Pith Number

pith:VN3XU4QF

pith:2009:VN3XU4QFNTJNIA5CPQ6GO5NUW7

not attested not anchored not stored refs pending

A mixing-like property and inexistence of invariant foliations for minimal diffeomorphisms of the 2-torus

Alejandro Kocsard, Andres Koropecki

arxiv:0902.2474 v1 · 2009-02-14 · 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{VN3XU4QFNTJNIA5CPQ6GO5NUW7}

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	2026-05-18T04:35:05.476546Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab777a72056cd2d403a27c3c6775b4b7ef3aa8b17f8c78d9e4b9ef91022de527

Aliases

arxiv: 0902.2474 · arxiv_version: 0902.2474v1 · doi: 10.48550/arxiv.0902.2474 · pith_short_12: VN3XU4QFNTJN · pith_short_16: VN3XU4QFNTJNIA5C · pith_short_8: VN3XU4QF

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/VN3XU4QFNTJNIA5CPQ6GO5NUW7 \
  | 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: ab777a72056cd2d403a27c3c6775b4b7ef3aa8b17f8c78d9e4b9ef91022de527

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc8fddea3cf69759324644722d2dde7d4a6a6af2def9455357322f1fb02439b6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-02-14T15:57:21Z",
    "title_canon_sha256": "430e8d0eff5dd5182363a650508534094b8545abcdae0e84e4da0ff82f70f412"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.2474",
    "kind": "arxiv",
    "version": 1
  }
}