Pith Number

pith:4U6TLNOA

pith:2014:4U6TLNOACPVOTTTQTGHAIVN3NH

not attested not anchored not stored refs pending

Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps

Artur Lopes, Benoit Kloeckner (LAMA), Manuel Stadlbauer

arxiv:1412.0848 v3 · 2014-12-02 · 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{4U6TLNOACPVOTTTQTGHAIVN3NH}

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	2026-05-18T01:34:55.196757Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e53d35b5c013eae9ce70998e0455bb69e000ae7356ca3328b367a50dda8d0634

Aliases

arxiv: 1412.0848 · arxiv_version: 1412.0848v3 · doi: 10.48550/arxiv.1412.0848 · pith_short_12: 4U6TLNOACPVO · pith_short_16: 4U6TLNOACPVOTTTQ · pith_short_8: 4U6TLNOA

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/4U6TLNOACPVOTTTQTGHAIVN3NH \
  | 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: e53d35b5c013eae9ce70998e0455bb69e000ae7356ca3328b367a50dda8d0634

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e741a0514f7c540c9a4b1e4b0282c9fa7e16c7daab5f9a686e31656f507f64ff",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2014-12-02T10:35:32Z",
    "title_canon_sha256": "47dbc046593511894187ef5810c5702ae6742947242f42a34fda26a1a27d816e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.0848",
    "kind": "arxiv",
    "version": 3
  }
}