Pith Number

pith:4ZWMZU4H

pith:2026:4ZWMZU4HJ6NGGEAH7GZCVXP4RO

not attested not anchored not stored refs pending

Structure-Oriented Randomized Neural Networks for Poisson-Nernst-Planck and Poisson-Nernst-Planck-Navier-Stokes Systems

Fei Wang, Yunlong Li

arxiv:2606.19912 v1 · 2026-06-18 · math.NA · cs.LG · cs.NA · 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{4ZWMZU4HJ6NGGEAH7GZCVXP4RO}

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	2026-06-19T16:12:38.496519Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e66cccd3874f9a631007f9b22addfc8ba374e19713dc349fb3f77aeb0d525e3b

Aliases

arxiv: 2606.19912 · arxiv_version: 2606.19912v1 · doi: 10.48550/arxiv.2606.19912 · pith_short_12: 4ZWMZU4HJ6NG · pith_short_16: 4ZWMZU4HJ6NGGEAH · pith_short_8: 4ZWMZU4H

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/4ZWMZU4HJ6NGGEAH7GZCVXP4RO \
  | 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: e66cccd3874f9a631007f9b22addfc8ba374e19713dc349fb3f77aeb0d525e3b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af59b1190dcd182fd57d0f27032ff5f4e4c75fcb1769c25ba4608a24ea60841d",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "physics.comp-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-06-18T08:07:58Z",
    "title_canon_sha256": "b4ba57e4b78eab3cabe9711932a37252623b36e2c39065407e20315d738d4812"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.19912",
    "kind": "arxiv",
    "version": 1
  }
}