Pith Number

pith:L4B42HCF

pith:2012:L4B42HCFDQZ3BKKLJKH6NDNERU

not attested not anchored not stored refs pending

Low red-shift formula for the luminosity distance in a LTB model with cosmological constant

Antonio Enea Romano, Pisin Chen

arxiv:1207.5572 v5 · 2012-07-24 · 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{L4B42HCFDQZ3BKKLJKH6NDNERU}

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	2026-05-18T02:52:23.796800Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f03cd1c451c33b0a94b4a8fe68da48d217cb61ed48ae706be25fd7c42a5029c

Aliases

arxiv: 1207.5572 · arxiv_version: 1207.5572v5 · doi: 10.48550/arxiv.1207.5572 · pith_short_12: L4B42HCFDQZ3 · pith_short_16: L4B42HCFDQZ3BKKL · pith_short_8: L4B42HCF

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/L4B42HCFDQZ3BKKLJKH6NDNERU \
  | 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: 5f03cd1c451c33b0a94b4a8fe68da48d217cb61ed48ae706be25fd7c42a5029c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8617dc71ce6a8ee2ba0e3a9bbce758d3f94be3b81706ab258675abdea8f26493",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2012-07-24T01:16:53Z",
    "title_canon_sha256": "4f4581942d8de244006c88eac801873946f13b87cafbaef06c1e23210b50c147"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.5572",
    "kind": "arxiv",
    "version": 5
  }
}