Pith Number

pith:O2PQ3SYE

pith:2014:O2PQ3SYE6VM7FFKCNZWSXI2L3N

not attested not anchored not stored refs pending

Hawking's singularity theorem for $C^{1,1}$-metrics

James A. Vickers, Michael Kunzinger, Milena Stojkovic, Roland Steinbauer

arxiv:1411.4689 v3 · 2014-11-17 · gr-qc · math-ph · math.DG · 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{O2PQ3SYE6VM7FFKCNZWSXI2L3N}

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	2026-05-18T01:04:41.796988Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

769f0dcb04f559f295426e6d2ba34bdb6671f04d6ad378ff7d7945ad5be9a241

Aliases

arxiv: 1411.4689 · arxiv_version: 1411.4689v3 · doi: 10.48550/arxiv.1411.4689 · pith_short_12: O2PQ3SYE6VM7 · pith_short_16: O2PQ3SYE6VM7FFKC · pith_short_8: O2PQ3SYE

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/O2PQ3SYE6VM7FFKCNZWSXI2L3N \
  | 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: 769f0dcb04f559f295426e6d2ba34bdb6671f04d6ad378ff7d7945ad5be9a241

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ea4194de2aaebc698c7bd2e62a1e0a2bc460fb2a303ca49dad0b865de54d16e",
    "cross_cats_sorted": [
      "math-ph",
      "math.DG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2014-11-17T22:46:42Z",
    "title_canon_sha256": "eea7b3635624b981831995a4fe11a85dfdd2a606bb4f76bc53b3bab903794b49"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.4689",
    "kind": "arxiv",
    "version": 3
  }
}