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10 · The same machinery everywhere — the point of the whole exercise

One measurement, three systems, no re-derivation:

A road network (Sioux Falls, real data). Logit route choice over BPR travel times. Toll a link, watch flows re-equilibrate, read the cross-response matrix. ℛ = 5.7×10⁻¹⁷ — zero. The system is an exact potential game (Beckmann's landscape exists), and the meter knows.

Colonel Blotto (budgets over battlefields). Same solve, same perturbation logic, same meter. ℛ = 0.12, α = 0.69 — strongly but not purely circulating (zero-sum ≠ pure harmonic, a fact the meter taught us).

Rock–paper–scissors. ℛ = 0.69, α = 1 — the pure extreme, with the dissipation meter showing the probability current physically circulating.

That is the thesis of this project in one table: potentiality is not a modelling assumption you make, it is a quantity you measure — the same instrument reading 0 where a potential exists, and loudly not-0 where strategy chases strategy in circles. Between the anchors sits everything interesting: pricing, electricity bidding, allocation contests — systems whose α nobody knows yet, and which these calibrated meters can now be pointed at.

Every number above regenerates from a fixed seed; the calibration gates, adversarial reviews, and the two occasions the meters corrected us (ℛ's λ-scaling; the response/dissipation decoupling) are all in the open repository. Instruments first; the readings decide the rest.

So what would you do differently?

The pricing answer, the bidding answer and the routing answer come out of one piece of arithmetic. If you have solved one of these decisions well, you already know how to set up the others.

The same machinery on five decisions