Pith Number

pith:Y5SOQXPF

pith:2011:Y5SOQXPFTRW3H4GKJILFCVHFVR

not attested not anchored not stored refs pending

Elements of causality theory

Piotr T. Chru\'sciel

arxiv:1110.6706 v1 · 2011-10-31 · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y5SOQXPFTRW3H4GKJILFCVHFVR}

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.

Cited by

2 papers in Pith

Stability of Synthetic Timelike Ricci Bounds under $C^0$-Limits and Applications to Impulsive Gravitational Waves

Hausdorff-type metric geometry of the space of Cauchy hypersurfaces

Receipt and verification

First computed	2026-05-18T04:09:54.765460Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c764e85de59c6db3f0ca4a165154e5ac7709f30ff692dbf718d6db4ff924e281

Aliases

arxiv: 1110.6706 · arxiv_version: 1110.6706v1 · doi: 10.48550/arxiv.1110.6706 · pith_short_12: Y5SOQXPFTRW3 · pith_short_16: Y5SOQXPFTRW3H4GK · pith_short_8: Y5SOQXPF

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/Y5SOQXPFTRW3H4GKJILFCVHFVR \
  | 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: c764e85de59c6db3f0ca4a165154e5ac7709f30ff692dbf718d6db4ff924e281

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68b1fc2f2231b8996800bf9d5984ecc567ba0261980ae4edb76faeb56d79cb80",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2011-10-31T07:02:58Z",
    "title_canon_sha256": "ea9c48f9651ffa1b59c1be227ede6b3daf7020ddf991859507b5704e5769833f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.6706",
    "kind": "arxiv",
    "version": 1
  }
}