Pith Number

pith:H2IGTTMN

pith:2026:H2IGTTMNPOPAPJXK5KJ2HM6HYG

not attested not anchored not stored refs pending

Explicit Hamiltonian structure of the Flaschka-Newell Painlev\'{e} II hierarchy via symmetry reduction of the Painlev\'{e} IV hierarchy

Mohamad Alameddine, Olivier Marchal, Sergej Laub

arxiv:2607.20106 v1 · 2026-07-22 · math-ph · math.AP · math.MP · math.SG · nlin.SI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{H2IGTTMNPOPAPJXK5KJ2HM6HYG}

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	2026-07-23T01:25:01.658722Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e9069cd8d7b9e07a6eaea93a3b3c7c1aa5b1669b56179f91a9cb313daaaefa9

Aliases

arxiv: 2607.20106 · arxiv_version: 2607.20106v1 · doi: 10.48550/arxiv.2607.20106 · pith_short_12: H2IGTTMNPOPA · pith_short_16: H2IGTTMNPOPAPJXK · pith_short_8: H2IGTTMN

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/H2IGTTMNPOPAPJXK5KJ2HM6HYG \
  | 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: 3e9069cd8d7b9e07a6eaea93a3b3c7c1aa5b1669b56179f91a9cb313daaaefa9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd51d4caeafc8f521a13faa8baf2fb7a8e456aad9b062a9b3ff63235c2c9e4b6",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP",
      "math.SG",
      "nlin.SI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-07-22T13:07:05Z",
    "title_canon_sha256": "abd66b676bd30681c51e0d69f5a1d7054c07283c3ba2f3c60275ae851d1badf0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.20106",
    "kind": "arxiv",
    "version": 1
  }
}