Pith Number

pith:DPAL7M7L

pith:2009:DPAL7M7L76P5ZB4I4PKG3QM7HE

not attested not anchored not stored refs pending

Iteration theory of $L$-index and Multiplicity of brake orbits

Chungen Liu, Duanzhi Zhang

arxiv:0908.0021 v2 · 2009-07-31 · math.SG · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DPAL7M7L76P5ZB4I4PKG3QM7HE}

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	2026-05-18T04:20:51.381878Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1bc0bfb3ebff9fdc8788e3d46dc19f3906f577f4e0eacde72eb2717300c82534

Aliases

arxiv: 0908.0021 · arxiv_version: 0908.0021v2 · doi: 10.48550/arxiv.0908.0021 · pith_short_12: DPAL7M7L76P5 · pith_short_16: DPAL7M7L76P5ZB4I · pith_short_8: DPAL7M7L

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/DPAL7M7L76P5ZB4I4PKG3QM7HE \
  | 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: 1bc0bfb3ebff9fdc8788e3d46dc19f3906f577f4e0eacde72eb2717300c82534

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af6752735cdbedc5045626b22e0c5863258aed0e9bae9811ae4fcb045f59f4a5",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2009-07-31T22:58:09Z",
    "title_canon_sha256": "83da8dd80bf374f837085da528e982cf2a376de344d307530e5bcbfc040bb517"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0908.0021",
    "kind": "arxiv",
    "version": 2
  }
}