Pith Number

pith:Z2D46QAJ

pith:2012:Z2D46QAJL7Z52NBYSSVAVNGQZM

not attested not anchored not stored refs pending

Concentration inequalities for Markov chains by Marton couplings and spectral methods

Daniel Paulin

arxiv:1212.2015 v5 · 2012-12-10 · 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{Z2D46QAJL7Z52NBYSSVAVNGQZM}

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	2026-05-18T00:01:01.079672Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce87cf40095ff3dd343894aa0ab4d0cb33196b9d484d66c3e9f4184ceac87e29

Aliases

arxiv: 1212.2015 · arxiv_version: 1212.2015v5 · doi: 10.48550/arxiv.1212.2015 · pith_short_12: Z2D46QAJL7Z5 · pith_short_16: Z2D46QAJL7Z52NBY · pith_short_8: Z2D46QAJ

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/Z2D46QAJL7Z52NBYSSVAVNGQZM \
  | 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: ce87cf40095ff3dd343894aa0ab4d0cb33196b9d484d66c3e9f4184ceac87e29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "633ee6ca7b97b792f24843dd4779875279e5e2b12513e9bf31d819594bb766e1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-12-10T10:04:11Z",
    "title_canon_sha256": "0d2b5e46b834af407df344a4cd062706fbe03cd9e3e5e9388041546eb13be42f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.2015",
    "kind": "arxiv",
    "version": 5
  }
}