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Will not fit

Does the CBE Engage fit a Bowtech Core SR?

Not in the riser slot. The Core SR in-riser mount is Bowtech's Center Mass bar, not a dovetail, so the CBE Engage cannot use the slot. Mount the CBE Engage on the conventional side bracket holes instead.

Bow sight mount

Bowtech Center Mass through-riser sight bar (not a dovetail, not Picatinny)

Sight

CBE Engage, a Bridge-Lock-capable dovetail sight

Whether the CBE Engage fits the Core SR comes down to its Center Mass sight mount.

The two ends

Bow sight mountBowtech Center Mass through-riser sight bar (not a dovetail, not Picatinny)
SightCBE Engage, a Bridge-Lock-capable dovetail sight
What to orderCBE Engage on the side bracket holes (the Center Mass slot takes only a Bowtech sight)
Trapthe Center Mass slot is not a dovetail and not Picatinny

The Bowtech Core SR sight mount is a Center Mass interface, so whether the CBE Engage fits depends on the mounting bar, not the sight head.

The CBE Engage is a dovetail sight offered in a Bridge-Lock version, which is why it drops into a Mathews slot but needs a base change for a Picatinny rail and cannot use a Center Mass slot.

Related

Sources: Custom Bow Equipment: Bridge-Lock Conversion Bar (3 detents, CBE sights) ยท Hoyt Archery: In-Line system FAQ (Picatinny sights and adapters)