Pith Number

pith:BW2W5XDE

pith:2012:BW2W5XDE63DFFKDJYBSSGAFYW2

not attested not anchored not stored refs pending

On the mixing properties of piecewise expanding maps under composition with permutations

Mark Holland, Nigel P. Byott, Yiwei Zhang

arxiv:1203.5145 v3 · 2012-03-22 · math.DS · math.CO · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BW2W5XDE63DFFKDJYBSSGAFYW2}

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	2026-05-18T01:25:16.566575Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0db56edc64f6c652a869c0652300b8b6a12b4c0d59fd02ff44836b9a180cd7cf

Aliases

arxiv: 1203.5145 · arxiv_version: 1203.5145v3 · doi: 10.48550/arxiv.1203.5145 · pith_short_12: BW2W5XDE63DF · pith_short_16: BW2W5XDE63DFFKDJ · pith_short_8: BW2W5XDE

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/BW2W5XDE63DFFKDJYBSSGAFYW2 \
  | 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: 0db56edc64f6c652a869c0652300b8b6a12b4c0d59fd02ff44836b9a180cd7cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cac6e5efe3b4580b25e8bf71b46c945c91fdc2b7fd920dff4bbda75947a55b50",
    "cross_cats_sorted": [
      "math.CO",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-03-22T23:05:16Z",
    "title_canon_sha256": "ff7e44a28b5841f9519d2f507a1cefa5e3a11cb3b7e079298b606f3665560d4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.5145",
    "kind": "arxiv",
    "version": 3
  }
}