Friction cycles and the Four Horsemen

Many relationship failures follow the same trajectory: a small model error is left uncorrected → friction rises → models drift in defence → feedback loop → \(\mathcal{R} < 1\) → breakup, burnout, or chronic hostility.

Gottman’s Four Horsemen (criticism, contempt, defensiveness, stonewalling) are, in FPE terms, behavioural signatures of rising \(d\Gamma/dt\) and \(\mathcal{D}_{KL}\).

The \(\mathcal{D}_{KL}\)–\(\Gamma\) loop

Uncorrected D_KL  →  surprise / hurt  →  defensive update of Q
        ↑                                    ↓
   more D_KL  ←  contempt, stonewall  ←  Γ rises (unresolved C)

\(\mathcal{D}_{KL}\): “What I thought about you / us” ≠ what happened.
\(\Gamma\): each unresolved fight adds to set \(C\); cost ~quadratic in overlapping conflicts.
Prediction: early \(d\Gamma/dt\) predicts long-term outcome (Gottman) because it measures whether the two operations are being performed.

Four Horsemen → FPE terms

Horseman	What it does	Term
Criticism	Global attack on ISM, not behaviour	Low-\(\eta\) aggression; raises partner’s \(\mathcal{D}_{KL}\)
Contempt	Disgust, superiority	Maximises \(\Gamma\); predicts dissolution strongest
Defensiveness	Refuses model update	Maintains self-\(\mathcal{D}_{KL}\); blocks operation 1
Stonewalling	Withdraws from coupling	Decouples without clean exit; leaves \(\Gamma\) in graph

Stonewalling often follows flooding (HPA overload): \(\Phi\) too low to run high-\(\eta\) assertion — not “indifference” but substrate-limited \(P_{in}\eta\).

Passive aggression

Passive aggression is low-\(\eta\) numerator disguised as denominator compliance:

sarcasm, procrastination, “forgetting”
appears low-conflict (\(\Gamma\) delayed)
raises \(\mathcal{D}_{KL}\) (“they said yes but model says no”)

It is the Persecutor who refuses to pay \(\eta\) cost of open assertion.

Rupture and repair

Gottman’s repair attempts are \(\Gamma\)-reducers:

humour, touch, meta-comment (“I’m flooded”)
successful repair before contempt installs → keeps \(C\) small

Accountability (not forced apology theatre) is \(\mathcal{D}_{KL}\)-reduction:

“I raised my voice” (observable) vs “I’m a terrible person” (identity → defensive loop)

Interruption checklist

Stop the loop — physiological reset (\(\Phi\)): 20+ min sub-threshold arousal if flooded.
Lower \(\mathcal{D}_{KL}\) — each party states observables + own affect without global labels.
Lower \(\Gamma\) — one conflict per conversation; schedule return; or exit if repair refused.
Raise \(\eta\) — consequence under own control, not punishment fantasy.

Institutions

The same loop appears in teams and states:

small factual error → blame culture → silos → contempt between factions
institutional \(\Gamma\) = technical debt + grievance backlog

Voice/exit/loyalty: voice_exit_loyalty.md.