Pith Number

pith:Z7JW7ZMU

pith:2010:Z7JW7ZMUYRNWVHNSHH44JAPLZX

not attested not anchored not stored refs pending

From efficient symplectic exponentiation of matrices to symplectic integration of high-dimensional Hamiltonian systems with slowly varying quadratic stiff potentials

Houman Owhadi, Jerrold E. Marsden, Molei Tao

arxiv:1006.4659 v3 · 2010-06-23 · math.NA · math.DS · 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{Z7JW7ZMUYRNWVHNSHH44JAPLZX}

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	2026-05-18T04:24:35.233830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfd36fe594c45b6a9db239f9c481ebcdfda6f8daf0370eac7a651ed74b8cd703

Aliases

arxiv: 1006.4659 · arxiv_version: 1006.4659v3 · doi: 10.48550/arxiv.1006.4659 · pith_short_12: Z7JW7ZMUYRNW · pith_short_16: Z7JW7ZMUYRNWVHNS · pith_short_8: Z7JW7ZMU

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/Z7JW7ZMUYRNWVHNSHH44JAPLZX \
  | 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: cfd36fe594c45b6a9db239f9c481ebcdfda6f8daf0370eac7a651ed74b8cd703

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b87905a5b48aaedbc8f6689d270c00cb436129ad2728c851f2dae6a0c5b0e66",
    "cross_cats_sorted": [
      "math.DS",
      "physics.comp-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2010-06-23T22:54:31Z",
    "title_canon_sha256": "b3bd35fe2cc9d52bebac50ca85e5a386ec9d6a5af71407766297f259a7c8383c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.4659",
    "kind": "arxiv",
    "version": 3
  }
}