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Data and Codes for the work published in NSE. Start by downloading scripts and reading the README. (Original training data h5 files are not included but can be made available on request, as these data…

Data and Codes for the work published in NSE. Start by downloading scripts and reading the README. (Original training data h5 files are not included but can be made available on request, as these data total over 300 GBs.)

Coupled OpenMC to the analytical GCR model for publication on NSTOR.

Abstract:The digitalisation of healthcare is transforming not only clinical practice but also the legal architecture through which health rights are protected, coordinated, and operationalised. Using …

Abstract:The digitalisation of healthcare is transforming not only clinical practice but also the legal architecture through which health rights are protected, coordinated, and operationalised. Using Italy as a doctrinal case study within the European Union (EU) framework shaped by the General Data Protection Regulation, the European Health Data Space, and artificial intelligence (AI) regulation, this article argues that digital healthcare is moving beyond consent-centred protection toward governance-based safeguards. The Italian trajectory is especially revealing because regionalised healthcare governance intersects with centralised digital coordination through the Fascicolo Sanitario Elettronico, the Ecosystem of Health Data, and EU rules on the secondary use of health data. The article contends that this shift does not displace consent as a legal or constitutional value, but requires stronger substitute and complementary safeguards when consent can no longer operate as an effective practical control mechanism. These include clear legal bases, differentiated access regimes, data minimisation, secure processing environments, meaningful patient information, democratic accountability, human oversight, anti-discrimination duties, and clearer allocations of responsibility among clinicians, institutions, and technology providers. AI-mediated care is treated as a downstream test case for whether governance-based legality remains compatible with autonomy, dignity, and responsibility in clinical care.

The prerequisites for transforming the analytical support for the comprehensive assessment of corporate structure development are examined. The content of the analytical toolkit is clarified, and its …

The prerequisites for transforming the analytical support for the comprehensive assessment of corporate structure development are examined. The content of the analytical toolkit is clarified, and its informational, methodological, technological, and process-and-outcome components are identified. Digital technologies are systematized according to the stages of data collection, integration and storage, analysis, modelling, forecasting, and visualization. The principles and levels of integrating economic analysis methods with digital tools are substantiated. A structural-logical model for the formation and application of the analytical toolkit is developed, combining functional blocks, stages of the analytical process, and a feedback mechanism. The practical value of the results lies in their potential use for generating predictive assessments and supporting strategic and operational management decisions.

The Architecture of Physical Reality A Comprehensive Analysis of the Constraint of Change, Algebraic Restructuring, and Wave Equation Derivation   Driven by Dean Kulik July 2026   The histor…

The Architecture of Physical Reality A Comprehensive Analysis of the Constraint of Change, Algebraic Restructuring, and Wave Equation Derivation   Driven by Dean Kulik July 2026   The historical trajectory of scientific inquiry, spanning from the atomistic propositions of Democritus in classical antiquity to the sophisticated gauge symmetries and quantum fields of the modern Standard Model, has been overwhelmingly predicated upon a substance-based ontology. This classical paradigm operates on the foundational assumption that the universe is constructed from fundamental "nouns"—static, enduring entities such as point masses, particles, and pre-existing geometric spacetime vacuums. Within this Newtonian and relativistic architecture, objects are treated as passive variables that proceed along trajectories dictated by independent, external laws. However, the progression of theoretical physics, advanced computational modeling, and mathematical logic has increasingly confronted irreducible boundary conditions that classical reductionism appears fundamentally unequipped to resolve. The pursuit of a rigorous unification of quantum mechanics and gravity has exposed the limits of treating spacetime and matter as separate, fundamental axioms. In response to this crisis of distinction, a paradigm-shifting theoretical model—often referred to as the Nexus Framework, the C1 Series, or the Recursive Harmonic Architecture (RHA)—has emerged. This framework executes an absolute "Ontological Inversion". It abandons the substance-based ontology in favor of a strictly process-oriented computational substrate, proposing that reality is fundamentally structured as a recursive lattice (a Cosmic Field Programmable Gate Array, or FPGA) where phenomena across all domains are governed by iterative processes and inviolable topological constraints. Within this architecture, stability does not arise from fixed points or unchanging foundational particles, but rather from continuously repeating feedback cycles and harmonic resonances. This report provides an exhaustive, rigorously detailed analysis of this ontological