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10 KiB
10 KiB
Equation Forest Topology Map
Last Updated: 2026-04-28 Total Nodes: 14 Total Connections: 10 Total Paths: 6
Forest Structure
Domain Clusters
┌─────────────────────────────────────────────────────────────────┐
│ COGNITIVE LOAD DOMAIN │
│ ┌──────────────┐ variableShared (100) ┌──────────────┐ │
│ │intrinsicLoad │─────────────────────────────►│totalCognitive│ │
│ └──────────────┘ │ Load │ │
│ └──────────────┘ │
└─────────────────────────────────────────────────────────────────┘
┌─────────────────────────────────────────────────────────────────┐
│ FRAMEWORK/BRIDGE DOMAIN │
│ ┌──────────────┐ leanBridge (500) ┌──────────────┐ │
│ │couchEquation │─────────────────────────────►│frameEvolution│ │
│ └──────────────┘ │ Continuous │ │
│ └──────────────┘ │
└─────────────────────────────────────────────────────────────────┘
┌─────────────────────────────────────────────────────────────────┐
│ THERMODYNAMICS DOMAIN │
│ ┌──────────────┐ familyConnection (300) ┌──────────────┐ │
│ │pressurePiling│─────────────────────────────►│hugoniotTemp │ │
│ └──────────────┘ │ erature │ │
│ └──────────────┘ │
└─────────────────────────────────────────────────────────────────┘
┌─────────────────────────────────────────────────────────────────┐
│ ELECTROCHEMISTRY DOMAIN (MOF) │
│ ┌──────────────┐ electrochemical (150) ┌──────────────┐ │
│ │mofCO2_2e_ │─────────────────────────────►│mofCO2_2e_ │ │
│ │HCOOH │ │CO │ │
│ └──────────────┘ └──────────────┘ │
│ │ │ │
│ │ │ │
│ │ electronTransfer (400) │ │
│ └────────────────────────────────────────────┘ │
│ │ │
│ ▼ │
│ ┌──────────────┐ │
│ │mofCO2_6e_ │ │
│ │CH3OH │ │
│ └──────────────┘ │
│ │ │
│ │ │
│ electronTransfer (200)│ │
│ ▼ │
│ ┌──────────────┐ │
│ │mofCO2_8e_ │ │
│ │CH4 │ │
│ └──────────────┘ │
└─────────────────────────────────────────────────────────────────┘
┌─────────────────────────────────────────────────────────────────┐
│ TIME SERIES DOMAIN (AFFINE) │
│ ┌──────────────┐ timeSeries (250) ┌──────────────┐ │
│ │affineLinear │─────────────────────────────►│affineDecomp │ │
│ │Layer │ │osition │ │
│ └──────────────┘ └──────────────┘ │
│ │ │
│ │ │
│ timeSeries (300) │ │
│ ▼ │
│ ┌──────────────┐ │
│ │affinePeriodic│ │
│ └──────────────┘ │
│ │ │
│ │ │
│ timeSeries (200) │ │
│ ▼ │
│ ┌──────────────┐ │
│ │affineScaled │ │
│ │Periodic │ │
│ └──────────────┘ │
└─────────────────────────────────────────────────────────────────┘
Connection Type Distribution
| Connection Type | Count | Gradient Range | Usage |
|---|---|---|---|
| variableShared | 1 | 100 | Cognitive load relationships |
| familyConnection | 1 | 300 | Thermodynamic families |
| leanBridge | 1 | 500 | Framework bridging |
| electrochemical | 1 | 150 | MOF reaction pathways |
| electronTransfer | 2 | 200-400 | MOF electron transfer chains |
| timeSeries | 3 | 200-300 | Affine time series decomposition |
Gradient Path Summary
| Path ID | Domain | Connections | Cost | Description |
|---|---|---|---|---|
| 0 | Framework + Cognitive | couchToFrame + loadToCognitive | 600 | Bridge to frame evolution |
| 1 | Thermodynamics | pressureToHugoniot | 300 | Pressure to temperature |
| 2 | MOF Electrochemical | mof2eCO_to_6eCH3OH + mof6eCH3OH_to_8eCH4 | 600 | CO → CH3OH → CH4 chain |
| 3 | MOF Electrochemical | mof2eHCOOH_to_2eCO | 150 | HCOOH → CO conversion |
| 4 | Affine Time Series | affineLinear_to_decomposition + affineDecomposition_to_periodic | 550 | Linear → Decomposition → Periodic |
| 5 | Affine Time Series | affinePeriodic_to_scaled | 200 | Periodic → Scaled Periodic |
Domain Isolation Analysis
Highly Connected Domains:
- MOF Electrochemistry: 3 connections, 2 paths (internal chain structure)
- Affine Time Series: 3 connections, 2 paths (linear decomposition chain)
Sparse Domains:
- Cognitive Load: 1 connection, 1 path (isolated pair)
- Framework/Bridge: 1 connection, 1 path (isolated pair)
- Thermodynamics: 1 connection, 1 path (isolated pair)
Cross-Domain Connections: None currently - domains are isolated
Forest Shape Characteristics
- Clustered Structure: Forest consists of 5 isolated domain clusters
- No Cross-Domain Bridges: No connections between different domains
- Linear Chains: MOF and Affine domains form linear chains
- Gradient Distribution: Costs range from 100-600 milli-units
- Path Length: Paths range from 1-2 connections
Potential Expansion Opportunities
- Cross-Domain Bridges: Could connect thermodynamics to electrochemistry (temperature effects on reaction rates)
- Cognitive-MOF Integration: Load monitoring for catalyst performance
- Framework-Affine Bridge: Couch equation to time series forecasting
- Unified Gradient Surface: Currently fragmented - could be unified with cross-domain connections