Pith Number

pith:BX3SPMZM

pith:2013:BX3SPMZMQE4UTIW72SVZH2JHJN

not attested not anchored not stored refs pending

Multiplier Hopf algebroids. Basic theory and examples

Alfons Van Daele, Thomas Timmermann

arxiv:1307.0769 v6 · 2013-07-02 · 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{BX3SPMZMQE4UTIW72SVZH2JHJN}

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	2026-05-18T00:40:08.788386Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0df727b32c813949a2dfd4ab93e9274b53b8d8a692debf4b23aa3e8a84faaa0b

Aliases

arxiv: 1307.0769 · arxiv_version: 1307.0769v6 · doi: 10.48550/arxiv.1307.0769 · pith_short_12: BX3SPMZMQE4U · pith_short_16: BX3SPMZMQE4UTIW7 · pith_short_8: BX3SPMZM

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/BX3SPMZMQE4UTIW72SVZH2JHJN \
  | 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: 0df727b32c813949a2dfd4ab93e9274b53b8d8a692debf4b23aa3e8a84faaa0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8229b82b7b9d524cf4cf231c1de78a00178da5b87735a3c64c6d5a5d14797091",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2013-07-02T17:24:12Z",
    "title_canon_sha256": "1d048c1c44491d9f870117de106bf1f1202d6b40dc3b732bbfa31cb441ae4569"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.0769",
    "kind": "arxiv",
    "version": 6
  }
}