## DPTS + Tree of Thoughts

### Phase 1: Initial Parallel Expansion
- Spawn N workers for Level 0 branches (N = 5-10)
- Each worker explores one branch independently
- Workers report confidence scores as they complete

### Phase 2: Dynamic Reallocation
- As Level 0 completes, rank branches by score
- Top 2 branches get 3 workers each for Level 1
- Remaining branches get 1 worker each
- Prune branches below dynamic threshold

### Phase 3: Convergence
- Continue reallocation until:
  - Winning branch confidence > 85%
  - OR all branches at Level 4+
  - OR diminishing returns detected

### Pruning Threshold Formula
dynamic_threshold = max(0.40, best_confidence - 0.30)

Level 0: 5 branches, 5 workers (parallel)
├─ Branch A: 75% confidence (3 workers assigned for L1)
├─ Branch B: 68% confidence (2 workers assigned for L1)
├─ Branch C: 52% confidence (1 worker, threshold = 45%)
├─ Branch D: 48% confidence (1 worker, threshold = 45%)
└─ Branch E: 35% confidence (PRUNED, below threshold)

Level 1: 8 workers reallocated
├─ A.1, A.2, A.3: parallel (3 workers)
├─ B.1, B.2: parallel (2 workers)
├─ C.1: sequential (1 worker)
└─ D.1: sequential (1 worker)

Best found: A.2 at 82% → New threshold: 52%
→ Branch D PRUNED (48% < 52%)
→ 1 worker reallocated to Branch A

## Branch Phase (Decomposition)
1. Analyze problem structure
2. Identify independent sub-problems
3. Define interfaces between sub-problems
4. Create sub-problem specifications

## Solve Phase (Parallel Execution)
1. Spawn worker per sub-problem
2. Each worker solves independently
3. Workers report partial solutions
4. Monitor for blocking dependencies

## Merge Phase (Aggregation)
1. Collect all partial solutions
2. Apply merge strategy (see below)
3. Resolve conflicts
4. Synthesize final solution

## Branch: "Design authentication system"
Sub-problems:
1. Token format selection (JWT vs Session vs API Key)
2. Storage strategy (Redis vs DB vs Memory)
3. Security requirements (MFA, encryption, audit)
4. Performance requirements (latency, throughput)

## Solve: 4 parallel workers
Worker 1: Evaluates token formats → JWT (85%)
Worker 2: Evaluates storage → Redis (78%)
Worker 3: Analyzes security → MFA required (92%)
Worker 4: Benchmarks performance → < 50ms needed (88%)

## Merge: Aggregation strategy
- JWT + Redis + MFA + 50ms latency
- Check compatibility: All compatible
- Synthesize: "JWT tokens stored in Redis with MFA, target 50ms"

┌─────────────────────────────────────────────────┐
│                 Aggregator Layer                 │
│  (Synthesizes proposals, resolves conflicts)    │
└────────────────────┬────────────────────────────┘
                     │ Proposals flow up
┌─────────────────────────────────────────────────┐
│                 Proposer Layer                   │
│  ┌─────────┐ ┌─────────┐ ┌─────────┐           │
│  │Proposer1│ │Proposer2│ │Proposer3│  ...      │
│  │ (ToT)   │ │ (BoT)   │ │ (AT)    │           │
│  └─────────┘ └─────────┘ └─────────┘           │
└─────────────────────────────────────────────────┘

## Proposer Configuration

### Proposer 1: Optimization Focus (ToT)
- Objective: Find optimal solution
- Evaluation: Score-based ranking
- Output: Single best path with confidence

### Proposer 2: Exploration Focus (BoT)
- Objective: Map solution space
- Evaluation: Coverage-based
- Output: Top 5 viable options

### Proposer 3: Analogy Focus (AT)
- Objective: Cross-domain insights
- Evaluation: Structural mapping quality
- Output: Transferred principles

## Aggregator Configuration

### Aggregation Method: Weighted Synthesis
- Weight by proposer confidence
- Identify common themes across proposers
- Flag disagreements for explicit resolution

### Conflict Resolution
- If proposers agree: Boost confidence +5%
- If 2/3 agree: Use majority, document minority
- If no agreement: Escalate to DR (Dialectical Reasoning)

## Problem: "Choose database for new microservice"

### Proposer 1 (ToT): Score-optimized
→ PostgreSQL (Score: 87/100)
  - Best for ACID compliance
  - Strong query performance

### Proposer 2 (BoT): Option-mapped
→ Top 3: PostgreSQL (72%), MongoDB (68%), DynamoDB (65%)
  - PostgreSQL: Relational, ACID
  - MongoDB: Flexible schema
  - DynamoDB: Serverless scale

### Proposer 3 (AT): Analogy-based
→ Recommendation: PostgreSQL
  - Analogy: Banking systems use relational for audit trails
  - Our use case: Financial transactions need same guarantees

