Pith Number

pith:YAUT6CBH

pith:2021:YAUT6CBHZHB74I3VSXVDLKBRVR

not attested not anchored not stored refs pending

Strong lensing systems and galaxy cluster observations as probe to the cosmic distance duality relation

Akshay Rana, Deepak Jain, F. S. Lima, R. F. L. Holanda

arxiv:2104.01614 v2 · 2021-04-04 · 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{YAUT6CBHZHB74I3VSXVDLKBRVR}

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	2026-07-05T03:59:16.642177Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c0293f0827c9c3fe237595ea35a831ac7e34e8238089ff22930a1fe9dff20038

Aliases

arxiv: 2104.01614 · arxiv_version: 2104.01614v2 · doi: 10.48550/arxiv.2104.01614 · pith_short_12: YAUT6CBHZHB7 · pith_short_16: YAUT6CBHZHB74I3V · pith_short_8: YAUT6CBH

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/YAUT6CBHZHB74I3VSXVDLKBRVR \
  | 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: c0293f0827c9c3fe237595ea35a831ac7e34e8238089ff22930a1fe9dff20038

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b84df59eb8c0f43dffd40b10e67d81a02e289770c1077cb85d0a0386af377da",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2021-04-04T13:45:32Z",
    "title_canon_sha256": "dddf1f1f76ada686b14d84c429d9917e0d8109446c9105135fb444b8d334312d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2104.01614",
    "kind": "arxiv",
    "version": 2
  }
}