Pith Number

pith:HDY4XMB4

pith:2005:HDY4XMB4SJPI4OANS2SPGRZ2S3

not attested not anchored not stored refs pending

A spectral gap property for random walks under unitary representations

Bachir Bekka, Yves Guivarc'h

arxiv:math/0508195 v1 · 2005-08-11 · math.DS · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HDY4XMB4SJPI4OANS2SPGRZ2S3}

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	2026-05-18T02:27:59.022739Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

38f1cbb03c925e8e380d96a4f3473a96fe1330d4e9cf38eb63fc1a7e8295d175

Aliases

arxiv: math/0508195 · arxiv_version: math/0508195v1 · doi: 10.48550/arxiv.math/0508195 · pith_short_12: HDY4XMB4SJPI · pith_short_16: HDY4XMB4SJPI4OAN · pith_short_8: HDY4XMB4

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/HDY4XMB4SJPI4OANS2SPGRZ2S3 \
  | 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: 38f1cbb03c925e8e380d96a4f3473a96fe1330d4e9cf38eb63fc1a7e8295d175

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82764b07e17c2d88fdcbb9dde1df336501c1b5eafc3cf06e2320723439462019",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2005-08-11T10:05:34Z",
    "title_canon_sha256": "814374ba7a0dfc02bb5acd4b3e98074d8c6abbd815520e627a221bf8596c170e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0508195",
    "kind": "arxiv",
    "version": 1
  }
}