Mathematical Implementation of the Investment Prioritization Rubric

Location: data/mathmatical_rubric.mdPurpose: Internal reference document for agents (risk-analyst, roadmap-planner, knowledge-graph-engineer) to translate the qualitative rubric in outputs/1b_investment_rubric.md into mathematical queries against Jena Fuseki.

Revision history:

• v1.0 (2026-03-25): Original complex formula — Part A (Weighted Gap Analysis) + Part B (Network Criticality Multiplier).
• v2.0 (2026-06-10): Part A replaced with simplified two-factor model. Part B archived for observatory-level use.
• v3.0 (2026-06-17): Three-factor model — added Recovery Factor derived from principle violation triples. Retired 2026-06-22.
• v4.0 (2026-07-06): Aligned to the approved two-track framework (outputs/1b_investment_rubric.md v3.0, approved by Nick Brown July 2026). Operational track = two-factor score (no 1.2× boost, no Recovery Factor); governance track = qualitative principle findings (rubric Part D). Documents the 2026-06-22 scoring run that produced the authoritative scores in https://w3id.org/ggsc/graph/tier-risk-scores-2026-06-22.

---

1. Introduction

The rubric produces a Tier Risk Score for each of the 25 supply chain tiers across the five EGV workflows, using two separate tracks:

Operational track (numeric):

Tier Risk Score = PPTD_Gap × Step_Criticality

• PPTD_Gap — reliability proxy: how mature are the capabilities at this tier? (higher gap = more likely to fail under normal conditions; carries P5)
• Step_Criticality — asset criticality: how consequential is failure at this tier? (structural redundancy in the supply chain; implicitly carries P1)

Governance track (qualitative): each tier is assessed for gaps against P2 (political concentration), P3 (absence of a governing agreement or mandate), P4 (proprietary critical-path software or restricted data), and P6 (absence of independent monitoring). Governance findings are not folded into the numeric score. They are reported alongside it and elevate investment urgency — a High operational score with severe governance gaps is treated as urgent, and a Significant score with severe governance gaps can warrant earlier action than a higher score with sound governance. See outputs/1b_investment_rubric.md Part D for the policy rationale.

Two distinct scopes:

• Workflow-tier risk scoring (this document, Part A v4.0): scores the 25 tiers to identify priority investment targets.
• Observatory-level network analysis (this document, Part B — archived): applies network topology multipliers to individual sites and centres.

---

2. Part A: Two-Track Tier Risk Model (v4.0 — Current)

Step 1: Compute PPTD_Gap for a Tier

1. Collect all capabilities linked to the tier via ggsc:requiredCapability.
2. For each capability, compute a straight unweighted average across all four dimensions (People, Process, Technology, Data). No boost is applied to any dimension.
3. Where the published State of Geodesy 2026 shows a dimension as NA, the stored dimension score is 0.00 and the tier-level average divides by 4 regardless (NA = 0 convention, per scoring run urn:ggsc:activity:wa3-risk-scoring-2026-06-22).
   • Note: this differs from the capability-level ggsc:averageMaturityScore in the capability DataBook, which follows the SoG 2026 published convention (mean of applicable dimensions only). Tier gap computation must use the NA = 0 / divide-by-4 convention, not the stored capability average.
4. Average all per-capability averages across the tier: this is tier_PPTD_avg.
5. PPTD_Gap = 5 − tier_PPTD_avg

SPARQL — compute PPTD_Gap per tier:

PREFIX ggsc: <https://w3id.org/ggsc/>

SELECT ?tier (AVG(?capAvg) AS ?tierPPTDAvg) (5 - AVG(?capAvg) AS ?pptdGap) WHERE {
  ?tier a ggsc:WorkflowTier ;
        ggsc:requiredCapability ?cap .
  ?cap ggsc:peopleMaturityScore     ?p ;
       ggsc:processMaturityScore    ?pr ;
       ggsc:technologyMaturityScore ?t ;
       ggsc:dataMaturityScore       ?d .
  BIND((?p + ?pr + ?t + ?d) / 4.0 AS ?capAvg)
}
GROUP BY ?tier

Capability scores are read from the canonical maturity graph https://w3id.org/ggsc/graph/capability-maturity-2026-05-12 (DataBook v1.3.0, re-verified 2026-06-15 against the published State of Geodesy 2026).

Step 2: Assign Step_Criticality

Assign an integer 1–5 per tier based on the supply chain architecture. Step_Criticality implicitly carries P1 (Geographic Distribution) — where no regional alternative exists, geographic scarcity raises the score.

