Pith Number

pith:764ZAQWQ

pith:2011:764ZAQWQCWFLYQYXLU3RHKDFNF

not attested not anchored not stored refs pending

A Spectral Gap Theorem in $SU(d)$

Alex Gamburd, Jean Bourgain

arxiv:1108.6264 v1 · 2011-08-31 · math.GR · math.CO · 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{764ZAQWQCWFLYQYXLU3RHKDFNF}

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.

Cited by

1 paper in Pith

Quantum Circuit Overhead

Receipt and verification

First computed	2026-05-18T04:14:26.653813Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffb99042d0158abc43175d3713a865696be8aa73fa7cdaf5ed6df5b8a08940ce

Aliases

arxiv: 1108.6264 · arxiv_version: 1108.6264v1 · doi: 10.48550/arxiv.1108.6264 · pith_short_12: 764ZAQWQCWFL · pith_short_16: 764ZAQWQCWFLYQYX · pith_short_8: 764ZAQWQ

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/764ZAQWQCWFLYQYXLU3RHKDFNF \
  | 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: ffb99042d0158abc43175d3713a865696be8aa73fa7cdaf5ed6df5b8a08940ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40001af93ca0da1f6723fd236e0c12f7fbab0e07fb46ebca47f3b45dfb426dfe",
    "cross_cats_sorted": [
      "math.CO",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-08-31T15:27:46Z",
    "title_canon_sha256": "848ade9b7836c6e680cb117683d1e8135dece13f2031e2b38dc910c54b484535"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.6264",
    "kind": "arxiv",
    "version": 1
  }
}