Why it is a question
A22 §4 revised the loop of CLAIM-297 and CLAIM-330, interpretive advantage → authority → further interpretive advantage, by inserting a “Legibility regime” (“Attention, categories, representation, available evidence, interpretive resources”) between the world and the problems an institution recognizes, with “Feedback: authority can alter the future legibility regime”. It tied the layer to the existing mathematics: “the coefficient γ, representing interpretation’s effect on future authority, implicitly depends on how evidence is registered and scored”, and “Legibility helps us see that the reading of evidence is itself an organized activity.”
What the record holds:
- CLAIM-330 (Active, demonstrated): two arrows, β (authority shaping interpretation) and γ (interpretation shaping endorsement). The symmetric state is unstable when βγ > (1 − α)(1 − δ).
- CLAIM-340 (Active, demonstrated): with committed predictions, γ = 4ηs(κ′ − κ̄), where κ′ is how far the shared meaning bends the reading of the evidence.
- CLAIM-338: influence “decides which operators retrieve and so what the next judgement observes”, which is β by retrieval.
- CLAIM-342: “a loop that selects its own evidence can lock in”.
So there are two readings of A22’s layer.
- Renamed. Legibility is κ′, or β’s retrieval, already in the model, and the categories and reporting requirements an institution keeps are how κ′ is set. Then nothing new needs deriving.
- A third, slower variable. If authority changes the categories (call their lean r) on a slower time-scale than it changes the reading, and r sets κ′, the model gains a state and a longer loop: authority → r → κ′ → γ → authority. Its linearization is 3×3, and its instability condition need not be CLAIM-330’s. Even where it is stable, a slow r relaxes slowly, so a lean could outlast the return of m and a, which the two-variable model cannot show.
What would count as an answer
A three-variable linearization of CASE-099 with a legibility state r, its instability condition, and a showing either that the condition reduces to CLAIM-330’s with κ′ replaced by a function of r (the layer is κ′ renamed) or that it allows an instability, or a slow mode, that no choice of the two-variable parameters gives. CASE-106 is the construction it would extend.
What it does not ask
Whether any institution’s categories follow such dynamics. That needs cases the record does not hold. The readings of 2026-10-21 do not supply one. Agenda-setting (THEORY-842; THEORY-838, Proposed) is an empirical candidate for which facts become legible enough to count as evidence, but it is an aggregate cross-section with no dynamics. Szeidl and Szucs’s endogenous-ownership counterfactual has the shape of the slower variable, authority setting owners’ ideology and ideology setting slant (THEORY-852), but only across episodes in a static model, not as a dynamical one. Nor whether legibility should be adopted as a term (TERM-064 is Proposed).
Answer, 2026-10-21
CLAIM-400 (demonstrated, Active), on the construction CASE-124. Both readings above hold, for different questions about the model. For whether symmetry breaks, the regime is renamed: det(I − J₃) is (1 − λ) times CLAIM-330’s expression with β + νε/(1 − λ) for β and δ + με/(1 − λ) for δ, and the slower the regime the more it adds. For how long a lean lasts and how the system returns, it is not: the regime is a third mode, and in the second witness a lean in r holds m and a off symmetry long after the two-variable system would have returned. The construction was proposed in the owner’s review of 2026-10-21 with the route r → m; the route r → a, the reduction and the stable witness were added when it was checked. The route r → a is a direct effect of the regime on scoring. This question’s own reading, r setting κ′, is different: because γ = 4ηs(κ′ − κ̄), a regime that only varies κ′ enters the authority update as r·m, second order at symmetry, and changes no linear threshold (noted at the owner’s second review of 2026-10-21). What this question does not ask, whether any institution’s categories have such dynamics, stays open.