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.
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<h2>Important beliefs <span class="muted small"><a href="/minds/{{$m.Slug}}/beliefs">{{.Data.BeliefStats.Total}} total</a></span></h2>
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{{if .Data.Beliefs}}<table class="table compact"><tbody>{{range .Data.Beliefs}}<tr><td><span class="badge st-{{.Status}}">{{.Status}}</span></td><td><a href="/minds/{{$m.Slug}}/beliefs/{{.ID}}">{{.Proposition}}</a></td><td class="num"><span class="conf"><span class="conf-bar"><i style="width:{{pct .Confidence}}"></i></span> {{conf .Confidence}}</span></td></tr>{{end}}</tbody></table>
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{{else}}<p class="muted small">No beliefs yet.</p>{{end}}
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<h2>Personality brief <span class="muted small">what cognitive prompts receive</span></h2>
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