framework, proving its mathematical assertions and detailing its physical logic. Relying fundamentally on the extraction of text, mathematical expressions, formulas, and equations from the core documentation of the constraint framework , the report systematically deconstructs the foundational Constraints of Change (C0 through C5). It elucidates the derivation of the Topological Laws (L3 and L4), conducts a deep dive into the Admissible Scalar Continuation Algebra Theorem (the T2 Architecture) which structurally supersedes the Frobenius and Solèr theorems, and finally traces the explicit mechanical derivation of the wave equation and field theory. I. The Fundamental Constraints: Redefining the State Space At the bedrock of this computational framework lies a strictly ordered sequence of primitive physical constraints. Crucially, these are not prescriptive laws imposed by an external mathematical evaluator upon a pre-existing physical substance. Instead, they function as fundamental topological boundaries that define the admissibility of any physical state. They dictate the parameters of existence by actively pruning the mathematical space, entirely prohibiting configurations that would result in a cessation of dynamic flow. Constraint 0 (C0): The Wash and the Absolute Ground State Constraint 0 (C0) establishes the pre-geometric baseline of the universe, representing an undifferentiated condition termed "the Wash". In this absolute ground state, every spatial direction and relational connection is perfectly equivalent and strictly isotropic. Because all relations are perfectly symmetric, every local signal propagated through this substrate perfectly cancels against its exact counterpart. Consequently, total global connection is physically read at the local level as absolute absence or void. To prove the operational properties of C0, the framework translates this condition into graph-theoretic terms. The C0 state is modeled mathematically as a complete graph on  nodes, , where every node is connected to every other node with identical weight. The dynamic behavior of such a network is governed by its Laplacian matrix, , where  is the degree matrix and  is the adjacency matrix. For the complete graph , the degree of every node is , meaning . The adjacency matrix  consists of zeros on the diagonal and ones elsewhere. The eigenvalues (spectrum) of this Laplacian matrix  define the vibrational and communicative modes of the C0 ground state. The characteristic equation yields exactly two distinct eigenvalues, mathematically verified as:   This spectrum possesses a network diameter of exactly one hop, meaning any perturbation reaches the entire system instantly. The physical implications of this exact mathematical structure are profound. The single zero mode ( with multiplicity 1) represents the global constant—the entirety of the system translating or phase-shifting together as a monolithic whole, which inherently produces no internal, local distinction or measurement. The massive degeneracy of the excited level ( with multiplicity ) represents a flat band of maximal connectivity. In physical terms, this extreme macroscopic connectivity is read as maximal stiffness; the system is so tightly coupled that any internal variance is immediately distributed and neutralized. Therefore, what macroscopic, classical physics interprets as an empty vacuum or a sterile spatial void is, in reality, a fully balanced, maximally connected computational ledger that is perfectly folded onto a single indistinguishable readout. Constraint 1 (C1): The Supreme Mandate of Change Operationally inseparable from the C0 baseline is Constraint 1 (C1), which serves as the supreme mandate, the single overarching axiom, and the thermodynamic engine of the entire framework: all things must change. Formally defined, C1 dictates that "no admissible state of any system may be one from which change is impossible". Expressed with mathematical precision, for every admissible physical state , there must exist an admissible state  such that , and  is reachable from  by a legal dynamical transition. Under this constraint, every admissible state is forced to possess at least one legal successor distinct from itself. The theoretical subtlety of C1—a concept that recurs iteratively at every hierarchical level of the framework—is that C1 defines an admissible boundary rather than acting as a test applied to a pre-existing state space. In classical computer science or physics, a system might evolve into a state, run a logical check, and halt. C1 rejects this topology. There is no external evaluator standing outside the universe checking and rejecting frozen states; instead, frozen states simply do not possess membership in the mathematical state space to begin with. A configuration lacking a legal successor is physically nonexistent. By demanding perpetual transition, C1 acts as the ultimate prohibition against fixed points (places in phase space where the dynamical flow terminates). However, C1 does not forbid invariants (quantities, such as energy or momentum, that the flow conserves). C1 itself is an invariant of the meta-dynamics—the continuous preservation of change. Topologically, the C1 mandate requires that the phase space of the universe must support a nowhere-vanishing vector field. According to the Poincaré-Hopf theorem in differential topology, the Euler characteristic  of a compact manifold  is directly related to the sum of the indices of the isolated zeros (fixed points) of a vector field defined on it:   Because C1 rigorously forbids the existence of any zeros in the transition vector field ( for all ), the sum on the left side is