Pith Number

pith:MPRMIH7A

pith:2010:MPRMIH7AVNR6WSBLCXR3HFV2IG

not attested not anchored not stored refs pending

Ratner's property and mixing for special flows over two-dimensional rotations

K. Fraczek, M. Lemanczyk

arxiv:1002.2734 v2 · 2010-02-13 · 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{MPRMIH7AVNR6WSBLCXR3HFV2IG}

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	2026-05-18T04:33:18.073709Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63e2c41fe0ab63eb482b15e3b396ba41a5065fd344e7979f809e5427f00b1293

Aliases

arxiv: 1002.2734 · arxiv_version: 1002.2734v2 · doi: 10.48550/arxiv.1002.2734 · pith_short_12: MPRMIH7AVNR6 · pith_short_16: MPRMIH7AVNR6WSBL · pith_short_8: MPRMIH7A

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/MPRMIH7AVNR6WSBLCXR3HFV2IG \
  | 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: 63e2c41fe0ab63eb482b15e3b396ba41a5065fd344e7979f809e5427f00b1293

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c82171f0c118d0170589bc624aa607d34e98422129529db2bd90e3d21d43548",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-02-13T22:10:20Z",
    "title_canon_sha256": "1f2630caad17894dc4deb249e1a272787f24bc5d464ed01b0ade78d6ea5acb1f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.2734",
    "kind": "arxiv",
    "version": 2
  }
}