Pith Number

pith:I2VURE5I

pith:2010:I2VURE5IY4MBRD3DVZLEDAMRWE

not attested not anchored not stored refs pending

Growth of matrix products and mixing properties of the horocycle flow

Ekaterina Shulman, F\"edor Nazarov

arxiv:1008.3077 v1 · 2010-08-18 · 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{I2VURE5IY4MBRD3DVZLEDAMRWE}

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	2026-05-18T04:42:03.628957Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46ab4893a8c718188f63ae56418191b1143512e7946b84813ff9e8e48c034f10

Aliases

arxiv: 1008.3077 · arxiv_version: 1008.3077v1 · doi: 10.48550/arxiv.1008.3077 · pith_short_12: I2VURE5IY4MB · pith_short_16: I2VURE5IY4MBRD3D · pith_short_8: I2VURE5I

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/I2VURE5IY4MBRD3DVZLEDAMRWE \
  | 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: 46ab4893a8c718188f63ae56418191b1143512e7946b84813ff9e8e48c034f10

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e0b9d39c7c78f12a093fab69ac24dee74e56aa4718e5ef00e43127a0d59d2871",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-08-18T11:20:13Z",
    "title_canon_sha256": "70e3abecb69f6f0da9c92bf065903079a2372ecb63211f03ace68664cf92f1af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.3077",
    "kind": "arxiv",
    "version": 1
  }
}