Pith Number

pith:DGOYY5WL

pith:2016:DGOYY5WLXKD2FLDKBIFDHO6A2E

not attested not anchored not stored refs pending

Two minimal unique ergodic diffeomorphisms on a manifolds and their smooth crossed product algebras

Hongzhi Liu

arxiv:1605.00226 v2 · 2016-05-01 · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DGOYY5WLXKD2FLDKBIFDHO6A2E}

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	2026-05-18T01:14:20.242949Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

199d8c76cbba87a2ac6a0a0a33bbc0d12c3736dde36bc57eaceb7aef7f7adff9

Aliases

arxiv: 1605.00226 · arxiv_version: 1605.00226v2 · doi: 10.48550/arxiv.1605.00226 · pith_short_12: DGOYY5WLXKD2 · pith_short_16: DGOYY5WLXKD2FLDK · pith_short_8: DGOYY5WL

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/DGOYY5WLXKD2FLDKBIFDHO6A2E \
  | 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: 199d8c76cbba87a2ac6a0a0a33bbc0d12c3736dde36bc57eaceb7aef7f7adff9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3105791778b168545478565d16390b6a98bf14cbc40aa040ce41a83bdd609827",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2016-05-01T09:47:56Z",
    "title_canon_sha256": "cf9645a6f8fe84041d680906e056ff26f00826863bcebea0477273f9449ed6b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.00226",
    "kind": "arxiv",
    "version": 2
  }
}