Pith Number

pith:MPMVCCVD

pith:2015:MPMVCCVDGMNZ6GOEJRXC7FKCHK

not attested not anchored not stored refs pending

Examples of extensions of Hopf algebras

Monique M\"uller, Nicol\'as Andruskiewitsch

arxiv:1503.07344 v1 · 2015-03-25 · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MPMVCCVDGMNZ6GOEJRXC7FKCHK}

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	2026-05-18T02:20:21.322926Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63d9510aa3331b9f19c44c6e2f95423a88e06d9a3a09c2b05b52e20fba147f69

Aliases

arxiv: 1503.07344 · arxiv_version: 1503.07344v1 · doi: 10.48550/arxiv.1503.07344 · pith_short_12: MPMVCCVDGMNZ · pith_short_16: MPMVCCVDGMNZ6GOE · pith_short_8: MPMVCCVD

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/MPMVCCVDGMNZ6GOEJRXC7FKCHK \
  | 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: 63d9510aa3331b9f19c44c6e2f95423a88e06d9a3a09c2b05b52e20fba147f69

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86470236492f033422794a502881150ae82ca41686d3b4268d996c0ae464e9e5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2015-03-25T11:40:26Z",
    "title_canon_sha256": "5d5f562db0c666a43d3c5bd2fed4b013183a26201b39783df4290ea8c68f987a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.07344",
    "kind": "arxiv",
    "version": 1
  }
}