Pith Number

pith:7L7F4ZOV

pith:2016:7L7F4ZOVNOQZ7MAVNQRYRKPM3T

not attested not anchored not stored refs pending

Shuffle and Fa\`a di Bruno Hopf Algebras in the Center Problem for Ordinary Differential Equations

Alexander Brudnyi

arxiv:1602.08655 v1 · 2016-02-28 · math.CA · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7L7F4ZOVNOQZ7MAVNQRYRKPM3T}

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	2026-05-18T01:19:52.288670Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fafe5e65d56ba19fb0156c2388a9ecdce4cb790490c7cce3612c8a700118bb3f

Aliases

arxiv: 1602.08655 · arxiv_version: 1602.08655v1 · doi: 10.48550/arxiv.1602.08655 · pith_short_12: 7L7F4ZOVNOQZ · pith_short_16: 7L7F4ZOVNOQZ7MAV · pith_short_8: 7L7F4ZOV

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/7L7F4ZOVNOQZ7MAVNQRYRKPM3T \
  | 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: fafe5e65d56ba19fb0156c2388a9ecdce4cb790490c7cce3612c8a700118bb3f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1890991dcfa2567911d7688f632be0032065fe2e55b6d3205f6e998efc91d86d",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-02-28T01:33:35Z",
    "title_canon_sha256": "db8cf2277611535d27ef5aedc4d31553cec83d44b23fbdf05b6d73a3607540dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.08655",
    "kind": "arxiv",
    "version": 1
  }
}