Pith Number

pith:FLJLBNJ7

pith:2009:FLJLBNJ7U4AQJ76TMCJE7EVWSE

not attested not anchored not stored refs pending

A spectral gap property for subgroups of finite covolume in Lie groups

Bachir Bekka, Yves Cornulier

arxiv:0903.4367 v1 · 2009-03-25 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FLJLBNJ7U4AQJ76TMCJE7EVWSE}

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	2026-05-18T04:42:43.348621Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ad2b0b53fa70104ffd360924f92b6912537f7d7894afc2990d564bf5dd6915c

Aliases

arxiv: 0903.4367 · arxiv_version: 0903.4367v1 · doi: 10.48550/arxiv.0903.4367 · pith_short_12: FLJLBNJ7U4AQ · pith_short_16: FLJLBNJ7U4AQJ76T · pith_short_8: FLJLBNJ7

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/FLJLBNJ7U4AQJ76TMCJE7EVWSE \
  | 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: 2ad2b0b53fa70104ffd360924f92b6912537f7d7894afc2990d564bf5dd6915c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6cf39c544887fc06c3db25915bdb402d879bcdfb6ff5d9d6c305c09cc18d67d4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-03-25T15:14:05Z",
    "title_canon_sha256": "d624010e672bb93b2fd03826720479ccb09c291845f9599375c4b616cd949a7f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.4367",
    "kind": "arxiv",
    "version": 1
  }
}