Pith Number

pith:PMVG2ZES

pith:2022:PMVG2ZESCGOK64BYCTBMBHRO5H

not attested not anchored not stored refs pending

On the equilibrium of the Poisson-Nernst-Planck-Bikermann model equipping with the steric and correlation effects

Jian-Guo Liu, Yijia Tang, Yu Zhao

arxiv:2201.01423 v1 · 2022-01-05 · 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{PMVG2ZESCGOK64BYCTBMBHRO5H}

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	2026-07-05T03:46:05.572575Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b2a6d6492119caf703814c2c09e2ee9d0edd805f1916a6f6c3d9736fe204c90

Aliases

arxiv: 2201.01423 · arxiv_version: 2201.01423v1 · doi: 10.48550/arxiv.2201.01423 · pith_short_12: PMVG2ZESCGOK · pith_short_16: PMVG2ZESCGOK64BY · pith_short_8: PMVG2ZES

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/PMVG2ZESCGOK64BYCTBMBHRO5H \
  | 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: 7b2a6d6492119caf703814c2c09e2ee9d0edd805f1916a6f6c3d9736fe204c90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bcfa25a026b121b1423a629e5864018f5176984d9689f7a65098d32bdcda865c",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2022-01-05T02:56:53Z",
    "title_canon_sha256": "854a536c69d717f51aec3231294b3cf6dd2f2b77856268303b9d798a933a2552"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2201.01423",
    "kind": "arxiv",
    "version": 1
  }
}