Pith Number

pith:HQTLBTEW

pith:2012:HQTLBTEWCQW5KJNXEVDU23P4Z7

not attested not anchored not stored refs pending

The strongest gravitational lenses: II. Is the large Einstein radius of MACS J0717.5+3745 in conflict with LCDM?

Jean-Claude Waizmann, Matthias Bartelmann, Matthias Redlich

arxiv:1207.0801 v2 · 2012-07-03 · 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{HQTLBTEWCQW5KJNXEVDU23P4Z7}

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	2026-05-18T03:41:58.524309Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c26b0cc96142dd525b725474d6dfccfca81ac209a7dd4c4e8c074db862c5011

Aliases

arxiv: 1207.0801 · arxiv_version: 1207.0801v2 · doi: 10.48550/arxiv.1207.0801 · pith_short_12: HQTLBTEWCQW5 · pith_short_16: HQTLBTEWCQW5KJNX · pith_short_8: HQTLBTEW

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/HQTLBTEWCQW5KJNXEVDU23P4Z7 \
  | 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: 3c26b0cc96142dd525b725474d6dfccfca81ac209a7dd4c4e8c074db862c5011

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8036420047ba4b8d98c3faf998a0c9a7b6bd8aabfaeb5db7c51ad62abd5ec0de",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2012-07-03T19:57:10Z",
    "title_canon_sha256": "2892c51fc9407629f10dcf005528b6f79051456822cd8a1b1b52ac143627cb7f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.0801",
    "kind": "arxiv",
    "version": 2
  }
}