Pith Number

pith:ZOQ5SPOF

pith:2013:ZOQ5SPOFQXMUXP65ZKUD7USNXQ

not attested not anchored not stored refs pending

A Computational Framework for the Mixing Times in the QBD Processes with Infinitely-Many Levels

Jing Cao, Quan-Lin Li

arxiv:1308.4227 v1 · 2013-08-20 · math.PR · cs.PF · cs.SY · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZOQ5SPOFQXMUXP65ZKUD7USNXQ}

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	2026-05-18T03:15:33.367737Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cba1d93dc585d94bbfddcaa83fd24dbc1c2a3b8e9e6fce5e22cee0271b4c9cb7

Aliases

arxiv: 1308.4227 · arxiv_version: 1308.4227v1 · doi: 10.48550/arxiv.1308.4227 · pith_short_12: ZOQ5SPOFQXMU · pith_short_16: ZOQ5SPOFQXMUXP65 · pith_short_8: ZOQ5SPOF

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/ZOQ5SPOFQXMUXP65ZKUD7USNXQ \
  | 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: cba1d93dc585d94bbfddcaa83fd24dbc1c2a3b8e9e6fce5e22cee0271b4c9cb7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36561bb13bc5af1df11d752b1b2c4b928b7f95141459ba53c397891ce4e28a3e",
    "cross_cats_sorted": [
      "cs.PF",
      "cs.SY",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-08-20T04:36:39Z",
    "title_canon_sha256": "441cab2d974e1a6eccedf5645149f4121cb3d96ef34a5aac12bb3f9b56c132b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.4227",
    "kind": "arxiv",
    "version": 1
  }
}