Threat-Communication Viability Index

• Threat-Communication Viability Index is a quantitative metric that assesses communication viability by modeling threat urgency, timing, and success probability.
• It integrates algorithms, Bayesian analysis, and reinforcement learning to guide decision-making in applications from cyber threat filtering to strategic interstellar protocols.
• By mapping raw metrics to actionable thresholds, the TCVI supports risk assessment, resource allocation, and adaptive communications in high-stakes environments.

A Threat-Communication Viability Index (TCVI) is a quantitative or algorithmic metric designed to assess the effectiveness, urgency, and risk trade-offs when communicating under active threat conditions. The index is used in diverse domains such as email threat filtering, cyber-physical systems, adversarial reinforcement learning settings, and scenarios involving human or machine negotiation under risk. Its fundamental function is to provide an actionable score or decision metric that guides operators, systems, or stakeholders in determining when communication is beneficial, how viable successful transmission or negotiation is under given threat constraints, and what defensive or escalation measures should be employed.

1. Mathematical Foundations and Formalization

Central to the TCVI framework is the explicit mathematical modeling of trade-offs between threat urgency and communication success viability. For example, in interstellar threat contexts, the TCVI is formally defined as:

$\text{TCVI} = \frac{T_{\ell}}{\sqrt{t_r}\, W P}$

where $T_\ell$ is a threat level (on the Loeb Scale), $t_r$ is the remaining time until closest approach, $W$ is the communication window, and $P$ is the estimated probability of successful communication (Gruber, 4 Oct 2025). The numerator captures the pressure to communicate rising with increased threat and urgency, while the denominator reflects logistical and probabilistic barriers. This structure ensures that high threat and short time increase the TCVI (driving communication urgency), whereas longer windows and higher success rates decrease it (improving communication viability).

A similar trade-off is formalized in adversarial learning environments via Critical Information Acquisition Cost (CIAC) and Base Information Acquisition Cost (BIAC):

$$\alpha_c^\text{Query} = \sup\left\{\alpha_p^\text{Query} \mid \max_{\Omega_{NE}[\alpha_p^\text{Query}]} \mathbb{E}[P_p] \geq 0\right\}$$

$$\text{BIAC} = \frac{\mathbb{E}[P_p \mid \alpha_p^\text{Query}=0]}{\mathbb{E}[N_p^\text{Query}]}$$

where $\alpha_p^\text{Query}$ is the penalty or risk of communication, and $P_p$ measures the pursuer's expected payoff. BIAC sets a threshold for when communication remains viable in pursuit-evasion settings (Gatta et al., 9 Oct 2025).

In statistical classification of threat e-mails, viability is characterized by aggregate scoring (such as Bayesian context weighted threat scores) and performance indices like Total Cost Ratio (TCR), ROC analysis, false positive/negative rates, and weighted accuracy (Banday et al., 2011). These metrics together define a multidimensional viability space.

2. Methodological Variants and Application Scenarios

The TCVI appears across several methodologies, each tuned for domain-specific considerations:

• Bayesian Filtering in Threat Detection: Used to score and prioritize threat communications in mail, the index combines keyword weighting, contextual matching, and probabilistic inference to estimate classification viability and cost-benefit tradeoffs (Banday et al., 2011).
• Strategic Communication Protocols for High-Threat Scenarios: The TCVI helps decision-makers move between observation, debate, standard communication, and emergency protocols depending on quantified risk thresholds. Each TCVI range maps to a prescribed action (from surveillance to escalation) (Gruber, 4 Oct 2025).
• Reinforcement Learning in Adversarial Environments: TCVI is fundamentally linked to the agent's willingness to communicate based on learned risk-reward equilibria, cost of exposure, and the adaptive modulation of information-gathering rates (Gatta et al., 9 Oct 2025).
• Risk Assessment in Autonomous Systems: Here, the index emerges from systematic threat modeling across communication links, where risks are numerically scored via DREAD and STRIDE, directly informing aggregate viability (Paz et al., 4 May 2025).
• Cyber Threat Intelligence (CTI) Contexts: In CTI, viability is expressed through composite, metric-driven indices such as the Threat Intelligence Effectiveness Index (using geometric mean to penalize poor dimensions), or via trust-modeling frameworks that aggregate multi-dimensional evidence to yield a final viability score (Strada, 23 Jul 2025, Bobelin et al., 2 Apr 2025).

3. Metrics, Performance Indicators, and Threshold Mapping

Operationalization of the TCVI universally relies on robust, domain-specific metrics. These include:

• Statistical Classifier Metrics: Precision, recall, FPR, FNR, weighted error, and TCR, relevant for filtering threat communication (Banday et al., 2011).
• Temporal and Quantitative KPIs: Time-based indicators (e.g., Mean Time to Detect, Mean Time to Respond, adversary dwell time) and composite indices (e.g., TIEI) form the backbone in CTI ROI quantification (Strada, 23 Jul 2025).
• Probabilistic Simulation Outputs: In cyber resilience or POMDP-based models, overall attack campaign risk is aggregated into a unified index analogous to market indices, with continuous updates based on observed TTP flows and defense performance (Alevizos et al., 27 Jun 2024).
• Multi-Dimensional Trust Modeling: Aggregating reliability, competence, plausibility, and credibility via logic-based systems yields an actionable composite for communication viability where trust is uncertain or multi-sourced (Bobelin et al., 2 Apr 2025).

