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README.md

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+---
+license: mit
+tags:
+- formal-verification
+- coq
+- threshold-logic
+- neuromorphic
+- modular-arithmetic
+---
+
+# tiny-mod12-verified
+
+Formally verified MOD-12 circuit. Single-layer threshold network computing modulo-12 arithmetic with 100% accuracy.
+
+## Architecture
+
+| Component | Value |
+|-----------|-------|
+| Inputs | 8 |
+| Outputs | 1 (per residue class) |
+| Neurons | 12 (one per residue 0-11) |
+| Parameters | 108 (12 × 9) |
+| Weights | [1, 1, 1, 1, 1, 1, 1, 1] |
+| Bias | 0 |
+| Activation | Heaviside step |
+
+## Key Properties
+
+- 100% accuracy (256/256 inputs correct)
+- Coq-proven correctness
+- All-ones weight pattern (m > input width)
+- Computes Hamming weight mod 12
+- Compatible with neuromorphic hardware
+
+## Algebraic Pattern
+
+MOD-12 uses all-ones weights because the reset position (position 12) is beyond the 8-bit input width:
+- All positions 1-8: weight = 1
+- Position 12 (beyond input): would be weight = 1-12 = -11
+
+The circuit tracks cumulative sum mod 12 using the Hamming weight directly.
+
+## Usage
+
+```python
+import torch
+from safetensors.torch import load_file
+
+weights = load_file('mod12.safetensors')
+
+def mod12_circuit(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.item()) % 12
+
+# Test
+print(mod12_circuit([1,1,1,1,1,1,1,1]))  # 8 mod 12 = 8
+print(mod12_circuit([1,1,1,1,0,0,0,0]))  # 4 mod 12 = 4
+```
+
+## Verification
+
+**Coq Theorem**:
+```coq
+Theorem mod12_correct_residue_0 : forall x0 x1 x2 x3 x4 x5 x6 x7,
+  mod12_is_zero [x0; x1; x2; x3; x4; x5; x6; x7] =
+  Z.eqb ((Z.of_nat (hamming_weight [x0; x1; x2; x3; x4; x5; x6; x7])) mod 12) 0.
+```
+
+Proven axiom-free using algebraic weight patterns.
+
+Full proof: [coq-circuits/Modular/Mod12.v](https://github.com/CharlesCNorton/coq-circuits/blob/main/coq/Modular/Mod12.v)
+
+## Residue Distribution
+
+For 8-bit inputs (256 total), limited to residues 0-8:
+- Residue 0: 1 inputs
+- Residue 1: 8 inputs
+- Residue 2: 28 inputs
+- Residue 3: 56 inputs
+- Residue 4: 70 inputs
+- Residue 5: 56 inputs
+- Residue 6: 28 inputs
+- Residue 7: 8 inputs
+- Residue 8: 1 inputs
+- Residues 9-11: 0 inputs (unreachable with 8-bit input)
+
+## Citation
+
+```bibtex
+@software{tiny_mod12_verified_2025,
+  title={tiny-mod12-verified: Formally Verified MOD-12 Circuit},
+  author={Norton, Charles},
+  url={https://huggingface.co/phanerozoic/tiny-mod12-verified},
+  year={2025}
+}
+```