Pith Number

pith:FUZRVIWO

pith:2009:FUZRVIWOPPKIX6I2PQVEQEPILU

not attested not anchored not stored refs pending

A note on the global structure of proper Lie groupoids in low codimensions

Giorgio Trentinaglia

arxiv:0907.2856 v1 · 2009-07-16 · math.RT · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FUZRVIWOPPKIX6I2PQVEQEPILU}

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	2026-05-18T04:30:12.768731Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d331aa2ce7bd48bf91a7c2a4811e85d17c04dc19ceaeef2bdaa581ffd9b7512

Aliases

arxiv: 0907.2856 · arxiv_version: 0907.2856v1 · doi: 10.48550/arxiv.0907.2856 · pith_short_12: FUZRVIWOPPKI · pith_short_16: FUZRVIWOPPKIX6I2 · pith_short_8: FUZRVIWO

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/FUZRVIWOPPKIX6I2PQVEQEPILU \
  | 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: 2d331aa2ce7bd48bf91a7c2a4811e85d17c04dc19ceaeef2bdaa581ffd9b7512

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef804b395d7b0149d50e2daa94338917c5f1386be537e9dea0d5fae88ea13e6e",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2009-07-16T14:44:18Z",
    "title_canon_sha256": "fbde661e6a8dc96b388b2bea807b7313c135f5151a4c498cff49e5d7908767b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.2856",
    "kind": "arxiv",
    "version": 1
  }
}