Mapping raw scores to actionable thresholds is critical. For example, the interstellar TCVI spectrum partitions into ranges dictating escalation from observation (<0.15) to full emergency communication (>3.5) (Gruber, 4 Oct 2025). In pursuit-evasion, BIAC and CIAC bound feasible communication under penalty risk (Gatta et al., 9 Oct 2025).

4. Challenges, Limitations, and Domain-Specific Caveats

Across deployments, several recurring challenges affect the fidelity and reliability of the TCVI:

• Metric Sensitivity and Cost Penalties: When misclassification, exposure, or operation under high risk is heavily penalized (e.g., high cost of false positives in mail or exposure cost in adversarial settings), TCVI or analogous indices can indicate negative viability even for high-performance filters (Banday et al., 2011, Gatta et al., 9 Oct 2025).
• Data and Corpus Generalizability: Viability estimates are only as robust as the datasets and threat models they are built upon. Threat e-mail corpora, simulation environments, or TTP databases may not cover full real-world diversity (Banday et al., 2011, Alevizos et al., 27 Jun 2024).
• Evolving Threat Surface and Adaptivity: Dynamic adjustment of TCVI to new threat TTPs, adversary learning, or systemic changes is non-trivial—hence, models that allow for continuous, threat-informed recalibration (as with POMDP or federated learning approaches) are preferred, yet computationally expensive (Alevizos et al., 27 Jun 2024, Ongun et al., 2022).
• Composite Index Bottleneck Effects: Indices based on geometric mean (e.g., TIEI) are highly sensitive to weakest components—a low score in any one area can sharply reduce overall viability, meaning investment must address all dimensions in tandem (Strada, 23 Jul 2025).
• Communication Paradox in Strategic Scenarios: The Information-Communication Paradox predicts a domain where risk and need are tightly, inversely coupled, producing situations where the TCVI explodes due to both rising urgency and falling chance of success (Gruber, 4 Oct 2025). Analytical models must cohere with this structure.

5. Practical Implementations and Case Studies

Implementation exemplars demonstrate the utility, adaptability, and interpretability of the TCVI:

• Threat E-mail Detection: The Bayesian context-weighted approach achieved ~97% accuracy, 1.86% FPR, nearly 97% f-measure, illustrating high viability for operational deployment, provided TCR remains above viable thresholds for cost (Banday et al., 2011).
• Federated Threat Detection: The CELEST system leverages federated learning to deliver global detection performance beyond local-only models, with PR-AUC tripling and false positives as low as $10^{-5}$; this collective intelligence supports a robust global TCVI (Ongun et al., 2022).
• Strategic Interstellar Communication: Computed TCVI values for different ISO scenarios inform discrete protocol steps, determining escalation or restraint based on real-time risk and logistics (Gruber, 4 Oct 2025).
• Adversarial Pursuit-Evasion: The learned communication policy in SHADOW consistently optimizes the trade-off between information gain and exposure, with BIAC and CIAC providing explicit thresholds for communication viability (Gatta et al., 9 Oct 2025).

The following table presents a summary of how TCVI is instantiated across domains:

Domain	Core Formula / Metric	Action Thresholds/Use
Threat e-mail detection	TCR, F-measure, ROC analysis	Deploy filter if TCR > 1
Interstellar object protocols	$\frac{T_\ell}{\sqrt{t_r}\,W P}$	TCVI bins map to SCP activation levels
Adversarial pursuit-evasion (SHADOW)	BIAC, CIAC	Communicate if cost $<$ BIAC
Cyber threat intelligence ROI (TIEI)	Weighted geometric mean across key dimensions	Composite score; bottleneck-limited performance
AV communication risk	DREAD (weighted security risk)	Channels prioritized as per DREAD-driven impact

6. Broader Implications and Future Research

The development and application of TCVI-type metrics reveal several avenues for future research:

• Generalizability to Complex, Evolving Environments: There is ongoing need for models that remain stable under evolving threat actor TTPs, changes in system topology, or adversarial adaptation (hence, the use of POMDPs or federated learning (Alevizos et al., 27 Jun 2024, Ongun et al., 2022)).
• Integration with Trust and Actionability Models: Future TCVIs may aggregate not only performance and risk but also multi-dimensional trust, particularly in multi-node or federated communication ecosystems (Bobelin et al., 2 Apr 2025, Papanikolaou et al., 2023).
• Multi-level Interpretability: Explicit mapping from technical scores to operational actions is required for high-stakes decisions, as shown by the direct binding of TCVI bands to SCPs or communication policies in recent work (Gruber, 4 Oct 2025, Gatta et al., 9 Oct 2025).
• Composite Metric Construction: Adopting non-linear aggregation methods (e.g., geometric mean for bottleneck sensitivity) addresses issues of hidden vulnerabilities, but also raises the bar for minimum acceptable performance across dimensions (Strada, 23 Jul 2025).
• Quantitative-Semantic Bridging: In management of spectral efficiency, control, and knowledge accumulation (as in 6G and TOC domains), future TCVIs may increasingly balance semantic/transfer entropy with safety margins in viability kernel models (Ercetin et al., 2023).

7. Conclusion

The Threat-Communication Viability Index is a unifying quantitative framework for understanding, prioritizing, and orchestrating communication strategies under threat. Its mathematical construction varies by domain but consistently integrates urgency, risk, resource constraints, and the expected value of success into actionable indices. By making the trade-offs between threat level, cost, timing, and success probability explicit, the TCVI facilitates rational, evidence-based decisions in high-stakes, adversarial, or safety-critical communication environments. Its continued evolution will depend on advances in trust modeling, dynamic risk assessment, adaptive protocol design, and integration with multi-modal security and organizational metrics.