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Mathematical Implementation of the Investment Prioritization Rubric ​

Location: data/mathmatical_rubric.md
Purpose: Internal reference document for agents (risk-analyst, roadmap-planner, knowledge-graph-engineer) to translate qualitative UN-GGCE guiding principles into mathematical queries within the Context Graph Architecture (RDF/OWL/SPARQL).

1. Introduction ​

To generate an objective, risk-based roadmap for the Joint Development Plan (JDP), the qualitative rules from the Investment Prioritization and Risk Rubric (outputs/1b_investment_rubric.md) must be translated into a mathematical model.

Because flat spreadsheets treat all Member States, observatories, and centres equally, we rely on a Context Graph Architecture. This allows us to mathematically weight the systemic importance of individual entities based on topology and science (aligned with IAG/GGOS standards), rather than political equivalence.

2. Part A: Weighted Gap Analysis (The Capability Deficit) ​

Capabilities are graded across People, Process, Technology, and Data (PPTD) on a scale of 1 to 5.

Step 1: Invert the Maturity Scores ​

Calculate the "Gap" for each PPTD dimension. Since 1 is high risk and 5 is optimized, we invert the scores so that higher numbers equal higher priority.

  • Gap = 5 - Maturity_Score
  • (Example: A People score of 2 becomes a Gap of 3).

Step 2: Apply Rubric Multipliers (The Weights) ​

Map the Critical and High Risks from the rubric to mathematical multipliers:

  • People (Sustainable Operations): Single retiring expert, no succession.
    • IF People_Score <= 2 THEN People_Weight = 3.0 ELSE 1.0
  • Process (Formal Governance): Lack of SLAs/MOUs or formal mandates.
    • IF Process_Score <= 2 THEN Process_Weight = 3.0 ELSE 1.0
  • Data (FAIR Interoperability): Proprietary or black-box data pipelines.
    • IF Data_Score <= 2 THEN Data_Weight = 3.0 ELSE 1.0
  • Technology (Hardware Lifecycle): End-of-life legacy hardware.
    • IF Tech_Score <= 2 THEN Tech_Weight = 2.0 ELSE 1.0

Step 3: Base Capability Priority Index ​

For every geodetic capability in the matrix:

text
Capability_Priority_Index = 
  (People_Gap * People_Weight) + 
  (Process_Gap * Process_Weight) + 
  (Tech_Gap * Tech_Weight) + 
  (Data_Gap * Data_Weight)

3. Part B: Network Criticality Multiplier (The Topological Weight) ​

Not all observatories or processing centres are equal. Importance is derived topologically and scientifically based on architecture rules defined by the International Association of Geodesy (IAG) and its Global Geodetic Observing System (GGOS).

The Capability_Priority_Index is multiplied by a Network Criticality Multiplier (NCM), automatically calculated by the graph based on three factors:

Factor 1: The EGV Bottleneck Weight (Role in the Supply Chain) ​

The graph traces the workflow of Essential Geodetic Variables (EGVs).

  • Combination Centres (Highest Multiplier): A centre that produces the final combined official product. If it fails, the global product fails.
  • Analysis/Data Centres (Medium Multiplier): If a Global Data Centre (GDC) goes down, others can mirror the data, so the risk is shared.
  • Math: The fewer alternative centres that exist for a specific EGV workflow, the higher the multiplier.

Factor 2: Multi-Technique Co-location Weight (Geometric Importance) ​

The integrity of the global reference frame relies disproportionately on "core" sites that host multiple geodetic techniques (VLBI, SLR, GNSS, DORIS) in one physical location, providing mathematical "local ties".

  • Math: An observatory with 4 techniques receives a 4.0x multiplier. A single-technique station receives a 1.0x multiplier.

Factor 3: Geopolitical Scarcity & Redundancy Weight (Principle 1) ​

Aligning with Guiding Principle 1, the algorithm calculates the spatial density of the network within a Member State or region.

  • High Scarcity: If an observatory is the only tracking station within a large radius (e.g., parts of Africa, South America, or ocean islands), its loss creates a massive geometric hole in the Earth observation model.
  • High Redundancy: If an observatory is in a region with 50 other overlapping stations, its individual loss is negligible.
  • Math: High spatial scarcity = High Multiplier.

4. Part C: The Final Prioritization Formula & Roadmap Roll-Up ​

The Final Formula ​

When generating the investment roadmap, the SPARQL query executes this combined math for each node (observatory/centre):

text
Final_Investment_Priority = Capability_Priority_Index * (EGV_Bottleneck_Weight + Colocation_Weight + Scarcity_Weight)

JDP Activity Roll-Up ​

Because the Joint Development Plan (JDP) maps specific Capabilities to overarching JDP Activities (e.g., "Objective 1.2 Establish Regional Hubs"):

  • Find all Capabilities mapped to the JDP Activity.
  • JDP_Activity_Score = SUM(Final_Investment_Priority of mapped capabilities) / Total_Mapped_Capabilities

Automated Sequencing ​

The algorithm sorts all JDP Activities in descending order based on their JDP_Activity_Score:

  • Top 25% of Scores: Sequenced into Phase 1 (Immediate Action).
  • Middle 50% of Scores: Sequenced into Phase 2 (Near-Term Investment).
  • Bottom 25% of Scores: Sequenced into Phase 3 (Optimization/Maintenance).

5. Traceability Example ​

Why prioritize an observatory in Brazil over upgrading one in Germany? The Context Graph provides a mathematically traceable answer: "Because the Brazilian observatory is a 3-technique co-location site operating with Level 2 Technology (failing legacy hardware) in a geographically scarce region, meaning its failure degrades the global EGV calculation significantly. The German observatory, while important, is in a redundant region and currently operates at Level 4 maturity."