Computer Science and Mathematics

Abstract: Frequent innovations in digital technology are driving the need for digital transformation in today’s companies. Although dedicated methods and frameworks exist to support the planning and execution of digital transformation, the corresponding organizational change remains a challenging endeavor. This is particularly true for small and medium-sized enterprises (SMEs), whose core business does not involve digital technology. These companies are often overwhelmed by the plethora of available technologies and struggle to comprehend their economic impact. Their main challenges include limited resources and the complexity of existing digital transformation frameworks. This paper presents a Design Science research project aimed at developing a lightweight approach to address the needs of SMEs initiating a digital transformation. The approach is based on the concept of managed evolution and is extended to include the development of a vision and guardrails. These elements help maintain the balance between fulfilling business needs and introducing digital technology.

Abstract: We investigate mechanisms by which natural systems store data across multi-dimensional spaces, integrating principles from information theory, probability, algebra, and geometry. We propose that simple Lie groups (SLGs) govern these encoding processes and act as basic information spaces. We start by showing that Euclidean space turns computationally unsolvable in higher dimensions. If we do not notice the "curse of dimensionality," it is likely because nature uses geometric positional notation at a rudimentary level. Using Benford's law, we extend the definition of radix economy to m physical dimensions. The new function measures a system's storage cost and has interesting properties. It grows as (Log_r(N))^m, rather than as N^m, providing radix r and rank m invariance, and attaining a "natural" minimum at r = e^m. This cost accommodates a homogeneous distribution of the space with a centripetal bias, avoiding the curse, and diverges when we abandon the positional system (i.e., as r->1 or r->∞) or when the dimensionality explodes (as m->∞). We review the SLGs central to modern geometry and physics. We note that they have irreducible representations of order s ≈ e^m and storage cost sorted by s, as expected. We suggest a universal notation based on balanced ternary to uniquely encode integers as the difference of two natural numbers in bijective notation. Structure and information are coupled so that the unit vectors of an s-dimensional irrep each have a label used by the radix r as an alphabetic symbol of the proposed symmetric bijective system to represent data. Finally, we examine the Weyl order of some of these SLGs, showing that Weyl divisors give rise to a logarithmic scale consistent with Benford's Law with radix r = s. This means that an SLG is autonomous to serve as an information space of non-Euclidean geometry.

Abstract: Beam Hopping (BH) technology is adopted in satellite communication systems primarily to address the rigid resource allocation issue of traditional fixed beam coverage. By dynamically adjusting beam pointing and dwell time, it achieves efficient utilization and flexible allocation of resources. This paper addresses the beam hopping scheduling problem in Low-Earth-Orbit (LEO) satellite networks for high-priority and time-sensitive services. We establish a system gain maximization model and propose a heuristic beam scheduling algorithm (HBSA) that pre-schedules critical traffic and greedily allocates remaining resources under interference and fairness constraints. We further extend the framework with a graph reinforcement learning beam-hopping scheduling scheme (GRL-BHS) that captures structural network dependencies for near-optimal adaptive scheduling. Extensive simulations against seven benchmarks demonstrate that HBSA delivers near-optimal gain (within 2% of MWC and GRL-BHS), ensures high-priority satisfaction, maintains a Jain fairness index above 0.84 under heavy load, and reduces signaling overhead by an order of magnitude, while preserving a low polynomial complexity of O(T × J × K). GRL-BHS offers the highest gain at the cost of offline training. HBSA thus emerges as the most balanced and practically deployable solution, providing a solid foundation for future intelligent BH scheduling in mega constellations.

