Pith Number

pith:W3KOMMXF

pith:2026:W3KOMMXFDI65JLAE7CQ622WOYG

not attested not anchored not stored refs pending

A Doeblin-Anchored Contrastive Chart for Learning Markov Transition Kernels

Ao Xu

arxiv:2606.02232 v1 · 2026-06-01 · 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{W3KOMMXFDI65JLAE7CQ622WOYG}

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	2026-06-02T03:04:53.724365Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6d4e632e51a3dd4ac04f8a1ed6acec18bd2a2d9db67a22ceaffb61b8d432bfc

Aliases

arxiv: 2606.02232 · arxiv_version: 2606.02232v1 · doi: 10.48550/arxiv.2606.02232 · pith_short_12: W3KOMMXFDI65 · pith_short_16: W3KOMMXFDI65JLAE · pith_short_8: W3KOMMXF

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/W3KOMMXFDI65JLAE7CQ622WOYG \
  | 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: b6d4e632e51a3dd4ac04f8a1ed6acec18bd2a2d9db67a22ceaffb61b8d432bfc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d6c1b88c03ba0b1be029e6f4fbfa98993590ff48f005fa1ece60c3b74950eea",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-01T13:26:44Z",
    "title_canon_sha256": "17e6564f8015e37d6f25c90f4a89af4259eab5182272ae333de4df46312bd6b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.02232",
    "kind": "arxiv",
    "version": 1
  }
}