exactly zero. Therefore, C1 mathematically proves that the topological manifold of the universe must possess a zero Euler characteristic (). This establishes reality not as a static geometric container filled with resting states, but as an active, measure-preserving unitary flow characterized by continuous dynamical evolution. The Intersection of C0 and C1: The Gap and the Origin of Distinction When the C1 mandate is applied to the C0 ground state, the physical universe is born. A perfect, symmetrical, static void (the pure C0 state) represents the ultimate fixed point—a state with no internal difference and therefore no possibility of sequential transition. Because the C1 axiom aggressively executes any state lacking a legal successor, the absolute void is mathematically disallowed from sustaining itself. In this framework, physical matter and energy are not miraculously inserted into nothingness; rather, "something" is simply the precise mathematical shape of nothingness actively failing to hold still. The intersection between the C0 singularity and the C1 mandate produces what the architecture terms "the gap". This gap is the permanent, oscillating interstice between a physical entity (the answering state) and its computational description (the asking state), enabling measurable physical distinction. Crucially, because a lone, self-identical unit with no complement would form an isolated fixed point (violating C1), the framework forces the first foundational distinction to intrinsically possess two asymmetric sides. Consequently, the integer "two" acts as the absolute baseline floor of numerical counting and geometry in this universe; the concept of "one" only exists a posteriori as a singular abstracted side of a pre-existing dual relationship. II. Hierarchical Constraints: Possibility, Exchange, and Symmetry With the state space actively prevented from freezing by C1, the framework projects this mandate upward through the structural hierarchies of the universe, generating new constraints that govern thermodynamics, momentum, and symmetry. Constraint 2 (C2): Infinite Degrees of Freedom and Location Inheritance Constraint 2 (C2) is conceptually defined as "C1, one level up". While C1 dictates that an individual state must change, C2 applies the mandate of change to the specific degree of freedom defined as "the set of futures still reachable" from a given state. To prove the physical necessity of C2, consider a deterministic universe with a finite number of discrete states. Let  represent the finite set of all possible futures available to the system. As the system undergoes transition via a function , the set of still-reachable futures from the current moment can only shrink or hold constant. This dynamic inherently generates a descending chain of finite sets:   According to foundational set theory and dynamical systems analysis, any descending chain of finite sets must eventually terminate. At some iteration , the sets stabilize such that . When this mathematical termination occurs, the set of reachable futures has hit an absolute fixed point. Even if the individual states within that final subset continue to move endlessly in a closed periodic loop, the "flow of possibility" itself has completely frozen. This freezing of possibility constitutes a direct violation of the C1 mandate when read one hierarchical level up. Because a finite world inevitably and mathematically forces this fixed point in possibility, the universe cannot be finite. To satisfy C2 and keep the flow of possibility open permanently, the physical universe is strictly forced to possess infinite degrees of freedom. Furthermore, C2 operates as the framework's Location Inheritance constraint. It dictates that any conserved computational content must have a verifiable distribution across physical locations; it cannot simply float free of the topological geometry without breaking the inheritance of sequential position. Matter cannot hold a specific spatial location without possessing the active potential to be moved from it, guaranteeing dynamic circulation and the impossibility of a terminal thermodynamic freeze. Constraint 3 (C3): The Isotropic Cost of Change Constraint 3 (C3) establishes the thermodynamic and mechanical rule that "all change is equal". The framework dictates that the base computational substrate privileges no specific physical channel, axis, or direction over another. The proof for C3 relies on a contradiction with C2. If the thermodynamic or computational cost of physical transition differed by direction—if some paths were "cheaper" to execute than others—the dynamic flow of the universe would instantly seek the path of least resistance. These cheap channels would saturate immediately, isolating other regions of the state space and functionally reducing the available degrees of freedom. This saturation would break the infinite circulation mandated by C2. Therefore, the cost of change must be strictly isotropic. This isotropic requirement is the geometric bedrock that formally derives the equal a priori probability postulate utilized in statistical mechanics. At the macroscopic and mechanical level, C3 manifests as the inheritance constraint read at the exact moment of physical contact. The principle that "equal rules plus interaction equates to equal exchange" produces the fundamental equation of interaction:   If the total energy or momentum shifted asymmetrically during a transformation, certain transformations would inherently cost more than others, violating the isotropic mandate and breaking the chain of inheritance. At the precise moment of a collision, this equal exchange manifests as the physical law:   