Pith Number

pith:PP24JBMH

pith:2015:PP24JBMH2QZWCUQDBJUNW2VV6T

not attested not anchored not stored refs pending

Uniqueness of photon spheres in electro-vacuum spacetimes

Carla Cederbaum, Gregory J. Galloway

arxiv:1508.00355 v2 · 2015-08-03 · math.DG · gr-qc · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PP24JBMH2QZWCUQDBJUNW2VV6T}

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

Photon Surfaces in Higher-Curvature Gravity: Implications for Quasinormal Modes and Gravitational Lensing

Receipt and verification

First computed	2026-05-18T01:18:33.462601Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bf5c48587d4336152030a68db6ab5f4ee1e94db2004e69782ceab5b97742b95

Aliases

arxiv: 1508.00355 · arxiv_version: 1508.00355v2 · doi: 10.48550/arxiv.1508.00355 · pith_short_12: PP24JBMH2QZW · pith_short_16: PP24JBMH2QZWCUQD · pith_short_8: PP24JBMH

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/PP24JBMH2QZWCUQDBJUNW2VV6T \
  | 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: 7bf5c48587d4336152030a68db6ab5f4ee1e94db2004e69782ceab5b97742b95

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f996d8009b9984f2679c5bf0b76767e69769eebcd5ec7aeb2414ba687f4ad3c3",
    "cross_cats_sorted": [
      "gr-qc",
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-08-03T09:29:43Z",
    "title_canon_sha256": "df9bfa9490b432020078554ba82a4ff8b272c64ecaeb892aab5271cba782c45a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.00355",
    "kind": "arxiv",
    "version": 2
  }
}