Abstract: Large ontologies constantly evolve to adapt to their original purpose. Ontology evolution refers to the process of modification in response to a change in the domain or its conceptualization. This evolution must address changes in the ontology and guarantee the consistency of both the ontology and all dependent objects. Therefore, the impacts of a change in an ontological entity must be managed before beginning any evolution process. Maintaining large ontologies, such as the NCI Thesaurus and the Gene Ontology, is complex because it is often entrusted to groups of experts who only support the part of the ontology they created. Another problem related to ontology evolution is tracking the propagation of inconsistencies among the entities of the modified ontology. Existing work does not adequately address this important aspect. We propose an approach that partitions a large ontology to track propagation impacts and resolve inconsistencies. Our approach first determines communities in the ontology, marks impacted entities and uses a Markov decision process to resolve inconsistencies.

Abstract: We are developing the information-theoretical method proposed by Ryabko and Savina (the RS-method) and applying it to several machine translation systems and four different languages belonging to different language families. The RS method is based on an evaluation according to the following well-known fundamental principle: the better a translation preserves the author’s style, the better that translation is. (It should be noted that an author’s style is inherent to every writer and, in a sense, is as unique as a fingerprint. It is important to know that individual style is inherent not only to writers, but also to ordinary people.) For our study, as an example, we selected texts by famous writers because their authorial writing style is most clearly expressed and obvious, but our research can be applied for any other texts. It turned out that the machine translation systems under consideration differ significantly, and some of them show quite good results within the framework of this approach.

Abstract: The decarbonisation of the energy system is accelerating the uptake of distributed and renewable energy resources. Nevertheless, this stresses already-constrained distribution networks, and it can lead to expensive grid infrastructure upgrades. Demand-side flexibility offers a non-network solution that can reduce power grid reinvestment and reinforcement. This paper investigates the potential of demand-side flexibility, where we explore community energy sharing and coordinated demand response through a data-driven case study for Waiheke Island, New Zealand. In particular, a demand response management framework is developed that coordinates household hot-water cylinders, EV charging, rooftop solar power, and home and community battery storage. The framework is first evaluated in a community-scale energy-sharing scenario that incorporates flexible load scheduling and market-level settlement. The analysis is then extended to the entire Waiheke Island under a realistic demand-response setting, supported by a digital representation of the island’s electricity network and energy system. The study integrates real household smart-meter data, feeder-level consumption data, and information obtained from multiple publicly available sources to assess the island-wide potential for demand-side flexibility. Detailed simulations show that rescheduling hot-water cylinder operation, EV charging, and household battery storage can substantially reduce the island’s evening peak demand, thereby delaying network reinforcement and generating significant economic benefits.

Abstract: The identification of emerging research trends from large bibliographic databases heavily relies on extracting textual information from publication titles and abstracts. However, robust computational workflows are required to efficiently process and synthesize these rapidly expanding textual spaces. To address this challenge, this study aims to develop and validate a structured text-mining pipeline, using global research on energy security and energy politics as a case study. The empirical analysis utilizes a corpus of 2,692 research and review articles published between 2022 and 2026 retrieved from the ScienceDirect database. The study demonstrates the feasibility of this integrated pipeline, which systematically combines text retrieval, Stanza-based syntactic noun phrase extraction, and the FP-Growth algorithm with VOSviewer mapping. Applied to the energy domain, the pipeline successfully unveiled critical structural shifts: while the thematic core remains highly persistent, peripheral research highlights a distinct movement away from abstract, high-level discussions toward more operational and solution-oriented perspectives. The empirical findings hold practical utility for streamlining information retrieval and supporting systematic literature reviews within specialized research domains. Future development of the method involves refining key-term ranking strategies and transitioning to higher-order community detection utilizing a hypergraph approach.

