Pith Number

pith:KIOCU6NG

pith:2017:KIOCU6NG4ZYA5HXXRQV7LR6GG5

not attested not anchored not stored refs pending

Weak multiplier Hopf algebras III. Integrals and duality

Alfons Van Daele, Shuanhong Wang

arxiv:1701.04951 v4 · 2017-01-18 · 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{KIOCU6NG4ZYA5HXXRQV7LR6GG5}

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	2026-05-18T00:34:10.062816Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

521c2a79a6e6700e9ef78c2bf5c7c6376e65baff6b0e912692ca497ae68b1d99

Aliases

arxiv: 1701.04951 · arxiv_version: 1701.04951v4 · doi: 10.48550/arxiv.1701.04951 · pith_short_12: KIOCU6NG4ZYA · pith_short_16: KIOCU6NG4ZYA5HXX · pith_short_8: KIOCU6NG

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/KIOCU6NG4ZYA5HXXRQV7LR6GG5 \
  | 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: 521c2a79a6e6700e9ef78c2bf5c7c6376e65baff6b0e912692ca497ae68b1d99

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ee61e495cd5ee9b8af1713b0e1d50bc4ff5f43c4ba65234bec91b7c67aa3014",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2017-01-18T05:28:44Z",
    "title_canon_sha256": "81718fe71d1a8e909eb75eac1e937471076a022250d4857108bec1ad2fcecfcb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.04951",
    "kind": "arxiv",
    "version": 4
  }
}