# 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- `superseded` when replaced by a newer proposition.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.