Pith Number

pith:SWLKT6AG

pith:2012:SWLKT6AGLPGTNAVRXWWBLHVQEX

not attested not anchored not stored refs pending

Perturbation bounds for the stationary distributions of Markov chains

Yuanyuan Liu

arxiv:1208.4974 v1 · 2012-08-24 · 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{SWLKT6AGLPGTNAVRXWWBLHVQEX}

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	2026-05-18T03:47:52.141920Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9596a9f8065bcd3682b1bdac159eb025f3a34598ee1b8f7d853d725d7951e313

Aliases

arxiv: 1208.4974 · arxiv_version: 1208.4974v1 · doi: 10.48550/arxiv.1208.4974 · pith_short_12: SWLKT6AGLPGT · pith_short_16: SWLKT6AGLPGTNAVR · pith_short_8: SWLKT6AG

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/SWLKT6AGLPGTNAVRXWWBLHVQEX \
  | 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: 9596a9f8065bcd3682b1bdac159eb025f3a34598ee1b8f7d853d725d7951e313

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c49d709aa5539a4ad09af9aa694a50ad9536fbb7fdd13eb055382a19c15ec4ed",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-08-24T13:34:54Z",
    "title_canon_sha256": "e96166b90cf21bb5d2b6467627020408409d87d29a32d93e0aa8fa9f81b6c2dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.4974",
    "kind": "arxiv",
    "version": 1
  }
}