Pith Number

pith:QR7CMJ25

pith:2013:QR7CMJ25ZN6SY6J3ZXNJDE3PPZ

not attested not anchored not stored refs pending

Reduction of Markov chains with two-time-scale state transitions

Chen Jia

arxiv:1311.2196 v3 · 2013-11-09 · 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{QR7CMJ25ZN6SY6J3ZXNJDE3PPZ}

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	2026-05-18T01:37:08.018514Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

847e26275dcb7d2c793bcdda91936f7e42d54433eb81619c1372978417c73553

Aliases

arxiv: 1311.2196 · arxiv_version: 1311.2196v3 · doi: 10.48550/arxiv.1311.2196 · pith_short_12: QR7CMJ25ZN6S · pith_short_16: QR7CMJ25ZN6SY6J3 · pith_short_8: QR7CMJ25

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/QR7CMJ25ZN6SY6J3ZXNJDE3PPZ \
  | 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: 847e26275dcb7d2c793bcdda91936f7e42d54433eb81619c1372978417c73553

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7b7b6633c1b2013232c7553c67fb6c73fa6d4ecfd88815c4c5654bef24b86de",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-11-09T18:33:20Z",
    "title_canon_sha256": "5d0b6b01c44d20780926620d99517ccfc72416d54027a39f9eac36cefaba421f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.2196",
    "kind": "arxiv",
    "version": 3
  }
}