Pith Number

pith:CBPNUM3C

pith:2026:CBPNUM3C4SAVPEVTFKMYRFN7NK

not attested not anchored not stored refs pending

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics

Truong Xuan Khanh

arxiv:2607.06639 v1 · 2026-07-07 · cs.LG · cs.AI

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CBPNUM3C4SAVPEVTFKMYRFN7NK}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-09T00:19:21.372436Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

105eda3362e4815792b32a998895bf6ab464dacd7e013df19527288d44536027

Aliases

arxiv: 2607.06639 · arxiv_version: 2607.06639v1 · doi: 10.48550/arxiv.2607.06639 · pith_short_12: CBPNUM3C4SAV · pith_short_16: CBPNUM3C4SAVPEVT · pith_short_8: CBPNUM3C

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CBPNUM3C4SAVPEVTFKMYRFN7NK \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 105eda3362e4815792b32a998895bf6ab464dacd7e013df19527288d44536027

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6aff299ea4a80dd361d810085f37c792abc09a629ce24707b4c08c36b83ee168",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-07T14:44:18Z",
    "title_canon_sha256": "6a31cfe07d367f51ce775ba0d6bf1d9bd1be9f49319db1cd81f5f0ec1fd530fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.06639",
    "kind": "arxiv",
    "version": 1
  }
}