Pith Number

pith:4CYTRFKF

pith:2022:4CYTRFKFZKCAIPGL6NL4D3GKTZ

not attested not anchored not stored refs pending

Dark matter effect on the weak deflection angle by black holes at the center of Milky Way and M87 galaxies

Ali \"Ovg\"un, Reggie C. Pantig

arxiv:2201.03365 v3 · 2022-01-10 · 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{4CYTRFKFZKCAIPGL6NL4D3GKTZ}

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.

Cited by

1 paper in Pith

Equatorial periodic orbits and gravitational wave signatures in Euler-Heisenberg black holes surrounded by perfect fluid dark matter

Receipt and verification

First computed	2026-07-05T04:19:51.651990Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0b1389545ca84043ccbf357c1ecca9e6205420d2f28697f5ad57ebe0f868a78

Aliases

arxiv: 2201.03365 · arxiv_version: 2201.03365v3 · doi: 10.48550/arxiv.2201.03365 · pith_short_12: 4CYTRFKFZKCA · pith_short_16: 4CYTRFKFZKCAIPGL · pith_short_8: 4CYTRFKF

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/4CYTRFKFZKCAIPGL6NL4D3GKTZ \
  | 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: e0b1389545ca84043ccbf357c1ecca9e6205420d2f28697f5ad57ebe0f868a78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec367a6d4162e03292bcb8c8c28ccc44a747da1b8ffdf62b6d62b3847674e742",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2022-01-10T14:30:38Z",
    "title_canon_sha256": "487794ce349dc6402d509bee29be81fcd1b0f68efe74524ed4f2c47d1f676b01"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2201.03365",
    "kind": "arxiv",
    "version": 3
  }
}