Abstract: LLM-based conversational agents generate fluent responses but remain limited in adapting their supportive style to individual personality and emotional needs. We address this gap through a theory-grounded personality-adaptive conversational AI architecture that performs turn-by-turn Big Five trait detection and applies Zurich Model-aligned behavioural regulation, orchestrated with PROMISE (a model-driven framework for state-based LLM orchestration). We generated 20 simulated dialogue sessions (120 assistant turns) comparing regulated and non-adaptive assistants across two boundary-condition Big Five profiles (all traits +1 vs. −1), scored by a structured LLM-based evaluator with author review retained as an internal audit. Under these conditions the pipeline executed as designed: holistic detection was correct on 59/60 turns (98.3%) and regulation adherence was complete (100%), although dimension-level accuracy was lower (macro mean 83.3%). The turn-level Personality Needs Yes rate rose from 8.3% (5/60) at baseline to 100% (60/60) under regulation, and all 10 conversation pairs favoured regulation; emotional tone was not estimable (both arms at ceiling) and relevance did not differ—a pattern of selective enhancement. Mixed-profile testing reduced dimension-level accuracy to 58.1%, locating the boundary result as an upper bound. A two-rater verify-and-revise audit on an n = 66 overlap supports detection-label convergence (mean linear κ = 0.731) but does not validate the outcome rubrics, which remain LLM-rated. The contribution is a reproducible detection→regulation→evaluation architecture for controlled simulation, implemented on closed cloud-hosted models whose computational footprint and detector interpretability are not characterised here. The Zurich mapping is implemented as a design choice rather than validated as psychological theory; the system is not evaluated as a therapeutic or clinical intervention, and clinical value remains to be demonstrated in human-participant studies.

Abstract: This article provides a comprehensive analysis of the fake Webometrics University Rankings (WURs) phenomenon observed in the first half of 2026. Based on an analysis of 300 publications gathered from 39 countries between January 6 and July 6, 2026, the study reveals that approximately 65% of cases involving the dissemination of inaccurate ranking data were initiated by news outlets and consulting agencies. The research confirms a pronounced geographical imbalance: 81.3% of fake publications originate from the Global South, with Indonesia serving as the primary epicenter of activity (accounting for 50.7% of publications). A retrospective analysis is conducted on the “first wave” of fake WURs (spring–summer 2025), which utilized domains such as webometrics.org, webometricsranking.com, and webometrics.online. These domains remained largely obscured from the European academic community throughout 2026 due to Geo-IP masking tactics. Furthermore, the paper analyzes the “July 2026 wave,” which confirms the further scaling of this network through domains such as webometrics.one, webometrics.top, and webometric.org. The article concludes by proposing institutional measures to enhance vigilance and safeguard the integrity and authority of academic rankings.

Abstract: Certificate request procedures across public administrations (PAs) often depend on heterogeneous repositories, data models, and validation rules, thereby limiting interoperability and automation. This study presents a semantic digital library built on an RDF/OWL ontology and a knowledge graph representing certificates, administrative entities, required documents, attributes, dependencies, and processing rules. Linked Open Data and SPARQL interfaces extend the initially centralized model and connect it to certificate-management microservices. The resulting architecture enables distributed access to shared semantic definitions and supports the Once-Only principle. To inform implementation priorities, we compare five graph measures with certificate request volumes from the Italian National Resident Population Registry (ANPR). PageRank yields the highest observed correlation (r = 0.6455), narrowly exceeding Betweenness and Closeness Centrality (r = 0.6386). This result suggests that indirect structural dependencies may help identify high-priority services; however, the limited matched dataset makes the analysis exploratory. The framework provides a foundation for interoperable certificate services and future integration with national semantic infrastructures such as SCHEMA.gov.it.

Abstract: This paper develops a Quantum-Institutional Automated Negotiation (QIAN) algorithm as an intelligent decision support system for carbon credit markets, contributing to quantum game theory applications in automated negotiation and institutional decision-making. We extend the Eisert–Wilkens–Lewenstein (EWL) framework by introducing an Institutional Filter Function Φ_C that maps continuous quantum strategies—phase shifts and superpositions—onto finite, legally viable contract archetypes. This filter models regulatory, political, and organizational constraints that collapse the infinite quantum strategy space into a tractable finite set, enabling computationally efficient decision support. We prove convergence of the automated negotiation algorithm to a Pareto-superior Nash Equilibrium and demonstrate, through Monte Carlo simulation with literature-calibrated parameters, that the collapsed quantum equilibrium yields a mean joint utility uplift of 13.5% over classical cooperation (95% CI: 9.8%–17.3%, p < 0.001), with the upper bound reaching 17.3% and 26.8% of simulations achieving uplifts in the 15–30% range. The framework maps directly to blockchain-based smart contracts, providing a deployable mechanism for sustainable carbon markets that aligns with SDG 13 (Climate Action) and SDG 17 (Partnerships). This work advances quantum game theory from abstract formalism to computational institutional design, offering a novel decision support approach for negotiation analysis under real-world constraints.

