Pith Number

pith:CQRBZG4A

pith:2021:CQRBZG4AYEP4FUIABMNNHA2LE4

not attested not anchored not stored refs pending

The Ponzano-Regge cylinder and Propagator for 3d quantum gravity

Etera R. Livine

arxiv:2107.03264 v2 · 2021-07-07 · hep-th · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CQRBZG4AYEP4FUIABMNNHA2LE4}

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	2026-07-05T03:32:07.506181Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14221c9b80c11fc2d1000b1ad3834b2710ee1279b404a7aa63a3be32de2d1403

Aliases

arxiv: 2107.03264 · arxiv_version: 2107.03264v2 · doi: 10.48550/arxiv.2107.03264 · pith_short_12: CQRBZG4AYEP4 · pith_short_16: CQRBZG4AYEP4FUIA · pith_short_8: CQRBZG4A

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/CQRBZG4AYEP4FUIABMNNHA2LE4 \
  | 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: 14221c9b80c11fc2d1000b1ad3834b2710ee1279b404a7aa63a3be32de2d1403

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "52475644c0342a73740503dfa0fd892269015ff2570fcececf7e1e9577c0e2d3",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2021-07-07T15:00:37Z",
    "title_canon_sha256": "c4e95d4f97d70b7b7cabebff0ce711b0c1bc0ac1cde48079badda734706732c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.03264",
    "kind": "arxiv",
    "version": 2
  }
}