Pith Number

pith:CXWBXHN5

pith:2017:CXWBXHN5QL43CVYMFU4DRBC6G2

not attested not anchored not stored refs pending

A Liouville theorem for stationary and ergodic ensembles of parabolic systems

Alberto Chiarini, Benjamin Fehrman, Peter Bella

arxiv:1706.03440 v1 · 2017-06-12 · math.AP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CXWBXHN5QL43CVYMFU4DRBC6G2}

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	2026-05-18T00:42:35.679595Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15ec1b9dbd82f9b1570c2d3838845e3694be4b61316549124bf2e28610468a10

Aliases

arxiv: 1706.03440 · arxiv_version: 1706.03440v1 · doi: 10.48550/arxiv.1706.03440 · pith_short_12: CXWBXHN5QL43 · pith_short_16: CXWBXHN5QL43CVYM · pith_short_8: CXWBXHN5

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/CXWBXHN5QL43CVYMFU4DRBC6G2 \
  | 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: 15ec1b9dbd82f9b1570c2d3838845e3694be4b61316549124bf2e28610468a10

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1596e71d1dc47ba06f36bd65cb689f0a2ceff3a69c4c5c0e9a11cf1ff567e264",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-06-12T02:22:03Z",
    "title_canon_sha256": "19914f73971962fdad202a190584d3170adbac13e3b6c70240ef20c6f938770a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.03440",
    "kind": "arxiv",
    "version": 1
  }
}