Pith Number

pith:52ALWOV5

pith:2026:52ALWOV5M3ABHMV2YQADNG5NZ4

not attested not anchored not stored refs pending

Periodic orbits and gravitational waveforms of black holes in bumblebee gravity

Xiangdong Zhang, Yunlong Liu, Zijian Shi

arxiv:2603.14413 v1 · 2026-03-15 · 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{52ALWOV5M3ABHMV2YQADNG5NZ4}

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	2026-06-08T01:04:00.993695Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee80bb3abd66c013b2bac400369badcf1c1ff6c4eb9575533084d102e0852ba2

Aliases

arxiv: 2603.14413 · arxiv_version: 2603.14413v1 · doi: 10.48550/arxiv.2603.14413 · pith_short_12: 52ALWOV5M3AB · pith_short_16: 52ALWOV5M3ABHMV2 · pith_short_8: 52ALWOV5

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/52ALWOV5M3ABHMV2YQADNG5NZ4 \
  | 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: ee80bb3abd66c013b2bac400369badcf1c1ff6c4eb9575533084d102e0852ba2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ce8398c5d9d668620813d7007c411f71992c657f56f04b9341eab5a475bdf67",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-03-15T14:56:13Z",
    "title_canon_sha256": "f57ead364f43ea27f7aa19d0297bf6c6478cea3a659999fdbc52d7c0ca0ea7e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.14413",
    "kind": "arxiv",
    "version": 1
  }
}