Pith Number

pith:RUZC3DJT

pith:2025:RUZC3DJTKCHHTOYRV3YBEGAL23

not attested not anchored not stored refs pending

On Limiting Probability Distributions of Higher Order Markov Chains

Jianhong Xu, Lixing Han

arxiv:2506.08874 v2 · 2025-06-10 · math.PR · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RUZC3DJTKCHHTOYRV3YBEGAL23}

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	2026-07-17T00:20:39.614641Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8d322d8d33508e79bb11aef012180bd6cc3c0334e0ce35f10d882a889b5d5ac5

Aliases

arxiv: 2506.08874 · arxiv_version: 2506.08874v2 · doi: 10.48550/arxiv.2506.08874 · pith_short_12: RUZC3DJTKCHH · pith_short_16: RUZC3DJTKCHHTOYR · pith_short_8: RUZC3DJT

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/RUZC3DJTKCHHTOYRV3YBEGAL23 \
  | 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: 8d322d8d33508e79bb11aef012180bd6cc3c0334e0ce35f10d882a889b5d5ac5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b68141934b2143498fc126d70f2cb7dc46e584390da72e20fc8b2e43b6739f36",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-06-10T15:06:30Z",
    "title_canon_sha256": "fd0a7614845db715516b2df7ccd0651531b7806b2fd9efb769e9d0ccbe604e6e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.08874",
    "kind": "arxiv",
    "version": 2
  }
}