Abstract: As industries increasingly transition manufacturing and production systems toward enabled smart factories, governments and policymakers assume a critical role in establishing regulatory frameworks that enable emerging Industry 4.0 ecosystems to develop and remain competitive. While existing scholarship has devoted substantial attention to technological capabilities and innovation potential, comparatively limited emphasis has been placed on the policy, regulatory, and governance structures that shape organizational readiness and workforce transformation in this digital industrial era. This study examines how institutional arrangements—encompassing public policy, regulatory regimes, and governance mechanisms—influence organizations’ capacity to adopt Industry 4.0 technologies and to effectively transform their workforce. Grounded in institutional theory and sociotechnical perspectives, the research adopts a multilevel analytical approach to explore the interactions between macro-level policy and regulatory environments, meso-level organizational readiness, and micro-level workforce outcomes. The study used the systematic literature review SLR to investigate 80 scholarly studies on key dimensions of organizational readiness, including digital maturity, leadership commitment, IT–OT integration, and change management capabilities, and analyzes how these factors mediate the relationship between external governance frameworks and Industry 4.0 implementation. In parallel, the research examines workforce transformation processes, with particular attention to reskilling and upskilling initiatives, job redesign, human–machine collaboration, and employee acceptance of AI-driven systems. Drawing on a comprehensive review of existing literature, supplemented by insights from organizational leaders and technical professionals operating within Industry 4.0 environments, the study evaluates the impact of policy and regulatory oversight on organizational readiness. The findings highlight the importance and impact of the organizational framework as an essential ingredient to organizational readiness and workforce transformation in Industry 4.0, spanning policy to governance practices, regulatory compliance challenges, and the human-centered implications of automation. Additionally, the study addresses ethical, social, and labor-related considerations, including data governance, algorithmic accountability, and workforce inclusion. The analysis reveals a consistent emphasis on workforce reskilling across national Industry 4.0 strategies, although significant variation exists in policy implementation approaches. Overall, the findings demonstrate that organizational readiness for Industry 4.0 is strongly associated with organizations' internal architecture, with leadership commitment and workforce digital literacy, underscoring the central role of governance and human-centered capabilities in enabling sustainable digital industrial transformation.

Abstract: We present an extension of our study on the discovery of useful journal-to-journal associations from bibliography data. Association Rule Mining (ARM) is applied under the market basket analysis (MBA) paradigm: cited journals are treated as "items" within an article’s "transaction", and the traditional market basket model is enhanced with a numerical dimension, namely the weight of referencing (WoR): the percentage of an article’s references to journals that target a given journal. The predictive ability of the ARM output is enhanced by ranking the rules by means of a Skyline operator that integrates the interdependence of the numerical variables involved (Spearman’s rho) with the ARM conviction interestingness measure. The approach is evaluated against a standard ARM-only implementation on the bibliographic record of the Hellenic Academic Libraries Link (HEAL-Link) consortium, and the enhanced results are integrated into the publicly available HEAL-Link J2J-GR web service (https://j2j.heal-link.gr/j2javis/).

