How is octane rating defined for negative values and those over 100?
I recommend the @Stanley Yu own answer, as I admit I was not particular familiar with the shape of the ON number curve.



It is done by an extrapolation of the critical compression ratios of mixtures 0-100% of isooctane and 100-0% of n-heptane for ON values &lt;0 and >100. 

If, just illustratively, 100% isooctane had the critical compression ratio 1:20, 90% isooctane 1:19 ,... 90% n-heptane 1:11, 100% n-heptane 1:10, then the fuel with the critical compression ratio 1:21 would have the octane number 110.

The octane number/rating differs for different procedures. See Research octane number RON, Motor octane number MON,  Anti-knock index AKI=(RON + MON )/2 and Observed Road octane number RdON.



As seen in the OP own answer, the extrapolation of the octane number (ON) scale  above 100 is done by linear  extrapolation by the empirical aviation formula for performance number $$PN=100 + 3 * ( ON - 100 )
where on the graph is coordinate ON substituted by tetraethyllead addition.