Pith Number

pith:KRXTQKOS

pith:2016:KRXTQKOSDLSQP4R7CKZOAYTU7B

not attested not anchored not stored refs pending

Estimating the Spectral Gap of a Reversible Markov Chain from a Short Trajectory

David A. Levin, Yuval Peres

arxiv:1612.05330 v1 · 2016-12-16 · math.ST · math.PR · stat.TH

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KRXTQKOSDLSQP4R7CKZOAYTU7B}

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	2026-05-18T00:54:52.051963Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

546f3829d21ae507f23f12b2e06274f8403987bd5ec0bcd7e32960f86b35e55f

Aliases

arxiv: 1612.05330 · arxiv_version: 1612.05330v1 · doi: 10.48550/arxiv.1612.05330 · pith_short_12: KRXTQKOSDLSQ · pith_short_16: KRXTQKOSDLSQP4R7 · pith_short_8: KRXTQKOS

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/KRXTQKOSDLSQP4R7CKZOAYTU7B \
  | 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: 546f3829d21ae507f23f12b2e06274f8403987bd5ec0bcd7e32960f86b35e55f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "64e4d0cffac07555dd34170b76ff0dc4db12d28494f9b022f01ec38a12668126",
    "cross_cats_sorted": [
      "math.PR",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2016-12-16T01:28:41Z",
    "title_canon_sha256": "08e93e1aed536023d9f62154c4b9f079f15d0d74601cc912e0a34dd64bd0cb2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.05330",
    "kind": "arxiv",
    "version": 1
  }
}