The smooth faithfulness conjecture for tame tangles

A smooth tangle is a tame smooth embedding $W\to\mathbb{I}^n$, and two such tangles are framed stratified homeomorphic when their framed stratified structures are related by such a homeomorphism.

Framed homeomorphism of tame smooth tangles implies diffeomorphism. If two tame smooth tangles $W\to\mathbb{I}^n$ and $W'\to\mathbb{I}^n$ are framed stratified homeomorphic, then $W$ and $W'$ are diffeomorphic.

The proposed argument assumes standard smooth disks and is motivated by recovering smooth structures from tame tangle data. The source notes that the issue is tied to open questions in dimensions $4$ and $5$, including SPC4.