Pith Number

pith:QDUVJ5GM

pith:2002:QDUVJ5GMOTNOO6SAD7K6KDBI2P

not attested not anchored not stored refs pending

Tannaka-Krein duality for Hopf algebroids

Phung Ho Hai

arxiv:math/0206113 v2 · 2002-06-11 · math.QA · math.CT · 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{QDUVJ5GMOTNOO6SAD7K6KDBI2P}

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	2026-05-17T23:45:55.727624Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80e954f4cc74dae77a401fd5e50c28d3ddda5bbf7ffb6f8b3ab13e3ab1edff21

Aliases

arxiv: math/0206113 · arxiv_version: math/0206113v2 · doi: 10.48550/arxiv.math/0206113 · pith_short_12: QDUVJ5GMOTNO · pith_short_16: QDUVJ5GMOTNOO6SA · pith_short_8: QDUVJ5GM

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/QDUVJ5GMOTNOO6SAD7K6KDBI2P \
  | 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: 80e954f4cc74dae77a401fd5e50c28d3ddda5bbf7ffb6f8b3ab13e3ab1edff21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc643937bc7c8dcafac2de59e12b331a8791b1f5ef82d3f311e9fd0c029cbd84",
    "cross_cats_sorted": [
      "math.CT",
      "math.RA"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2002-06-11T08:58:19Z",
    "title_canon_sha256": "ccd7120a71c368c5c1f55548a5fdc5c3d0973943bf0062b5ba81dc7899394a4f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0206113",
    "kind": "arxiv",
    "version": 2
  }
}