Pith Number

pith:V3EQXIUI

pith:2018:V3EQXIUILERLGY5UYKML7XDHYO

not attested not anchored not stored refs pending

A Hopf algebra without modular pair in involution

Sebastian Halbig, Ulrich Kraehmer

arxiv:1810.03350 v1 · 2018-10-08 · 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{V3EQXIUILERLGY5UYKML7XDHYO}

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	2026-05-18T00:03:51.597637Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aec90ba2885922b363b4c298bfdc67c3aaf18aec85825777db8e18451571b918

Aliases

arxiv: 1810.03350 · arxiv_version: 1810.03350v1 · doi: 10.48550/arxiv.1810.03350 · pith_short_12: V3EQXIUILERL · pith_short_16: V3EQXIUILERLGY5U · pith_short_8: V3EQXIUI

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/V3EQXIUILERLGY5UYKML7XDHYO \
  | 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: aec90ba2885922b363b4c298bfdc67c3aaf18aec85825777db8e18451571b918

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ede44f2862b8e6e50d64676b66210f0f6bc48764f2ebe587e57dc9f0d127fbd1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2018-10-08T09:53:09Z",
    "title_canon_sha256": "3a4caa031988fb39394a9f089682d5c6c9f3bb6073c5aad55d1d875330d88606"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.03350",
    "kind": "arxiv",
    "version": 1
  }
}