Pith Number

pith:ZKOD3YYW

pith:2017:ZKOD3YYWZ73IA43TBJAAGAYEGE

not attested not anchored not stored refs pending

Transient behavior of the solutions to the second order difference equations by the renormalization method based on Newton-Maclaurin expansion

Cheng-shi Liu

arxiv:1709.02044 v1 · 2017-09-07 · math-ph · math.AP · math.CA · math.DS · math.MP · 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{ZKOD3YYWZ73IA43TBJAAGAYEGE}

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	2026-05-18T00:35:50.400047Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca9c3de316cff68073730a40030304310a018766767f7eb264f47f67ac98dacc

Aliases

arxiv: 1709.02044 · arxiv_version: 1709.02044v1 · doi: 10.48550/arxiv.1709.02044 · pith_short_12: ZKOD3YYWZ73I · pith_short_16: ZKOD3YYWZ73IA43T · pith_short_8: ZKOD3YYW

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/ZKOD3YYWZ73IA43TBJAAGAYEGE \
  | 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: ca9c3de316cff68073730a40030304310a018766767f7eb264f47f67ac98dacc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2df3a76c4eba2d8c02f6c464832e948cfd094ac6f2bd2750a35319e84bdb97c4",
    "cross_cats_sorted": [
      "math.AP",
      "math.CA",
      "math.DS",
      "math.MP",
      "physics.comp-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2017-09-07T01:48:52Z",
    "title_canon_sha256": "901b383b16ea9e87be4fdd098f9d7d8832f10cf6de72f35dfb4f2f368e8a2c0d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.02044",
    "kind": "arxiv",
    "version": 1
  }
}