Pith Number

pith:YX3DUGXV

pith:2026:YX3DUGXV26MMDHO6YMHUEKTCYZ

not attested not anchored not stored refs pending

Mean First Passage Times and Fundamental Tensors of Higher Order Markov Chains

Jianhong Xu

arxiv:2606.10058 v1 · 2026-06-08 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YX3DUGXV26MMDHO6YMHUEKTCYZ}

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	2026-06-10T00:08:46.830022Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5f63a1af5d798c19ddec30f422a62c646a80ac0bf9ed28d49f5c4d5ed7ed58a

Aliases

arxiv: 2606.10058 · arxiv_version: 2606.10058v1 · doi: 10.48550/arxiv.2606.10058 · pith_short_12: YX3DUGXV26MM · pith_short_16: YX3DUGXV26MMDHO6 · pith_short_8: YX3DUGXV

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/YX3DUGXV26MMDHO6YMHUEKTCYZ \
  | 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: c5f63a1af5d798c19ddec30f422a62c646a80ac0bf9ed28d49f5c4d5ed7ed58a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "57e5ae56ab6196b2666ee205408b7c7aa965bcbbc3ed5e19ba02ba65d77e1cf5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-08T18:34:00Z",
    "title_canon_sha256": "3436513aaa2b4a6ee788bf278245f8cc953b4548af28b7236ee5e80d6274a767"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.10058",
    "kind": "arxiv",
    "version": 1
  }
}