Pith Number

pith:CLROYBLF

pith:2026:CLROYBLFHH5TWLKFHPJABVGNHP

not attested not anchored not stored refs resolved

Uniqueness for embeddings of nuclear $C^*$-algebras into type II$_{1}$ factors

Shanshan Hua, Stuart White

Unital full nuclear maps from separable exact C*-algebras satisfying the UCT into ultraproducts of finite factors are unitarily equivalent whenever they agree on traces and total K-theory.

arxiv:2601.08779 v2 · 2026-01-13 · math.OA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CLROYBLFHH5TWLKFHPJABVGNHP}

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.

Claims

C1strongest claim

any two such maps agreeing on traces and total K-theory are unitarily equivalent

C2weakest assumption

A is a separable, unital and exact C*-algebra satisfying the universal coefficient theorem; the maps are unital, full and nuclear

C3one line summary

Uniqueness up to unitary conjugacy holds for nuclear maps from separable exact C*-algebras satisfying the UCT into ultraproducts of finite factors when the maps agree on traces and total K-theory.

References

82 extracted · 82 resolved · 1 Pith anchors

[1] R. Antoine, J. Bosa, and F. Perera. Completions of monoids with applications to the Cuntz semigroup.Internat. J. Math., 22(6):837–861, 2011 2011

[2] W. Arveson. Notes on extensions ofC∗-algebras.Duke Math. J., 44(2):329–355, 1977 1977

[3] S. Barlak and X. Li. Cartan subalgebras and the UCT problem.Adv. Math., 316:748– 769, 2017 2017

[4] Blackadar.K-theory for operator algebras, volume 5 ofMathematical Sciences Re- search Institute Publications 1998

[5] Blackadar.Operator algebras, volume 122 ofEncyclopaedia of Mathematical Sci- ences 2006

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:16.664284Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12e2ec056539fb3b2d453bd200d4cd3bf11fa143daa4392242ffa2f33f38cd03

Aliases

arxiv: 2601.08779 · arxiv_version: 2601.08779v2 · doi: 10.48550/arxiv.2601.08779 · pith_short_12: CLROYBLFHH5T · pith_short_16: CLROYBLFHH5TWLKF · pith_short_8: CLROYBLF

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/CLROYBLFHH5TWLKFHPJABVGNHP \
  | 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: 12e2ec056539fb3b2d453bd200d4cd3bf11fa143daa4392242ffa2f33f38cd03

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e532b73ba7aecf8352cb0200774825b53de0ff14d58ad4a57ea4c4a2d54ff4c5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-01-13T18:09:47Z",
    "title_canon_sha256": "59cd0c4eff394e28330d78342bcc4d697e4cb2c910719f2cbb1c03780c308860"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.08779",
    "kind": "arxiv",
    "version": 2
  }
}