nucleation

CASE-156: A legibility filter as the ν of the meaning–authority–legibility model: in a safe world where 15% of raw cues are alarms, an admission rule P(admit | y, r) = σ(c + χry) with c = 0 and χr = 2 admits 88.1% of alarms and 11.9% of reassurances, so 56.6% of the admitted record is alarms with the world and the sensors unchanged; at symmetry the mean admitted evidence is χσ′(c)r to first order, so ν = η_m χ σ′(c); and r_t = λᵗr₀ + ε Σ λ^(t−1−j) a_j is an exponentially weighted history of authority

5 min read

Properties9
StatusActive
Version2
Standingstipulated
Kindconstruction
Tagscomplex-systems, self-governance, epistemology
Linedistributed-agency
IllustratesCLAIM-400 — In the meaning–authority model linearized at symmetry, a third, maintained legibility state that authority moves (ε) and that moves interpretation (ν) or endorsement (μ), with persistence λ < 1 and nonnegative couplings, destabilizes the symmetric state exactly when the two-variable condition holds with β + νε/(1 − λ) in place of β and δ + με/(1 − λ) in place of δ: at the threshold the regime is indistinguishable from stronger two-variable couplings, and the slower it is the more it adds, while away from the threshold it adds a mode that no two-variable model has, so a lean in the regime can outlast the advantages it was built from, CLAIM-448 — An ordinal potential describes only the winning-move relation it is computed on; where an organization's legibility regime selects which contests are admitted or recorded, an acyclic record, even a persistent potential, can be the product of selective contestation, so observed coherence is not evidence that the organization's perspectives are integrated, and an intervention that improves its self-governance may at first increase the disagreement observed
Variant ofCASE-124 — A maintained legibility lean as a third state of the linearized meaning–authority model: authority moves the lean r of the categories through which evidence is read, and r feeds interpretation or authority, with its own persistence λ
VariantsCASE-162 — Capture and selectively admitted evidence in two lab realizations: in a four-variable model of authority, record and competence the equilibrium fold under self-scoring is at c ≈ 0.4247 while the declared history is trapped from c ≈ 0.4469, and in a 32-member event-level population, admission of cues that depends on the record reverses the sign of the admitted evidence and leaves the worse alternative in charge in 41 of 64 worlds, which exact inverse-propensity weighting brings to 0 of 64 below full selectivity

Graph View

The case

The filter. An objectively safe environment. An independent observer emits cues y_t ∈ {−1, +1}, +1 an alarm, with 85% accuracy, so P(y = +1 | safe) = 0.15. The governing regime decides whether a cue enters the record: P(k = 1 | y, r) = σ(c + χ r y). At r = 0 alarms and reassurances are admitted equally; for r > 0 alarms are favoured. With c = 0 and χr = 2, σ(2) = 0.881 and σ(−2) = 0.119, and

P(y = +1 | k = 1) = 0.15·0.881 / (0.15·0.881 + 0.85·0.119) ≈ 0.566.

Alarms go from 15% of the raw stream to 56.6% of the admitted record. The world has not changed and the sensors are as accurate as before. An evaluator who analyses the admitted record faithfully, without modelling the admission rule, concludes that alarms are common.

The microfoundation. Write the admitted evidence v_t = k_t y_t (zero when not admitted). At a symmetric point with equally frequent raw cues,

E[v | r] = ½σ(c + χr) − ½σ(c − χr) = χσ′(c) r + O(r³).

With the meaning update m′ = tanh(αm + βa + η_m v), the mean dynamics have, to first order, CASE-124’s ν = η_m χ σ′(c). The r → m coupling is then a mechanism, selective admission, and not a stipulated influence. CASE-124’s μ, the effect of r on scoring authority (CLAIM-400), is a different route and is not produced by this filter: experts whose reports fit the official categories scored higher with no better accuracy.

Legibility as memory of authority. Without inputs or nonlinearity, r_{t+1} = λr_t + εa_t unrolls to r_t = λᵗr₀ + ε Σ_{j<t} λ^(t−1−j) a_j. A once-dominant perspective leaves reporting conventions, attentional habits and evaluative standards that keep operating after its authority has faded. That is one more route of amortization (CLAIM-358’s note of 2026-10-23), adaptive while the settlement fits and self-protecting when it blocks revision.

What it can show

That filtering alone can turn a mostly reassuring stream into a mostly alarming record; that one of CASE-124’s couplings has a concrete mechanism; and why, at threshold, legibility acts like stronger coupling (CLAIM-400’s β_eff, δ_eff) while away from it r carries a memory of its own.

What it cannot show

  • Lock-in. A statistically sophisticated evaluator that knows the admission probabilities can correct for the selection, so long as the cues remain identifiable and have nonzero admission probability. The pathology needs more than filtering: the selection unmodelled, unaudited, or protected against correction.
  • That linear instability is lock-in. CASE-124’s witness (ρ(J₂) ≈ 0.724, ρ(J₃) ≈ 1.033) shows instability of the symmetric state. Lock-in also needs a persistent state, measured misalignment with the environment, and a maintaining path through r or a.

The mean-field witness the exchange reported

At U22 the exchange reported a deterministic mean-field run: sensor 70% correct, danger for 100 steps then safety for 500, a Jacobian at the neutral point with entries (0.5, 0.1, 1.25; 0.5, 0.5, 0; 0, 0.5, 0.5) and spectral radius about 1.203, a final lean r ≈ 0.225 with about 80.2% of admitted cues alarms in the safe phase, and a correction threshold (one step of independent evidence did not change the regime, three did). The script was not provided and the run is not reproduced here. The record holds it as reported, not checked.

Note of 2026-10-25: the reported run, checked

At U32 of the exchange of 2026-10-24, continued, the mean-field model was published as an interactive app, and its update rule was carried inline in the share:

m′ = tanh(0.5m + 0.1a + 0.5e),  a′ = tanh(0.5m + 0.5a + μr),
r′ = tanh(εa + λr),  e = qσ(χr) − (1 − q)σ(−χr),

with χ = 10, λ = ε = 0.5, μ = 0, a 70% sensor, danger for 100 steps and safety for 500. Transcribed and run, it reproduces every number A22 reported, which this case held as reported and not checked:

  • the Jacobian at the neutral point is (0.5, 0.1, 1.25; 0.5, 0.5, 0; 0, 0.5, 0.5), with spectral radius 1.2032;
  • the final lean is r = 0.2248, at which 80.2% of admitted cues are alarms in the safe phase;
  • the coupled run ends threat-leaning (m = +0.241), neutral reporting ends at m = −0.237, and with χ = 0 the coupled run ends at the neutral value;
  • an audit of 1 or 2 steps of neutral reporting leaves the coupled run threat-leaning, and 3 steps send it to the safe attractor (m = −0.601).

Two further results. With these parameters, lock-in needs χ above about 9.8: at χ = 9 the coupled run turns to safety by itself (m = −0.597), and at χ = 4 it ends at m = −0.513. And the shortest audit that corrects grows with χ: 3 steps at χ = 10, 4 at 12 and 5 at 16. That is CASE-155’s correction threshold in this model. That the app is the same script as A22’s is inferred from the matching numbers. The run is no longer only reported. The case is unchanged.

Backlinks