Pith Number

pith:QWY5FWA2

pith:2012:QWY5FWA2FHRSCNLB54RKWRA7U4

not attested not anchored not stored refs pending

Duality for groupoid (co)actions

Antonio Paques, Daiana Fl\^ores

arxiv:1209.3681 v1 · 2012-09-17 · 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{QWY5FWA2FHRSCNLB54RKWRA7U4}

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	2026-05-18T01:27:15.522311Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

85b1d2d81a29e3213561ef22ab441fa73acd992836b26cb221a9cd606bcb0162

Aliases

arxiv: 1209.3681 · arxiv_version: 1209.3681v1 · doi: 10.48550/arxiv.1209.3681 · pith_short_12: QWY5FWA2FHRS · pith_short_16: QWY5FWA2FHRSCNLB · pith_short_8: QWY5FWA2

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/QWY5FWA2FHRSCNLB54RKWRA7U4 \
  | 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: 85b1d2d81a29e3213561ef22ab441fa73acd992836b26cb221a9cd606bcb0162

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ee3afe563eb7aab5f953029bf3ecf352f16ba1626b34f46cc8f3aa414c44af3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2012-09-17T15:07:05Z",
    "title_canon_sha256": "bf7a2cca3e15626bd52a737dd6c836b4c60c80b10702e943081564f75ff9de8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3681",
    "kind": "arxiv",
    "version": 1
  }
}