I read your latest missive on debt to GDP ratio, the first part. Again, you assumed fixed sample periods and lost me. Maybe you introduced variable sampling periods later on, but I didn't get that far, I don't get past the fixed period assumptions anymore.

Treasury Curve spreads over time

I guess I should give my lecture in fairness. I will speak to the chart above, which are the yields of the various terms in the Treasury curve. The quick summary is that as interest payments increase over time, the flexibility of Congress to maintain inventory decreases. At some point, bond market generates skepticism that interest payments can be made. When that happens, we dilate space and time. When we have those wide spreads, we are dilated. When the curve is nearly flat, that is because we have more levels of precision, each level handling a thinner slice of yield. The dilate state is the steep curve.

For the government, we adjust the relationship between state and federal government (space dilation) and estimate yields over longer time lines (time dilation) for a real example. The amount of time we spend in the dilated state depends upon the balance sheet adjustments that are made. If we do nothing, but stay in the dilated state, we will operate longer without inventory collapse. Normally we go through some government reorganization which reduces the constraint on government productions or pass them onto some lower level of the economy.

So, we move inventory with precision N, drop to precision N-1 for a while, sometimes hit precision N+1, and so one. Over time we have staved off negative inventory in government, but not completely corrected the problem as yield continue to decline. The bond market 'sees' government inventory with the current precision, or the current bounded calculus. When we say bounded, the bounds, the alarm level raised by uncertainty is proportional to the quantization error of the current calculus. Lower precision means inventory management has a large sigma in the variance to mean (= plan) ratio.

**The unit quant is larger in lower precision calculi, the quantization error greater, but inventory risk less. It seems contradictory, the the higher quantization error makes us more conservative, we delever.**
The take away is important, a infinite precision computation gives an alarm bell which is too risky. Underneath the lower precision means the bond market sees the alarms sooner than traditional, infinitely precise calculus would indicate. That is why we go into Recalc sooner than many of us expect.

What does the spread tell us now? This time is different! We are forced into a necessary restructuring of government, there is no more room for pretend and extend. We have done this before, we know how.