Pith Number

pith:2QSZAILD

pith:2012:2QSZAILDXO2ZUKNXANEW3T44KK

not attested not anchored not stored refs pending

Weak Multiplier Hopf Algebras. The main theory

Alfons Van Daele, Shuanhong Wang

arxiv:1210.4395 v1 · 2012-10-16 · math.RA · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2QSZAILDXO2ZUKNXANEW3T44KK}

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	2026-05-18T03:43:06.090640Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d425902163bbb59a29b703496dcf9c529547781e7ed1665ccb33c7fb9c76b8c8

Aliases

arxiv: 1210.4395 · arxiv_version: 1210.4395v1 · doi: 10.48550/arxiv.1210.4395 · pith_short_12: 2QSZAILDXO2Z · pith_short_16: 2QSZAILDXO2ZUKNX · pith_short_8: 2QSZAILD

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/2QSZAILDXO2ZUKNXANEW3T44KK \
  | 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: d425902163bbb59a29b703496dcf9c529547781e7ed1665ccb33c7fb9c76b8c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e52ff96f10b7781db80a66d02d5ea4369096a78db6ee281b20ed2244d2fa3a3e",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2012-10-16T13:15:36Z",
    "title_canon_sha256": "29b6e6330bf4759361c5c1e9832bb74bd5f76cbc86e757a4b23ad22bf6ca7839"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.4395",
    "kind": "arxiv",
    "version": 1
  }
}