### Aggregator Synthesis
Agreement Level: FULL (3/3 on PostgreSQL)
Combined Confidence: max(87%, 72%, 75%) + 5% = 92%

Final Recommendation: PostgreSQL with high confidence
- Optimization confirms performance
- Exploration confirms no better alternatives
- Analogy confirms domain fit

     [Problem]
        │
    ┌───┴───┐
    ▼       ▼
  [A]     [B]
    │       │
    ▼       ▼
  [A.1]   [B.1]
    │       │
    └───┬───┘
        ▼
    [Merged]──────┐
        │         │
        ▼         │ Cycle
    [Refined] ◄───┘
        │
        ▼
    [Solution]

## GoT Reasoning Session

### Step 1: Branch (Problem → A, B, C)
Generate three distinct approaches in parallel

### Step 2: Refine (A → A', B → B')
Improve promising approaches through iteration

### Step 3: Merge (A' + B' → AB)
Combine best elements of top approaches

### Step 4: Cycle (AB → AB')
Re-evaluate merged solution with fresh perspective

### Step 5: Converge (AB' → Solution)
Finalize when confidence threshold met

## Phase 1: Parallel Path Generation
- Generate K reasoning paths (K = 5-10)
- Each path solves problem independently
- Collect both answer AND rationale

## Phase 2: Rationale Clustering
- Cluster paths by rationale similarity
- Identify distinct reasoning approaches
- Group paths with similar logic

## Phase 3: Representative Selection
- Select representative from each cluster
- Weight by cluster size (more paths = more weight)
- Eliminates redundant similar paths

## Phase 4: Aggregation
- Combine representatives (not all K paths)
- Apply weighted voting
- Confidence = agreement level among representatives

## Problem: "Should we use microservices or monolith?"

### Generated Paths (K=10):
Path 1: Microservices - "team autonomy" rationale
Path 2: Microservices - "scalability" rationale
Path 3: Microservices - "team autonomy" rationale (similar to 1)
Path 4: Monolith - "simplicity" rationale
Path 5: Microservices - "scalability" rationale (similar to 2)
Path 6: Microservices - "team autonomy" rationale (similar to 1)
Path 7: Monolith - "simplicity" rationale (similar to 4)
Path 8: Microservices - "tech diversity" rationale (new cluster)
Path 9: Monolith - "performance" rationale (new cluster)
Path 10: Microservices - "scalability" rationale (similar to 2)

### Clusters:
Cluster A (size 3): "team autonomy" → Path 1 representative
Cluster B (size 3): "scalability" → Path 2 representative
Cluster C (size 2): "simplicity" → Path 4 representative
Cluster D (size 1): "tech diversity" → Path 8 representative
Cluster E (size 1): "performance" → Path 9 representative

### Weighted Vote:
Microservices: Clusters A(3) + B(3) + D(1) = 7 weight
Monolith: Clusters C(2) + E(1) = 3 weight

### Final: Microservices (70% weighted agreement)
Rationales: Team autonomy, Scalability, Tech diversity

## BoT + Parallel Execution

### Standard BoT (Sequential):
Explore Approach 1 → Explore Approach 2 → ... → Explore Approach 8
Total time: 8 × T(explore)

### Parallel BoT:
Explore Approaches 1-8 simultaneously
Total time: 1 × T(explore) (with parallelism)

### Implementation:
1. Level 0: Spawn 8-10 parallel workers
2. Each worker explores one approach independently
3. Workers share evidence repository (./reasoning/evidence/)
4. Pruning happens after ALL Level 0 complete
5. Level 1: Spawn workers for retained approaches

### Pruning Threshold (BoT-specific):
Keep approaches with confidence > 40%
Do NOT dynamically adjust (conservative breadth philosophy)

## ToT + Monte Carlo Tree Search (MCTS)

### MCTS Integration:
1. **Selection**: UCB1 formula to balance explore/exploit
2. **Expansion**: Parallel branch generation
3. **Simulation**: Parallel rollouts to estimate branch value
4. **Backpropagation**: Update ancestor scores

### UCB1 Formula:
UCB1(branch) = avg_score + C × sqrt(ln(N) / n_branch)
- avg_score: Average score from simulations
- C: Exploration constant (typically 1.41)
- N: Total simulations across all branches
- n_branch: Simulations for this branch

### Parallel MCTS for ToT:
1. Run parallel rollouts from each Level 0 branch
2. Use UCB1 to decide which branches get more rollouts
3. After budget exhausted, select best-scoring branch
4. Recurse with same strategy for Level 1, 2, 3...

