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README.md

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+---
+license: mit
+tags:
+- formal-verification
+- coq
+- threshold-logic
+- neuromorphic
+---
+
+# tiny-1OutOf8-prover
+
+Formally verified 1-out-of-8 threshold gate. 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 | -1 |
+| Activation | Heaviside step |
+
+## Key Properties
+
+- 100% accuracy (256/256 inputs correct)
+- Coq-proven correctness
+- Single threshold neuron
+- Integer weights
+- Fires when at least 1 of 8 inputs are true
+
+
+## Usage
+
+```python
+import torch
+from safetensors.torch import load_file
+
+weights = load_file('oneoutof8.safetensors')
+
+def oneoutof8_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(oneoutof8_gate([0,0,0,0,0,0,0,0]))  # 0 (no bits set)
+print({func}_gate([1,0,0,0,0,0,0,0]))  # 1 (1/8, at threshold)
+print(oneoutof8_gate([1,1,1,1,1,1,1,1]))  # 1 (8/8, above threshold)
+```
+
+## Verification
+
+**Coq Theorem**:
+```coq
+Theorem oneout_eight_correct : forall x0 x1 x2 x3 x4 x5 x6 x7,
+  oneout_eight_circuit [x0; x1; x2; x3; x4; x5; x6; x7] =
+  oneout_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 ≥ 1
+
+Full proof: [coq-circuits/Threshold/OneOutOfEight.v](https://github.com/CharlesCNorton/coq-circuits)
+
+## Circuit Operation
+
+Input with h true bits (Hamming weight h):
+- Weighted sum: h - 1
+- Output: 1 if h ≥ 1, else 0
+
+## Citation
+
+```bibtex
+@software{tiny_1outof8_prover_2025,
+  title={tiny-1OutOf8-prover: Formally Verified 1-out-of-8 threshold gate},
+  author={Norton, Charles},
+  url={https://huggingface.co/phanerozoic/tiny-1OutOf8-prover},
+  year={2025}
+}
+```