Pith Number

pith:G3PSYRM5

pith:2010:G3PSYRM5JOP445KTAGRVLRK2SO

not attested not anchored not stored refs pending

Asymptotic Expansions and Amplification of a Gravitational Lens Near a Fold Caustic

A.N. Alexandrov, V.I. Zhdanov

arxiv:1006.5903 v2 · 2010-06-30 · 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{G3PSYRM5JOP445KTAGRVLRK2SO}

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	2026-05-18T04:10:12.596763Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

36df2c459d4b9fce755301a355c55a93959a2f3e1fb6b37414017091b510176f

Aliases

arxiv: 1006.5903 · arxiv_version: 1006.5903v2 · doi: 10.48550/arxiv.1006.5903 · pith_short_12: G3PSYRM5JOP4 · pith_short_16: G3PSYRM5JOP445KT · pith_short_8: G3PSYRM5

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/G3PSYRM5JOP445KTAGRVLRK2SO \
  | 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: 36df2c459d4b9fce755301a355c55a93959a2f3e1fb6b37414017091b510176f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97a4dcb3cfad0eb052ebb6375dd606940c8aaebe8355bfc92a06fe2c54269eee",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2010-06-30T16:18:46Z",
    "title_canon_sha256": "4b77b6f7bc2331a3a721a81add44b30d7b337204981f757a0724bb875d5a5eee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.5903",
    "kind": "arxiv",
    "version": 2
  }
}