Pith Number

pith:Q7VW76OE

pith:2011:Q7VW76OE2EKYMLQO5O55US2ZSC

not attested not anchored not stored refs pending

Derivative Formula and Gradient Estimates for Gruschin Type Semigroups

Feng-Yu Wang

arxiv:1109.6738 v4 · 2011-09-30 · 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{Q7VW76OE2EKYMLQO5O55US2ZSC}

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	2026-05-18T03:29:14.081029Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87eb6ff9c4d115862e0eebbbda4b5990b56554cd5eb508ac43620cc8d89e8356

Aliases

arxiv: 1109.6738 · arxiv_version: 1109.6738v4 · doi: 10.48550/arxiv.1109.6738 · pith_short_12: Q7VW76OE2EKY · pith_short_16: Q7VW76OE2EKYMLQO · pith_short_8: Q7VW76OE

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/Q7VW76OE2EKYMLQO5O55US2ZSC \
  | 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: 87eb6ff9c4d115862e0eebbbda4b5990b56554cd5eb508ac43620cc8d89e8356

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fdcf96f7de212c994b0d00cbe2a4ef36070702dd4c519c039350a71d649135f7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-09-30T07:51:22Z",
    "title_canon_sha256": "d832789167c250fb74e5f65174469f0203bf7dcfd9becf5aa5a773c0e1c10cd7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.6738",
    "kind": "arxiv",
    "version": 4
  }
}