Pith Number

pith:MIFOM3JD

pith:2013:MIFOM3JDYM6HH3SSP4DVJTZNPK

not attested not anchored not stored refs pending

Gravitational Lensing by Spherical Lenses

Juan M. Tejeiro, Leonardo Castaneda, Roger Hurtado

arxiv:1308.5271 v2 · 2013-08-24 · astro-ph.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MIFOM3JDYM6HH3SSP4DVJTZNPK}

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.

Receipt and verification

First computed	2026-05-18T02:47:23.181487Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

620ae66d23c33c73ee527f0754cf2d7ab00c826419a47d451c5082898e1ef8d8

Aliases

arxiv: 1308.5271 · arxiv_version: 1308.5271v2 · doi: 10.48550/arxiv.1308.5271 · pith_short_12: MIFOM3JDYM6H · pith_short_16: MIFOM3JDYM6HH3SS · pith_short_8: MIFOM3JD

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/MIFOM3JDYM6HH3SSP4DVJTZNPK \
  | 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: 620ae66d23c33c73ee527f0754cf2d7ab00c826419a47d451c5082898e1ef8d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cde91d34b2ccf7625adc6e07979fb2ce5b4e8e83ae7edc830436d5994a59b1a9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2013-08-24T01:08:48Z",
    "title_canon_sha256": "925a3eb00b4a295a75eaba0c5422c647e99f8a3f3cdf2a76e993bccfa7c3e1b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.5271",
    "kind": "arxiv",
    "version": 2
  }
}