Pith Number

pith:4YI27ZNJ

pith:2012:4YI27ZNJVDD7I2C7QWQJVJBFFU

not attested not anchored not stored refs pending

Statistical properties of coupled expanding maps on a lattice with general infinite range couplings and H\"older densities

Chinmaya Gupta, Nicolai Haydn

arxiv:1203.3992 v1 · 2012-03-18 · math.DS · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4YI27ZNJVDD7I2C7QWQJVJBFFU}

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	2026-05-18T03:59:48.485845Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e611afe5a9a8c7f4685f85a09aa4252d1b33bb239e90e14d039e026a12f5a589

Aliases

arxiv: 1203.3992 · arxiv_version: 1203.3992v1 · doi: 10.48550/arxiv.1203.3992 · pith_short_12: 4YI27ZNJVDD7 · pith_short_16: 4YI27ZNJVDD7I2C7 · pith_short_8: 4YI27ZNJ

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/4YI27ZNJVDD7I2C7QWQJVJBFFU \
  | 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: e611afe5a9a8c7f4685f85a09aa4252d1b33bb239e90e14d039e026a12f5a589

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e59e741b7bab60c195726a626a3a1827f3e6d31684e1f7d2ad021d479d42f64",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-03-18T19:21:32Z",
    "title_canon_sha256": "e8cc83109ad08e0a8f788ab5d36a0999714741f1530161e525a05f293b70f737"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.3992",
    "kind": "arxiv",
    "version": 1
  }
}