Consequently, C3 proves the conservation of total momentum. It is not a new, arbitrary physical axiom injected to match human observation; rather, Newton's third law of motion is geometrically forced by the requirement that change cannot possess an anisotropic cost gradient. Furthermore, because all change is equal, the flux of causal influence or "price" leaving any closed bounding surface around a continuous source must be completely symmetric. The surface area of a sphere in three dimensions scales as . For the flux to remain equal across any arbitrary boundary, the intensity must dilute proportionally to the inverse of the area. This topological necessity mathematically forces the inverse-square law of field propagation for forces such as gravity and electromagnetism. Constraint 5 (C5): Spontaneous Symmetry Breaking Constraint 5 (C5) formalizes the mandate that "Symmetry must break". As established by the interplay of C0 and C1, a perfect, unbroken vacuum (where all amplitudes cancel and nothing transitions) is a highly stable fixed point. Because the C1 axiom rigorously executes any fixed point from the admissible phase space, the perfectly symmetric vacuum is mathematically targeted for elimination. To survive as an active computational substrate, the void is forced to spontaneously select a broken configuration. The universe must adopt an asymmetry—a differential in state—to sustain its dynamic operation. Thus, spontaneous symmetry breaking is not an accidental feature of the early universe, but a persistent, continuously executed topological requirement of the architecture. Constraint Conceptual Definition Physical & Topological Consequence C0 The Wash / Absolute Ground State Total global connection reading as absence; Laplacian zero mode indicating a single monolithic ledger. C1 The Mandate of Change No fixed points; nowhere-vanishing vector field mathematically enforcing a zero Euler characteristic (). C2 Location Inheritance Infinite degrees of freedom forced by the mathematical termination of descending finite sets. C3 All Change is Equal Isotropic cost of change; mathematical derivation of momentum conservation () and the inverse-square law. C5 Symmetry Must Break Rejection of the unbroken vacuum as a forbidden fixed point; forced spontaneous differentiation. III. The T2 Architecture: The Admissible Scalar Continuation Algebra Theorem One of the most profound mathematical achievements of this constraint-based framework is the T2 Architecture. This formulation completely replaces existing abstract theorems regarding the foundations of quantum mechanics, deriving the absolute necessity of complex numbers () in quantum field theory through physical boundaries rather than axiomatic postulation. Traditionally, the mathematical justification for utilizing real, complex, or quaternionic Hilbert spaces in quantum logic relies heavily on Solèr's Theorem. Solèr's theorem, originally proved by Maria Pia Solèr in 1995, is a celebrated result concerning infinite-dimensional vector spaces. It states that for every star division ring  and every -module  equipped with an orthomodular Hermitian form, if the space possesses an infinite orthonormal sequence, then the division ring  is strictly forced to be isomorphic to either the real numbers (), the complex numbers (), or the quaternions (), and  must be a Hilbert space over . Physicists and mathematicians, notably John C. Baez, have characterized this theorem as quite "magical". The hypotheses are purely algebraic and completely ignore the continuum, yet they miraculously force the underlying geometry of the universe into one of these three highly specific division rings. While Solèr's theorem successfully fills a gap in rederiving quantum mechanics from information-theoretic postulates, it remains an abstract mathematical descriptor rather than a physical causal mechanism. The Nexus framework proposes an aggressive restructuring, replacing the Frobenius/Solèr mathematical discussion by tightening four specific physical lemmas (the T2 Architecture). This transition grounds the scalar algebra exclusively in the physical constraints C0-C5 rather than orthomodular lattice theory. The Four Lemmas of Continuation Let  denote the scalar algebra utilized by the computational substrate to encode the weights of independent continuation amplitudes (i.e., the probability amplitudes of quantum mechanics). The framework relies on four foundational lemmas to logically structure this algebra: Lemma A (Associativity as Representation Independence): Lemma A asserts that physical composition must be representation-independent. A physical continuation history is an ordered sequence of lawful, dynamic continuations. Any mathematical algebra attempting to represent that physical history must assign the exact same aggregate continuation map regardless of how the sequence of events is parenthesized. If associativity were to fail, the human accounting method and parenthesization, rather than the physical history itself, would dictate the physical outcome. This directly violates C0's underlying requirement that observable distinctions must correspond strictly to physical realities rather than arbitrary human bookkeeping conventions. Therefore,  must be associative. Lemma B (Identity as Representation Artifact): Lemma B proves that the identity element belongs strictly to the representation system rather than the physics itself. The continuation algebra represents the sequential composition of states. Any logical composition system fundamentally requires a mechanism to denote an empty composition—a zero-length sequence. While a zero-length physical continuation is not an