Value	Meaning
5	Single point of failure — no backup, no alternative exists globally
4	Dominant path — one main actor, limited alternatives not operationally ready
3	Important but substitutable — meaningful redundancy exists
2	Supported — multiple parallel operational institutions
1	Redundant — easily mitigated

Key reference: ACC/SPOCC at Satellite Orbits Tier 3 = 5 (canonical SPOF, validated by IGS shutdowns 2013, 2018–2019).

Step 3: Record Governance-Track Findings

Governance gaps are encoded per tier using ggsc:violatesPrinciple with the principle IRI as the object. These assertions drive the qualitative governance track — they do not modify the numeric score.

Principle	IRI	Why it matters
P2 — Political Resilience	ggsc:P2	Political concentration means stress cannot be absorbed by a neutral actor
P3 — Centralised Accountability	ggsc:P3	No SLA means no governed recovery response exists
P4 — Technical Interoperability	ggsc:P4	Proprietary software means the function cannot be independently replicated
P6 — Transparency	ggsc:P6	No monitoring means failure may not be detected promptly

Encoding pattern:

PREFIX ggsc: <https://w3id.org/ggsc/>

<https://w3id.org/ggsc/tier/Tier3_Combination>
    ggsc:violatesPrinciple ggsc:P2, ggsc:P3, ggsc:P4, ggsc:P6 .

Push to the relevant workflow named graph (e.g. https://w3id.org/ggsc/satellite-orbits/workflow).

SPARQL — governance findings per tier (for reporting alongside the operational score):

PREFIX ggsc: <https://w3id.org/ggsc/>

SELECT ?tier (GROUP_CONCAT(STR(?principle); separator=", ") AS ?governanceGaps)
       (COUNT(?principle) AS ?gapCount)
WHERE {
  ?tier a ggsc:WorkflowTier .
  OPTIONAL { ?tier ggsc:violatesPrinciple ?principle }
}
GROUP BY ?tier
ORDER BY DESC(?gapCount)

Urgency rule (rubric Part D): a tier whose operational score is High and which records governance gaps against P2 or P3 at a critical-path function is treated as urgent regardless of its numeric distance from the Critical band. Satellite Orbits Tier 3 (all four principles unmet) is the canonical case.

Step 4: Compute and Classify Tier Risk Score

Operational-track query (against the authoritative scores graph):

PREFIX ggsc: <https://w3id.org/ggsc/>

SELECT ?tier ?label ?pptdGap ?criticality ?tierRiskScore ?classification
WHERE {
  GRAPH <https://w3id.org/ggsc/graph/tier-risk-scores-2026-06-22> {
    ?tier ggsc:pptdGap            ?pptdGap ;
          ggsc:stepCriticality    ?criticality ;
          ggsc:tierRiskScore      ?tierRiskScore ;
          ggsc:riskClassification ?classification .
  }
  OPTIONAL { ?tier <http://www.w3.org/2000/01/rdf-schema#label> ?label }
}
ORDER BY DESC(?tierRiskScore)

Classification bands (unchanged from v3.0; maximum possible score is 5 × 5 = 25):

Range	Classification	Investment priority
≥ 20	Critical	Immediate action required
13–19.99	High	Near-term priority investment
7–12.99	Significant	Planned investment within JDP cycle
0–6.99	Minor	Monitoring and maintenance

No tier reaches the Critical band under the 2026-06-22 scoring run; the three High tiers (Satellite Orbits T3, ICRF T1, ITRF T3) are exactly the three Step Criticality 5 single points of failure.

Step 5: Persist Updated Scores to Jena

After computing updated scores, write back to a new dated named graph — never overwrite the current graph. Superseded graphs are dropped once the new graph is verified and referenced (the 2026-06-10 graph was dropped 2026-07-05; scores remain recoverable from git history).

PREFIX ggsc: <https://w3id.org/ggsc/>
PREFIX dcterms: <http://purl.org/dc/terms/>
PREFIX prov: <http://www.w3.org/ns/prov#>
PREFIX xsd: <http://www.w3.org/2001/XMLSchema#>

INSERT DATA {
  GRAPH <https://w3id.org/ggsc/graph/tier-risk-scores-YYYY-MM-DD> {
    <https://w3id.org/ggsc/tier/Tier3_Combination>
        ggsc:pptdGap            "3.65"^^xsd:decimal ;
        ggsc:stepCriticality    5 ;
        ggsc:tierRiskScore      "18.25"^^xsd:decimal ;
        ggsc:riskClassification "High" ;
        dcterms:created         "YYYY-MM-DD"^^xsd:date ;
        prov:wasGeneratedBy     <urn:ggsc:activity:wa3-risk-scoring-YYYY-MM-DD> .
  }
}

Use databook push --merge if writing via DataBook, or SPARQL UPDATE directly via the Fuseki endpoint. Record the new graph IRI in outputs/project/decisions.md and update every deliverable citation.

