Pith Number

pith:ZCD6ATTW

pith:2023:ZCD6ATTW6A2SNP2HXSC4HDP7IZ

not attested not anchored not stored refs pending

Strong Gravitational Lensing by Sgr A* and M87* Black Holes embedded in Dark Matter Halo exhibiting string cloud and quintessential field

Dhruv Arora, Farruh Atamurotov, G.Mustafa, Himanshu Chaudhary, Niyaz Uddin Molla, Ujjal Debnath

arxiv:2310.14234 v2 · 2023-10-22 · gr-qc · 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{ZCD6ATTW6A2SNP2HXSC4HDP7IZ}

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	2026-07-05T07:08:13.403611Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c887e04e76f03526bf47bc85c38dff46577a1aba39fb9f7c206c34b45ed0a9e4

Aliases

arxiv: 2310.14234 · arxiv_version: 2310.14234v2 · doi: 10.48550/arxiv.2310.14234 · pith_short_12: ZCD6ATTW6A2S · pith_short_16: ZCD6ATTW6A2SNP2H · pith_short_8: ZCD6ATTW

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/ZCD6ATTW6A2SNP2HXSC4HDP7IZ \
  | 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: c887e04e76f03526bf47bc85c38dff46577a1aba39fb9f7c206c34b45ed0a9e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07a2970b827c69f2bb77bc0146dbd868c4237b2d34ea34d4f858b8bafe1030eb",
    "cross_cats_sorted": [
      "astro-ph.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2023-10-22T08:59:35Z",
    "title_canon_sha256": "21deffc733be562b884e8dfabcf8e7e622d9af54b62c6805d208631d02709ecd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2310.14234",
    "kind": "arxiv",
    "version": 2
  }
}