Pith Number

pith:MUPL5APF

pith:2016:MUPL5APFQB3PEG22UXDKB4DO23

not attested not anchored not stored refs pending

Convergence Analysis and Numerical Implementation of a Second Order Numerical Scheme for the Three-Dimensional Phase Field Crystal Equation

Cheng Wang, Lixiu Dong, Steven M. Wise, Wenqiang Feng, Zhengru Zhang

arxiv:1611.06288 v1 · 2016-11-19 · 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{MUPL5APFQB3PEG22UXDKB4DO23}

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	2026-05-18T00:57:39.157009Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

651ebe81e58076f21b5aa5c6a0f06ed6dcbbfc4cb8dfa3a8cd6b90e0e9db0676

Aliases

arxiv: 1611.06288 · arxiv_version: 1611.06288v1 · doi: 10.48550/arxiv.1611.06288 · pith_short_12: MUPL5APFQB3P · pith_short_16: MUPL5APFQB3PEG22 · pith_short_8: MUPL5APF

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/MUPL5APFQB3PEG22UXDKB4DO23 \
  | 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: 651ebe81e58076f21b5aa5c6a0f06ed6dcbbfc4cb8dfa3a8cd6b90e0e9db0676

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fbbe44010bcc7485104a5e1044a3eb0d01f13ef4f99acc5d70b551c288703225",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2016-11-19T01:04:46Z",
    "title_canon_sha256": "f65dac368936e8cd41200f11d21fc008af003ba7603b029803c022085369efab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.06288",
    "kind": "arxiv",
    "version": 1
  }
}