Pith Number

pith:22HZ5D4A

pith:2026:22HZ5D4A7YWEHVUSCB6DM5OFBH

not attested not anchored not stored refs pending

Global Finite-Energy Weak Solutions and Sharp Entropy Decay for a Poisson-Nernst-Planck System with Interspecies Drag and Steric Effects

Baoli Hao, Chun Liu, Fanze Kong, Kei Fong Lam

arxiv:2607.21742 v1 · 2026-07-23 · math.AP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{22HZ5D4A7YWEHVUSCB6DM5OFBH}

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	2026-07-27T00:20:18.515030Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d68f9e8f80fe2c43d692107c3675c509f1ce5f9fd67419b6c7248c8760ca9624

Aliases

arxiv: 2607.21742 · arxiv_version: 2607.21742v1 · doi: 10.48550/arxiv.2607.21742 · pith_short_12: 22HZ5D4A7YWE · pith_short_16: 22HZ5D4A7YWEHVUS · pith_short_8: 22HZ5D4A

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/22HZ5D4A7YWEHVUSCB6DM5OFBH \
  | 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: d68f9e8f80fe2c43d692107c3675c509f1ce5f9fd67419b6c7248c8760ca9624

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37784b773096464de295b5c4d2e5d2ec3c1c37bec7ba0076f0934d4c517e4e3b",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-23T18:50:18Z",
    "title_canon_sha256": "ce5b780f84e96c951348398c63c3c4451ba84c6fa21f38005f5bbab7baf12ab7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.21742",
    "kind": "arxiv",
    "version": 1
  }
}