Pith Number

pith:NVUBU3PD

pith:2015:NVUBU3PD3QMNQ5JFPBIQSQ2M32

not attested not anchored not stored refs pending

Strong Gravitational Lensing in the Einstein-Proca Theory

Guoping Li, Li Zhang, Xiaotao Zu, Yan Zhang, Zhongwen Feng

arxiv:1507.03942 v1 · 2015-06-29 · physics.gen-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NVUBU3PD3QMNQ5JFPBIQSQ2M32}

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	2026-05-18T01:36:44.408683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d681a6de3dc18d87525785109434cde96d56842822278ce430b905f01d6b5aa

Aliases

arxiv: 1507.03942 · arxiv_version: 1507.03942v1 · doi: 10.48550/arxiv.1507.03942 · pith_short_12: NVUBU3PD3QMN · pith_short_16: NVUBU3PD3QMNQ5JF · pith_short_8: NVUBU3PD

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/NVUBU3PD3QMNQ5JFPBIQSQ2M32 \
  | 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: 6d681a6de3dc18d87525785109434cde96d56842822278ce430b905f01d6b5aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd20e20855618ab49ad007ee9635fc3c0924488d49ef81d1030affe23aafe9e9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.gen-ph",
    "submitted_at": "2015-06-29T13:31:06Z",
    "title_canon_sha256": "aebaa754d1ae9994a850655884fa833bf660241895b69944fe50678efd7b1358"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.03942",
    "kind": "arxiv",
    "version": 1
  }
}