Pith Number

pith:UD6CY4JQ

pith:2009:UD6CY4JQSMOLTIRCB5RK25GON5

not attested not anchored not stored refs pending

Towards the Koch Snowflake Fractal Billiard: Computer Experiments and Mathematical Conjectures

Michel L. Lapidus, Robert G. Niemeyer

arxiv:0912.3948 v1 · 2009-12-19 · 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{UD6CY4JQSMOLTIRCB5RK25GON5}

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	2026-05-18T03:29:28.114244Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a0fc2c7130931cb9a2220f62ad74ce6f7d35275ed0732689e613f4a326f47457

Aliases

arxiv: 0912.3948 · arxiv_version: 0912.3948v1 · doi: 10.48550/arxiv.0912.3948 · pith_short_12: UD6CY4JQSMOL · pith_short_16: UD6CY4JQSMOLTIRC · pith_short_8: UD6CY4JQ

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/UD6CY4JQSMOLTIRCB5RK25GON5 \
  | 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: a0fc2c7130931cb9a2220f62ad74ce6f7d35275ed0732689e613f4a326f47457

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "25337f0de169a57690a5e5711cf0f75f832ccce433db218e969eb19fc611c393",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-12-19T23:06:17Z",
    "title_canon_sha256": "07d7860923cc237a2a2305db2dc396fe70f1819a6fd673a5f4f0dbcd5458ff07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.3948",
    "kind": "arxiv",
    "version": 1
  }
}