Pith Number

pith:I4JRTPDA

pith:2016:I4JRTPDAB3PTEA5A5B4DPGAYBC

not attested not anchored not stored refs pending

Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus

Delfim F. M. Torres, Fr\'ed\'eric Pierret

arxiv:1601.02602 v3 · 2016-01-09 · math.OC · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I4JRTPDAB3PTEA5A5B4DPGAYBC}

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	2026-05-18T01:14:35.615239Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

471319bc600edf3203a0e87837981808b955d0f73da34129590f749193f71822

Aliases

arxiv: 1601.02602 · arxiv_version: 1601.02602v3 · doi: 10.48550/arxiv.1601.02602 · pith_short_12: I4JRTPDAB3PT · pith_short_16: I4JRTPDAB3PTEA5A · pith_short_8: I4JRTPDA

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/I4JRTPDAB3PTEA5A5B4DPGAYBC \
  | 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: 471319bc600edf3203a0e87837981808b955d0f73da34129590f749193f71822

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b2bcb62e3971e965f3e0d6766cf6c49176e3d77676f4d78155123bf1b5880508",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-01-09T15:38:53Z",
    "title_canon_sha256": "45f8a01968992dc7e0751915c33d16f65be9101fc8b4e6c36e57f1205bb3f9be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.02602",
    "kind": "arxiv",
    "version": 3
  }
}