Pith Number

pith:DJK2SILN

pith:2020:DJK2SILNKJSQPBXJ4ULYJFJ357

not attested not anchored not stored refs pending

Lower bound on the radii of black-hole photonspheres

Shahar Hod

arxiv:2012.03962 v1 · 2020-12-07 · gr-qc · astro-ph.HE · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DJK2SILNKJSQPBXJ4ULYJFJ357}

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	2026-07-05T01:59:36.334107Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1a55a9216d52650786e9e51784953befeeadda7e5674963cfa40d4a851824e0c

Aliases

arxiv: 2012.03962 · arxiv_version: 2012.03962v1 · doi: 10.48550/arxiv.2012.03962 · pith_short_12: DJK2SILNKJSQ · pith_short_16: DJK2SILNKJSQPBXJ · pith_short_8: DJK2SILN

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/DJK2SILNKJSQPBXJ4ULYJFJ357 \
  | 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: 1a55a9216d52650786e9e51784953befeeadda7e5674963cfa40d4a851824e0c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb63f19c1237a4b2526a4759328e8b00e02ca30168a94b3a5198637f560b5fa8",
    "cross_cats_sorted": [
      "astro-ph.HE",
      "hep-th"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2020-12-07T19:00:02Z",
    "title_canon_sha256": "4a08263f0d41379153759b0be1c80dd1cfdfcbffddab8942359e917bcd78b0cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.03962",
    "kind": "arxiv",
    "version": 1
  }
}