Pith Number

pith:BV6U5NVW

pith:2013:BV6U5NVWYPOMYQKTYPVQW73ULX

not attested not anchored not stored refs pending

A free energy satisfying finite difference method for Poisson--Nernst--Planck equations

Hailiang Liu, Zhongming Wang

arxiv:1308.6632 v3 · 2013-08-30 · 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{BV6U5NVWYPOMYQKTYPVQW73ULX}

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	2026-05-18T01:47:56.644759Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d7d4eb6b6c3dccc4153c3eb0b7f745dd9e00bd487abed99a479d5d0efb5f94d

Aliases

arxiv: 1308.6632 · arxiv_version: 1308.6632v3 · doi: 10.48550/arxiv.1308.6632 · pith_short_12: BV6U5NVWYPOM · pith_short_16: BV6U5NVWYPOMYQKT · pith_short_8: BV6U5NVW

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/BV6U5NVWYPOMYQKTYPVQW73ULX \
  | 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: 0d7d4eb6b6c3dccc4153c3eb0b7f745dd9e00bd487abed99a479d5d0efb5f94d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c65f8493a6ecddd786bc4dbeb69e9adf93c9c7fda7806a70423d872422ba2af6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2013-08-30T00:46:55Z",
    "title_canon_sha256": "557cff18b475cece06fba664dab6e140d9e6aa81852f450896302b7de67c0e1c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.6632",
    "kind": "arxiv",
    "version": 3
  }
}