Pith Number

pith:CDUJU4DX

pith:2026:CDUJU4DXL5CXI4B4374FRKIBPD

not attested not anchored not stored refs pending

On dense free subgroups of Lie groups -- revisited

Emmanuel Breuillard, Tsachik Gelander

arxiv:2605.20568 v1 · 2026-05-20 · 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{CDUJU4DXL5CXI4B4374FRKIBPD}

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	2026-05-21T01:04:42.721014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10e89a70775f4574703cdff858a90178e5cf15896d5479133a8fcc2cb6019a78

Aliases

arxiv: 2605.20568 · arxiv_version: 2605.20568v1 · doi: 10.48550/arxiv.2605.20568 · pith_short_12: CDUJU4DXL5CX · pith_short_16: CDUJU4DXL5CXI4B4 · pith_short_8: CDUJU4DX

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/CDUJU4DXL5CXI4B4374FRKIBPD \
  | 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: 10e89a70775f4574703cdff858a90178e5cf15896d5479133a8fcc2cb6019a78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d6ffa30a8deb0c91175d1d1becf0a88bf3832461b5683ee2310922e16100040",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-05-20T00:00:45Z",
    "title_canon_sha256": "85fad33e417a7882501d51b979432ec93cd076d33316fc846a495ed5160778fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.20568",
    "kind": "arxiv",
    "version": 1
  }
}