Pith Number

pith:PP73224Z

pith:2014:PP73224Z6CXETQYOYLEUL2USML

not attested not anchored not stored refs pending

Self-energy-modified Poisson-Nernst-Planck equations: WKB approximation and finite-difference approaches

Manman Ma, Pei Liu, Zhenli Xu

arxiv:1404.0253 v2 · 2014-04-01 · physics.comp-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{PP73224Z6CXETQYOYLEUL2USML}

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	2026-05-18T01:43:43.381459Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bffbd6b99f0ae49c30ec2c945ea9262eab41d50b268428c3f1417a7452718b1

Aliases

arxiv: 1404.0253 · arxiv_version: 1404.0253v2 · doi: 10.48550/arxiv.1404.0253 · pith_short_12: PP73224Z6CXE · pith_short_16: PP73224Z6CXETQYO · pith_short_8: PP73224Z

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/PP73224Z6CXETQYOYLEUL2USML \
  | 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: 7bffbd6b99f0ae49c30ec2c945ea9262eab41d50b268428c3f1417a7452718b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "650cdf86d3707001c472b19b86b8436da89d9fddd00d3becca534ff3cf89f98c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.comp-ph",
    "submitted_at": "2014-04-01T14:35:27Z",
    "title_canon_sha256": "223fd2598753bd19784b013c7230afe6687f15aeae9ba3a03097217195cf2712"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.0253",
    "kind": "arxiv",
    "version": 2
  }
}