Pith Number

pith:ZSJA5L6I

pith:2015:ZSJA5L6I4B6EYMJM53RJSJOTQ5

not attested not anchored not stored refs pending

Neutrino and Photon Lensing by Black Holes: Radiative Lens Equations and Post-Newtonian Contributions

Antonio Costantini, Claudio Coriano, Luigi Delle Rose, Marta Dell'Atti

arxiv:1504.01322 v3 · 2015-04-06 · hep-ph · astro-ph.HE · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZSJA5L6I4B6EYMJM53RJSJOTQ5}

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

2 papers in Pith

The Case for Astrons

Astrons: Reissner-Nordstr\"om Primordial Naked Singularities

Receipt and verification

First computed	2026-05-18T01:34:23.734428Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc920eafc8e07c4c312ceee29925d387459650eeb483d2c3dba5383406ab7128

Aliases

arxiv: 1504.01322 · arxiv_version: 1504.01322v3 · doi: 10.48550/arxiv.1504.01322 · pith_short_12: ZSJA5L6I4B6E · pith_short_16: ZSJA5L6I4B6EYMJM · pith_short_8: ZSJA5L6I

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/ZSJA5L6I4B6EYMJM53RJSJOTQ5 \
  | 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: cc920eafc8e07c4c312ceee29925d387459650eeb483d2c3dba5383406ab7128

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19d6172f5298754074c9c5b697e86769eaae549940879bd2b0456f5253c2dedb",
    "cross_cats_sorted": [
      "astro-ph.HE",
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2015-04-06T17:12:13Z",
    "title_canon_sha256": "e76aab262dc4662d465d9b74ca65d5e6d243105479508449dd5281c466384d23"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.01322",
    "kind": "arxiv",
    "version": 3
  }
}