Ask the boundary a better question.

The saved interval probe is a mathematical teaching tool with a declared circular boundary and a visible cutoff. At radius one, interval A runs from thirty to one hundred fifty degrees, a shortest separation of one hundred twenty degrees. Interval B runs from two hundred ten to three hundred twenty, a separation of one hundred ten. Its formula is chord equal to two R times sine of half the separation. That gives about one point seven three two one for A and one point six three eight three for B. Both circles use exactly one hundred forty pixels per radius unit, and each colored segment joins its actual angular endpoints. These chords are model evidence, not physical spacetime measurements. The exported regulated length is two times the natural logarithm of chord over epsilon. For the A chord at radius one and epsilon zero point zero five, the result is about seven point zero nine zero one. Halving epsilon to zero point zero two five leaves the chord unchanged but adds two times log two, about one point three eight six three, to this length. Doubling radius at fixed epsilon multiplies the chord by two and adds the same amount. Bars use seventy pixels per regulated model length unit. The tool exports the radius, cutoff, endpoints, all derived values and its explicit model limitations. Neither result is a cutoff independent universal distance. Change one interval to endpoints three hundred fifty and ten degrees. Their numeric difference is minus three hundred forty, but the source wraps onto the shortest signed separation, positive twenty degrees. Its midpoint is zero degrees. At radius one, the chord becomes two sine ten degrees, about zero point three four seven three. Compare the default one hundred twenty degree chord, one point seven three two one. Bars use two hundred fifty pixels per chord length unit. Calculate geometry validates positive radius and a positive cutoff smaller than radius; clear readout removes the saved result and hides export. Restore sample recalculates. This simplified regulated disk model does not prove reconstruction of a universe.