Pith Number

pith:5UGFPYBH

pith:2020:5UGFPYBHGE7LWNMFAMLXX6FABV

not attested not anchored not stored refs pending

Spectral invariants of convex billiard maps:a viewpoint of Mather's beta function

Jianlu Zhang

arxiv:2009.12513 v1 · 2020-09-26 · math.DS · math.GT · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5UGFPYBHGE7LWNMFAMLXX6FABV}

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	2026-07-05T01:38:05.930591Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed0c57e027313ebb358503177bf8a00d7fe89d32088b07ca0f34c600d9b64121

Aliases

arxiv: 2009.12513 · arxiv_version: 2009.12513v1 · doi: 10.48550/arxiv.2009.12513 · pith_short_12: 5UGFPYBHGE7L · pith_short_16: 5UGFPYBHGE7LWNMF · pith_short_8: 5UGFPYBH

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/5UGFPYBHGE7LWNMFAMLXX6FABV \
  | 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: ed0c57e027313ebb358503177bf8a00d7fe89d32088b07ca0f34c600d9b64121

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "34b40a893abbc49ce427e988ad27bde88499f451cd0df4d942df1d4a3d13899b",
    "cross_cats_sorted": [
      "math.GT",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2020-09-26T04:11:28Z",
    "title_canon_sha256": "4878c06a2cfaa7531715b64a9267b5321ba894f64aa18c7603b7126c0703f838"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2009.12513",
    "kind": "arxiv",
    "version": 1
  }
}