Pith Number

pith:4ZCASESR

pith:2016:4ZCASESRNF4BNDETTE6NU7OFXG

not attested not anchored not stored refs pending

Friedmann-Robertson-Walker models do not require zero active mass

Anthony N. Lasenby, Do Young Kim, Michael P. Hobson

arxiv:1601.07890 v2 · 2016-01-28 · 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{4ZCASESRNF4BNDETTE6NU7OFXG}

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	2026-05-18T01:15:42.701164Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6440912516978168c93993cda7dc5b9a8ced4cf492f0316586c6fcaebd42cff

Aliases

arxiv: 1601.07890 · arxiv_version: 1601.07890v2 · doi: 10.48550/arxiv.1601.07890 · pith_short_12: 4ZCASESRNF4B · pith_short_16: 4ZCASESRNF4BNDET · pith_short_8: 4ZCASESR

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/4ZCASESRNF4BNDETTE6NU7OFXG \
  | 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: e6440912516978168c93993cda7dc5b9a8ced4cf492f0316586c6fcaebd42cff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d36d0c87f24b0ad25974c30b70b93ff571ee4b0c34d6fb85733c2c6ae9ed907b",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2016-01-28T20:31:49Z",
    "title_canon_sha256": "4c934c9b8aadf8e28290495cb473cc676205f75d1c36baa526305e53c3940d06"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.07890",
    "kind": "arxiv",
    "version": 2
  }
}