Pith Number

pith:RZA2CTWI

pith:2009:RZA2CTWIZXKGNRFJZ4LFK7WU4P

not attested not anchored not stored refs pending

Hamilton-Jacobi theory and the evolution operator

E. Martinez, G. Marmo, J.F. Carinena, M.C. Munoz-Lecanda, N. Roman-Roy, X. Gracia

arxiv:0907.1039 v1 · 2009-07-06 · 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{RZA2CTWIZXKGNRFJZ4LFK7WU4P}

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	2026-05-18T01:24:31.163849Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8e41a14ec8cdd466c4a9cf16557ed4e3d4651c4019dcbc341a151cd8b561262d

Aliases

arxiv: 0907.1039 · arxiv_version: 0907.1039v1 · doi: 10.48550/arxiv.0907.1039 · pith_short_12: RZA2CTWIZXKG · pith_short_16: RZA2CTWIZXKGNRFJ · pith_short_8: RZA2CTWI

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/RZA2CTWIZXKGNRFJZ4LFK7WU4P \
  | 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: 8e41a14ec8cdd466c4a9cf16557ed4e3d4651c4019dcbc341a151cd8b561262d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5bfd92cd08e153384e3acba73a96a37d6e500b234eb02cd50a82d90a21f75c5",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2009-07-06T16:29:08Z",
    "title_canon_sha256": "c90036b44501b5db714a9cfe483e6d1fe36114863023338d3af852efb067e826"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.1039",
    "kind": "arxiv",
    "version": 1
  }
}