Pith Number

pith:GOTXSE5P

pith:2026:GOTXSE5PUKK5BCBQJAR5FMR56W

not attested not anchored not stored refs pending

The Active Ingredient in Muon's Grokking

Yufeng Wang

arxiv:2607.20512 v1 · 2026-07-06 · 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{GOTXSE5PUKK5BCBQJAR5FMR56W}

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	2026-07-24T00:23:19.729243Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33a77913afa295d088304823d2b23df593e7e5c82e3d9c14ca3bb37cb753e565

Aliases

arxiv: 2607.20512 · arxiv_version: 2607.20512v1 · doi: 10.48550/arxiv.2607.20512 · pith_short_12: GOTXSE5PUKK5 · pith_short_16: GOTXSE5PUKK5BCBQ · pith_short_8: GOTXSE5P

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/GOTXSE5PUKK5BCBQJAR5FMR56W \
  | 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: 33a77913afa295d088304823d2b23df593e7e5c82e3d9c14ca3bb37cb753e565

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2296a0c490be950a41c961eac5cf8b10fbfacc290dd9ef6fb8a1e69387a6014d",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-06T22:35:57Z",
    "title_canon_sha256": "f0c89356cd3c875bb7934638c42d5a216592519c50d3418968515c77ef229c79"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.20512",
    "kind": "arxiv",
    "version": 1
  }
}