Pith Number

pith:2P7K727L

pith:2014:2P7K727LU2UDH3M6FQQAB2X6MZ

not attested not anchored not stored refs pending

A link between the log-Sobolev inequality and Lyapunov condition

Yuan Liu

arxiv:1410.6080 v4 · 2014-10-22 · 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{2P7K727LU2UDH3M6FQQAB2X6MZ}

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	2026-05-18T01:16:07.376671Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3feafebeba6a833ed9e2c2000eafe666d45c805791f812bb3d2399f72bed8b6

Aliases

arxiv: 1410.6080 · arxiv_version: 1410.6080v4 · doi: 10.48550/arxiv.1410.6080 · pith_short_12: 2P7K727LU2UD · pith_short_16: 2P7K727LU2UDH3M6 · pith_short_8: 2P7K727L

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/2P7K727LU2UDH3M6FQQAB2X6MZ \
  | 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: d3feafebeba6a833ed9e2c2000eafe666d45c805791f812bb3d2399f72bed8b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8fff8e785cb42256eae2ae596d658cd98c5c3f1f6aab8baad0e21d0b93f65262",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-10-22T15:39:01Z",
    "title_canon_sha256": "26779cb2bc58c0b5a47247dd4bf8e6c73076e342f18c3b629816812a0b7d59ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.6080",
    "kind": "arxiv",
    "version": 4
  }
}