Pith Number

pith:YRYEEXAZ

pith:2020:YRYEEXAZCBBUDSJ4JMWB3RKVCR

not attested not anchored not stored refs pending

Gravitational deflection angle of light: Definition by an observer and its application to an asymptotically nonflat spacetime

Hideki Asada, Keita Takizawa, Toshiaki Ono

arxiv:2001.03290 v2 · 2020-01-10 · gr-qc · astro-ph.HE · 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{YRYEEXAZCBBUDSJ4JMWB3RKVCR}

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

2 papers in Pith

Boundary-only weak deflection angles from isothermal optical geometry

Reference-renormalized curvature-primitive Gauss-Bonnet formalism for finite-distance weak gravitational lensing in static spherical spacetimes

Receipt and verification

First computed	2026-07-05T01:05:41.611204Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c470425c19104341c93c4b2c1dc55514432e3c8e3d2689893e4ffcd68c7362b0

Aliases

arxiv: 2001.03290 · arxiv_version: 2001.03290v2 · doi: 10.48550/arxiv.2001.03290 · pith_short_12: YRYEEXAZCBBU · pith_short_16: YRYEEXAZCBBUDSJ4 · pith_short_8: YRYEEXAZ

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/YRYEEXAZCBBUDSJ4JMWB3RKVCR \
  | 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: c470425c19104341c93c4b2c1dc55514432e3c8e3d2689893e4ffcd68c7362b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e25f99278d646bb9e13a3f824d6299fff97960ebd776e56e8a715dc628ba0b8",
    "cross_cats_sorted": [
      "astro-ph.HE",
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2020-01-10T02:47:46Z",
    "title_canon_sha256": "430685870f61a4d8831aad5c0327b1fed89d5175eaebc05db9a107b28f9ce316"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2001.03290",
    "kind": "arxiv",
    "version": 2
  }
}