Pith Number

pith:WIMCNTZX

pith:2019:WIMCNTZXA77OT6GLLBPEBLSNMU

not attested not anchored not stored refs pending

Wasserstein Gradient Flow Formulation of the Time-Fractional Fokker-Planck Equation

Bangti Jin, Manh Hong Duong

arxiv:1908.09055 v2 · 2019-08-24 · math.NA · cs.NA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WIMCNTZXA77OT6GLLBPEBLSNMU}

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	2026-07-05T01:07:50.317324Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b21826cf3707fee9f8cb585e40ae4d652e954cce7bbe6bfa3e7bd4a6603ea8f5

Aliases

arxiv: 1908.09055 · arxiv_version: 1908.09055v2 · doi: 10.48550/arxiv.1908.09055 · pith_short_12: WIMCNTZXA77O · pith_short_16: WIMCNTZXA77OT6GL · pith_short_8: WIMCNTZX

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/WIMCNTZXA77OT6GLLBPEBLSNMU \
  | 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: b21826cf3707fee9f8cb585e40ae4d652e954cce7bbe6bfa3e7bd4a6603ea8f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db6d06c7950c62c01640f847f98a142b18015aeebc235f49931cf91c4fc5a361",
    "cross_cats_sorted": [
      "cs.NA",
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2019-08-24T00:19:22Z",
    "title_canon_sha256": "6b0cd555a26cc4a7faaf0f941592ed8691f24bf85d0db11fa7130b4a2ab09208"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.09055",
    "kind": "arxiv",
    "version": 2
  }
}