Pith Number

pith:4QQ2P7GI

pith:2021:4QQ2P7GI7OZ7DOFC537P5JQV3U

not attested not anchored not stored refs pending

Complete classification of Friedmann-Lema\^{i}tre-Robertson-Walker solutions with linear equation of state: parallelly propagated curvature singularities for general geodesics

Bernard Carr, Takahisa Igata, Takuma Sato, Tomohiro Harada

arxiv:2110.13421 v2 · 2021-10-26 · gr-qc · astro-ph.CO · hep-th

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4QQ2P7GI7OZ7DOFC537P5JQV3U}

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	2026-07-05T04:39:22.314291Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e421a7fcc8fbb3f1b8a2eefefea615dd1cbad2f585f14284649f65e834847b1b

Aliases

arxiv: 2110.13421 · arxiv_version: 2110.13421v2 · doi: 10.48550/arxiv.2110.13421 · pith_short_12: 4QQ2P7GI7OZ7 · pith_short_16: 4QQ2P7GI7OZ7DOFC · pith_short_8: 4QQ2P7GI

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/4QQ2P7GI7OZ7DOFC537P5JQV3U \
  | 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: e421a7fcc8fbb3f1b8a2eefefea615dd1cbad2f585f14284649f65e834847b1b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b847c56edca1eee995ebf9d5bfc80ba8aa6eecf4037c4263f1ccf98a3b055e7f",
    "cross_cats_sorted": [
      "astro-ph.CO",
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2021-10-26T05:42:23Z",
    "title_canon_sha256": "cd7f8461da735dff6e1242ba669cfc5cb85233c9bbf658229ace0e8d1ccee914"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2110.13421",
    "kind": "arxiv",
    "version": 2
  }
}