Pith Number

pith:FPBMCJY2

pith:2015:FPBMCJY2OARHERLUE6Z4RF67FB

not attested not anchored not stored refs pending

A Wasserstein gradient flow approach to Poisson-Nernst-Planck equations

David Kinderlehrer, L\'eonard Monsaingeon, Xiang Xu

arxiv:1501.04437 v3 · 2015-01-19 · 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{FPBMCJY2OARHERLUE6Z4RF67FB}

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	2026-05-18T01:33:56.853779Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2bc2c1271a702272457427b3c897df2850073f30717885afa69f46e5311fa03f

Aliases

arxiv: 1501.04437 · arxiv_version: 1501.04437v3 · doi: 10.48550/arxiv.1501.04437 · pith_short_12: FPBMCJY2OARH · pith_short_16: FPBMCJY2OARHERLU · pith_short_8: FPBMCJY2

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/FPBMCJY2OARHERLUE6Z4RF67FB \
  | 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: 2bc2c1271a702272457427b3c897df2850073f30717885afa69f46e5311fa03f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b096caa9bf1d234f6d5abe26a29de56bcb78ec50edfc1318c4b08ca8608f941",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-01-19T10:08:58Z",
    "title_canon_sha256": "be23b7be6f2a5b81569f70ca84ee0da81490d368846a6d6a197533e020a39024"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.04437",
    "kind": "arxiv",
    "version": 3
  }
}