Pith Number

pith:DG5IBPBE

pith:2026:DG5IBPBEGYWWWD4FBNV73KZR3R

not attested not anchored not stored refs pending

Learning Ergodic Dynamical Systems from a Finite Trajectory

Lorenzo Rosasco, Oleksii Kachaiev, Silvia Villa

arxiv:2607.22399 v1 · 2026-07-24 · stat.ML · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DG5IBPBEGYWWWD4FBNV73KZR3R}

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	2026-07-27T01:21:18.735375Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

19ba80bc24362d6b0f850b6bfdab31dc624d5d7badb08b976f911f5282e077ee

Aliases

arxiv: 2607.22399 · arxiv_version: 2607.22399v1 · doi: 10.48550/arxiv.2607.22399 · pith_short_12: DG5IBPBEGYWW · pith_short_16: DG5IBPBEGYWWWD4F · pith_short_8: DG5IBPBE

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/DG5IBPBEGYWWWD4FBNV73KZR3R \
  | 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: 19ba80bc24362d6b0f850b6bfdab31dc624d5d7badb08b976f911f5282e077ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "852c91f59c8678dec8c3e2dbd565306fb2155ee253661d4b87525f90379c2ad4",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-07-24T15:21:51Z",
    "title_canon_sha256": "1cc841ff7d9279190c0e3b2f71c2d3386c53ef105c38b4de06648ec25b773915"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.22399",
    "kind": "arxiv",
    "version": 1
  }
}