Pith Number

pith:THSNZRL6

pith:2019:THSNZRL6BCU63WIUZQUOF6QG7V

not attested not anchored not stored refs pending

Strong-field gravitational lensing by black holes

Jake O. Shipley

arxiv:1909.04691 v1 · 2019-09-10 · gr-qc · nlin.CD

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{THSNZRL6BCU63WIUZQUOF6QG7V}

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

Black hole spectroscopy: from theory to experiment

Receipt and verification

First computed	2026-07-05T00:03:59.608743Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

99e4dcc57e08a9edd914cc28e2fa06fd4af48834b4044bd4eab5cfbfbb5ddb48

Aliases

arxiv: 1909.04691 · arxiv_version: 1909.04691v1 · doi: 10.48550/arxiv.1909.04691 · pith_short_12: THSNZRL6BCU6 · pith_short_16: THSNZRL6BCU63WIU · pith_short_8: THSNZRL6

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/THSNZRL6BCU63WIUZQUOF6QG7V \
  | 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: 99e4dcc57e08a9edd914cc28e2fa06fd4af48834b4044bd4eab5cfbfbb5ddb48

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "616be1d4108e25026e5a7980250ee758c92e7bee2f0d904afccfe9934c6cad3b",
    "cross_cats_sorted": [
      "nlin.CD"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2019-09-10T18:10:09Z",
    "title_canon_sha256": "33d1b780c15622a1a1d775aa7bfa95cc34ff69029e7590da276b2cca2ff6ee79"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.04691",
    "kind": "arxiv",
    "version": 1
  }
}