7. How Doxa Is Built

Doxa is constructed, not handed down from the sky. It is built in layers from raw possibility to particular cultural form. Each layer is the maximum-entropy distribution compatible with all constraints so far—the minimal information add-on that encodes the new constraints while carrying earlier ones forward.

The stack (µ⁰ → µ⁴)

Layer	Content	Social?
µ⁰	Bare configuration space	Pre-social
µ¹	Symmetries physical law imposes	Pre-social
µ²	Salience perception supplies	Pre-social
µ³	Institutions a community consciously builds	Doxa proper begins
µ⁴	History it accumulates	Doxa proper

The framework’s distinctive claim is not “culture has layers” (Bourdieu and others already said that). It is that the layering is iterated maximum-entropy projection—one operation repeated.

Institutions as concentrations of µ

Once you see µ this way, major economic objects share one ontology:

Object	Domain of concentration
Money	Medium of exchange
Property	Resource ownership
Firm	Production organisation
Market	Coordination mechanism

Each is a maintained concentration of µ in some slice of configuration space, with mechanisms that resist drift: enforcement, ritual, reproduction, narrative. Unattended, µ relaxes toward scaffolding—institutions decay. Work must be done to hold them. Flourishing, on this reading, is activity that sustains doxic concentrations against drift. A community whose conventional GDP looks fine while µ decays faster than it is renewed is still at structural risk.

The foundation-model analogy (exact enough to use)

Look at how large models are built:

1. Pretraining — install linguistic and cultural scaffolding.
2. Instruction tuning — install institutional “how to respond.”
3. RLHF — install refined contextual preferences against a reference policy.

Deep layers are held by being what every later stage starts from. The surface stage is often anchored by explicit KL regularisation against a reference model—the same projection idea. Labs have been refining hierarchical doxa engineering computationally, named differently because it was not recognised as such.

RLHF is doxic alignment (box it)

The objective max E[V] − τ KL(ρ ∥ µ) is the choice objective. The pretrained policy is µ; the KL term is the cost of leaving doxa; τ is the rationality/attention scale. RLHF is economic optimisation on the contractive form of the structure with doxa as reference. What was missing was the name of the reference.

Two-factor alignment requirement

Behaviour follows the score:

∇log ρ = ∇V/τ + ∇log µ

So behavioural alignment with a human community needs both terms compatible:

1. Value alignment — V points at what humans want.
2. Doxic alignment — µ matches the community’s unspoken background.

An AI with aligned V and misaligned µ can pass every stated-values benchmark while pulling systematically toward directions the second term sets—failures hardest to detect because they live below articulation: what counts as obvious, what would never need to be said, what is “not the kind of thing we do.”

The framework names µ as a first-class alignment target beside V, and makes “which reference, by which procedure, at which hierarchy level” a precise question rather than an implicit accident of training data.

Next: prove the structure is not a rebrand by recovering classical economics as special cases—and showing what finite temperature returns that classics set to zero.