Pith Number

pith:7HPAPKMW

pith:2015:7HPAPKMW3O2FMMY4B2GN2NZQ45

not attested not anchored not stored refs pending

Computable bounds of ${\ell}^2$-spectral gap for discrete Markov chains with band transition matrices

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

arxiv:1511.01717 v1 · 2015-11-05 · 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{7HPAPKMW3O2FMMY4B2GN2NZQ45}

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	2026-05-18T01:27:39.982001Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9de07a996dbb456331c0e8cdd3730e740269c1fa409400e001d4cee4a74b1d3

Aliases

arxiv: 1511.01717 · arxiv_version: 1511.01717v1 · doi: 10.48550/arxiv.1511.01717 · pith_short_12: 7HPAPKMW3O2F · pith_short_16: 7HPAPKMW3O2FMMY4 · pith_short_8: 7HPAPKMW

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/7HPAPKMW3O2FMMY4B2GN2NZQ45 \
  | 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: f9de07a996dbb456331c0e8cdd3730e740269c1fa409400e001d4cee4a74b1d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b0c4fc2e2474aaa2791b7a1ffdd7727d10806b13bff651039d4ff5542ed7d87",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-11-05T12:45:02Z",
    "title_canon_sha256": "24c0711999fbe13582b440d3e422bce3ae4329c189b26be8786d22d306f2031e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.01717",
    "kind": "arxiv",
    "version": 1
  }
}