Pith Number

pith:RUO2TG6M

pith:2021:RUO2TG6M7VPER3FM5PMCJ7M56W

not attested not anchored not stored refs pending

Birkhoff Normal Form and Twist Coefficients of Periodic Orbits of Billiards

Pengfei Zhang, Xin Jin

arxiv:2108.12098 v3 · 2021-08-27 · 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{RUO2TG6M7VPER3FM5PMCJ7M56W}

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.

Cited by

1 paper in Pith

From bungee to $C^1$ and $C^0$ Hamiltonian systems and their integrability and nonintegrability

Receipt and verification

First computed	2026-07-05T08:02:18.593067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8d1da99bccfd5e48ecacebd824fd9df5b43e02c84e39b36539c8828fda6248f0

Aliases

arxiv: 2108.12098 · arxiv_version: 2108.12098v3 · doi: 10.48550/arxiv.2108.12098 · pith_short_12: RUO2TG6M7VPE · pith_short_16: RUO2TG6M7VPER3FM · pith_short_8: RUO2TG6M

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/RUO2TG6M7VPER3FM5PMCJ7M56W \
  | 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: 8d1da99bccfd5e48ecacebd824fd9df5b43e02c84e39b36539c8828fda6248f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b21366800b39a2a3375626c6c93ca0745fe9bd46f71bab866a9ba065151adae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2021-08-27T02:53:42Z",
    "title_canon_sha256": "a8cfec6a30ba3809994362e13bb0e8c7dc6a5181a987ae59a2a59a14532d85c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2108.12098",
    "kind": "arxiv",
    "version": 3
  }
}