Pith Number

pith:EH5GNGEN

pith:2012:EH5GNGENM6WSGQDX6GIUM63N6M

not attested not anchored not stored refs pending

Log-Harnack Inequality for Gruschin Type Semigroups

Feng-Yu Wang, Lihu Xu

arxiv:1206.0583 v1 · 2012-06-04 · 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{EH5GNGENM6WSGQDX6GIUM63N6M}

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	2026-05-18T03:54:17.201342Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

21fa66988d67ad234077f191467b6df3136995e80b3348af75b71c518ce5f6a1

Aliases

arxiv: 1206.0583 · arxiv_version: 1206.0583v1 · doi: 10.48550/arxiv.1206.0583 · pith_short_12: EH5GNGENM6WS · pith_short_16: EH5GNGENM6WSGQDX · pith_short_8: EH5GNGEN

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/EH5GNGENM6WSGQDX6GIUM63N6M \
  | 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: 21fa66988d67ad234077f191467b6df3136995e80b3348af75b71c518ce5f6a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3bda25a3d5ced85f3b8866eb205a437b7c21489612499dac0e0f3105d5b74f46",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-06-04T11:26:51Z",
    "title_canon_sha256": "180599830d1b96dac753ee3b79c7d350cfd35f743db601641a113c77a5a86fae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0583",
    "kind": "arxiv",
    "version": 1
  }
}