Pith Number

pith:XUDG7OSM

pith:2002:XUDG7OSMZAARSN62I7VKSZ2Q5S

not attested not anchored not stored refs pending

On spectral representation of coalgebras and Hopf algebroids

Janez Mrcun

arxiv:math/0208199 v1 · 2002-08-26 · math.QA · math.DG · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XUDG7OSMZAARSN62I7VKSZ2Q5S}

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	2026-05-18T04:08:43.190431Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd066fba4cc8011937da47eaa96750ecabc284a14439d1974cd7662685ee697d

Aliases

arxiv: math/0208199 · arxiv_version: math/0208199v1 · doi: 10.48550/arxiv.math/0208199 · pith_short_12: XUDG7OSMZAAR · pith_short_16: XUDG7OSMZAARSN62 · pith_short_8: XUDG7OSM

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/XUDG7OSMZAARSN62I7VKSZ2Q5S \
  | 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: bd066fba4cc8011937da47eaa96750ecabc284a14439d1974cd7662685ee697d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a399e0e47a03126d3ecece97b8a85b6af8f901f05d53935e8106ef8e73d86805",
    "cross_cats_sorted": [
      "math.DG",
      "math.OA"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2002-08-26T12:26:59Z",
    "title_canon_sha256": "70d79e9311fcff8e3e671114592d88893f8114192748705ae75a71cdf01eea91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0208199",
    "kind": "arxiv",
    "version": 1
  }
}