Pith Number

pith:CIXQDJMZ

pith:2006:CIXQDJMZAB6KJKDUWV5AI5H2LT

not attested not anchored not stored refs pending

Traces of symmetric Markov processes and their characterizations

Jiangang Ying, Masatoshi Fukushima, Zhen-Qing Chen

arxiv:math/0606784 v1 · 2006-06-30 · 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{CIXQDJMZAB6KJKDUWV5AI5H2LT}

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	2026-07-04T14:55:34.356917Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

122f01a599007ca4a874b57a0474fa5cd9d81005bc1a30e45023eacf142cc616

Aliases

arxiv: math/0606784 · arxiv_version: math/0606784v1 · doi: 10.48550/arxiv.math/0606784 · pith_short_12: CIXQDJMZAB6K · pith_short_16: CIXQDJMZAB6KJKDU · pith_short_8: CIXQDJMZ

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/CIXQDJMZAB6KJKDUWV5AI5H2LT \
  | 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: 122f01a599007ca4a874b57a0474fa5cd9d81005bc1a30e45023eacf142cc616

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "956b100ab8190cd5667870c4e5e51274775d537a23804ad641746f33020a7a1b",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2006-06-30T08:22:26Z",
    "title_canon_sha256": "537358265f9bb8a0d9c23a347a930727d60475c50149ee964b9e763889d4240a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0606784",
    "kind": "arxiv",
    "version": 1
  }
}