Pith Number

pith:VSB3WUM2

pith:2009:VSB3WUM2IOEJTGSYTWOCZZ7RLZ

not attested not anchored not stored refs pending

Measured Quantum Groupoids Associated with Matched Pairs of Locally Compact Groupoids

Jean-Michel Vallin

arxiv:0906.5247 v5 · 2009-06-29 · math.OA · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VSB3WUM2IOEJTGSYTWOCZZ7RLZ}

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	2026-05-18T04:21:13.746216Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac83bb519a4388999a589d9c2ce7f15e49823fd82f15c3ee19ad3f9847e384ae

Aliases

arxiv: 0906.5247 · arxiv_version: 0906.5247v5 · doi: 10.48550/arxiv.0906.5247 · pith_short_12: VSB3WUM2IOEJ · pith_short_16: VSB3WUM2IOEJTGSY · pith_short_8: VSB3WUM2

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/VSB3WUM2IOEJTGSYTWOCZZ7RLZ \
  | 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: ac83bb519a4388999a589d9c2ce7f15e49823fd82f15c3ee19ad3f9847e384ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3adc372607682385f9f4cff015d0348b356448e30e7586f39f05f87d841641ca",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2009-06-29T12:21:47Z",
    "title_canon_sha256": "9beaa45ebf462a4cb85c87122a37af3c9ae4e80881ab85e2894491f533f45533"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.5247",
    "kind": "arxiv",
    "version": 5
  }
}