feat: add beliefs with evidence-derived confidence, contradictions and corrections

Phase 6. Beliefs are propositions with a prior set by epistemic kind and a
confidence computed from typed evidence: sigmoid(logit(prior) + slope ×
(support × diversity − opposition)), where support from a single source
is discounted so repetition cannot manufacture certainty, and bounds keep
the mind away from absolute certainty. Every evaluation stores its
breakdown and appends a version row protected by the append-only
trigger; the belief page shows the arithmetic, evidence for and against,
alternatives, contradictions and history.

Contradiction detection is deterministic first (negation plus token
overlap): a hit emits contradiction_detected, links both beliefs and
makes each counter-evidence for the other so both trend to contested.
Operators can assert beliefs (their statement is the evidence), add
evidence, mark a belief wrong (pinned rejected, history kept) and forbid
an inference; do-not-infer corrections block matching hypotheses.
Retracting a memory retracts the evidence that cited it and re-evaluates
the beliefs concerned.

The associate process proposes low-confidence causal hypotheses from
co-occurring notable observations, and the hypothesis handler turns
admitted ones into beliefs with automatic alternatives, closing demo
scenarios 1 and 2 without any model call.

internal/ui/minds.go

@@ -9,6 +9,7 @@ import (
 	"time"
 
 	"github.com/andydixon/noema/internal/auth"
+	"github.com/andydixon/noema/internal/beliefs"
 	"github.com/andydixon/noema/internal/minds"
 	"github.com/andydixon/noema/internal/storage"
 	"github.com/andydixon/noema/pkg/ids"
@@ -98,7 +99,9 @@ func (u *UI) mindOverview(w http.ResponseWriter, r *http.Request) {
 	sm, _ := u.deps.Minds.GetSelfModel(r.Context(), m.ID)
 	st, _ := u.deps.Events.Stats(r.Context(), m.ID, time.Now().Add(-24*time.Hour))
 	ms, _ := u.deps.Memory.Stats(r.Context(), m.ID)
-	u.render(w, r, "mind", m.DisplayName, map[string]any{"Mind": m, "Brief": m.Personality.Brief(), "SelfModel": sm, "Stats": st, "MemStats": ms})
+	bs, _ := u.deps.Beliefs.Stats(r.Context(), m.ID)
+	top, _ := u.deps.Beliefs.List(r.Context(), m.ID, beliefs.Filter{Limit: 8})
+	u.render(w, r, "mind", m.DisplayName, map[string]any{"Mind": m, "Brief": m.Personality.Brief(), "SelfModel": sm, "Stats": st, "MemStats": ms, "BeliefStats": bs, "Beliefs": top})
 }
 
 func (u *UI) mindStatus(w http.ResponseWriter, r *http.Request) {