Pith Number

pith:BHYVH22B

pith:2012:BHYVH22BFPG4ZBIXBNSC6BRJ3T

not attested not anchored not stored refs pending

Applying MOG to lensing: Einstein rings, Abell 520 and the Bullet Cluster

J. W. Moffat, S. Rahvar, V. T. Toth

arxiv:1204.2985 v2 · 2012-04-13 · astro-ph.CO · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BHYVH22BFPG4ZBIXBNSC6BRJ3T}

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	2026-05-18T00:19:36.341759Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09f153eb412bcdcc85170b642f0629dcf85b4f5454db40f292a940505bd78f7e

Aliases

arxiv: 1204.2985 · arxiv_version: 1204.2985v2 · doi: 10.48550/arxiv.1204.2985 · pith_short_12: BHYVH22BFPG4 · pith_short_16: BHYVH22BFPG4ZBIX · pith_short_8: BHYVH22B

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/BHYVH22BFPG4ZBIXBNSC6BRJ3T \
  | 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: 09f153eb412bcdcc85170b642f0629dcf85b4f5454db40f292a940505bd78f7e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20d8e3f380b18b0f37af665fc904af32f880f6fcc265a39c97f4deb34ad65f1a",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2012-04-13T13:25:32Z",
    "title_canon_sha256": "5278eaa729e0a24105e0dc27e06652f888edd6a6b9c4322c66f5d96c5fe489df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.2985",
    "kind": "arxiv",
    "version": 2
  }
}