Pith Number

pith:MKIT5EO6

pith:2026:MKIT5EO6776LXUYXP7E3USCJGA

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Model theory and Connes' bicentralizer problem

Hiroshi Ando, Isaac Goldbring

The bicentralizer problem has a positive solution if and only if the bicentralizer functor is a zeroset relative to the theory of III1 factors.

arxiv:2605.12776 v1 · 2026-05-12 · math.OA · math.LO

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Claims

C1strongest claim

the bicentralizer problem has a positive solution if and only if the bicentralizer functor is a zeroset relative to the theory of III1 factors

C2weakest assumption

The Houdayer-Marrakchi equivalence between trivial bicentralizer and selflessness extends to all diffuse W*-probability spaces without separability or other hidden restrictions.

C3one line summary

The bicentralizer problem for III1 factors has a positive solution if and only if the bicentralizer functor is a zeroset in the theory of III1 factors, and the class of such factors with trivial bicentralizer is ∀∃-axiomatizable.

References

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[1] Matsumoto, Kengo , TITLE =. Proc. London Math. Soc. (3) , FJOURNAL =. 1997 , NUMBER =. doi:10.1112/S0024611597000166 , URL = 1997 · doi:10.1112/s0024611597000166

[2] Houdayer, Cyril , TITLE =. Proc. Amer. Math. Soc. , FJOURNAL =. 2009 , NUMBER =. doi:10.1090/S0002-9939-09-09923-7 , URL = 2009 · doi:10.1090/s0002-9939-09-09923-7

[3] Connes, A. , TITLE =. J. Functional Analysis , FJOURNAL =. 1974 , PAGES =. doi:10.1016/0022-1236(74)90059-7 , URL = 1974 · doi:10.1016/0022-1236(74)90059-7

[4] Houdayer, Cyril and Isono, Yusuke , TITLE =. Bull. Lond. Math. Soc. , FJOURNAL =. 2020 , NUMBER =. doi:10.1112/blms.12376 , URL = 2020 · doi:10.1112/blms.12376

[5] 2024 , eprint = 2024

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Cited by

1 paper in Pith

Ultrapowers of spectral subspaces

Receipt and verification

First computed	2026-05-18T03:09:13.210643Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62913e91defffcbbd3177fc9ba4849301fc548b11afc608513e38dc65ad31dbf

Aliases

arxiv: 2605.12776 · arxiv_version: 2605.12776v1 · doi: 10.48550/arxiv.2605.12776 · pith_short_12: MKIT5EO6776L · pith_short_16: MKIT5EO6776LXUYX · pith_short_8: MKIT5EO6

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MKIT5EO6776LXUYXP7E3USCJGA \
  | 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: 62913e91defffcbbd3177fc9ba4849301fc548b11afc608513e38dc65ad31dbf

Canonical record JSON

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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-05-12T21:43:49Z",
    "title_canon_sha256": "c037ec814bee2a8bb491e570a01d18098e0a4f45b1b72b90e8da39018a1e4b9f"
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  "source": {
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    "kind": "arxiv",
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}