Pith Number

pith:2DXMNZPL

pith:2020:2DXMNZPLFMBDWNPCR2NDYHOE3R

not attested not anchored not stored refs pending

Perturbative deflection angle, gravitational lensing in the strong field limit and the black hole shadow

Junji Jia, Ke Huang

arxiv:2011.08084 v1 · 2020-11-16 · 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{2DXMNZPLFMBDWNPCR2NDYHOE3R}

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	2026-07-05T02:29:35.299675Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d0eec6e5eb2b023b35e28e9a3c1dc4dc46593b1c3872fc2721e9ddda1a46361a

Aliases

arxiv: 2011.08084 · arxiv_version: 2011.08084v1 · doi: 10.48550/arxiv.2011.08084 · pith_short_12: 2DXMNZPLFMBD · pith_short_16: 2DXMNZPLFMBDWNPC · pith_short_8: 2DXMNZPL

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/2DXMNZPLFMBDWNPCR2NDYHOE3R \
  | 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: d0eec6e5eb2b023b35e28e9a3c1dc4dc46593b1c3872fc2721e9ddda1a46361a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00f5374f39164d43d00bee695a5dfe70746d1d32fa2c214013396671a25e0f7c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2020-11-16T16:32:28Z",
    "title_canon_sha256": "ce73b141f0e10b2246a7325c03b8c2bb7cbbdc047140d184e7aaaff3d1000e0b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2011.08084",
    "kind": "arxiv",
    "version": 1
  }
}