First we need to discuss knock...
Knock is traditionally referred to as "end gas autoignition"
End gas being the gasses at the ends of the combustion chamber, remote from the spark initiation point... (note, ring land failure...that's the last bit to get burned).
Increasing the turbulence in a combustion chamber actually INCREASES the burn speed, up to 10%, and that is one of the ways in which knock is reduced...so flame speed is NOT resistance to knock.
When the spark initiated a flame, the flame front progresses away from the spark at the local flame speed. The pressure in the chamber increases, and that pressure increase is transmitted through the chamber at the local speed of sound (KRT^0.5), K and R being constants, T being temperature in Kelvins (Celsius plus 273))...so the gasses at the end of the combustion process are increasing rapidly in pressure, and as per your bicycle pump experience, this makes them hot also).
If the pressure and temperature rise high enough for the fuel, the fuel/air … in the END GAS … autoigites (end gas autoignition) … and as it's an homogeneous mixture, it tends to all go off at once...with a bang...and all ahead of the flame front.
This event takes place all at the end of the chamber away from the flame front....if the flame had burned smoothly through, there would be no pressure spike.
"Octane rating" is the resistance to this end gas spontaneously "exploding"
Octane requirements near the plug are nil...further out, in the flame front proper, not much either...at the end gas phase...that's where you need the octane.
How it's measured ?
Iso-octane (2,2,4, trimethylpentane) is defined as 100, n-heptane is defined as zero. THe octane rating is the percentage of Isooctane and N-heptane that brackets the performance of a test fuel in a test engine under the various test methods.
QED...it has NOTHING to do with burn rate.
Quoting junk science and defending it to the death is becoming a major part of this board these days... I'm getting over it.