Pith Number

pith:ZVF44JTU

pith:2003:ZVF44JTUMLGN2PS5PIU7CYLVH3

not attested not anchored not stored refs pending

Causal Geometry of Einstein-Vacuum Spacetimes with Finite Curvature Flux

Igor Rodnianski, Sergiu Klainerman

arxiv:math/0308123 v2 · 2003-08-13 · math.AP · 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{ZVF44JTUMLGN2PS5PIU7CYLVH3}

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	2026-05-18T01:05:28.718513Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd4bce267462ccdd3e5d7a29f161753ee0470e69fd5ec947f8476d2f18d4f857

Aliases

arxiv: math/0308123 · arxiv_version: math/0308123v2 · doi: 10.48550/arxiv.math/0308123 · pith_short_12: ZVF44JTUMLGN · pith_short_16: ZVF44JTUMLGN2PS5 · pith_short_8: ZVF44JTU

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/ZVF44JTUMLGN2PS5PIU7CYLVH3 \
  | 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: cd4bce267462ccdd3e5d7a29f161753ee0470e69fd5ec947f8476d2f18d4f857

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b78ef0c29018a3ba3340554e5d9f6810c97a06994e590365567e6813ec1f7c9a",
    "cross_cats_sorted": [
      "gr-qc",
      "math-ph",
      "math.DG",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2003-08-13T19:20:39Z",
    "title_canon_sha256": "1d4bb68f8a3c603f24c11e2ce647eda6379a455c54104ffb6475d2157989f686"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0308123",
    "kind": "arxiv",
    "version": 2
  }
}