Pith Number

pith:Y5EAVU7S

pith:2011:Y5EAVU7SYIXTI23C2ZLR5ATOS7

not attested not anchored not stored refs pending

A Modified log-Harnack inequality and asymptotically strong Feller property

Lihu Xu

arxiv:1102.1162 v1 · 2011-02-06 · 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{Y5EAVU7SYIXTI23C2ZLR5ATOS7}

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	2026-05-18T04:29:54.880155Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7480ad3f2c22f346b62d6571e826e97df2c0c63c8af5f0345f159d236e168a4

Aliases

arxiv: 1102.1162 · arxiv_version: 1102.1162v1 · doi: 10.48550/arxiv.1102.1162 · pith_short_12: Y5EAVU7SYIXT · pith_short_16: Y5EAVU7SYIXTI23C · pith_short_8: Y5EAVU7S

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/Y5EAVU7SYIXTI23C2ZLR5ATOS7 \
  | 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: c7480ad3f2c22f346b62d6571e826e97df2c0c63c8af5f0345f159d236e168a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c886d90dbec347b965024152974afcb5f0ee5a0c1d2aa2b7c6bda92306aaced",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-02-06T16:05:00Z",
    "title_canon_sha256": "92da57e58c23dfaa94acc304a69eefcc7a4465cb3bd2292390d1fa8a9aecff2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.1162",
    "kind": "arxiv",
    "version": 1
  }
}