Pith Number

pith:Z4FQMEGS

pith:2010:Z4FQMEGSJW3K2LEPSYFV3QDR4X

not attested not anchored not stored refs pending

The symmetric operation in a free pre-Lie algebra is magmatic

Jean-Louis Loday, Nantel Bergeron

arxiv:1004.1204 v3 · 2010-04-07 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z4FQMEGSJW3K2LEPSYFV3QDR4X}

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	2026-05-18T01:00:10.733331Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf0b0610d24db6ad2c8f960b5dc071e5c717e1392bb0d15f4747f91f40ad69e8

Aliases

arxiv: 1004.1204 · arxiv_version: 1004.1204v3 · doi: 10.48550/arxiv.1004.1204 · pith_short_12: Z4FQMEGSJW3K · pith_short_16: Z4FQMEGSJW3K2LEP · pith_short_8: Z4FQMEGS

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/Z4FQMEGSJW3K2LEPSYFV3QDR4X \
  | 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: cf0b0610d24db6ad2c8f960b5dc071e5c717e1392bb0d15f4747f91f40ad69e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4fcc3fe854a5219ed95f196601f31bc189601490af0138c72ac454fbc76ea0f2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2010-04-07T22:49:52Z",
    "title_canon_sha256": "cf9231a8d35b1be5463c5eb29d55ac8013ee675d8578c254af1b85b1ad4ca137"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.1204",
    "kind": "arxiv",
    "version": 3
  }
}