://huggingface.co/phanerozoic/tiny-5OutOf8-verified},
+  year={2025}
+}
+```