Pith Number

pith:UH7N2MHN

pith:2012:UH7N2MHNHZLOO3A5TT5P2HBQYU

not attested not anchored not stored refs pending

The current state of fractal billiards

Michel L. Lapidus, Robert G. Niemeyer

arxiv:1210.0282 v3 · 2012-10-01 · 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{UH7N2MHNHZLOO3A5TT5P2HBQYU}

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	2026-05-18T02:55:48.613584Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a1fedd30ed3e56e76c1d9cfafd1c30c52b77a570d9343c1b066032c2628815fa

Aliases

arxiv: 1210.0282 · arxiv_version: 1210.0282v3 · doi: 10.48550/arxiv.1210.0282 · pith_short_12: UH7N2MHNHZLO · pith_short_16: UH7N2MHNHZLOO3A5 · pith_short_8: UH7N2MHN

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/UH7N2MHNHZLOO3A5TT5P2HBQYU \
  | 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: a1fedd30ed3e56e76c1d9cfafd1c30c52b77a570d9343c1b066032c2628815fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a479606c3b5bb2025e8efee40fc6289e9db5c89fc0f621aa1994b04cbeeb09ac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-10-01T03:32:55Z",
    "title_canon_sha256": "79447306ffb4e7686c0bf89c0865eea3480255f5bb731cf7fbb66ddcf4e829cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.0282",
    "kind": "arxiv",
    "version": 3
  }
}