Pith Number

pith:UST4L2FF

pith:2010:UST4L2FFZUWWMCSDXMEQ5FMMQJ

not attested not anchored not stored refs pending

Hopf monads on monoidal categories

Alain Brugui\`eres, Alexis Virelizier, Steve Lack

arxiv:1003.1920 v4 · 2010-03-09 · math.QA · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UST4L2FFZUWWMCSDXMEQ5FMMQJ}

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	2026-05-18T02:24:38.043847Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4a7c5e8a5cd2d660a43bb090e958c826ee20bd0dcb14d1b4db09e11209b5551

Aliases

arxiv: 1003.1920 · arxiv_version: 1003.1920v4 · doi: 10.48550/arxiv.1003.1920 · pith_short_12: UST4L2FFZUWW · pith_short_16: UST4L2FFZUWWMCSD · pith_short_8: UST4L2FF

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/UST4L2FFZUWWMCSDXMEQ5FMMQJ \
  | 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: a4a7c5e8a5cd2d660a43bb090e958c826ee20bd0dcb14d1b4db09e11209b5551

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a911bf5b92ed72e2ddc00caaff328b4254a1e6fb22e52139df7a35bd15767c6",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2010-03-09T16:27:11Z",
    "title_canon_sha256": "555f5b5e2708a23a1f8f7e67e83a0b31db8dc3b76d85c9794b609d976ea74d79"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.1920",
    "kind": "arxiv",
    "version": 4
  }
}