feat(finance): support weighted rent split

docs/specs/HOUSEBOT-077-custom-rent-split-weights.md

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+# HOUSEBOT-077 Custom Rent Split Weights
+
+## Summary
+
+Support unequal room rents by storing a deterministic rent-share weight per active household member and using those weights in monthly settlement calculations.
+
+## Goals
+
+- Preserve equal split as the default when all member weights are `1`.
+- Allow household admins to edit per-member rent weights from the mini app.
+- Keep settlement math deterministic and money-safe.
+- Reflect weighted rent shares consistently in statements and dashboard views.
+
+## Non-goals
+
+- Per-cycle rent weights.
+- Free-form percentage editing.
+- Automatic square-meter or room-type calculations.
+
+## Scope
+
+- In: member-level `rentShareWeight`, settlement-engine support, admin API/UI, tests.
+- Out: historical backfill UI, move-in/move-out proration logic, rent history analytics.
+
+## Data Model Changes
+
+- Add `members.rent_share_weight integer not null default 1`.
+- Existing members migrate to `1`.
+
+## Domain Rules
+
+- Rent weights must be positive integers.
+- Active members participate in rent splitting according to their weight.
+- Utility splitting remains independent from rent splitting.
+- The same input must always produce the same minor-unit allocation.
+
+## Interfaces
+
+- Household admin mini app payload includes member `rentShareWeight`.
+- Admin write endpoint updates one member rent weight at a time.
+
+## Acceptance Criteria
+
+- [ ] Settlement engine uses weighted rent shares.
+- [ ] Equal split still holds when all weights are `1`.
+- [ ] Admins can edit member rent weights in the mini app.
+- [ ] Dashboard and statements reflect the new rent shares.
+- [ ] Validation rejects zero or negative weights.