Pith Number

pith:OK2TACCF

pith:2022:OK2TACCFAMJNBPUMH7LFCSD7SL

not attested not anchored not stored refs pending

Fully nonlinear gravitational instabilities for expanding Newtonian universes with inhomogeneous pressure and entropy: Beyond the Tolman's solution

Chao Liu

arxiv:2210.04657 v3 · 2022-10-10 · gr-qc · astro-ph.CO · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OK2TACCFAMJNBPUMH7LFCSD7SL}

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	2026-07-05T06:28:32.348818Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

72b53008450312d0be8c3fd651487f92e2c19f7eba8c0a8731d1c1b8a40ed222

Aliases

arxiv: 2210.04657 · arxiv_version: 2210.04657v3 · doi: 10.48550/arxiv.2210.04657 · pith_short_12: OK2TACCFAMJN · pith_short_16: OK2TACCFAMJNBPUM · pith_short_8: OK2TACCF

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/OK2TACCFAMJNBPUMH7LFCSD7SL \
  | 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: 72b53008450312d0be8c3fd651487f92e2c19f7eba8c0a8731d1c1b8a40ed222

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7efd9a8c4cd5306eb9cf05ecf5c7ecafdae19b10199c1ad4f0273936502dc0a2",
    "cross_cats_sorted": [
      "astro-ph.CO",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2022-10-10T12:59:54Z",
    "title_canon_sha256": "b9b804994b985a2c85f4c47458ef73e10a7c7fec5b0676cba3de0dbfe89c176d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2210.04657",
    "kind": "arxiv",
    "version": 3
  }
}