Pith Number

pith:RWUW4V5W

pith:1999:RWUW4V5WEDASASOPJL2AFOEUNQ

not attested not anchored not stored refs pending

Generalized n-Poisson brackets on a symplectic manifold

Giuseppe Marmo, Janusz Grabowski

arxiv:math/9902129 v1 · 1999-02-23 · math.DG · 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{RWUW4V5WEDASASOPJL2AFOEUNQ}

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	2026-05-18T02:35:38.377204Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8da96e57b620c12049cf4af402b8946c06208c137bfa82403d4a192435eb9a73

Aliases

arxiv: math/9902129 · arxiv_version: math/9902129v1 · doi: 10.48550/arxiv.math/9902129 · pith_short_12: RWUW4V5WEDAS · pith_short_16: RWUW4V5WEDASASOP · pith_short_8: RWUW4V5W

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/RWUW4V5WEDASASOPJL2AFOEUNQ \
  | 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: 8da96e57b620c12049cf4af402b8946c06208c137bfa82403d4a192435eb9a73

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d40293fa18ee72af43a092973db188934322ea0280ef7a4468b87e64075f4c2",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "1999-02-23T09:36:26Z",
    "title_canon_sha256": "5134f9d0330e2af829ec8fb1e02033b7bd1c00393e814c398b33bc4a824f0923"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9902129",
    "kind": "arxiv",
    "version": 1
  }
}