Pith Number

pith:DM36LWNU

pith:2014:DM36LWNUESEOVIQEWBGBVS7UFU

not attested not anchored not stored refs pending

Multiplier Hopf algebroids arising from weak multiplier Hopf algebras

Alfons Van Daele, Thomas Timmermann

arxiv:1406.3509 v1 · 2014-06-13 · 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{DM36LWNUESEOVIQEWBGBVS7UFU}

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	2026-05-18T02:49:46.539092Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b37e5d9b42488eaa204b04c1acbf42d317912d6b396799af1beebd1dbd4dcf3

Aliases

arxiv: 1406.3509 · arxiv_version: 1406.3509v1 · doi: 10.48550/arxiv.1406.3509 · pith_short_12: DM36LWNUESEO · pith_short_16: DM36LWNUESEOVIQE · pith_short_8: DM36LWNU

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/DM36LWNUESEOVIQEWBGBVS7UFU \
  | 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: 1b37e5d9b42488eaa204b04c1acbf42d317912d6b396799af1beebd1dbd4dcf3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e1ba5e2a8b61c74608fa28b50a3901e9f5f62a35ad23ea6e8e95e79c9a581b1d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2014-06-13T11:37:44Z",
    "title_canon_sha256": "898b124ed8606ffc5af7d9b84d0609a8f421d59cb0a61fcc3e90d11e979973a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1406.3509",
    "kind": "arxiv",
    "version": 1
  }
}