Pith Number

pith:QXOM3DAK

pith:1999:QXOM3DAKUC7KJMBUC74NGNWBW2

not attested not anchored not stored refs pending

Gravity on Finite Groups

Leonardo Castellani

arxiv:gr-qc/9909028 v2 · 1999-09-07 · gr-qc · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QXOM3DAKUC7KJMBUC74NGNWBW2}

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	2026-07-04T16:13:54.335737Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

85dccd8c0aa0bea4b03417f8d336c1b6935970b3e672f9eaf27a54c26456259b

Aliases

arxiv: gr-qc/9909028 · arxiv_version: gr-qc/9909028v2 · doi: 10.48550/arxiv.gr-qc/9909028 · pith_short_12: QXOM3DAKUC7K · pith_short_16: QXOM3DAKUC7KJMBU · pith_short_8: QXOM3DAK

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/QXOM3DAKUC7KJMBUC74NGNWBW2 \
  | 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: 85dccd8c0aa0bea4b03417f8d336c1b6935970b3e672f9eaf27a54c26456259b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "142c6435bf85dff29a48d068feb2fc39b665b72d34cb480f0df554311dfce160",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "1999-09-07T17:55:25Z",
    "title_canon_sha256": "17eccd78d33b40adde873f368e6b9757b1f2c96e06537d5de242a1e02e9748b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/9909028",
    "kind": "arxiv",
    "version": 2
  }
}