Pith Number

pith:HQFVMLMI

pith:2006:HQFVMLMIKOYYVFYLSWRGSD2FSH

not attested not anchored not stored refs pending

The Chang-Refsdal Lens Revisited

2), (2) IoA Cambridge), J. An (1, N. W. Evans (2) ((1) MKI-MIT

arxiv:astro-ph/0601457 v2 · 2006-01-20 · astro-ph · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HQFVMLMIKOYYVFYLSWRGSD2FSH}

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	2026-07-04T15:17:29.683738Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c0b562d8853b18a970b95a2690f4591c3df11bf048c417498bcbdeb51b88b83

Aliases

arxiv: astro-ph/0601457 · arxiv_version: astro-ph/0601457v2 · doi: 10.48550/arxiv.astro-ph/0601457 · pith_short_12: HQFVMLMIKOYY · pith_short_16: HQFVMLMIKOYYVFYL · pith_short_8: HQFVMLMI

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/HQFVMLMIKOYYVFYLSWRGSD2FSH \
  | 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: 3c0b562d8853b18a970b95a2690f4591c3df11bf048c417498bcbdeb51b88b83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c71fe90f05adee8480cd13443d4906612485ee2f39b0b127b72bdff1e7911be9",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2006-01-20T19:38:26Z",
    "title_canon_sha256": "db14892602e9bf17db0a013c61b058ce12c64f76a404fb6830423286ae0a8584"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0601457",
    "kind": "arxiv",
    "version": 2
  }
}