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routing_schema.md

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-# Routing Schema for 8-bit Threshold Computer
-
-## Overview
-
-The routing file (`routing.json`) defines how gates are interconnected. Each entry maps a gate path to its input sources.
-
-## Schema Format
-
-```json
-{
-  "version": 1,
-  "external_inputs": {
-    "circuit_path": ["input_name", ...]
-  },
-  "routing": {
-    "gate_path": ["source1", "source2", ...]
-  }
-}
-```
-
-## Input Source Types
-
-1. **External input**: `"$input_name"` - Named input to the circuit
-   - Example: `"$a"`, `"$b"`, `"$cin"`
-
-2. **Gate output**: `"path.to.gate"` - Output of another gate
-   - Example: `"ha1.sum"`, `"layer1.or"`
-
-3. **Bit extraction**: `"$input[i]"` - Single bit from multi-bit input
-   - Example: `"$a[0]"` (LSB), `"$a[7]"` (MSB for 8-bit)
-
-4. **Constant**: `"#0"` or `"#1"` - Fixed value
-   - Example: `"#1"` for carry-in in two's complement
-
-5. **Relative reference**: `"../sibling.gate"` - Reference to sibling in hierarchy
-   - Example: `"../fa0.cout"` from fa1
-
-## Circuit Types
-
-### Single-Layer Gates
-Gates with just `.weight` and `.bias`:
-```json
-"boolean.and": ["$a", "$b"]
-```
-
-### Two-Layer Gates (XOR, XNOR)
-Gates decomposed into layer1 + layer2:
-```json
-"boolean.xor.layer1.or": ["$a", "$b"],
-"boolean.xor.layer1.nand": ["$a", "$b"],
-"boolean.xor.layer2": ["layer1.or", "layer1.nand"]
-```
-
-### Hierarchical Circuits
-Complex circuits with sub-components:
-```json
-"arithmetic.fulladder": {
-  "external_inputs": ["$a", "$b", "$cin"],
-  "gates": {
-    "ha1.sum.layer1.or": ["$a", "$b"],
-    "ha1.sum.layer1.nand": ["$a", "$b"],
-    "ha1.sum.layer2": ["ha1.sum.layer1.or", "ha1.sum.layer1.nand"],
-    "ha1.carry": ["$a", "$b"],
-    "ha2.sum.layer1.or": ["ha1.sum", "$cin"],
-    "ha2.sum.layer1.nand": ["ha1.sum", "$cin"],
-    "ha2.sum.layer2": ["ha2.sum.layer1.or", "ha2.sum.layer1.nand"],
-    "ha2.carry": ["ha1.sum", "$cin"],
-    "carry_or": ["ha1.carry", "ha2.carry"]
-  },
-  "outputs": {
-    "sum": "ha2.sum",
-    "cout": "carry_or"
-  }
-}
-```
-
-### Bit-Indexed Circuits
-Circuits operating on multi-bit values:
-```json
-"arithmetic.ripplecarry8bit": {
-  "external_inputs": ["$a[0:7]", "$b[0:7]"],
-  "gates": {
-    "fa0": {"inputs": ["$a[0]", "$b[0]", "#0"], "type": "fulladder"},
-    "fa1": {"inputs": ["$a[1]", "$b[1]", "fa0.cout"], "type": "fulladder"},
-    ...
-  }
-}
-```
-
-## Naming Conventions
-
-- External inputs: `$name` or `$name[bit]`
-- Constants: `#0`, `#1`
-- Internal gates: relative path from circuit root
-- Outputs: named in `outputs` section
-
-## Validation Rules
-
-1. Every gate in routing must exist in tensors file
-2. Every tensor must have routing entry
-3. Input count must match weight dimensions
-4. No circular dependencies (DAG only)
-5. All referenced sources must exist