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+# Architecture: Bounded-Range Dynamic Minimum Cut
+
+## Overview
+
+This crate implements the first deterministic exact fully-dynamic minimum cut
+algorithm with subpolynomial update time, based on arxiv:2512.13105 (December 2024).
+
+## System Architecture
+
+```
+┌─────────────────────────────────────────────────────────────────┐
+│                        MinCutWrapper                             │
+│  ┌─────────────────────────────────────────────────────────────┐ │
+│  │           O(log n) Bounded-Range Instances                   │ │
+│  │  ┌─────────┐ ┌─────────┐ ┌─────────┐      ┌─────────┐       │ │
+│  │  │ [1,1]   │ │ [1,1]   │ │ [2,2]   │ ... │ [λ,1.2λ]│       │ │
+│  │  └────┬────┘ └────┬────┘ └────┬────┘      └────┬────┘       │ │
+│  │       │           │           │                │             │ │
+│  │       ▼           ▼           ▼                ▼             │ │
+│  │  ┌──────────────────────────────────────────────────────┐   │ │
+│  │  │              ProperCutInstance Trait                  │   │ │
+│  │  │   - apply_inserts(edges)                             │   │ │
+│  │  │   - apply_deletes(edges)                             │   │ │
+│  │  │   - query() -> ValueInRange | AboveRange             │   │ │
+│  │  └──────────────────────────────────────────────────────┘   │ │
+│  └─────────────────────────────────────────────────────────────┘ │
+│                              │                                    │
+│  ┌───────────────────────────┴───────────────────────────────┐   │
+│  │              DynamicConnectivity                           │   │
+│  │   (Union-Find with rebuild on delete)                      │   │
+│  └───────────────────────────────────────────────────────────┘   │
+└─────────────────────────────────────────────────────────────────┘
+
+┌─────────────────────────────────────────────────────────────────┐
+│                    Supporting Components                         │
+├─────────────────────────────────────────────────────────────────┤
+│  LocalKCutOracle          │  DeterministicLocalKCut             │
+│  - search(graph, query)   │  - BFS exploration                  │
+│  - deterministic          │  - Early termination                │
+├───────────────────────────┼─────────────────────────────────────┤
+│  ClusterHierarchy         │  FragmentingAlgorithm               │
+│  - O(log n) levels        │  - Connected components             │
+│  - Recursive decomposition│  - Merge/split handling             │
+├───────────────────────────┼─────────────────────────────────────┤
+│  CutCertificate           │  AuditLogger                        │
+│  - Witness tracking       │  - Provenance logging               │
+│  - JSON export            │  - Thread-safe                      │
+└───────────────────────────┴─────────────────────────────────────┘
+```
+
+## Component Responsibilities
+
+### MinCutWrapper
+- Manages O(log n) bounded-range instances
+- Geometric ranges with factor 1.2
+- Lazy instantiation
+- Order invariant: inserts before deletes
+
+### ProperCutInstance
+- Abstract interface for cut maintenance
+- Implementations: StubInstance, BoundedInstance
+
+### DeterministicLocalKCut
+- BFS-based local minimum cut search
+- Fully deterministic (no randomness)
+- Configurable radius and budget
+
+### ClusterHierarchy
+- Multi-level vertex clustering
+- Fast boundary updates on edge changes
+
+### FragmentingAlgorithm
+- Handles graph disconnection
+- Tracks connected components
+
+## Data Flow
+
+1. **Update arrives** (insert/delete edge)
+2. **Wrapper buffers** the update with timestamp
+3. **On query**:
+   a. Check connectivity (fast path for disconnected)
+   b. Process instances in order
+   c. Apply buffered updates (inserts then deletes)
+   d. Query each instance
+   e. Stop at first ValueInRange or end
+4. **Return result** with witness
+
+## Invariants
+
+1. **Range invariant**: Instance never sees λ < λ_min during update
+2. **Order invariant**: Inserts applied before deletes
+3. **Certificate invariant**: Every answer can be verified
+4. **Determinism invariant**: Same sequence → same output
+
+## Complexity
+
+- **Update**: O(n^{o(1)}) amortized
+- **Query**: O(log n) instances × O(n^{o(1)}) per instance
+- **Space**: O(n + m) per instance