Pith Number

pith:QHFP5WAW

pith:2025:QHFP5WAWGKWOYF77HXLR6MHNTI

not attested not anchored not stored refs pending

Mixed Solutions to the Liouville Equation

Jan Troost, Sujay K. Ashok

arxiv:2506.02196 v1 · 2025-06-02 · hep-th · 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{QHFP5WAWGKWOYF77HXLR6MHNTI}

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	2026-07-05T11:14:34.160783Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81cafed81632acec17ff3dd71f30ed9a0b19b35854b46afb6fc61006bb217daa

Aliases

arxiv: 2506.02196 · arxiv_version: 2506.02196v1 · doi: 10.48550/arxiv.2506.02196 · pith_short_12: QHFP5WAWGKWO · pith_short_16: QHFP5WAWGKWOYF77 · pith_short_8: QHFP5WAW

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/QHFP5WAWGKWOYF77HXLR6MHNTI \
  | 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: 81cafed81632acec17ff3dd71f30ed9a0b19b35854b46afb6fc61006bb217daa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fdbf4f33a8a0b54581372f6bc60a60a50b48fdfccbd9f9d64b01087f4aa85e29",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2025-06-02T19:34:07Z",
    "title_canon_sha256": "68f83e4ff736624c98589b0b665ca88e01234620c943f52953745ed936569bb8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.02196",
    "kind": "arxiv",
    "version": 1
  }
}