Pith Number

pith:7U6J6V65

pith:2017:7U6J6V65DJ7AM64WUQRXLNTCAY

not attested not anchored not stored refs pending

Ergodicity in umbrella billiards

Christopher Cox, Hong-Kun Zhang, Maria Correia

arxiv:1702.05445 v1 · 2017-02-17 · 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{7U6J6V65DJ7AM64WUQRXLNTCAY}

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	2026-05-18T00:50:31.685288Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd3c9f57dd1a7e067b96a42375b6620630af8ed9235daeb6d13a8ac5a1d6ee4b

Aliases

arxiv: 1702.05445 · arxiv_version: 1702.05445v1 · doi: 10.48550/arxiv.1702.05445 · pith_short_12: 7U6J6V65DJ7A · pith_short_16: 7U6J6V65DJ7AM64W · pith_short_8: 7U6J6V65

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/7U6J6V65DJ7AM64WUQRXLNTCAY \
  | 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: fd3c9f57dd1a7e067b96a42375b6620630af8ed9235daeb6d13a8ac5a1d6ee4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7959fffb06f163010ffb5e9194e8ac71188460804807739fdd62c64f02b55ef6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-02-17T17:18:41Z",
    "title_canon_sha256": "daba9db6d72b54640b115c443287e1b38a2945af2447d958fe9f43907fae9f02"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.05445",
    "kind": "arxiv",
    "version": 1
  }
}