Pith Number

pith:QNKSSR2Q

pith:2015:QNKSSR2QK66PQGVLK5OZ775HNG

not attested not anchored not stored refs pending

Asymptotic and optimal Liouville properties for Wolff type integral systems

John Villavert

arxiv:1506.02579 v2 · 2015-06-08 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QNKSSR2QK66PQGVLK5OZ775HNG}

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	2026-05-18T01:11:27.377983Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

835529475057bcf81aab575d9fffa769ab04c82d74ffebd330a6881492a8442e

Aliases

arxiv: 1506.02579 · arxiv_version: 1506.02579v2 · doi: 10.48550/arxiv.1506.02579 · pith_short_12: QNKSSR2QK66P · pith_short_16: QNKSSR2QK66PQGVL · pith_short_8: QNKSSR2Q

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/QNKSSR2QK66PQGVLK5OZ775HNG \
  | 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: 835529475057bcf81aab575d9fffa769ab04c82d74ffebd330a6881492a8442e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b929e264cbcd434cf0997ca867d370a5b5def7dd88ed6eb7c4070d1f5547043f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-06-08T16:37:05Z",
    "title_canon_sha256": "3756d473374bc460e061cfaac5d729db2c9160afa3b09abfee7ca59b550a4d8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.02579",
    "kind": "arxiv",
    "version": 2
  }
}