Abstract: It has become increasingly clear to organizations that future decision-making, production optimization, and competitive edge within a digital economy would largely be data-driven and dependent on systematic collection and use of a data-driven approach necessary to rationalize strategic decision-making, the need to develop an organizational culture that enhances digitalization of business process activities becomes imperative to survive in a digital economy. As enterprises rapidly undergo digital transformation with various advanced digital technologies, they strive to implement measures to adapt their organizational culture to the changing economy in other to remain competitive and survive. Organizations have had to continuously adapt their business processes to the dynamic nature of the digital industry to support their businesses and provide value. The current advances in the digital space have provided enterprises with the opportunities to digitalize their business processes, integrating various advanced digital technologies such as artificial intelligence, robotics, and machine learning to automate and optimize business processes and boost workplace operational efficiency and productivity. As the society undergo digital transformation, enterprises are faced with the constant need to integrate new digital infrastructure to power their business processes, provide business value, and remain competitive in a dynamic market economy. While some organizations have immensely benefited from the integration of advanced digital technologies to support business processes others are facing challenges from stiff organizational culture, such as resistance from employees, due to fears of job loss. A Systematic Literature Review SLR was adopted to review 150 existing scholarly studies on organizational cultures thriving well in a digital society. Findings from the study review identifies the most effective adaptive organizational culture dimensions that support digital transformation and Industry 4.0 adoption. Findings reveal that learning culture, innovation culture, collaborative culture, agile culture, data-driven culture and Leadership support culture are the strongest predictors of successful digitalization. Hierarchical and rigid bureaucratic cultures were repeatedly linked to slow adoption and resistance to change .The study reveal a significant relationship between organizational culture and successful digitalization and integration of new digital technologies.

Abstract: This paper presents a critical analysis of the current system of scholarly communication, which has undergone a profound transformation under the influence of excessive commercialization within the neoliberal "publish or perish" paradigm. The study demonstrates that the Open Access movement, in its current form, has been co-opted by major commercial publishers through mechanisms such as Article Processing Charges (APCs) and "Transformative Agreements," which fail to solve the problem of creating a fair and accessible environment for the dissemination of knowledge. The work substantiates the thesis that the prestige of academic journals has ceased to be a reliable indicator of scientific quality, and that the traditional peer-review system is in a state of crisis, driven by the exponential growth of publications and a catastrophic shortage of qualified reviewers. The author analyzes potential solutions to this impasse, including a transition to platform-based publication and review models, as well as the advancement of Diamond Open Access. Particular attention is paid to the deconstruction of the English language monopoly in science: it is shown that the development of artificial intelligence (AI) technologies is neutralizing language barriers, making high-quality knowledge globally accessible regardless of the original language. The paper proposes a reform model for scholarly communication that combines elements of centralized access—based on adapting the Soviet VINITI experience to the digital environment—with decentralized Diamond Open Access platforms. Possible reactions of commercial publishers to such radical measures are discussed. In conclusion, a program for transforming the system of scholarly communication is formulated. This includes the reform of research assessment principles (shifting from quantitative metrics toward qualitative peer review), the assurance of technological sovereignty in metadata processing and bibliometrics, and the conceptual integration of Open Access to current publications, scientific heritage, and educational resources into a single framework under public control.

Abstract: Recent industry reporting indicates that meantime to exploit has become negative in several observed datasets, implying that exploitation may occur before patch availability for some classes of vulnerabilities. Adversarial use of artificial intelligence (AI) is a documented accelerant of this trend. This paper addresses the operational problem that follows in healthcare cybersecurity: the volume and velocity of vulnerability disclosure exceed human analytic capacity, which leads practitioners to under-prioritize, or defer entirely, individual Common Vulnerabilities and Exposures (CVEs) at precisely the moment their risk is rising. Adopting the design science research paradigm of Hevner et al. [8], the study develops and evaluates a purposeful information technology artifact intended to resolve this problem within a mid-sized United States healthcare system. The artifact is a three-application automated CVE intelligence, prioritization, and remediation-tracking pipeline implemented in Microsoft Azure Logic Apps, integrating the National Vulnerability Database (NVD), the CISA Known Exploited Vulnerabilities (KEV) catalog, the Microsoft Security Response Center (MSRC) CVRF API, Microsoft Defender, Claroty xDome, Microsoft Security Copilot, and ServiceNow, and operationalizing the four risk factors codified in CISA Binding Operational Directive (BOD) 26-04. In naturalistic operation across three CISA Weekly Vulnerability Summary bulletins, the artifact processed 5,216 unique CVE references and reduced them to 534 environment-relevant findings, an 89.8 percent exposure-first reduction, before expensive per-CVE enrichment and ticketing. Findings indicate that governed automation demonstrably increases CVE coverage, reduces low-value enrichment volume, and creates an auditable prioritization record. Because no controlled before-and-after time-and-motion study was conducted and no independent ground-truth severity labels were collected, remediation-speed and analyst-productivity outcomes remain future validation targets rather than demonstrated results.

