Pith Number

pith:ZGSJ63XM

pith:2003:ZGSJ63XMDQHSAVXBRGFQQ45MS4

not attested not anchored not stored refs pending

Hopf algebroids with bijective antipodes: axioms, integrals and duals

Gabriella B"ohm, Korn'el Szlach'anyi

arxiv:math/0302325 v1 · 2003-02-26 · 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{ZGSJ63XMDQHSAVXBRGFQQ45MS4}

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.

Cited by

1 paper in Pith

Examples of scalar extension Hopf algebroids over a universal enveloping algebra

Receipt and verification

First computed	2026-07-04T14:37:06.481821Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9a49f6eec1c0f2056e1898b0873ac9701ea6d49609a5d989c45f6eb2b1af719

Aliases

arxiv: math/0302325 · arxiv_version: math/0302325v1 · doi: 10.48550/arxiv.math/0302325 · pith_short_12: ZGSJ63XMDQHS · pith_short_16: ZGSJ63XMDQHSAVXB · pith_short_8: ZGSJ63XM

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/ZGSJ63XMDQHSAVXBRGFQQ45MS4 \
  | 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: c9a49f6eec1c0f2056e1898b0873ac9701ea6d49609a5d989c45f6eb2b1af719

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d90f82b0f6114d5718e031bbbf02bb619ca46a19476cda83506a4387ffa4ae2",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2003-02-26T11:49:00Z",
    "title_canon_sha256": "6a0994761289407164f21a38e523b8eac9bac6004488ddbb25ce594a57fc3451"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0302325",
    "kind": "arxiv",
    "version": 1
  }
}