Pith Number

pith:WWCDOSPB

pith:2020:WWCDOSPBE4IWAAI3CVW4ZFECH6

not attested not anchored not stored refs pending

On the Renyi entropy power and the Gagliardo-Nirenberg-Sobolev inequality on Riemannian manifolds

Songzi Li, Xiang-Dong Li

arxiv:2001.11184 v1 · 2020-01-30 · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WWCDOSPBE4IWAAI3CVW4ZFECH6}

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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

On Perelman's $W$-entropy and Shannon entropy power for super Ricci flows on metric measure spaces

Receipt and verification

First computed	2026-07-05T00:37:21.456059Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5843749e1271160011b156dcc94823f8395ef3ac550931e76219296e1685104

Aliases

arxiv: 2001.11184 · arxiv_version: 2001.11184v1 · doi: 10.48550/arxiv.2001.11184 · pith_short_12: WWCDOSPBE4IW · pith_short_16: WWCDOSPBE4IWAAI3 · pith_short_8: WWCDOSPB

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/WWCDOSPBE4IWAAI3CVW4ZFECH6 \
  | 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: b5843749e1271160011b156dcc94823f8395ef3ac550931e76219296e1685104

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9148d2dcdeba7458a3fbb2030d63419121dcb7f35b5e01f232e40ac6e3ec5274",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2020-01-30T05:59:02Z",
    "title_canon_sha256": "bfc88f4584cfa52c745853c83460af6c3c685e8025cd17c24aef7fa7d41d1927"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2001.11184",
    "kind": "arxiv",
    "version": 1
  }
}