Pith Number

pith:RY5Y6YNP

pith:2016:RY5Y6YNPYVEONRC25KJ6J3ZHN6

not attested not anchored not stored refs pending

On logarithmic Sobolev inequalities for the heat kernel on the Heisenberg group

Djalil Chafa\"i (CEREMADE, LAMA), Michel Bonnefont (IMB), PSL), Ronan Herry (Uni.lu

arxiv:1607.02741 v3 · 2016-07-10 · math.DG · 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{RY5Y6YNPYVEONRC25KJ6J3ZHN6}

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.

Cited by

1 paper in Pith

The Quasi Curvature-Dimension Condition with applications to sub-Riemannian manifolds

Receipt and verification

First computed	2026-07-05T01:34:03.116403Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8e3b8f61afc548e6c45aea93e4ef276f97e76429af10730d9759fcbaffaee39c

Aliases

arxiv: 1607.02741 · arxiv_version: 1607.02741v3 · doi: 10.48550/arxiv.1607.02741 · pith_short_12: RY5Y6YNPYVEO · pith_short_16: RY5Y6YNPYVEONRC2 · pith_short_8: RY5Y6YNP

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/RY5Y6YNPYVEONRC25KJ6J3ZHN6 \
  | 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: 8e3b8f61afc548e6c45aea93e4ef276f97e76429af10730d9759fcbaffaee39c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2976c8f872474814e30986691e899837ae8ca1151a9df7625c81c1b4cc5f5899",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-07-10T12:45:52Z",
    "title_canon_sha256": "02aa0c94c5b8cd74f575e125bdc488d5d61a69c5c954b4795205ebe8ccb2d35e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.02741",
    "kind": "arxiv",
    "version": 3
  }
}