Pith Number

pith:MQ7ZHBSC

pith:2016:MQ7ZHBSCZAGFSKAUD35KTU37AP

not attested not anchored not stored refs pending

Deflection angle in the strong deflection limit in a general asymptotically flat, static, spherically symmetric spacetime

Naoki Tsukamoto

arxiv:1612.08251 v2 · 2016-12-25 · 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{MQ7ZHBSCZAGFSKAUD35KTU37AP}

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

4 papers in Pith

Boundary-only weak deflection angles from isothermal optical geometry

Strong-deflection expansion of the deflection angle near a degenerate photon sphere

Effective null geodesics and black hole images in Kruglov nonlinear electrodynamics

Receipt and verification

First computed	2026-05-18T00:48:05.117955Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

643f938642c80c5928141efaa9d37f03fad1db79470ca2cce4b892ae19be28f0

Aliases

arxiv: 1612.08251 · arxiv_version: 1612.08251v2 · doi: 10.48550/arxiv.1612.08251 · pith_short_12: MQ7ZHBSCZAGF · pith_short_16: MQ7ZHBSCZAGFSKAU · pith_short_8: MQ7ZHBSC

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/MQ7ZHBSCZAGFSKAUD35KTU37AP \
  | 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: 643f938642c80c5928141efaa9d37f03fad1db79470ca2cce4b892ae19be28f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b05a685e369677ab9b63a74821e8b2983deda57c319c7e60862d0a0c407ef2b0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2016-12-25T08:47:04Z",
    "title_canon_sha256": "357406a921ffd2037422f148bbe8293e591fa13739722b0926aab4b7a0efa23f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.08251",
    "kind": "arxiv",
    "version": 2
  }
}