Pith Number

pith:35EJ3GQZ

pith:2026:35EJ3GQZSECS6WXXMEW5RIBSLF

not attested not anchored not stored refs pending

On the Maximal Size of Irredundant Generating Sets in Lie Groups and Algebraic Groups

Itamar Vigdorovich, Tal Cohen

A topologically generating set in a connected compact Lie group must be redundant if its size exceeds a polynomial in the group's rank.

arxiv:2603.09640 v3 · 2026-03-10 · math.GR

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\pithnumber{35EJ3GQZSECS6WXXMEW5RIBSLF}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

We show that a topologically generating set S of a connected compact Lie group G of size larger than a fixed polynomial in the rank of G must be redundant (i.e., some proper subset of S still topologically generates G).

C2weakest assumption

The quantitative bounds produced by the method are controlled by corresponding bounds for finite simple groups of Lie type; the argument assumes that sufficiently strong polynomial bounds already exist or can be established for those finite groups.

C3one line summary

In connected compact Lie groups the maximal size of an irredundant topologically generating set is bounded by a polynomial in the rank, with analogous statements for amenable Lie groups and reductive algebraic groups.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-07-02T00:18:27.818917Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

df489d9a1991052f5af7612dd8a0325946dfe8fd0bba9dec6da740438052edc9

Aliases

arxiv: 2603.09640 · arxiv_version: 2603.09640v3 · doi: 10.48550/arxiv.2603.09640 · pith_short_12: 35EJ3GQZSECS · pith_short_16: 35EJ3GQZSECS6WXX · pith_short_8: 35EJ3GQZ

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/35EJ3GQZSECS6WXXMEW5RIBSLF \
  | 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: df489d9a1991052f5af7612dd8a0325946dfe8fd0bba9dec6da740438052edc9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "30dc729d6958ee8023e77bbc9f92dcf2f929b614899d836f878379a0ac8108b7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-03-10T13:15:30Z",
    "title_canon_sha256": "e0f4456ac477fa8272c8811311de8f222d1d46383a3933a7176729fb876ca8a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.09640",
    "kind": "arxiv",
    "version": 3
  }
}