Pith Number

pith:D3X2OKO3

pith:2012:D3X2OKO3K2EDIYAQ7L5TSKFKII

not attested not anchored not stored refs pending

Sharkovsky's Theorem and one-dimensional combinatorial dynamics

Chris Bernhardt

arxiv:1201.3583 v1 · 2012-01-17 · math.DS · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D3X2OKO3K2EDIYAQ7L5TSKFKII}

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	2026-05-18T04:04:28.865813Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1eefa729db5688346010fafb3928aa42395af6ca6c61be81dec0d247a1e12483

Aliases

arxiv: 1201.3583 · arxiv_version: 1201.3583v1 · doi: 10.48550/arxiv.1201.3583 · pith_short_12: D3X2OKO3K2ED · pith_short_16: D3X2OKO3K2EDIYAQ · pith_short_8: D3X2OKO3

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/D3X2OKO3K2EDIYAQ7L5TSKFKII \
  | 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: 1eefa729db5688346010fafb3928aa42395af6ca6c61be81dec0d247a1e12483

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d098177282715cab83e1f671da96e9653f54f34d7ab3622d99b5fbbb3789167",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-01-17T18:18:19Z",
    "title_canon_sha256": "b99921ff2db6e725d9d43b2ea2c2928b7dac25141e4955454a1d93d38b82d077"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.3583",
    "kind": "arxiv",
    "version": 1
  }
}