Pith Number

pith:4R5JUJ3B

pith:2021:4R5JUJ3B367NNTF4ACXPLXA3U6

not attested not anchored not stored refs pending

Ringing of a black hole in a dark matter halo

Dong Liu, Shurui Wu, Yi Yang, Yujia Xing, Zhaoyi Xu, Zheng-Wen Long

arxiv:2104.04332 v3 · 2021-04-09 · 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{4R5JUJ3B367NNTF4ACXPLXA3U6}

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

Black holes surrounded by dark matter spike: Spacetime metrics and gravitational wave ringdown waveforms

Receipt and verification

First computed	2026-07-05T03:33:04.993247Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e47a9a2761dfbed6ccbc00aef5dc1ba79c81dc3290b5210b4ece092008b63140

Aliases

arxiv: 2104.04332 · arxiv_version: 2104.04332v3 · doi: 10.48550/arxiv.2104.04332 · pith_short_12: 4R5JUJ3B367N · pith_short_16: 4R5JUJ3B367NNTF4 · pith_short_8: 4R5JUJ3B

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/4R5JUJ3B367NNTF4ACXPLXA3U6 \
  | 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: e47a9a2761dfbed6ccbc00aef5dc1ba79c81dc3290b5210b4ece092008b63140

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dcf9762f14860af05fb7cd8e8602167c733ab50d84ddae9c6a05491bc6ac2392",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2021-04-09T12:29:35Z",
    "title_canon_sha256": "572efc3df7f9072d71b8bfc5b426856e9321fbecf4f092273705ba52db1a0f1d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2104.04332",
    "kind": "arxiv",
    "version": 3
  }
}