Pith Number

pith:U4NBU5WU

pith:2000:U4NBU5WUCKTRZGSZTFUNOAM4TP

not attested not anchored not stored refs pending

An Efficient Modified "Walk On Spheres" Algorithm for the Linearized Poisson-Boltzmann Equation

Chi-Ok Hwang, Michael Mascagni

arxiv:math-ph/0010032 v1 · 2000-10-23 · math-ph · cs.NA · math.MP · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U4NBU5WUCKTRZGSZTFUNOAM4TP}

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	2026-06-03T22:06:14.073944Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a71a1a76d412a71c9a599968d7019c9bc5e0aa45cfc7cedcebf412bac7a0dff1

Aliases

arxiv: math-ph/0010032 · arxiv_version: math-ph/0010032v1 · doi: 10.48550/arxiv.math-ph/0010032 · pith_short_12: U4NBU5WUCKTR · pith_short_16: U4NBU5WUCKTRZGSZ · pith_short_8: U4NBU5WU

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/U4NBU5WUCKTRZGSZTFUNOAM4TP \
  | 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: a71a1a76d412a71c9a599968d7019c9bc5e0aa45cfc7cedcebf412bac7a0dff1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5cb466128c61952c34419cd44cb202b774629456fd71a6eb3cd207f9831a10db",
    "cross_cats_sorted": [
      "cs.NA",
      "math.MP",
      "math.NA"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2000-10-23T15:05:32Z",
    "title_canon_sha256": "afbc29d2762715d07f621f0ea5a322426f1d4fe628b78cbd7be49226bd8871bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0010032",
    "kind": "arxiv",
    "version": 1
  }
}