Pith Number

pith:PN2LPKEE

pith:2012:PN2LPKEEW33KRAQ6DIY54LMGCA

not attested not anchored not stored refs pending

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients

Nataliya M. Shapoval, Roman O. Popovych, Vyacheslav M. Boyko

arxiv:1203.0387 v3 · 2012-03-02 · math.CA · 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{PN2LPKEEW33KRAQ6DIY54LMGCA}

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	2026-05-18T02:55:48.677882Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b74b7a884b6f6a8821e1a31de2d8610348aafc25693963cf3ae9038c8f6123c

Aliases

arxiv: 1203.0387 · arxiv_version: 1203.0387v3 · doi: 10.48550/arxiv.1203.0387 · pith_short_12: PN2LPKEEW33K · pith_short_16: PN2LPKEEW33KRAQ6 · pith_short_8: PN2LPKEE

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/PN2LPKEEW33KRAQ6DIY54LMGCA \
  | 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: 7b74b7a884b6f6a8821e1a31de2d8610348aafc25693963cf3ae9038c8f6123c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84ef5d89afa459953d0d60d771da144b6b4eaa2c6405bf271af2470207d26ce9",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-03-02T08:21:58Z",
    "title_canon_sha256": "177b98791d490e87ce90094a9b02de341d9554d8760346a0aa31449d52ee8999"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.0387",
    "kind": "arxiv",
    "version": 3
  }
}