Result stated and proved in the source manuscript; website restatementfusion-reconstruction
Statement
For an infinite-index subgroup inclusion, the adjacent algebraic multiplication maps on cannot all extend as bounded or closable operators on the corresponding levelwise Connes-fusion completions . Failure already occurs at depth two.
Meaning and scope
The algebraic multiplication identities still hold. The dual operator-valued weight still realizes the face on its finite ideal. This is an obstruction to the specified ordinary Hilbert-operator realization.
The paper page includes the reader corrections accompanying this edition.
Source
[Paper 1, Theorem 6.1](/public/papers/released/Paper I - Infinite Index Fusion.pdf#page=7). Research note — not peer reviewed.
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Where this object sits in the mathematics
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