# Three-Tier Verification Report

- Bundle: `sum_monoid`
- Impossible: 1
- Rare: 0
- Emergent: 0
- External: 2
- Verified: 0

| Obligation | Declared | Evidence | Verified | Statistical |
|---|---|---|---|---|
| `associativity` | `External` | `Impossible` | `false` | `Impossible` at p=0 (bound 0.05) |
| `left_identity` | `External` | `External` | `false` | - |
| `right_identity` | `External` | `External` | `false` | - |

Report files:
- Schema version: `1`
- JSON: `target/karpal-verify-golden/summary.three-tier.json`
- Markdown: `target/karpal-verify-golden/summary.three-tier.md`
