8. Classical Economics at the Limit

If economics is choice under doxa on this structure, it must answer for the economics that already exists. The answer: classical results are special cases of the same object—each recovered under the reference and limit its field assumed.

Recovery map (plain version)

Classical idea	How it falls out	What finite τ adds back
Demand & Slutsky	Value linear in prices inside the forced law	Price-dependent µ → measurable asymmetry (doxa estimator)
Multinomial logit	Uniform µ on finite options	Doxic term in log-odds
Euler equation / dynamic optimisation	τ → 0 mode over plans	Correction −τ ∇log µ
Exponential discounting	Independence read along the clock	Time-consistency as independence
Nash equilibrium	τ → 0 of coupled soft best responses (QRE)	Equilibrium selection by reference
Black–Scholes risk-neutral measure	Minimal-entropy tilt of physical measure	Incomplete markets price the reference
Landauer bound	Two-state erasure cost τ ln 2 at physical T	Physical floor of complexity cost C
Rational expectations	Fixed point µ ← ρ*	Lucas critique as motion of µ
Condorcet jury theorem	Shared µ, independent signals	Mean-bias failure when µ diverge
Aumann agreement	Common µ, tilts combine	Disagreement measures reference divergence
Clearing & welfare	Convex program over prices	Welfare at temperature; efficiency is doxa-conditional

Two kinds of recovery matter. Some reproduce a formula the field already had—a check. Others identify a field’s object with one the structure carries—and earn keep only by transfer: the rest of the machinery (score, temperature, V/µ split) must yield a new constraint the source field did not build in. Renaming is not unification. Transfer is.

Demand without positing utility first

With linear value tilt V = −p · x, average choice is the gradient of a log-partition function. Compensated price responses form the Slutsky matrix—symmetric and negative semidefinite because that log-partition is a convex cumulant generator. Textbook demand properties fall out of one fact. Income effects need richer V; they are not smuggled in here.

Slutsky asymmetry as a doxic meter. If the reference itself depends on prices (fairness anchors, “the usual price”), part of measured demand response becomes asymmetric. The antisymmetric piece estimates how µ depends on p. What classical theory assumed away becomes measurable.

Lucas critique as dynamics, not only prohibition

Lucas: estimated policy relationships are not invariant because expectations adapt. Rational-expectations macro often answered by assuming expectations already consistent—immune by construction, sometimes unrealistically fast.

Here expectations live in µ. A policy change is a change in V. Within a round, agents relax toward new ρ. Across rounds, the settled distribution becomes the next reference: µ ← ρ**.

• Slow adaptation ≈ fixed expectations.
• Fast adaptation ≈ rational expectations.
• Real life sits between—and the adaptation rate is in principle estimable.

The critique becomes an equation of motion, not only a ban on naive policy. The same iteration, when a system trains on its own output, is the skeleton of model collapse in generative AI: annealing the reference toward degeneracy. Reward over-optimisation is the fixed-V cousin.

Games, agreement, aggregation

The chain forces structure per agent. Multi-agent results need no new axioms: couple through the free slots.

• Couple through V (my payoff depends on your action) → strategic interaction; quantal response equilibrium at τ > 0; Nash as τ → 0.
• Couple through µ (shared or split references) → agreement, aggregation, maintenance contests.

Aumann: with common µ, combining tilts yields agreement; with different µ, exchanging posteriors cannot fix a reference mismatch. Persistent disagreement is often doxic.

Condorcet: shared µ and independent signals recover majority wisdom. If mean doxic bias exceeds signal information, more voters can converge confidently on the wrong answer. Polarisation resists “more facts” when facts are processed through divergent references; repair is rebuilding common µ.

Schools as specialisations

School	Where it sits on the object
Neoclassical / Walrasian / rational expectations	Zero-temperature boundary
Behavioural / rational inattention	Finite-τ interior; “biases” as pull of µ
HANK / distributional macro	Evolution of ρ itself
Marxian accumulation themes	Circulation-dominant non-reciprocal values
Austrian / institutional (Hayek, North)	Construction and information in µ

The framework does not declare them wrong. It locates them: mainstream on the boundary, heterodox in the interior, institutional work on the reference the structure is defined against.

Next: where prices come from, how markets clear as a convex program, and what a firm is when culture is a reference.