Pith Number

pith:N32TT7LO

pith:2011:N32TT7LOLPWOHZ3WPJ7KJO42YM

not attested not anchored not stored refs pending

Black Holes in the Universe: Generalized Lemaitre-Tolman-Bondi Solutions

Changjun Gao, Valerio Faraoni, Xuelei Chen, You-Gen Shen

arxiv:1110.6708 v3 · 2011-10-31 · 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{N32TT7LOLPWOHZ3WPJ7KJO42YM}

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	2026-05-18T01:59:49.802477Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ef539fd6e5bece3e7767a7ea4bb9ac31c824b21f374d638d0d8f4df43feb1c4

Aliases

arxiv: 1110.6708 · arxiv_version: 1110.6708v3 · doi: 10.48550/arxiv.1110.6708 · pith_short_12: N32TT7LOLPWO · pith_short_16: N32TT7LOLPWOHZ3W · pith_short_8: N32TT7LO

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/N32TT7LOLPWOHZ3WPJ7KJO42YM \
  | 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: 6ef539fd6e5bece3e7767a7ea4bb9ac31c824b21f374d638d0d8f4df43feb1c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0afb3ea61d620829d12e41ec85219a397bb19a1d1bb3f8b1b956e6516e127c74",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2011-10-31T07:26:02Z",
    "title_canon_sha256": "a870817b67d337f99d7f4a3a8a32a7861189c0cd33ff2b6cb77897256e2a217b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.6708",
    "kind": "arxiv",
    "version": 3
  }
}