Pith Number

pith:VZEL5FTN

pith:2017:VZEL5FTNCEUSUR2WJG7ZLEKK6I

not attested not anchored not stored refs pending

Local spectral gap in the group of Euclidean isometries

Adrian Ioana, R\'emi Boutonnet

arxiv:1702.06323 v2 · 2017-02-21 · math.GR · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VZEL5FTNCEUSUR2WJG7ZLEKK6I}

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	2026-05-18T00:23:45.919863Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae48be966d11292a475649bf95914af21a9be5dcec92bebbb2f1cd49402092ba

Aliases

arxiv: 1702.06323 · arxiv_version: 1702.06323v2 · doi: 10.48550/arxiv.1702.06323 · pith_short_12: VZEL5FTNCEUS · pith_short_16: VZEL5FTNCEUSUR2W · pith_short_8: VZEL5FTN

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/VZEL5FTNCEUSUR2WJG7ZLEKK6I \
  | 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: ae48be966d11292a475649bf95914af21a9be5dcec92bebbb2f1cd49402092ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "906b0655e711ef83f9c1aedc4928010efd363377bdccb1cbdb7e44d3c5ae7826",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-02-21T10:49:55Z",
    "title_canon_sha256": "16dcfb7d7c876ecf4c137372434d319741734d17f32b180dac760419ddbf5219"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.06323",
    "kind": "arxiv",
    "version": 2
  }
}