Top 3 Investment Targets (v4.0 — authoritative, from tier-risk-scores-2026-06-22)

Rank	Workflow	Tier	Gap	Criticality	Score	Class	Governance gaps
1	Satellite Orbits	T3: ACC/SPOCC Combination	3.65	5	18.25	High	P2, P3, P4, P6
2	ICRF	T1: Archiving & Correlation	3.00	5	15.00	High	P2, P3, P4
3	ITRF	T3: ITRS Combination (IGN)	2.75	5	13.75	High	P2, P3

---

3. Part B: Network Criticality Multiplier — Archived (Observatory-Level Analysis)

Status: Archived for workflow-tier scoring. Remains applicable and recommended for observatory-level and centre-level network analysis where topological factors (co-location, geographic scarcity) are the primary discriminator.

The Capability_Priority_Index is multiplied by a Network Criticality Multiplier (NCM) based on three factors:

Factor 1: The EGV Bottleneck Weight

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.
• Math: The fewer alternative centres that exist for a specific EGV workflow, the higher the multiplier.

Factor 2: Multi-Technique Co-location Weight

The integrity of the global reference frame relies disproportionately on core sites hosting multiple geodetic techniques (VLBI, SLR, GNSS, DORIS) providing local ties.

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

Factor 3: Geopolitical Scarcity & Redundancy Weight

Aligning with P1, 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, its loss creates a geometric hole in the observation model.
• High Redundancy: If an observatory is in a region with 50 overlapping stations, its individual loss is negligible.
• Math: High spatial scarcity = High Multiplier.

The Part B Formula

Final_Investment_Priority = Capability_Priority_Index × (EGV_Bottleneck_Weight + Colocation_Weight + Scarcity_Weight)

JDP Activity Roll-Up

JDP_Activity_Score = SUM(Final_Investment_Priority of mapped capabilities) / Total_Mapped_Capabilities

Sorted descending: top 25% → Phase 1, middle 50% → Phase 2, bottom 25% → Phase 3.

---

4. Future Model Evolution — MTBF/MTBR

The current PPTD_Gap is a structural proxy for reliability: low maturity predicts higher failure likelihood. A mature version of this model would replace this proxy with empirically observed metrics derived from the GGSC event graph:

• Mean Time Between Failures (MTBF): Average operational time between disruption events at a tier
• Mean Time Between Repairs (MTBR): Average time to restore the tier to full operation after disruption

These become computable from Jena once the event graph (https://w3id.org/ggsc/graph/events-2026-05-07) is extended as a historical record of operational disruptions with timestamped start and restore events. The SPARQL pattern would aggregate ggsc:disruptionStart and ggsc:serviceRestored triples per tier.

Until the event graph contains sufficient historical data, PPTD_Gap remains the appropriate proxy.

---

5. Traceability Example

Why is Satellite Orbits T3 the top priority across all five workflows?

Using the Part A v4.0 operational track:

• PPTD_Gap = 3.65 — the highest gap of any tier in the assessment, driven by Risk Management (avg 1.00), Knowledge Management (avg 1.30), and Disaster Recovery and Supply Chain Continuity (avg 1.70)
• Step_Criticality = 5 (canonical SPOF — all upstream redundancy from Tiers 0–2 converges through a single pipeline with no governed failover)
• Score = 3.65 × 5 = 18.25 → High (highest of all 25 tiers)

Why does the governance track matter here?

The numeric score alone understates this tier. It is the only tier in the assessment with governance gaps against all four governance-track principles simultaneously: P2 (US federal jurisdiction concentration), P3 (no SLA or mandate governing the combination function), P4 (SPOCC proprietary software with GFZ dependency), and P6 (no independent monitoring). Under the rubric's urgency rule, a High operational score combined with P2/P3 gaps at a critical-path function is treated as urgent — this tier is the unconditional first priority for governance action even though no tier reaches the numeric Critical band. A hypothetical tier with the same operational score but operated under a multilateral SLA, with open-source combination software, distributed across two jurisdictions, and subject to independent monitoring, would be a manageable high-priority investment rather than a supply chain emergency.