Pith Number

pith:NIBH2VUB

pith:2026:NIBH2VUBGYE3K3ZV4GQBYMZ4FS

not attested not anchored not stored refs pending

Post-Grokking Collapse at the Representation-Readout Interface in Muon-Trained Transformers

Ali Janati, Anass Belfatmi, Andrei Kanavalau, Kaoutar El Maghraoui

arxiv:2608.07436 v1 · 2026-08-07 · cs.AI · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NIBH2VUBGYE3K3ZV4GQBYMZ4FS}

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	2026-08-10T01:15:23.479189Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a027d56813609b56f35e1a01c333c2ca73f6f9168e8394863a93635174187a8

Aliases

arxiv: 2608.07436 · arxiv_version: 2608.07436v1 · doi: 10.48550/arxiv.2608.07436 · pith_short_12: NIBH2VUBGYE3 · pith_short_16: NIBH2VUBGYE3K3ZV · pith_short_8: NIBH2VUB

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/NIBH2VUBGYE3K3ZV4GQBYMZ4FS \
  | 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: 6a027d56813609b56f35e1a01c333c2ca73f6f9168e8394863a93635174187a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f58aa7a8a9038a1b7b69b51558b478b84b212e46a0e015bab91f2892507e4a76",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.AI",
    "submitted_at": "2026-08-07T17:21:49Z",
    "title_canon_sha256": "3ef0a167a73288550de906ea9e6dbfcf0b6284730d070602e4584d2651f2b41e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.07436",
    "kind": "arxiv",
    "version": 1
  }
}