Pith Number

pith:OB4QLO4G

pith:2026:OB4QLO4GTJ2JIIGIHZ3OYXHFZL

not attested not anchored not stored refs pending

Shadows and photon spheres of static black holes embedded in a Dehnen-(1,4,5/2)-type dark matter halo with a quintessential field

Bofeng Wu, Enwei Liang, Hong-Er Gong, Junlin Qin, Xiao Zhang, Yusen Wang, Zhan-Feng Mai

arxiv:2605.19567 v1 · 2026-05-19 · 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{OB4QLO4GTJ2JIIGIHZ3OYXHFZL}

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	2026-05-20T01:05:52.158816Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

707905bb869a749420c83e76ec5ce5cad0f03032ce00a132c432228e64074ec6

Aliases

arxiv: 2605.19567 · arxiv_version: 2605.19567v1 · doi: 10.48550/arxiv.2605.19567 · pith_short_12: OB4QLO4GTJ2J · pith_short_16: OB4QLO4GTJ2JIIGI · pith_short_8: OB4QLO4G

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/OB4QLO4GTJ2JIIGIHZ3OYXHFZL \
  | 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: 707905bb869a749420c83e76ec5ce5cad0f03032ce00a132c432228e64074ec6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c1f5200da2ca58dd9af8daba6a51319279a80aafd8f7e3821824f08bc65f9b4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-05-19T09:13:06Z",
    "title_canon_sha256": "30e058882668c475ba8f011632defeef98dd04b404cafdd63e43f31aede70461"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.19567",
    "kind": "arxiv",
    "version": 1
  }
}