Pith Number

pith:6NP3IQ7B

pith:2013:6NP3IQ7B5FS7G4SPLZH7YR3MP3

not attested not anchored not stored refs pending

A numerical lower bound for the spectral radius of random walks on surface groups

Sebastien Gouezel (IRMAR)

arxiv:1310.4265 v2 · 2013-10-16 · 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{6NP3IQ7B5FS7G4SPLZH7YR3MP3}

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	2026-05-18T01:31:46.800579Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f35fb443e1e965f3724f5e4ffc476c7efe154ad1fe6d2edfc864d7f586a4b8fb

Aliases

arxiv: 1310.4265 · arxiv_version: 1310.4265v2 · doi: 10.48550/arxiv.1310.4265 · pith_short_12: 6NP3IQ7B5FS7 · pith_short_16: 6NP3IQ7B5FS7G4SP · pith_short_8: 6NP3IQ7B

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/6NP3IQ7B5FS7G4SPLZH7YR3MP3 \
  | 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: f35fb443e1e965f3724f5e4ffc476c7efe154ad1fe6d2edfc864d7f586a4b8fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66d5a47d7cc7e72258997a99573977efe6e1ba75061fb138412023ad32e5c0be",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-10-16T04:27:06Z",
    "title_canon_sha256": "2c3e0294b35678c89d4bade426b8b58880a31ba4cadd6330e4f7b6be60b49bf8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.4265",
    "kind": "arxiv",
    "version": 2
  }
}