Pith Number

pith:VYVAN5LI

pith:2024:VYVAN5LIIUAE5MFDFZ5Y6G2CB5

not attested not anchored not stored refs pending

Gravitational lensing effect of black holes in effective quantum gravity

De-Cheng Zou, Hao Liu, Hyat Huang, Meng-Yun Lai, Xiao-Yin Pan

arxiv:2408.11603 v2 · 2024-08-21 · 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{VYVAN5LIIUAE5MFDFZ5Y6G2CB5}

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

2 papers in Pith

Particle motions and gravitational waveforms in rotating black hole spacetimes of loop quantum gravity

Reference-renormalized curvature-primitive Gauss-Bonnet formalism for finite-distance weak gravitational lensing in static spherical spacetimes

Receipt and verification

First computed	2026-07-05T09:37:09.817087Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae2a06f56845004eb0a32e7b8f1b420f4bc2a4c3e1345d664b38b4ab8cf326d1

Aliases

arxiv: 2408.11603 · arxiv_version: 2408.11603v2 · doi: 10.48550/arxiv.2408.11603 · pith_short_12: VYVAN5LIIUAE · pith_short_16: VYVAN5LIIUAE5MFD · pith_short_8: VYVAN5LI

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/VYVAN5LIIUAE5MFDFZ5Y6G2CB5 \
  | 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: ae2a06f56845004eb0a32e7b8f1b420f4bc2a4c3e1345d664b38b4ab8cf326d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab1de9c13aae3a41636dee2f4f2b8a4e5039d82db94b088e4c5c012f003847a0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2024-08-21T13:20:51Z",
    "title_canon_sha256": "003aed31cf5c9f9b3c05ef05f7ab7170a3088dad30d50b5ec01bef9e88dd2b1b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2408.11603",
    "kind": "arxiv",
    "version": 2
  }
}