Pith Number

pith:WLFLZNRD

pith:2017:WLFLZNRDCBEZPK2YVKKX5PPZCX

not attested not anchored not stored refs pending

$W$-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds

Songzi Li, Xiang-Dong Li

arxiv:1710.05750 v1 · 2017-10-12 · 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{WLFLZNRDCBEZPK2YVKKX5PPZCX}

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	2026-05-18T00:32:48.289081Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2cabcb623104997ab58aa957ebdf915ece284101494f9be4e310d48b0835427

Aliases

arxiv: 1710.05750 · arxiv_version: 1710.05750v1 · doi: 10.48550/arxiv.1710.05750 · pith_short_12: WLFLZNRDCBEZ · pith_short_16: WLFLZNRDCBEZPK2Y · pith_short_8: WLFLZNRD

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/WLFLZNRDCBEZPK2YVKKX5PPZCX \
  | 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: b2cabcb623104997ab58aa957ebdf915ece284101494f9be4e310d48b0835427

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a06d47d78e7490aaf0678fa0c35f16db885f65327cae429fbd24c26988141a5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2017-10-12T21:28:53Z",
    "title_canon_sha256": "9f6a9abd86e06456d295f39e0883dd8fd9a36535707dfc24ba683bced901ab71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.05750",
    "kind": "arxiv",
    "version": 1
  }
}