Pith Number

pith:XYZT6FVA

pith:2021:XYZT6FVAQVWQQ4AV2OB3JBLYJB

not attested not anchored not stored refs pending

Motion of Particles and Gravitational Lensing Around (2+1)-dimensional BTZ black holes in Gauss-Bonnet Gravity

Ahmadjon Abdujabbarov, Bakhtiyor Narzilloev, Bobomurat Ahmedov, Cosimo Bambi, Ibrar Hussain, Sanjar Shaymatov

arxiv:2109.02816 v1 · 2021-09-07 · 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{XYZT6FVAQVWQQ4AV2OB3JBLYJB}

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

Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A$^*$

Receipt and verification

First computed	2026-07-05T03:17:59.129973Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be333f16a0856d087015d383b4857848689c04a6e99d2841ef7bf91f858b22bc

Aliases

arxiv: 2109.02816 · arxiv_version: 2109.02816v1 · doi: 10.48550/arxiv.2109.02816 · pith_short_12: XYZT6FVAQVWQ · pith_short_16: XYZT6FVAQVWQQ4AV · pith_short_8: XYZT6FVA

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/XYZT6FVAQVWQQ4AV2OB3JBLYJB \
  | 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: be333f16a0856d087015d383b4857848689c04a6e99d2841ef7bf91f858b22bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aafdfbb00d8b2cca19d075e17e94da61856c1dac447a55f47404e7879d0d25a1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2021-09-07T02:02:38Z",
    "title_canon_sha256": "0ea5adb7bf94e6e643bf0ee69667237b0896f8a937786dbff41f9551eb02fe3a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.02816",
    "kind": "arxiv",
    "version": 1
  }
}