Pith Number

pith:PTW72PKT

pith:2010:PTW72PKT43E326Y53UYK7B5IKP

not attested not anchored not stored refs pending

Strong gravitational lensing in a noncommutative black-hole spacetime

Chang-Yong Chen, Chikun Ding, Jiliang Jing, Shuai Kang, Songbai Chen

arxiv:1012.1670 v3 · 2010-12-08 · gr-qc · astro-ph.CO · 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{PTW72PKT43E326Y53UYK7B5IKP}

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	2026-05-18T04:23:45.625676Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cedfd3d53e6c9bd7b1ddd30af87a853f6d5234800ef5cdbc1b04dcb135f60f3

Aliases

arxiv: 1012.1670 · arxiv_version: 1012.1670v3 · doi: 10.48550/arxiv.1012.1670 · pith_short_12: PTW72PKT43E3 · pith_short_16: PTW72PKT43E326Y5 · pith_short_8: PTW72PKT

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/PTW72PKT43E326Y53UYK7B5IKP \
  | 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: 7cedfd3d53e6c9bd7b1ddd30af87a853f6d5234800ef5cdbc1b04dcb135f60f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "afbcad04676e108eb63be7c43d1584cb68e4c712555ebfdaa21428241607458d",
    "cross_cats_sorted": [
      "astro-ph.CO",
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2010-12-08T01:55:10Z",
    "title_canon_sha256": "104720f085c89b56e64ae32e85dd0ed7d7d552f74e4d521e6787f1b86d228a38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1670",
    "kind": "arxiv",
    "version": 3
  }
}