Pith Number

pith:3RZLL7KF

pith:2015:3RZLL7KFTYQS6LS3OYMUDMLOXJ

not attested not anchored not stored refs pending

Additional material on bounds of $\ell^2$-spectral gap for discrete Markov chains with band transition matrices

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

arxiv:1503.02206 v2 · 2015-03-07 · 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{3RZLL7KFTYQS6LS3OYMUDMLOXJ}

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	2026-05-18T01:22:54.220093Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc72b5fd459e212f2e5b761941b16eba7d8d4ae97bcd12f25b0e7621cbd85a0a

Aliases

arxiv: 1503.02206 · arxiv_version: 1503.02206v2 · doi: 10.48550/arxiv.1503.02206 · pith_short_12: 3RZLL7KFTYQS · pith_short_16: 3RZLL7KFTYQS6LS3 · pith_short_8: 3RZLL7KF

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/3RZLL7KFTYQS6LS3OYMUDMLOXJ \
  | 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: dc72b5fd459e212f2e5b761941b16eba7d8d4ae97bcd12f25b0e7621cbd85a0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b664cb05ca1c419d044211693f8ec066337672c97975914a504668800e5b4d46",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-03-07T19:41:41Z",
    "title_canon_sha256": "0e6f5c9ab7ca93574f5c5ac24876a332bcfd2b76f25a29dd22d76a47367cc7a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.02206",
    "kind": "arxiv",
    "version": 2
  }
}