Pith Number

pith:3QLXIK55

pith:2010:3QLXIK55KOVLEVAT6LFPPVSSLW

not attested not anchored not stored refs pending

A Series Solution to the Luminosity Distance in a Flat LCDM Universe

2), (2) Center for High Energy Physics, Beijing Normal University, De-Zi Liu (1), Nan-Nan Yue (1), Peking University), Tong-Jie Zhang (1, Xiao-Lei Meng (1), Zhi-Liang Yang (1) ((1) Department of Astronomy

arxiv:1011.2525 v2 · 2010-11-10 · astro-ph.CO · 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{3QLXIK55KOVLEVAT6LFPPVSSLW}

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	2026-05-18T03:48:13.853014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc17742bbd53aab25413f2caf7d6525da233d9d5a5eb785e56a4cda8c363c39c

Aliases

arxiv: 1011.2525 · arxiv_version: 1011.2525v2 · doi: 10.48550/arxiv.1011.2525 · pith_short_12: 3QLXIK55KOVL · pith_short_16: 3QLXIK55KOVLEVAT · pith_short_8: 3QLXIK55

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/3QLXIK55KOVLEVAT6LFPPVSSLW \
  | 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: dc17742bbd53aab25413f2caf7d6525da233d9d5a5eb785e56a4cda8c363c39c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c48b153105d389432b13c71347c4d0165967a40840585999e6f0f36e8f8ce004",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2010-11-10T23:16:58Z",
    "title_canon_sha256": "f8bbd675396467b28cc792efd1b3723e6b3b1a841747d8587c79d85381f4e23c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2525",
    "kind": "arxiv",
    "version": 2
  }
}