# RCIG K3 Canonical Kernel v0.3

This runtime is the first RCIG verifier that can genuinely accept:

```text
canonicality = "certified"
```

for the restricted profile:

```text
finite_state_critical_pairs_v0.1
```

## What K3 checks

1. ordinary CDIR trace soundness through the v0.2 reference semantics;
2. explicit finite state model;
3. all valid certificate-induced transitions;
4. exact equality between kernel-derived and declared transitions;
5. strict natural-number rank descent on every transition;
6. reachability of every declared state;
7. complete enumeration of every local transition fork;
8. replayed left/right join paths;
9. selected trace embedding;
10. unique reachable normal-form debt set.

## Scope

The canonicality theorem is **package-local**.

It covers the finite rewrite universe induced by the package's checked certificates and registered built-in rule semantics.

It does not claim absolute mathematical terminality.

## Windows / PowerShell

```powershell
py -m pip install jsonschema

py .\rcig_k3_canonical_kernel_v0_3.py .\samples\canonical_closed.json --schema .\RCIG_CDIR_v0.3.schema.json

py .\test_rcig_k3_canonical_kernel_v0_3.py
```

## Current attack result

12 / 12 expected outcomes passed.