Mechanisms
The machinery our pieces lean on, written out once and kept here. Each one is a formula you can drive. Pieces link to these instead of re-deriving them, so the derivation lives in one place and gets corrected in one place.
Capital recovery factor
The annual payment that repays a dollar of capital over its useful life at a given rate. It is how a one-time hardware bill becomes a yearly cost, and why the same satellite is far more expensive per year when it lives five years at 15% than when a building lives fifteen years at 10%.
Annual charge per dollar of capital, rate r, life L years
K(r, L) = r / [1 − (1 + r)^(−L)]
Orbit base: K(0.15, 5) = 0.298 Ground facility: K(0.103, 15) = 0.134
Common misreading
Treating a longer physical life as a longer economic life. A processor can survive in orbit and still be economically tired; L is the useful life, not the survival time.
Markers show the two cases the orbital piece uses. Move the rate to 12% and the life to 7 years to see K fall to 0.219.
Break-even launch price
The most an orbital compute stack could pay for launch and still match the ground’s cost per useful IT-kilowatt-year. Solve the two cost identities for the launch price and everything that isn’t launch becomes a single number the rocket has to beat.
Costs per useful IT-kW-year; P in $/kg; A is launch mass per IT-kW-year
C_ground = 8.76 × e × PUE + F × K_ground + g × I_ground
C_orbit = A × P + (h/η) × K_orbit × b + O + a × I_orbit
P* = [C_ground − (h/η) K_orbit b − O − a I_orbit] / A
Base: P* ≈ −$275/kg. Negative means the non-launch costs already exceed the ground bill.
Common misreading
Reading a falling launch price as progress toward parity. If P* is negative, launch at any price is not the constraint; the satellite bill is.
Each $1/MWh of ground power moves the ground bill by $11.83 per IT-kW-year, and the ceiling by $1.31/kg at the base mass.
Learning curves
Unit cost falls by a fixed share each time cumulative production doubles. The rate is a property of a specific product made the same way many times; it is not transferable from a different product, and it does not tick with the calendar.
Cost index after x times cumulative production, learning rate LR per doubling
index(x) = x ^ log₂(1 − LR)
doublings needed for a decline D: n = ln(1 − D) / ln(1 − LR) → x = 2ⁿ
80% decline at 20% learning: n = 7.21 doublings, x ≈ 148× production.
Common misreading
Counting the wrong denominator. Rocket flights carrying other payloads do not teach the compute-satellite factory; a redesign improves cost but changes the product being measured.
The curve is drawn on a log production axis. At 10% learning, 148\u00d7 only gets the index to 0.47.
Debt dynamics
Debt as a share of GDP changes with the gap between the effective interest rate and nominal growth, scaled by the debt level, less the primary balance. It is an identity, not a theory, which is why it is a good place to check a story about cheaper work shrinking the debt burden.
d = debt/GDP, r = effective interest, g = nominal growth, pb = primary balance (surplus positive), sfa = stock-flow adjustment
Δd = ((r − g) / (1 + g)) × d − pb + sfa
pb* = ((r − g) / (1 + g)) × d primary balance that holds d constant
FY2026 inputs from the piece: r ≈ 3.49%, g ≈ 5.77%, d: 99.0% → 100.0%. With sfa = 0 that implies pb ≈ −3.2%.
Common misreading
Treating a saving as a fiscal gain. Cheaper work only reaches pb if the saving becomes taxable domestic income and someone keeps it; otherwise it shows up in g, if anywhere.
Dashed line is CBO’s February 2026 projection, for scale. The toy holds r, g and pb fixed; CBO does not.
Inelastic markets
If the investors who would sell into a price rise adjust their portfolios only modestly, a flow into equities has to move prices a lot to find a counterparty. The aggregate response is summarized as a multiplier on the flow’s share of market capitalization.
Price change from a net flow f, as a share of market cap, with aggregate multiplier M
ΔP / P ≈ M × f
Gabaix and Koijen estimate M around 5 for the aggregate US market; a frictionless benchmark would put it near zero.
Common misreading
Reading fund assets as flow. Assets rise when holdings appreciate; only net new money, net of what it was switched out of, is f.
M is an estimate with a wide range, not a constant. The point of the mechanism is that the counterparty’s capacity is a market variable, not a given.