Pith Number

pith:TBZC6TVW

pith:2011:TBZC6TVW5H2ATEAG6UVIWOADWH

not attested not anchored not stored refs pending

Effect of the cosmological constant on the bending of light and the cosmological lens equation

Hideyoshi Arakida, Masumi Kasai

arxiv:1110.6735 v4 · 2011-10-31 · 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{TBZC6TVW5H2ATEAG6UVIWOADWH}

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

Gravitational lensing time delay beyond the Shapiro/geometry split

Receipt and verification

First computed	2026-05-18T04:03:08.930844Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

98722f4eb6e9f4099006f52a8b3803b1fbf99600c27d9994bf1a607b0b2aaf8a

Aliases

arxiv: 1110.6735 · arxiv_version: 1110.6735v4 · doi: 10.48550/arxiv.1110.6735 · pith_short_12: TBZC6TVW5H2A · pith_short_16: TBZC6TVW5H2ATEAG · pith_short_8: TBZC6TVW

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/TBZC6TVW5H2ATEAG6UVIWOADWH \
  | 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: 98722f4eb6e9f4099006f52a8b3803b1fbf99600c27d9994bf1a607b0b2aaf8a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7116791aaa1854d70c001f93aa1b9fe46bb2b8df5a3dd47c033edb5d26dbb1e4",
    "cross_cats_sorted": [
      "astro-ph.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2011-10-31T10:01:18Z",
    "title_canon_sha256": "69d1099ca0a705000ee56a773cf90bef84bf51d34cfe329a91446a2f498f4fd8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.6735",
    "kind": "arxiv",
    "version": 4
  }
}