Pith Number

pith:MMBLLVEB

pith:2022:MMBLLVEB2LK3BFQXD7WDAHBKYO

not attested not anchored not stored refs pending

Gravitational lensing by using the 0th order of affine perturbation series of the deflection angle of a ray near a photon sphere

Naoki Tsukamoto

arxiv:2211.04239 v2 · 2022-11-08 · 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{MMBLLVEB2LK3BFQXD7WDAHBKYO}

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

Observing of background electromagnetic radiation of the real sky through the throat of a wormhole

Receipt and verification

First computed	2026-07-05T06:00:33.259375Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6302b5d481d2d5b096171fec301c2ac3ac96ed3f37173d28c76a6f3fc82b1690

Aliases

arxiv: 2211.04239 · arxiv_version: 2211.04239v2 · doi: 10.48550/arxiv.2211.04239 · pith_short_12: MMBLLVEB2LK3 · pith_short_16: MMBLLVEB2LK3BFQX · pith_short_8: MMBLLVEB

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/MMBLLVEB2LK3BFQXD7WDAHBKYO \
  | 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: 6302b5d481d2d5b096171fec301c2ac3ac96ed3f37173d28c76a6f3fc82b1690

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c170f5c5e1bc1ddb64aa0cc9b8f46ed425f751f10f860c89f4d4554e09c457e5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2022-11-08T13:34:37Z",
    "title_canon_sha256": "815a3df2ae0cd57f394194f1f10776c42ffd4f143dac17b7082176657521b575"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2211.04239",
    "kind": "arxiv",
    "version": 2
  }
}