Pith Number

pith:MBVCXYHP

pith:2011:MBVCXYHPU4RGNDFJ7TRJP56WPM

not attested not anchored not stored refs pending

Families of Periodic Orbits of the Koch Snowflake Fractal Billiard

Michel L. Lapidus, Robert G. Niemeyer

arxiv:1105.0737 v1 · 2011-05-04 · 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{MBVCXYHPU4RGNDFJ7TRJP56WPM}

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	2026-05-18T02:22:00.615707Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

606a2be0efa722668ca9fce297f7d67b09c2eb784b371926b07b01d6d416b8fa

Aliases

arxiv: 1105.0737 · arxiv_version: 1105.0737v1 · doi: 10.48550/arxiv.1105.0737 · pith_short_12: MBVCXYHPU4RG · pith_short_16: MBVCXYHPU4RGNDFJ · pith_short_8: MBVCXYHP

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/MBVCXYHPU4RGNDFJ7TRJP56WPM \
  | 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: 606a2be0efa722668ca9fce297f7d67b09c2eb784b371926b07b01d6d416b8fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "528c81189745baa19a709178d0374fca5126c11123184761de97c0011ef9e505",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-05-04T05:48:23Z",
    "title_canon_sha256": "d1ae1fff65d291567cc90d1a392981ca05f06c6f0f0e79c5783dbf692d5945b8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.0737",
    "kind": "arxiv",
    "version": 1
  }
}