Pith Number

pith:A6XYHSGW

pith:2013:A6XYHSGWPHLPO3TOWGQJ7Q4PJX

not attested not anchored not stored refs pending

Spectral analysis of Markov kernels and application to the convergence rate of discrete random walks

James Ledoux (IRMAR), Lo\"ic Herv\'e (IRMAR)

arxiv:1312.1656 v1 · 2013-12-05 · 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{A6XYHSGWPHLPO3TOWGQJ7Q4PJX}

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	2026-05-18T03:05:26.605082Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07af83c8d679d6f76e6eb1a09fc38f4de2e47587388b8703fff29f9f18d6effc

Aliases

arxiv: 1312.1656 · arxiv_version: 1312.1656v1 · doi: 10.48550/arxiv.1312.1656 · pith_short_12: A6XYHSGWPHLP · pith_short_16: A6XYHSGWPHLPO3TO · pith_short_8: A6XYHSGW

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/A6XYHSGWPHLPO3TOWGQJ7Q4PJX \
  | 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: 07af83c8d679d6f76e6eb1a09fc38f4de2e47587388b8703fff29f9f18d6effc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00a70d369eac81d7834f8c17f6fae58cb1229c7170bf20185bb92c590274e197",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-12-05T19:48:40Z",
    "title_canon_sha256": "109439724f3a645f3b3542149c54a98a18e92b14e21c8a3cf3a13957a6de19b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.1656",
    "kind": "arxiv",
    "version": 1
  }
}