Pith Number

pith:JHR5X2IK

pith:2021:JHR5X2IKYYCOODJVZRJWF72JIT

not attested not anchored not stored refs pending

Gravitational lensing by a black hole in effective loop quantum gravity

Qi-Ming Fu, Xin Zhang

arxiv:2111.07223 v2 · 2021-11-14 · gr-qc · hep-ph · hep-th

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JHR5X2IKYYCOODJVZRJWF72JIT}

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

3 papers in Pith

Strong-deflection expansion of the deflection angle near a degenerate photon sphere

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

Relative Magnification Factor of Point Sources on Accretion Disks

Receipt and verification

First computed	2026-07-05T04:07:27.683582Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

49e3dbe90ac604e70d35cc5362ff4944d97c677c26d9ef28b9e746a3eeecf2cb

Aliases

arxiv: 2111.07223 · arxiv_version: 2111.07223v2 · doi: 10.48550/arxiv.2111.07223 · pith_short_12: JHR5X2IKYYCO · pith_short_16: JHR5X2IKYYCOODJV · pith_short_8: JHR5X2IK

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/JHR5X2IKYYCOODJVZRJWF72JIT \
  | 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: 49e3dbe90ac604e70d35cc5362ff4944d97c677c26d9ef28b9e746a3eeecf2cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9453835b733fbd72d102a7d8c3a4df5e6e8140d06ed02d80584c2a9f21f33209",
    "cross_cats_sorted": [
      "hep-ph",
      "hep-th"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2021-11-14T02:25:41Z",
    "title_canon_sha256": "e727cd6463c41754a10955d4a14a5dcdfbdfa0edde54e000969bcd60e1b7da70"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.07223",
    "kind": "arxiv",
    "version": 2
  }
}