Pith Number

pith:VE4KXGC5

pith:2026:VE4KXGC54LH6PIKAEVAY7ADSN6

not attested not anchored not stored refs pending

Ergodicity of (co)expanding on average random dynamical systems

Dmitry Dolgopyat, Jonathan DeWitt, Zhiyuan Zhang

arxiv:2605.21199 v1 · 2026-05-20 · 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{VE4KXGC54LH6PIKAEVAY7ADSN6}

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	2026-05-21T01:05:43.078453Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a938ab985de2cfe7a14025418f80726faed4fb98ddcc1e4ec77b9acd4bc066b1

Aliases

arxiv: 2605.21199 · arxiv_version: 2605.21199v1 · doi: 10.48550/arxiv.2605.21199 · pith_short_12: VE4KXGC54LH6 · pith_short_16: VE4KXGC54LH6PIKA · pith_short_8: VE4KXGC5

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/VE4KXGC54LH6PIKAEVAY7ADSN6 \
  | 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: a938ab985de2cfe7a14025418f80726faed4fb98ddcc1e4ec77b9acd4bc066b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b31ce3923d077a7cc237182dd50702e74fce026e234ea954aebfd79e1f13afd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-20T14:00:15Z",
    "title_canon_sha256": "e12fd3e354e70fb9e02ed661b7db226d199b91b3314f61a2b9253ab789927251"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.21199",
    "kind": "arxiv",
    "version": 1
  }
}