Pith Number

pith:AZG5LXKC

pith:2010:AZG5LXKC3X2KFVXLM4UNUSRNZ5

not attested not anchored not stored refs pending

Grand canonical ensembles in general relativity

David Klein, Wei-Shih Yang

arxiv:1009.3846 v2 · 2010-09-20 · math-ph · gr-qc · 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{AZG5LXKC3X2KFVXLM4UNUSRNZ5}

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	2026-05-18T04:00:01.369087Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

064dd5dd42ddf4a2d6eb6728da4a2dcf5ad32b72b3ac776445911c04b8ded5f0

Aliases

arxiv: 1009.3846 · arxiv_version: 1009.3846v2 · doi: 10.48550/arxiv.1009.3846 · pith_short_12: AZG5LXKC3X2K · pith_short_16: AZG5LXKC3X2KFVXL · pith_short_8: AZG5LXKC

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/AZG5LXKC3X2KFVXLM4UNUSRNZ5 \
  | 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: 064dd5dd42ddf4a2d6eb6728da4a2dcf5ad32b72b3ac776445911c04b8ded5f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "146831c6060a8c881859a9ea46658c96a38a1fdc30904604c1dd8c5984a81d88",
    "cross_cats_sorted": [
      "gr-qc",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-09-20T14:58:59Z",
    "title_canon_sha256": "5c5d72d5c24adb3beb8eafeb5a958a27e522527730531152c5ab671909d47710"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.3846",
    "kind": "arxiv",
    "version": 2
  }
}