Pith Number

pith:ZNM6C4B7

pith:2026:ZNM6C4B7X7STVJULJW5SCRIIBZ

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Geometric duality, perfect graphs, and the Sierpi\'nski space

Anna Pelczar-Barwacz, Barnab\'as Farkas, Piotr Borodulin-Nadzieja

Duality between combinatorial Banach spaces holds precisely when the families are finite cliques and anti-cliques of a perfect graph on the naturals.

arxiv:2605.14072 v1 · 2026-05-13 · math.FA · math.CO · math.LO

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\pithnumber{ZNM6C4B7X7STVJULJW5SCRIIBZ}

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Claims

C1strongest claim

This duality holds iff there is a perfect graph G on NN such that F0 consists of all finite cliques of G and F1 consists of all finite anti-cliques of G.

C2weakest assumption

The precise definition of the 'duality phenomenon' between the two combinatorial Banach spaces is taken from the Bang-Odell paper and is assumed to be the correct notion of duality for the characterization to apply.

C3one line summary

Duality between combinatorial Banach spaces holds precisely when the families are the finite cliques and anti-cliques of a perfect graph on the naturals, making Lovász' perfect graph theorem a corollary, with further study of the Sierpiński graph case.

References

27 extracted · 27 resolved · 0 Pith anchors

[1] D. E. ALSPACH ANDS. ARGYROS,Complexity of weakly null sequences, vol. 321 of Dissertationes Math. (Rozprawy Mat.), 1992 1992

[2] APATSIDIS,Operators on the stopping time space, Studia Math., 228 (2015), pp 2015

[3] K. A. BAKER, P. FISHBURN,ANDF. S. ROBERTS,Partial orders of dimension2, Networks, 2 (1972), pp. 11–28 1972

[4] H. BANG ANDE. ODELL,On the stopping time Banach space, Quart. J. Math. Oxford Ser. (2), 40 (1989), pp. 257–273 1989

[5] K. BEANLAND, N. DUNCAN, M. HOLT,ANDJ. QUIGLEY,Extreme points for combinatorial Banach spaces, Glasg. Math. J., 61 (2019), pp. 487–500 2019

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-17T23:39:12.398162Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb59e1703fbfe53aa68b4dbb2145080e47d60b177a54aaa7d91a4af44a0a0e38

Aliases

arxiv: 2605.14072 · arxiv_version: 2605.14072v1 · doi: 10.48550/arxiv.2605.14072 · pith_short_12: ZNM6C4B7X7ST · pith_short_16: ZNM6C4B7X7STVJUL · pith_short_8: ZNM6C4B7

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZNM6C4B7X7STVJULJW5SCRIIBZ \
  | 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: cb59e1703fbfe53aa68b4dbb2145080e47d60b177a54aaa7d91a4af44a0a0e38

Canonical record JSON

{
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    "abstract_canon_sha256": "82e15a33c589bcaa9d068478cee864ce0224e9384a15c7c8e0723150f7eef5ab",
    "cross_cats_sorted": [
      "math.CO",
      "math.LO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-05-13T19:48:20Z",
    "title_canon_sha256": "3d1dd036eab5677d6e0c29833862081bc50ea4e819a42afccd039b969374c21c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14072",
    "kind": "arxiv",
    "version": 1
  }
}