Pith Number

pith:LQE4YNQY

pith:2012:LQE4YNQYFA5N2545VE3YR5CKOK

not attested not anchored not stored refs pending

Homogenization of the Poisson-Nernst-Planck Equations for Ion Transport in Charged Porous Media

Markus Schmuck, Martin Z. Bazant

arxiv:1202.1916 v2 · 2012-02-09 · math-ph · math.AP · math.MP · physics.bio-ph · physics.chem-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LQE4YNQYFA5N2545VE3YR5CKOK}

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	2026-05-18T02:47:41.468839Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5c09cc3618283add779da93788f44a728802f46857962367d429ae02b9308751

Aliases

arxiv: 1202.1916 · arxiv_version: 1202.1916v2 · doi: 10.48550/arxiv.1202.1916 · pith_short_12: LQE4YNQYFA5N · pith_short_16: LQE4YNQYFA5N2545 · pith_short_8: LQE4YNQY

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/LQE4YNQYFA5N2545VE3YR5CKOK \
  | 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: 5c09cc3618283add779da93788f44a728802f46857962367d429ae02b9308751

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d2801affcc4b5d6f8a05b6c388bfb9d899614e8e11c4811cac6ac2b154799a7",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP",
      "physics.bio-ph",
      "physics.chem-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-02-09T09:03:21Z",
    "title_canon_sha256": "0611644b51083ea10e592909963947cf6d409bbfb46df7686c48f2681530492e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.1916",
    "kind": "arxiv",
    "version": 2
  }
}