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.

docs/beliefs.md

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+# Belief system
+
+A **belief** is a proposition the mind holds with an explicit, evidence-derived confidence and a status. Beliefs are never edited in place: every change appends a `belief_versions` row (append-only trigger) and an event.
+
+## Structure
+
+| Table | Contents |
+|---|---|
+| `beliefs` | proposition, optional subject, epistemic kind, status, confidence, prior, version, source, origin event, operator-pinned status |
+| `belief_evidence` | typed references (event, memory, belief, prediction, operator, note) with direction for/against, weight (how much it bears on the proposition), credibility (trust in the source), retracted flag |
+| `belief_alternatives` | competing explanations kept alongside (open, dismissed, promoted) |
+| `belief_links` | contradicts / supports / alternative_to / derived_from between beliefs |
+| `belief_versions` | append-only history with the confidence breakdown and the event that caused each change |
+| `corrections` | operator statements: belief wrong, memory inaccurate, do not infer, entity same/different |
+
+## Confidence arithmetic
+
+Confidence is never typed in by a person or produced by a model. It is:
+
+```
+for      = Σ weight × credibility over supporting evidence
+against  = Σ weight × credibility over opposing evidence
+diversity = 0.6 + 0.4 × min(1, (distinct supporting sources − 1) / 2)
+confidence = sigmoid( logit(prior) + 1.5 × (for × diversity − against) )   clamped to [0.02, 0.98]
+```
+
+- The **prior** depends on the epistemic kind: hypothesis 0.25, assumption/opinion 0.4, claim 0.5, observation/memory 0.6, fact 0.8.
+- **Diversity** discounts support that all comes from one source, so repetition from a single feed cannot manufacture certainty (threat T4).
+- Absolute certainty is unreachable; the bounds are deliberate (spec §10).
+
+The breakdown (prior, for, against, sources, diversity, log-odds, formula, notes) is stored with every version and shown on the belief page.
+
+## Status
+
+Derived from the breakdown unless an operator pinned it:
+
+- `contested` when both sides carry real weight (against ≥ half of the discounted support) and confidence is mid-range;
+- `rejected` below 0.15; `hypothesis` for hypotheses without support or below 0.5; `tentative` below 0.7; `likely` below 0.85; `accepted` above;
+- `superseded` when replaced by a newer proposition.
+
+## Contradictions
+
+On creation and on gaining support, a belief is compared with the mind's live beliefs. The deterministic pass detects the same content with flipped polarity (negation words plus token Jaccard ≥ 0.6). A hit emits `contradiction_detected`, links both beliefs, and makes each counter-evidence for the other weighted by the other's confidence, so both move towards `contested` until more evidence arrives. Paraphrase-level judgement is added by an LLM-assisted process once providers exist; it can only propose, and the same arithmetic applies.
+
+## Hypothesis generation
+
+The `associate` process proposes causal hypotheses when two notable observations occur within a window ("deployment … may have caused: latency alert"). Each observation is weak evidence (weight 0.15) so the belief starts as a hypothesis around 0.3–0.4; independent support is needed to move it. Alternatives ("coincidence", "a third factor") are recorded automatically.
+
+## Corrections
+
+- **This belief is wrong** pins the status to rejected, adds operator counter-evidence, records a `belief_wrong` correction and a `belief_retracted` event. History is kept.
+- **Do not infer this again** stores a `do_not_infer` correction; future creations of a matching proposition (token Jaccard ≥ 0.7) are refused and logged as metacognition.
+- **This memory is inaccurate** retracts the memory and marks belief evidence citing it as retracted; affected beliefs are re-evaluated with a `belief_updated` event.