Pith Number

pith:FABQTFHE

pith:2011:FABQTFHESXO72YLTX5XJ7NJNYQ

not attested not anchored not stored refs pending

Light propagation and the average expansion rate in near-FRW universes

Syksy Rasanen

arxiv:1107.1176 v2 · 2011-07-06 · 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{FABQTFHESXO72YLTX5XJ7NJNYQ}

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

Light path averages in spacetimes with non-vanishing average spatial curvature

Receipt and verification

First computed	2026-05-18T03:56:35.375911Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28030994e495ddfd6173bf6e9fb52dc416ceb7c36c7b0bb9f8d7fad489729ad4

Aliases

arxiv: 1107.1176 · arxiv_version: 1107.1176v2 · doi: 10.48550/arxiv.1107.1176 · pith_short_12: FABQTFHESXO7 · pith_short_16: FABQTFHESXO72YLT · pith_short_8: FABQTFHE

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/FABQTFHESXO72YLTX5XJ7NJNYQ \
  | 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: 28030994e495ddfd6173bf6e9fb52dc416ceb7c36c7b0bb9f8d7fad489729ad4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12e187b61fd6fb11e8f5727076685b52380e5f21f7f5b11375e48b6c5a524494",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2011-07-06T16:12:25Z",
    "title_canon_sha256": "1e4a6cdbe5dda088543bb4d06b65ad755fde5af8ace5060c1071ad1c0d7f41ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.1176",
    "kind": "arxiv",
    "version": 2
  }
}