Abstract: Trust is the invisible glue that binds together economic transactions, human machine partnerships, organizational cohesion, and decentralized governance. Yet despite its centrality, the vast majority of mathematical trust models remain confined to dyadic relationships—one trustor assessing one trustee. The real world, however, routinely demands trust in groups, teams, swarms, and institutions, where emergent outcomes depend on internal coordination, heterogeneity, and decision rules (e.g., quorums, weakest link dependencies, or majority votes). This paper presents a Unified Multi Layer Mathematical Framework that seamlessly integrates both dyadic and collective trust. The framework synthesizes seven core layers—perceived trustworthiness (ability, benevolence, integrity), behavioral risk thresholding (with a full utility theoretic justification), Bayesian learning with recency weighted evidence, temporal dynamics with asymmetric build destroy rates, game theoretic sustainability (with a smooth logistic override), social network propagation, and a coupled dynamical system. We introduce the Group Trust Extension (GTE), which generalizes the framework to collective trustees via three aggregation architectures: series (weakest link), parallel (redundancy), and quorum (k of m) systems. Crucially, we replace the simple cohesion penalty with a flexible cohesion–diversity function that can either penalize excessive variance or reward useful diversity (e.g., wisdom of crowds), and we extend the quorum model to account for correlated failures via a beta binomial formulation. We provide a formal unification theorem proving that the dyadic model is a special case of the GTE, and we present a sensitivity analysis and empirical comparison against baseline models using synthetic data calibrated to real world trust phenomena. We demonstrate the practical application of the framework through ten distinct real world case studies and one extended illustrative example (Amazon.ca e commerce, Appendix D) that shows how the model integrates reputation, risk, strategic incentives, social recommendations, and reviewer credibility into a single quantitative assessment. For each case, we provide domain specific parameterizations and executable Python code snippets from our open source library trustlib, demonstrating how the framework generates actionable decisions. The result is a mathematically consistent, computationally tractable, and empirically grounded theory of trust applicable to a wide range of multi agent systems.

Abstract: Analyzing the thematic content of bibliometric records through titles and abstracts is essential for understanding how research topics are defined, articulated, and transformed over time. As these publication components concentrate the most visible and representative terminology, they provide a compact yet informative basis for identifying recurring concepts, emerging terms, and shifts in thematic emphasis across a research corpus. This study aimed to evaluate the utility of a hybrid Stanza–FP-Growth approach for terminological pattern recognition in ScienceDirect bibliometric records addressing energy security indicators. The dataset comprised 830 bibliometric records retrieved from the open ScienceDirect abstract database using the search query “Energy security” AND (indicators OR indication OR metrics OR index) within titles, abstracts, and keywords, with the document types limited to review and research articles. The extraction procedure identified well-established scientific terms, including renewable energy source, energy security indicator, national energy security, cleaner energy system, energy security, technological trajectory, clean technology transfer, lithium battery, and sustainable innovation. More specific research themes were characterized by the co-occurrence of multiple key terms, including the term sets energy trilemma; environmental sustainability; energy security and energy trilemma; energy equity; environmental sustainability. Notably, although energy trilemma was not included in the original ScienceDirect search query, it emerged naturally through the proposed extraction pipeline. The findings demonstrate that the Stanza–FP-Growth framework constitutes a viable proof-of-concept approach for structuring bibliometric records and transforming unstructured textual data into a systematic terminological representation. The proposed approach may support domain experts in identifying promising research directions and emerging thematic relationships. Future research should explore the use of Stanza’s default_accurate module for named entity recognition and implement domain-specific recalibration of stop-word and exception dictionaries to improve extraction fidelity.

