Pith Number

pith:YMR5DI2C

pith:2014:YMR5DI2CVOOMZQLGSM7Q5XGLE5

not attested not anchored not stored refs pending

Strong gravitational lensing and black hole quasinormal modes: Towards a semiclassical unified description

Bernard Raffaelli

arxiv:1412.7333 v1 · 2014-12-23 · 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{YMR5DI2CVOOMZQLGSM7Q5XGLE5}

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

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

Receipt and verification

First computed	2026-05-18T01:22:14.769437Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c323d1a342ab9cccc166933f0edccb2771141a709c5d8ea5ea81d14e71a73f7f

Aliases

arxiv: 1412.7333 · arxiv_version: 1412.7333v1 · doi: 10.48550/arxiv.1412.7333 · pith_short_12: YMR5DI2CVOOM · pith_short_16: YMR5DI2CVOOMZQLG · pith_short_8: YMR5DI2C

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/YMR5DI2CVOOMZQLGSM7Q5XGLE5 \
  | 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: c323d1a342ab9cccc166933f0edccb2771141a709c5d8ea5ea81d14e71a73f7f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f267b001524cf578f019beda045bcd88373dd9437d18408aea486c95e5b7575",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2014-12-23T11:56:35Z",
    "title_canon_sha256": "28338437580ce81d78cb0a88041290cb8c34433c9db2c80063cefe6d628b285a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.7333",
    "kind": "arxiv",
    "version": 1
  }
}