Pith Number

pith:ZPAZZQJK

pith:2009:ZPAZZQJKYRMWPEBIGLLX7BYZZU

not attested not anchored not stored refs pending

On Marginal Markov Processes of Quantum Quadratic Stochastic Processes

Farrukh Mukhamedov

arxiv:0904.3790 v2 · 2009-04-24 · math.FA · 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{ZPAZZQJKYRMWPEBIGLLX7BYZZU}

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	2026-05-18T04:36:59.487663Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbc19cc12ac45967902832d77f8719cd265ea4f0812fd51e6ce74289576cd821

Aliases

arxiv: 0904.3790 · arxiv_version: 0904.3790v2 · doi: 10.48550/arxiv.0904.3790 · pith_short_12: ZPAZZQJKYRMW · pith_short_16: ZPAZZQJKYRMWPEBI · pith_short_8: ZPAZZQJK

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/ZPAZZQJKYRMWPEBIGLLX7BYZZU \
  | 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: cbc19cc12ac45967902832d77f8719cd265ea4f0812fd51e6ce74289576cd821

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7a94212c5af6792ddaebbe669aa8bcf11d2baf89417522c0c291a384cb5fc3b",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2009-04-24T03:34:02Z",
    "title_canon_sha256": "9713a26935d5335e4ef504421692e57969420faedad43da1e8b1536e4d4d60ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.3790",
    "kind": "arxiv",
    "version": 2
  }
}