Pith Number

pith:66P5FVGT

pith:2013:66P5FVGTNOFBRLUJSSZRUEA4BZ

not attested not anchored not stored refs pending

Objects Appear Smaller as They Recede: How Proper Motions Can Directly Reveal the Cosmic Expansion, Provide Geometric Distances, and Measure the Hubble Constant

Jeremy Darling

arxiv:1310.0500 v2 · 2013-10-01 · 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{66P5FVGTNOFBRLUJSSZRUEA4BZ}

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	2026-05-18T01:47:16.755887Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f79fd2d4d36b8a18ae8994b31a101c0e515646dc59dab762274c5f7a13e1f1ca

Aliases

arxiv: 1310.0500 · arxiv_version: 1310.0500v2 · doi: 10.48550/arxiv.1310.0500 · pith_short_12: 66P5FVGTNOFB · pith_short_16: 66P5FVGTNOFBRLUJ · pith_short_8: 66P5FVGT

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/66P5FVGTNOFBRLUJSSZRUEA4BZ \
  | 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: f79fd2d4d36b8a18ae8994b31a101c0e515646dc59dab762274c5f7a13e1f1ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e5c25adfae8b62c3b4e100c910d5880d0de7e8a44f7ab46e844e962fd4d31c23",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2013-10-01T22:02:56Z",
    "title_canon_sha256": "53eff86c4152fb045e4af214b061903ed161e74c32fc8723b6b3f582e391c6d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.0500",
    "kind": "arxiv",
    "version": 2
  }
}