Pith Number

pith:FC6VAYS4

pith:2026:FC6VAYS4IX6I7ZS7UOMNF3EBFX

not attested not anchored not stored refs pending

Periodic orbits and gravitational waveforms around a Schwarzschild black hole with a cloud of strings embedded in perfect fluid dark matter

Qi-Qi Liang, Zhenglong Ban, Zheng-Wen Long, Zhi Li, Ziqiang Cai

arxiv:2605.25625 v1 · 2026-05-25 · 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{FC6VAYS4IX6I7ZS7UOMNF3EBFX}

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	2026-05-26T02:04:47.084887Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28bd50625c45fc8fe65fa398d2ec812dd81e39a6443793a4746855295b669bc8

Aliases

arxiv: 2605.25625 · arxiv_version: 2605.25625v1 · doi: 10.48550/arxiv.2605.25625 · pith_short_12: FC6VAYS4IX6I · pith_short_16: FC6VAYS4IX6I7ZS7 · pith_short_8: FC6VAYS4

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/FC6VAYS4IX6I7ZS7UOMNF3EBFX \
  | 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: 28bd50625c45fc8fe65fa398d2ec812dd81e39a6443793a4746855295b669bc8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2aeeca432c216a8ffbd3239559a554fbce53f107795f28ff292a492e36924be1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-05-25T09:28:15Z",
    "title_canon_sha256": "4ac4d9fba1c1715006da713a63ae16ae3f28a0576befc3079711423f28594eb0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.25625",
    "kind": "arxiv",
    "version": 1
  }
}