actual physical event (as C1 forbids zero-length stasis), it is the mathematically required neutral element for the algebra to function coherently. Therefore, every valid representation of physical continuation possesses a unital identity element. Lemma C (Commutativity of Scalar Weights): Lemma C restricts the claim of commutativity specifically to the scalar continuation algebra used for the weights of independent amplitudes. It acknowledges that general physical symmetry operators (such as spin rotations, Lorentz boosts, and gauge generators) are distinctly non-commutative. However, the underlying scalar algebra  that weights these amplitudes must commute to ensure that the combination of independent probabilities is not path-dependent at the scalar level. Lemma D (Methodological Dimensionality): Lemma D formulates dimensional minimality as an explicit methodological principle rather than a blind physical law, drawing directly on Methodological Principle M1 (Minimal Compilation). M1 states: "When multiple mathematical structures satisfy the primitive constraints, the compiled theory adopts the structure containing no unconstrained degrees of freedom". C5 (Symmetry breaking) physically forces the existence of at least two real degrees of freedom to prevent the collapse into a 1D fixed point. M1 dictates that the system compiles with exactly two real degrees of freedom, carrying zero unconstrained excess. The Algebraic Classification and the Elimination of Alternatives Under the primitives C0, C1, C2, and C5, paired with the M1 Minimal Compilation principle, the Admissible Scalar Continuation Algebra theorem asserts that the algebra  must be associative (Lemma A), unital (Lemma B), commutative (Lemma C), and strictly two-dimensional over  (Lemma D). By importing the standard mathematical classification theorem of two-dimensional real unital commutative associative algebras, there are exactly four structural possibilities available up to isomorphism. The framework evaluates each candidate and systematically eliminates all alternatives except the complex numbers () through direct, rigorous contradiction with the upstream physical primitives. Algebra Type Mathematical Structure Eliminated By Physical Reason for Execution Dual Numbers   C2 Possesses nilpotent elements (); violates the infinite descending chain logic and location inheritance. Split-Complex   C0 Contains nontrivial idempotents; breaks the absolute symmetry requirements of the isotropic ground state.  Space  (Direct product) C1 + C0 Possesses zero divisors. Annihilation of two lawful amplitudes creates a forbidden fixed point (detailed below). Complex Numbers   Survives Forms a true mathematical field lacking zero divisors or nilpotents; satisfies all dynamic constraints. The Rigorous Execution of The elimination of the  direct product algebra is the most vital step in the proof, as  is heavily utilized in standard real-vector space physics. In abstract algebra,  is not a valid mathematical field because it contains zero divisors—non-zero elements whose algebraic product equals zero. An explicit isomorphism links  to the split-complex numbers, matching non-trivial idempotents to demonstrate the presence of these zero divisors. Rather than discarding  purely by citing the abstract algebraic existence of zero divisors, the framework grounds the elimination directly in the physical interpretation of wave annihilation under Constraint 1 (C1). Consider the direct product space  with element-wise multiplication defined as . Let  and  be elements within this algebra. Both  and  are non-zero elements. Physically, this means they represent valid, non-zero, lawful continuation amplitudes. However, their mathematical composition yields:   Translated back into physical dynamics, this equation asserts that two lawful, independently continuable amplitudes compose together into a state of absolute termination (zero). However, C1 mandates that every lawful continuation must admit further lawful continuation; nothing in the physical universe may end in a configuration from which change is impossible. Because the direct product operation in  permits two valid, energetic states to mutually annihilate into a forbidden fixed point (the zero vector), it permits a computational dead-end. Therefore, it cannot represent an admissible scalar continuation algebra. Thus, , alongside the dual and split-complex numbers, is structurally executed by the C1 mandate. The complex field  emerges as the unique survivor, proving why quantum mechanics absolutely requires complex amplitudes. IV. Topological Laws: Conservation, Locality, and the Wave Equation Having secured the complex numbers as the substrate's operating algebra, the framework compresses its primitive set by formally compiling the topological laws of macroscopic physics from the base constraints. Law 3 (L3): The Conservation of Change Law 3 (L3) dictates the "Conservation of change," asserting that the net change across any closed topological boundary must identically equal zero. Every physical transformation introduced into the computational substrate strictly requires a displaced counter-transformation. The framework formally bridges this from a primitive constraint (C3) to a compiled consequence (L3) using the mathematics of continuous symmetries. Let  denote the continuous group of admissible continuation transformations. Let  represent an invariant quantity satisfying the symmetry condition . In the case of a physical collision or localized interaction between entities A and B, the equal exchange mandated by C3 () enforces that the total invariant quantity before and after the transformation remains constant :   The logical progression is unbroken: the isotropic nature of change (equal rules) geometrically forces transformation symmetry; transformation symmetry, via Noether's paradigm, guarantees the existence of a mathematical invariant; and this invariant manifests physically as a continuous conservation law. Because net change is conserved and inherently requires a displaced counter-transformation, any displaced physical pair propagating oppositely acts fundamentally as a topological wave. Law 4 (L4): Statistics Fixed by Parity Law 4 (L4) establishes that the statistical behavior of all physical states is strictly fixed by their topological parity. When physical states close back on themselves in the substrate, they exhibit specific parity constraints. Even-parity topological closures are permitted to smoothly share a degree of freedom, causing them to behave statistically as bosons. Conversely, odd-parity closures must cross the topological seam of the manifold. They are geometrically prohibited from sharing an identical state space, forcing them to behave as fermions subject to Pauli exclusion. This topological necessity ensures that exactly two primary particle species are forced to exist by the base geometry of the substrate, without requiring the ad hoc insertion of particle physics tables. The Mechanical Derivation of Locality and the Wave Equation Following the establishment of the scalar algebra and L3, the system forces the derivation of quantum field theory and the classical wave equation through three mechanical, logical steps. New Constraint (Location Placement): Because L3 dictates that conserved content exists and must be tracked, this content must possess a defined distribution across physical locations. It cannot exist free of the background geometry without violating C2's location inheritance. New Path (Strict Locality): The conserved computational content can only move between physically adjacent locations. If a non-adjacent transfer (a true non-local jump) occurred, it would flagrantly violate C2, which strictly requires that every intermediate spatial location—possessing the potential to hold content—must be traversed and accounted for in the state ledger. Therefore, the redistribution of change flows exclusively through local adjacency. New Computation (The Wave Equation): The universe now features a locally-redistributing conserved quantity operating over a symmetric geometry, constrained entirely by C3 (all change is equal, hence no spatial direction is preferred). Under these highly specific topological conditions, the unique free-field Lagrangian representing this dynamic is forced to take the exact shape of the canonical wave equation ( in the formal documentation), which governs all classical and quantum free-field propagation. The Dual Wave Formalism and the Inescapable Gap Velocity To explain how these topological wave structures propagate outward without resulting in a static, frozen universe, the architecture strictly employs a Dual Wave Formalism. The physical universe is not a static geometric entity, but rather a continuously moving, phase-localized oscillation operating fundamentally at the Planck frequency. The interface between what is successfully resolved by the computational substrate and what remains unresolved forms a moving, dynamic boundary, which corresponds mathematically to the C0/C1 Gap. This gap is located exactly where the absolute magnitudes of its two interactive components (conceptually termed "Answering" and "Asking" within the computational logic) are perfectly equal. Mathematically, this condition of equality is expressed in the phase domain as:   Assuming a standard linear variation of phase with respect to position, we define the phase function as . The physical trajectory of the gap boundary is tracked by taking the temporal derivative to find the point where the total phase change is zero:     Substituting the spatial derivative of the linear phase (), we arrive at the equation for the gap's physical translation:     This equation is of paramount ontological and physical importance. If this gap boundary were ever to stop moving (i.e., if the velocity ), the underlying mathematics would strictly require one of three catastrophic conditions to be met : , which corresponds to the absolute cessation of temporal progression (time stops). , which represents a complete structural collapse of spatial extent. , representing an undefined, infinite phase singularity. Because all three of these mathematical scenarios violently violate the foundational C1 mandate (that things must change and absolute fixed points cannot exist), the gap boundary is absolutely forced by the substrate geometry to oscillate continuously. This forced, inescapable oscillation guarantees Lyapunov stability across the entire universe, structurally preventing the computational lattice from ever collapsing into a static, terminal fixed state. V. Implications of the Recursive Harmonic Architecture The constraints, topological laws, and algebraic derivations detailed above coalesce into the comprehensive Recursive Harmonic Architecture (RHA). This framework achieves unification not by searching for a smaller physical particle, but by mapping physics, mathematics, and computation onto the same self-organizing computational substrate. The Harmonic Resonance Constant (H) At the core of the RHA is the assertion that this universal computational system continuously seeks a state of dynamic equilibrium defined by a universal Harmonic Resonance Constant, mathematically approximated as . Within this architecture, stability is achieved entirely through repeating, dynamic feedback cycles