### Configuration:
- Rollouts per branch: 10-20
- Exploration constant: 1.41
- Minimum rollouts before pruning: 5

## HE + Parallel Execution

### Sequential HE (Standard):
Test H1 → Test H2 → Test H3 → ...
Each test may affect others (evidence dependencies)

### Parallel HE (Accelerated):
Phase 1: Generate all hypotheses (8-15)
Phase 2: Identify INDEPENDENT evidence gathering
  - Evidence that affects only one hypothesis → parallelize
  - Evidence that affects multiple → sequence based on discrimination power
Phase 3: Parallel evidence gathering
Phase 4: Synchronized hypothesis update

### Evidence Parallelization Rules:
- Log analysis: Usually parallelizable (independent sources)
- Metrics queries: Parallelizable (independent systems)
- Reproduction tests: May conflict (shared test environment)
- Code tracing: Parallelizable (read-only)

### Synchronization Points:
After each parallel batch, synchronize to:
1. Update ALL hypothesis probabilities
2. Check for eliminations
3. Decide next evidence batch

## AT + Mixture of Agents

### Standard AT:
Investigate Analogy 1 → Investigate Analogy 2 → ... → Synthesize

### MoA-Enhanced AT:
Layer 1 (Proposers): Parallel analogy investigation
  - Worker 1: Technology domain analogies
  - Worker 2: Nature/biology analogies
  - Worker 3: Business/economics analogies
  - Worker 4: Historical analogies

Layer 2 (Aggregator): Cross-analogy synthesis
  - Identify common principles across domains
  - Weight by structural mapping quality
  - Synthesize unified transferable insights

### Aggregation Strategy for AT:
- Principles appearing in 3+ analogies: High confidence
- Principles appearing in 2 analogies: Medium confidence
- Principles appearing in 1 analogy: Low confidence (needs validation)

## Fan-Out/Fan-In Structure

### Fan-Out Phase:
1. Identify parallelizable work units
2. Create work unit specifications
3. Spawn workers (one per work unit)
4. Track worker status (pending/running/complete/failed)

### Fan-In Phase:
1. Wait for all workers OR timeout
2. Collect results from completed workers
3. Handle failed workers (retry/skip/abort)
4. Apply merge strategy

### Implementation with Task Tool:

# Fan-out
for approach in approaches:
    spawn_task(
        description=f"Explore {approach.name}",
        input=approach.specification,
        pattern="BoT-L1"
    )

# Fan-in
results = await_all_tasks(timeout=30min)
merged = apply_merge_strategy(results, strategy="aggregation")

## Parallel Execution + Handover Protocol

### Checkpoint Timing:
- Before fan-out: Checkpoint work unit specifications
- After fan-out: Checkpoint spawned worker IDs
- During execution: Workers checkpoint individually
- After fan-in: Checkpoint merged results

### Recovery from Parallel Failure:
1. Load checkpoint with worker states
2. Identify failed workers
3. Retry failed workers only
4. Resume fan-in when complete

### State File Structure:
.reasoning/session-{id}/
├── parallel/
│   ├── fan-out-spec.json      # Work unit specifications
│   ├── worker-status.json     # Worker states
│   ├── worker-001/            # Individual worker state
│   ├── worker-002/
│   └── fan-in-result.json     # Merged result

Is the task decomposable?
├─ NO → Use sequential execution
└─ YES → Are sub-tasks independent?
    ├─ NO → Use sequential with checkpoints
    └─ YES → Is merge strategy clear?
        ├─ NO → Define merge strategy first
        └─ YES → Is parallelization worth the overhead?
            ├─ NO (< 3 sub-tasks) → Sequential may be simpler
            └─ YES → Parallelize with fan-out/fan-in

Step 1: Get user input (parallel) ─┐
Step 2: Validate input (parallel) ─┼─ WRONG: Step 2 needs Step 1!
Step 3: Process input (parallel) ──┘

Step 1: Get user input
  └─→ Step 2: Validate input
      └─→ Step 3: Process input

Level 0: 20 branches (overwhelming, redundant)
Level 1: 100 sub-branches (unmanageable)

Level 0: 5-10 branches (diverse, manageable)
Level 1: 5 sub-branches per retained branch

Fan-out: Spawn 5 workers to explore approaches
Fan-in: ??? (no plan to combine results)

Fan-out: Spawn 5 workers to explore approaches
Fan-in: Apply weighted voting based on confidence scores
        If disagreement > 30%, escalate to DR pattern

{
  "parallel_execution": {
    "max_workers": 10,
    "worker_timeout_minutes": 30,
    "fan_in_timeout_minutes": 60,

    "pruning": {
      "bot_threshold": 0.40,
      "tot_keep_top": 2,
      "dpts_margin": 0.30,
      "min_confidence_to_continue": 0.40
    },

    "merge_strategies": {
      "default": "aggregation",
      "conflict_resolution": "weighted_voting",
      "confidence_agreement_boost": 0.05,
      "confidence_disagreement_penalty": 0.10
    },

    "checkpointing": {
      "checkpoint_on_fan_out": true,
      "checkpoint_on_fan_in": true,
      "worker_checkpoint_interval_minutes": 10
    },

    "mcts": {
      "exploration_constant": 1.41,
      "min_rollouts_per_branch": 5,
      "max_rollouts_per_branch": 20
    }
  }
}