Abstract: Physical AI is conventionally associated with robots, vehicles, and other mechanically embodied systems. This article extends Physical AI to electromagnetic-field embodiment, where RF-programmable hardware acts on real electromagnetic fields and propagation environments via phased arrays, reconfigurable intelligent surfaces, and programmable wireless environments. We define electromagnetic-field Physical AI through a perception–modeling–decision–execution–feedback loop, introduce a four-level hierarchy from passive perception to closed-loop field-state regulation, and propose five identification criteria to distinguish field-level intelligence from conventional parameter optimization. We further position this perspective relative to emerging world-model-based wireless intelligence, arguing that the two are complementary: world models emphasize predictive internal cognition, whereas electromagnetic-field Physical AI emphasizes physical-layer embodiment through which intelligent policies act on propagation environments. We examine the control-theoretic structure of distributed-parameter field dynamics, discuss reduced-order modeling and structured physical priors, and analyze implications for 6G architecture and standardization. A concept-validation example suggests that explicit field-level optimization can outperform parameter-centric baselines under simplified but explicit controlled assumptions. This work also proposes a layered standardization framework with field-level intent descriptors and capability abstractions, offering a starting point for future programmable wireless environment standards.

Abstract:

The Possibilistic Cramér–Rao Bound (PCRB) of the Theory of Epistemic Abductive Geometry (TEAG) floors the rate at which evidence may delete admissible microstates: \(H_π^{+} \geq H_π^{-} + \tfrac{n}{2}\log(1-I_k)\), with \(n\) the state dimension and \(I_k\) the Choquet information content of the observation. This paper corrects and strengthens the bound by exploiting a structural fact the earlier formulation ignored: possibilistic entropy lives on state space, but evidence deforms the impossibility field through the state-to-measurement map, which is not injective — many states produce the same evidence. For a measurement of rank m ≤ n, the surprisal field is the pullback of an \(m\)-dimensional field and is constant on the (n-m)-dimensional fibers of the measurement map. Three results follow. (1) Fiber conservation: a single observation leaves the fiber-direction geometry of every admissible \(\alpha\)-cut exactly invariant; the entire entropy change is the admissibility-integral of the log base-mass retained, an identity we prove by exact Fubini factorization. Ignorance is conserved along every direction the evidence cannot compare — the Principle of Comparative Information as a conservation law. (2) The rank-aware PCRB: under an explicit base-marginal coupling condition that formalizes the innovation–state isotropy assumption in its correct (\(m\)-dimensional) home, \(H_π^{+} \geq H_π^{-} + \tfrac{m}{2}\log(1-I_k)\) — a strictly stronger floor than the state-dimension version whenever \(m < n\), recovering it at full rank. (3) Falsifiability–observability: over \(\ell\) observations with dynamics, a direction of state space is falsifiable if and only if it lies in the accumulated pulled-back row space; the state is totally falsifiable if and only if the system is observable; and evidence-versus-evidence falsification — the detection of inconsistency, bias, and model stress through joint total falsification — is possible if and only if the stacked system is overdetermined, \(\ell m > n\) after accounting for rank. Consequences for the PCRB-admissible basin, for the ESPF reference implementation, and a falsifiable prediction about previously reported over-pruning in rank-deficient tracking are derived. Tightness of the corrected floor remains open and is inherited, not resolved, by the rank refinement.