Pith Number

pith:TZSFQJMW

pith:2014:TZSFQJMW5IP6UQOIMTEL7YGFG2

not attested not anchored not stored refs pending

The time delay in strong gravitational lensing with Gauss-Bonnet correction

Hongbo Cheng, Jingyun Man

arxiv:1409.3921 v1 · 2014-09-13 · 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{TZSFQJMW5IP6UQOIMTEL7YGFG2}

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	2026-05-18T01:42:02.893892Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e64582596ea1fea41c864c8bfe0c536b368092c053d9bbe1d50ba498e9174f2

Aliases

arxiv: 1409.3921 · arxiv_version: 1409.3921v1 · doi: 10.48550/arxiv.1409.3921 · pith_short_12: TZSFQJMW5IP6 · pith_short_16: TZSFQJMW5IP6UQOI · pith_short_8: TZSFQJMW

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/TZSFQJMW5IP6UQOIMTEL7YGFG2 \
  | 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: 9e64582596ea1fea41c864c8bfe0c536b368092c053d9bbe1d50ba498e9174f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba0adb8de773a83c9e906728ec54eca06c4c2802bd534b21abcf2ca2e46aad16",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2014-09-13T07:20:18Z",
    "title_canon_sha256": "d12d0d7c28258b649ea5aedf81c240357ecb1e66de29e0e68e581cb1b9d35218"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.3921",
    "kind": "arxiv",
    "version": 1
  }
}