Pith Number

pith:BJFW6EBF

pith:2019:BJFW6EBFJX5CMG7WPPOC4XIBX6

not attested not anchored not stored refs pending

Triple-lens Gravitational Microlensing: Critical Curves for Arbitrary Spatial Configuration

David Heyrovsky, Kamil Danek

arxiv:1901.08610 v2 · 2019-01-24 · astro-ph.EP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BJFW6EBFJX5CMG7WPPOC4XIBX6}

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	2026-05-17T23:39:25.034106Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a4b6f10254dfa261bf67bdc2e5d01bf8e9d0a6c8f0e4d0027c760f518b4286b

Aliases

arxiv: 1901.08610 · arxiv_version: 1901.08610v2 · doi: 10.48550/arxiv.1901.08610 · pith_short_12: BJFW6EBFJX5C · pith_short_16: BJFW6EBFJX5CMG7W · pith_short_8: BJFW6EBF

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/BJFW6EBFJX5CMG7WPPOC4XIBX6 \
  | 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: 0a4b6f10254dfa261bf67bdc2e5d01bf8e9d0a6c8f0e4d0027c760f518b4286b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c75e5cb2058f128448793c2c2369908652670e0153075b88df05706537bf564",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.EP",
    "submitted_at": "2019-01-24T19:06:39Z",
    "title_canon_sha256": "168f6717f138779cb08d66e736ccf38efb5053fc631856e09f1569bbc2b66e53"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.08610",
    "kind": "arxiv",
    "version": 2
  }
}