tuned to this specific harmonic ratio. The framework posits that fundamental physical constants (such as the fine-structure constant or the gravitational constant) are not arbitrary numeric values injected into the universe; rather, they are emergent properties of a massive cosmic feedback loop scaling infinitely across the dimensional folds of the substrate. This shifts the scientific epistemology from classical derivation to "proof in alignment". It suggests a holistic, pattern-recognition approach where complexity and unity are inherent properties arising exclusively from iterative, self-referential mathematical processes such as Kulik Recursive Reflection (KRR) and Phase-Conjugate Recursive Expansion (PRSEQ). Redefining Gravity, Randomness, and Computation The RHA models the universe as a "Cosmic FPGA" where the base physical lattice is termed the "Alpha Layer". This layer is the fundamental geometry—the grid of logic and memory itself, whose emergent macroscopic expression is observed as spacetime. Standard general relativity posits gravity as the curvature of a continuous spacetime manifold. The RHA fundamentally contextualizes this by describing gravity not as an independent, fundamental force acting over a distance, but as a direct manifestation of substrate fold curvature—a literal topological warping of the discrete computational grid caused by the presence of mass-energy. Mass-energy is redefined simply as a form of dense, highly folded informational logic within the lattice. This interpretation fundamentally redefines the concept of randomness. In classical paradigms, randomness is viewed as an inherent unpredictability central to quantum mechanics. In the RHA, randomness is reinterpreted strictly as a manifestation of "unresolved recursion". The universe processes physical information at such immense computational depth that localized, finite observer frames perceive the recursive depth as stochastic noise. In reality, the system is fully deterministic when viewed from the highest dimensional fold of the harmonic architecture. Furthermore, the principles of the RHA extend directly into cryptography and computer science. Standard cryptographic hashing algorithms like SHA-256 are re-contextualized not merely as human-engineered security tools, but as direct, parallel mathematical models of the universe's harmonic folding logic, which inherently records the thermodynamic history of state changes. The framework establishes a strict isomorphism between physical thermodynamic dissipation and computational information erasure. Just as C1 mandates change and C2 collapses possibility spaces, erasing information in any computational substrate fundamentally generates physical emanation. This mechanism links the precision loss in computational factorization directly to actual physical energy costs, proving that computation and physical thermodynamic search are governed by the exact same constraint ledger. Synthesis The comprehensive framework outlined by the Constraint of Change and the Recursive Harmonic Architecture presents a formidable, mathematically rigorous challenge to standard substance-based physical models. By completely replacing abstract axiomatic postulates with inviolable topological boundaries—specifically the absolute mandate of change (C1) and the prohibition of a static vacuum (C5)—the framework achieves an unparalleled level of theoretical compilation. It successfully replaces the magical, purely mathematical constraints of Solèr's theorem with the physically grounded T2 Architecture. It derives the absolute necessity of complex numbers () in quantum mechanics through the rigorous algebraic elimination of any system that permits fixed points via zero divisors (such as  and split-complex spaces). Furthermore, it mechanizes the derivation of the wave equation, proving that a locally-redistributing conserved quantity on a symmetric geometry, governed by the isotropic cost of change (C3), must uniquely result in continuous oscillatory wave dynamics to prevent the mathematical collapse of time and spatial extent. Ultimately, this ontological inversion maps continuous field physics, quantum mechanics, cryptography, and topological geometry onto a single, self-regulating computational lattice. By redefining reality not as a collection of static geometric nouns, but as a perpetual, recursively harmonic verb constrained by the fundamental mandate that all things must change, this architecture provides a radically unified, rigorously proven lens through which the fundamental mechanics of the universe must be understood.  

Compendium of R code and data for “Estimation of the Degree of Decomposition of Peat and Past Net Primary Production from Mid-Infrared Spectra” This repository contains the data and code …

Compendium of R code and data for “Estimation of the Degree of Decomposition of Peat and Past Net Primary Production from Mid-Infrared Spectra” This repository contains the data and code for our manuscript: Teickner, H., Arsenault, J., Gałka, M., Knorr, K.-H., 2025. Estimation of the degree of decomposition of peat and past net primary production from mid-infrared spectra. https://doi.org/10.5194/egusphere-2025-5819 How to cite Please cite this compendium as: Teickner, H., Arsenault, J., Galka, M., Knorr, K.