Pith Number

pith:ZZM4K2K3

pith:2013:ZZM4K2K3WDO7RXBL2NALX5JCGU

not attested not anchored not stored refs pending

Trace formula for linear Hamiltonian systems with its applications to elliptic Lagrangian solutions

Penghui Wang, Xijun Hu, Yuwei Ou

arxiv:1308.4745 v1 · 2013-08-22 · math-ph · math.DS · math.FA · 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{ZZM4K2K3WDO7RXBL2NALX5JCGU}

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	2026-05-18T01:48:04.853475Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce59c5695bb0ddf8dc2bd340bbf522350acd89947fa051585f63c2b33583192b

Aliases

arxiv: 1308.4745 · arxiv_version: 1308.4745v1 · doi: 10.48550/arxiv.1308.4745 · pith_short_12: ZZM4K2K3WDO7 · pith_short_16: ZZM4K2K3WDO7RXBL · pith_short_8: ZZM4K2K3

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/ZZM4K2K3WDO7RXBL2NALX5JCGU \
  | 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: ce59c5695bb0ddf8dc2bd340bbf522350acd89947fa051585f63c2b33583192b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f29171164a0e26f2053750b177b9abbdd98cd3aa68470eb26063bb17c5141e9b",
    "cross_cats_sorted": [
      "math.DS",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-08-22T00:21:40Z",
    "title_canon_sha256": "2f1af17547549f04f48c472af5fe51131fc6f2f24e8ff7fab27a57819d23ad6e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.4745",
    "kind": "arxiv",
    "version": 1
  }
}