Pith Number

pith:VTIAASGC

pith:2019:VTIAASGCEUMAO3K3MCKMJXBF5D

not attested not anchored not stored refs pending

Null geodesic incompleteness of spacetimes with no CMC Cauchy surfaces

Daniel Pollack, Madeleine Burkhart, Martin Lesourd

arxiv:1902.07411 v3 · 2019-02-20 · gr-qc · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VTIAASGCEUMAO3K3MCKMJXBF5D}

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	2026-05-17T23:52:26.661555Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

acd00048c22518076d5b6094c4dc25e8c1a5e4edce5d5380a35ebd5f8743e818

Aliases

arxiv: 1902.07411 · arxiv_version: 1902.07411v3 · doi: 10.48550/arxiv.1902.07411 · pith_short_12: VTIAASGCEUMA · pith_short_16: VTIAASGCEUMAO3K3 · pith_short_8: VTIAASGC

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/VTIAASGCEUMAO3K3MCKMJXBF5D \
  | 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: acd00048c22518076d5b6094c4dc25e8c1a5e4edce5d5380a35ebd5f8743e818

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3344c5d11eb617347ce3c453716846a29201ef3a8abc2539c467f7d5564ec44c",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2019-02-20T05:27:40Z",
    "title_canon_sha256": "2b3a7ac09cac51301291bc44fae5c092d965bba250710d623d61025d6544783c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.07411",
    "kind": "arxiv",
    "version": 3
  }
}