Pith Number

pith:5N6LNFCE

pith:2026:5N6LNFCE65PMTCH5NAYBDGZVLG

not attested not anchored not stored refs pending

Strict comparison holds in the uniform Roe algebra of a discrete amenable group

Chun Guang Li, George A. Elliott, Jianguo Zhang, Zhuang Niu

If d_τ(a) < d_τ(b) for all traces τ then a is Cuntz subequivalent to b in A ⊗ K where A is the uniform Roe algebra or minimal crossed product of a countable discrete amenable group.

arxiv:2605.01053 v2 · 2026-05-01 · math.OA · math.DS

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\usepackage{pith}
\pithnumber{5N6LNFCE65PMTCH5NAYBDGZVLG}

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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

It is shown that if a, b ∈ A ⊗ K are positive elements such that d_τ(a) < d_τ(b), τ ∈ T(A), then a is Cuntz subequivalent to b, where A = l^∞(Γ) ⋊ Γ or A = C(M) ⋊ Γ with (M, Γ) the universal minimal set of the countable discrete amenable group Γ.

C2weakest assumption

The assumption that Γ is amenable is load-bearing, as the proof relies on approximation properties and Følner sequences available only for amenable groups; the result is stated specifically for these crossed products and may fail without amenability or for other choices of A.

C3one line summary

For countable discrete amenable groups, strict comparison holds in A ⊗ K where A is l^∞(Γ) ⋊ Γ or C(M) ⋊ Γ with M the universal minimal set: d_τ(a) < d_τ(b) for all traces τ implies a is Cuntz subequivalent to b.

Receipt and verification

First computed	2026-06-12T01:09:28.351285Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb7cb69444f75ec988fd6830119b3559ba26be2ad8cd86328a54de8eb5cc6eff

Aliases

arxiv: 2605.01053 · arxiv_version: 2605.01053v2 · doi: 10.48550/arxiv.2605.01053 · pith_short_12: 5N6LNFCE65PM · pith_short_16: 5N6LNFCE65PMTCH5 · pith_short_8: 5N6LNFCE

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5N6LNFCE65PMTCH5NAYBDGZVLG \
  | 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: eb7cb69444f75ec988fd6830119b3559ba26be2ad8cd86328a54de8eb5cc6eff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db871437e779f998030f702ec2202ea7684c642b58a8d362787fad26e28fecbd",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-05-01T19:34:15Z",
    "title_canon_sha256": "0aca1992cfb52301cfe188b69749322fb52202f65bd5bd015e7ab1360ac6825f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.01053",
    "kind": "arxiv",
    "version": 2
  }
}