Pith Number

pith:W4D3ZJO6

pith:2019:W4D3ZJO6YV3YDZSR6DJJ4KGCZI

not attested not anchored not stored refs pending

Causal concept for black hole shadows

Masaru Siino

arxiv:1908.02921 v2 · 2019-08-08 · gr-qc · astro-ph.HE

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W4D3ZJO6YV3YDZSR6DJJ4KGCZI}

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

1 paper in Pith

Gravitational lensing inside and outside of a marginally unstable photon sphere in a general, static, spherically symmetric, and asymptotically-flat spacetime in strong deflection limits

Receipt and verification

First computed	2026-07-05T01:42:52.137908Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b707bca5dec57781e651f0d29e28c2ca2b26890594b3e5dd29c25f8d1af8726b

Aliases

arxiv: 1908.02921 · arxiv_version: 1908.02921v2 · doi: 10.48550/arxiv.1908.02921 · pith_short_12: W4D3ZJO6YV3Y · pith_short_16: W4D3ZJO6YV3YDZSR · pith_short_8: W4D3ZJO6

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/W4D3ZJO6YV3YDZSR6DJJ4KGCZI \
  | 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: b707bca5dec57781e651f0d29e28c2ca2b26890594b3e5dd29c25f8d1af8726b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c4e6973bf0311f329b49dce98485b650362853148ed7166f724ed3f0a97b3c0",
    "cross_cats_sorted": [
      "astro-ph.HE"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2019-08-08T03:51:32Z",
    "title_canon_sha256": "588a65cc2fbd54a7a818fe109ca65dce5e572d4475805447fa4dbfd727b8fa40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.02921",
    "kind": "arxiv",
    "version": 2
  }
}