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An isotope effect from a retained labeled bond adjacent to the reaction centre, often influenced by hyperconjugation and its geometry.

The natural mechanism is ionizing solvolysis: C-OTs cleavage gives a cyclopentyl cation/ion pair, capture by acetic acid gives the protonated acetate ester, and deprotonation gives product.

The $1.15$ effect from H/D at the leaving-group carbon is normal alpha-secondary: that carbon develops trigonal carbocation character. The $2.06$ effect from four neighboring labels is a combined beta-secondary effect. Adjacent C-H sigma bonds stabilize the developing empty p orbital by hyperconjugation; replacing H by D changes the vibrational stabilization and slows ionization. If the four contributions were equal and independent, each would be $2.06^{1/4}=1.198$.

None of those labeled C-H bonds is broken. The isotope effects support substantial carbocation character, although distinguishing a free cation from an intimate ion pair needs additional evidence.

Bridgehead substitution proceeds by ionization and solvent capture; backside displacement at the adamantyl bridgehead is geometrically inaccessible. The rigid cage prevents the labeled bonds from sampling all the favorable alignments available in cyclopentyl solvolysis.

The two labeled bonds in the adjacent methylene group are poorly oriented for ordinary C-H-to-empty-orbital hyperconjugation, explaining an effect close to $1.000$. Cage C-C sigma donation and geometrical relaxation can still stabilize the developing adamantyl cation. The three remote bridgehead labels perturb that coupled framework and give the smaller normal effect $1.073$, or about $1.024$ per label if contributions are equivalent.

This is a geometrical and remote secondary isotope effect. It does not imply cleavage of the remote C-H bonds, and absence of a beta effect at one selected site does not establish absence of a cation.