switching-cost — L3 attention-switch scorer

Framework context

Flagship L3 skill. The only quantified attention-economics tool in the suite. Score is a deterministic function of current-domain open-question count, current-domain thinking stage, and concept overlap between domains.

Formula (copied from tools_prosthetic.py:683-686):

oq_cost         = min(len(cur_open_questions) / 10.0, 1.0)
overlap_discount = min(len(shared_concepts) / max(len(cur_concepts), 1), 1.0)
stage_cost      = {executing: 0.8, refining: 0.6, crystallizing: 0.4, exploring: 0.2}[cur_stage]
score           = (oq_cost * 0.35) + (stage_cost * 0.35) - (overlap_discount * 0.3)

Score thresholds: <0.3 low / 0.3–0.6 moderate / >0.6 high.

When to invoke

• User says "should I switch to X" / "is it worth pausing Y for Z"
• Auto-invoke before tunnel-state(target) when user was just in a different tunnel-state
• Pair with context-recovery when score is high but switch is necessary

Input

current_domain: str
target_domain: str

Output contract

## 🔀 Switching Cost: {current} → {target}
**Score**: 0.XX (✅ Low / ⚠️ Moderate / 🔴 High)
**Recommendation**: "Low cost — go for it" | "Moderate — consider noting open questions first" | "High — significant unfinished work"

### Breakdown
- oq_cost: X.XX (N open questions in current)
- stage_cost: X.XX (current stage: {stage})
- overlap_discount: X.XX ({shared} shared concepts out of {total})

### Questions you'd leave behind (top 5)
- {question} [conv_id · date]

### Shared concept bridges
{concept}, {concept}, ...

Does NOT do

• Recommend which domain is "better"
• Factor in deadlines or external constraints (user does that)
• Cache the score — always recomputed from latest summaries
• Extrapolate to 3+ domains (pairwise only)

Fallback

Without summaries: heuristic based on (question count, message volume, shared conversation titles). Returns a score of same range but with different weights. Output explicitly labels [heuristic fallback].

Verification checklist

• [ ] Score clamped to [0.0, 1.0]
• [ ] Formula weights are 0.35/0.35/-0.30 (hardcoded — not tunable in this version)
• [ ] Recommendation string matches the three threshold bands
• [ ] Leave-behind questions cite source
• [ ] Score is deterministic — same inputs → same score