Pith Number

pith:X7QY3FMX

pith:2011:X7QY3FMXWHBE6WO45E7OK4RDRV

not attested not anchored not stored refs pending

Gr\"obner-Shirshov bases for free partially commutative Lie algebras

Qiuhui Mo, Yuqun Chen

arxiv:1105.4796 v1 · 2011-04-21 · 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{X7QY3FMXWHBE6WO45E7OK4RDRV}

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	2026-05-18T03:01:11.622212Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfe18d9597b1c24f59dce93ee572238d75f3d4558ba1eff273b7c0d637f95220

Aliases

arxiv: 1105.4796 · arxiv_version: 1105.4796v1 · doi: 10.48550/arxiv.1105.4796 · pith_short_12: X7QY3FMXWHBE · pith_short_16: X7QY3FMXWHBE6WO4 · pith_short_8: X7QY3FMX

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/X7QY3FMXWHBE6WO45E7OK4RDRV \
  | 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: bfe18d9597b1c24f59dce93ee572238d75f3d4558ba1eff273b7c0d637f95220

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b2a1d2d2a65c45935bc1bb58f9f4ac1af7095adfc1ea45d262448db4f78ea5e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2011-04-21T14:52:46Z",
    "title_canon_sha256": "292c26e97429caa6c63a06867ccf65d04a153d2b63dc3f241538ba34f2a11f3b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.4796",
    "kind": "arxiv",
    "version": 1
  }
}