Pith Number

pith:5YOP5TUS

pith:2010:5YOP5TUSJEF3QPZ2TLAA7RG73H

not attested not anchored not stored refs pending

The frequency map for billiards inside ellipsoids

Pablo S. Casas, Rafael Ramirez-Ros

arxiv:1004.5499 v2 · 2010-04-30 · math.DS · nlin.SI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5YOP5TUSJEF3QPZ2TLAA7RG73H}

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	2026-05-18T02:17:22.236957Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee1cfece92490bb83f3a9ac00fc4dfd9ebd5da3f4c36943fc75aff9596b808c3

Aliases

arxiv: 1004.5499 · arxiv_version: 1004.5499v2 · doi: 10.48550/arxiv.1004.5499 · pith_short_12: 5YOP5TUSJEF3 · pith_short_16: 5YOP5TUSJEF3QPZ2 · pith_short_8: 5YOP5TUS

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/5YOP5TUSJEF3QPZ2TLAA7RG73H \
  | 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: ee1cfece92490bb83f3a9ac00fc4dfd9ebd5da3f4c36943fc75aff9596b808c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb4567cd37d29796fc6107f46c3a56af1f48951b39b4d41a077c5641670ce39d",
    "cross_cats_sorted": [
      "nlin.SI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-04-30T11:19:39Z",
    "title_canon_sha256": "0fb932b6bd7f39db44da0c24aede1a110d474756070813a5b31cb1e15fb6d71f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.5499",
    "kind": "arxiv",
    "version": 2
  }
}