Pith Number

pith:GOHU4ASL

pith:2011:GOHU4ASLE63NUUT3Y6LV34E4MF

not attested not anchored not stored refs pending

Gravitational Lensing with Three-Dimensional Ray Tracing

Chris J. Fluke, Geraint F. Lewis, Madhura Killedar, Paul D. Lasky

arxiv:1110.4894 v1 · 2011-10-21 · 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{GOHU4ASLE63NUUT3Y6LV34E4MF}

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	2026-05-18T02:00:07.036521Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

338f4e024b27b6da527bc7975df09c6174e921496bcbe9e515a8ab6251b06638

Aliases

arxiv: 1110.4894 · arxiv_version: 1110.4894v1 · doi: 10.48550/arxiv.1110.4894 · pith_short_12: GOHU4ASLE63N · pith_short_16: GOHU4ASLE63NUUT3 · pith_short_8: GOHU4ASL

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/GOHU4ASLE63NUUT3Y6LV34E4MF \
  | 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: 338f4e024b27b6da527bc7975df09c6174e921496bcbe9e515a8ab6251b06638

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd529bacd863a069067ed529a92cd63777d4327510206cf590625d21419c2a8e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2011-10-21T20:04:49Z",
    "title_canon_sha256": "86aa93555aaac429beba32102347a33111a4b93501ca78bfb4d3f72ee12693b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.4894",
    "kind": "arxiv",
    "version": 1
  }
}