# Executable verification and canonical identity

For responses already decoded to the task's verifier surface, the supplied `code/oat_drgrpo/math_grader.py` entry point is `validated_modebench_outcome_key(response, row["answer"])`. It returns a canonical key only when that same response passes the executable task verifier; invalid responses return `None`.

| Domain | Executable acceptance | Canonical identity |
| --- | --- | --- |
| Graph Coloring | Parse assignments; preserve fixed colors and satisfy every edge | Complete color vector |
| Countdown | Restricted arithmetic AST, exact operand multiplicities and exact target value | Normalized expression AST with registered commutative normalization |
| Python Factors | Restricted function AST executed in the bounded external worker on the specified cases | Executed return vector |
| MathIR | Restricted action menu expanded and executed using exact equation transformations | Executed normalized state trajectory |
| PantryPlan | Bounded ingredient quantities, serving steps, mass/nutrient constraints and dietary restrictions | Ingredient support |

Install the versioned dependencies recorded in `MANIFEST.json`/`requirements-verifier.txt`; prepend the release's `code` directory to Python's import path. The code is supplied as inspectable ordinary source, not automatically executed by the datasets loader.

```python
import sys
sys.path.insert(0, "path/to/ModeBench/code")
from oat_drgrpo.math_grader import validated_modebench_outcome_key

key = validated_modebench_outcome_key(response, row["answer"])
verified = key is not None
```

Policy action adapters must run before this grader when the registered interface uses them. In particular, Pantry's six-bit support mask is not an allocation string: use `decode_pantry_support_mask(mask, json.loads(row["answer"]))` from `oat_drgrpo.pantry_support_action`, then grade the returned allocation. The frozen adapter searches only the chosen support's registered quantity grid and returns an invalid sentinel when infeasible; it does not consult a gold support catalogue. `canonical_actions.py` preserves the other registered action-to-verifier adapters.

Python Factors retains its original separate, syntax-restricted worker. Use the supplied implementation for model outputs rather than evaluating arbitrary response strings in a notebook. The code also contains imported legacy task support needed by the original module; this release's dataset configurations contain only the five listed domains.

All copied verifier/template dependencies are authenticated against the completed Level-3 confirmation's source hashes. The release validation checks canonical *problem* identity uniqueness and disjointness, row/feature preservation, and the original structural/support-histogram records. It does not regenerate every exhaustive answer catalogue, retrain models, or claim a new model-admission result.