Pith Number

pith:4XGXAOPZ

pith:2013:4XGXAOPZ5GCSTB3ACJF473OZ5R

not attested not anchored not stored refs pending

Weak multiplier bialgebras

Esperanza L\'opez-Centella, Gabriella B\"ohm, Jos\'e G\'omez-Torrecillas

arxiv:1306.1466 v2 · 2013-06-06 · 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{4XGXAOPZ5GCSTB3ACJF473OZ5R}

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	2026-05-18T03:08:47.068523Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5cd7039f9e985298760124bcfedd9ec6b8407636883c1803c42bfad621c23b8

Aliases

arxiv: 1306.1466 · arxiv_version: 1306.1466v2 · doi: 10.48550/arxiv.1306.1466 · pith_short_12: 4XGXAOPZ5GCS · pith_short_16: 4XGXAOPZ5GCSTB3A · pith_short_8: 4XGXAOPZ

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/4XGXAOPZ5GCSTB3ACJF473OZ5R \
  | 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: e5cd7039f9e985298760124bcfedd9ec6b8407636883c1803c42bfad621c23b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c90742de0c551e5ed5f9e6766c3cb070f8842469aed7de72a6897c313f6aadf2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2013-06-06T16:35:18Z",
    "title_canon_sha256": "1dca27c9beaa5833f6f95d11c73709531b5c91d552406653c7162be1244cfdc8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.1466",
    "kind": "arxiv",
    "version": 2
  }
}