Pith Number

pith:4WP7DRF2

pith:2012:4WP7DRF2ZGRGKKJSVSKVMC2IER

not attested not anchored not stored refs pending

On the causal characterization of singularities in spherically symmetric spacetimes

Francesc Fayos, Ramon Torres

arxiv:1204.4651 v1 · 2012-04-20 · 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{4WP7DRF2ZGRGKKJSVSKVMC2IER}

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	2026-05-18T03:57:25.803722Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e59ff1c4bac9a2652932ac95560b482445d1cc9b76cf58f0a2a2b3e343728830

Aliases

arxiv: 1204.4651 · arxiv_version: 1204.4651v1 · doi: 10.48550/arxiv.1204.4651 · pith_short_12: 4WP7DRF2ZGRG · pith_short_16: 4WP7DRF2ZGRGKKJS · pith_short_8: 4WP7DRF2

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/4WP7DRF2ZGRGKKJSVSKVMC2IER \
  | 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: e59ff1c4bac9a2652932ac95560b482445d1cc9b76cf58f0a2a2b3e343728830

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "445f20fdaf42907e7c6cc49b3a0e5492415072c66d44d5a4641dcdb5c58a3dd0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2012-04-20T14:52:26Z",
    "title_canon_sha256": "70a05b13bb74616e06de933b2b8a01e97cd9fcd5f92a3157f34d871052cc54c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.4651",
    "kind": "arxiv",
    "version": 1
  }
}