Pith Number

pith:URKEUVCK

pith:2025:URKEUVCKQRWZKOG3QX63R7ZYBI

not attested not anchored not stored refs pending

The existence and upper bound for stable photon spheres in static spherically symmetric black holes

Jiaqi Fu, Yiting Cen, Yong Song

arxiv:2508.19823 v2 · 2025-08-27 · 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{URKEUVCKQRWZKOG3QX63R7ZYBI}

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	2026-07-05T12:11:20.166607Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4544a544a846d9538db85fdb8ff380a3eac8a3ef10308d8c5fd5505fa78761d

Aliases

arxiv: 2508.19823 · arxiv_version: 2508.19823v2 · doi: 10.48550/arxiv.2508.19823 · pith_short_12: URKEUVCKQRWZ · pith_short_16: URKEUVCKQRWZKOG3 · pith_short_8: URKEUVCK

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/URKEUVCKQRWZKOG3QX63R7ZYBI \
  | 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: a4544a544a846d9538db85fdb8ff380a3eac8a3ef10308d8c5fd5505fa78761d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "16a8fd19b9ba6afa1e86e11e0b8a74946d34a0718190ac18d72a30670bd1923a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2025-08-27T12:14:20Z",
    "title_canon_sha256": "aba3c33b1bc0c2521300f811274f80e8ae53aeb8b82a969ce730fc7b537a873b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.19823",
    "kind": "arxiv",
    "version": 2
  }
}