-H., 2025. Compendium of R code and data for “Estimation of the Degree of Decomposition of Peat and Past Net Primary Production from Mid-Infrared Spectra.” https://doi.org/10.5281/ZENODO.17209547 How to use Instructions how to set up the Docker containers to reproduce the computations are available from the Dockerfile. The Dockerfile also provides instructions to run the targets workflow to reproduce all computations and eventually the manuscript and supporting information. Licenses Text and figures : CC-BY-4.0 Code : GPL-3 Data : CC-0 attribution requested in reuse. See the sources section for licenses for data derived from external sources, their licenses, and how to give credit to the original author(s) and the source. Sources Data in folder data/raw_data are derived from different sources. To use these data and give credit to data authors, please follow the following information: 📁 pmird: This is a template folder in which the folder pmird_prepared_data from the pmird database needs to be stored to reproduce the computations. This folder is available from https://doi.org/10.5281/zenodo.17092587. 📁 ecy2462-sup-0005-npp_moss.csv: This is one of the csv files contained in the Peatland Decomposition and Productivity Database (Bona et al. 2018). The reproduction is a copy of an official work that is published by Natural Resources Canada (NRCan) and has not been produced in affiliation with, or with the endorsement of, NRCan. Commercial reproduction and distribution are prohibited except with written permission from NRCan. For more information, contact NRCan at copyright.droitdauteur@nrcan-rncan.gc.ca. The full copyright statement is: © Her Majesty the Queen in Right of Canada, 2018. Information contained in this publication or product may be reproduced, in part or in whole, and by any means, for personal or public noncommercial purposes, without charge or further permission, unless otherwise specified. You are asked to exercise due diligence in ensuring the accuracy of the materials reproduced; indicate the complete title of the materials reproduced, and the name of the author organization; and indicate that the reproduction is a copy of an official work that is published by Natural Resources Canada (NRCan) and that the reproduction has not been produced in affiliation with, or with the endorsement of, NRCan. Commercial reproduction and distribution are prohibited except with written permission from NRCan. For more information, contact NRCan at copyright.droitdauteur@nrcan-rncan.gc.ca. See Bona et al. (2018) (https://esajournals.onlinelibrary.wiley.com/doi/full/10.1002/ecy.2462) for details. 📁 Bengtsson_etal_sph_holarctic_growth.csv: csv file from Bengtsson et al. (2020) (these data are described in more detail in Bengtsson et al. (2021)). License: CC-0. See http://datadryad.org/stash/dataset/doi:10.5061/dryad.1ns1rn8rm for details. 📁 d88_2.rds, d89_2.rds, d90_1.rds: These are average testate amoebae-reconstructed water table depth for the peat cores analyzed in our manuscript, digitized from figures in the original publications (Gałka, Diaconu, et al. 2022; Gałka, Hölzer, et al. 2022; Diaconu et al. 2020). License: CC-0 📁 pangaea_metadata_reuter2019.rds: rds file with the metadata from Reuter et al. (2019), extracted from the Pangaea repository using the pangaear R package (Chamberlain et al. 2025). License: CC-BY-4.0. For details, see https://doi.pangaea.de/10.1594/PANGAEA.902181. 📁 eb1064: Folder with preprocessed data from Arsenault et al. (2024a) (the contents of the folder were not directly derived from Arsenault et al. (2024a), but processed from the same original raw data files) and containing in addition the mid-infrared spectra for the samples in Arsenault et al. (2024a) (for an overview on the data, see Arsenault et al. (2024b)). Contributions We welcome contributions from everyone. Please note that the eb1149 project is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms. Funding This study was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) grant no. KN 929/23-1 to Klaus-Holger Knorr and grant no. PE 1632/18-1 to Edzer Pebesma. References Arsenault, Julien, Julie Talbot, Tim R. Moore, Klaus-Holger Knorr, Henning Teickner, and Jean-François Lapierre. 2024a. “Patterns and Drivers of Organic Matter Decomposition in Peatland Open-Water Pools.” Zenodo. https://doi.org/10.5281/ZENODO.10581235. ———. 2024b. “Patterns and Drivers of Organic Matter Decomposition in Peatland Open-Water Pools.” Biogeosciences 21 (15): 3491–3507. https://doi.org/10.5194/bg-21-3491-2024. Bengtsson, Fia, Håkan Rydin, Jennifer L. Baltzer, Luca Bragazza, Zhao-Jun Bu, Simon J. M. Caporn, Ellen Dorrepaal, et al. 2021. “Environmental Drivers of Sphagnum Growth in Peatlands Across the Holarctic Region.” Edited by Rien Aerts. Journal of Ecology 109 (1): 417–31. https://doi.org/10.1111/1365-2745.13499. Bengtsson, Fia, Håkan Rydin, Jennifer Baltzer, Luca Bragazza, Zhao-Jun Bu, Simon Caporn, Ellen Dorrepaal, et al. 2020. “Environmental Drivers of Sphagnum Growth in Peatlands Across the Holarctic Region.” Dryad. https://doi.org/10.5061/DRYAD.1NS1RN8RM. Bona, Kelly Ann, Arlene Hilger, Magdalena Burgess, Nicole Wozney, and Cindy Shaw. 2018. “A Peatland Productivity and Decomposition Parameter Database.” Ecology 99 (10): 2406–6. https://doi.org/10.1002/ecy.2462. Chamberlain, Scott, Kara Woo, Andrew MacDonald, Naupaka Zimmerman, and Gavin Simpson. 2025. pangaear: Client for the ’Pangaea’ Database. Manual. Diaconu, Andrei-Cosmin, Ioan Tanţău, Klaus-Holger Knorr, Werner Borken, Angelica Feurdean, Andrei Panait, and Mariusz Gałka. 2020. “A Multi-Proxy Analysis of Hydroclimate Trends in an Ombrotrophic Bog over the Last Millennium in the Eastern Carpathians of Romania.” Palaeogeography, Palaeoclimatology, Palaeoecology 538 (January): 109390. https://doi.org/10.1016/j.palaeo.2019.109390. Gałka, Mariusz, Andrei-Cosmin Diaconu, Angelica Feurdean, Julie Loisel, Henning Teickner, Tanja Broder, and Klaus-Holger Knorr. 2022. “Relations of Fire, Palaeohydrology, Vegetation Succession, and Carbon Accumulation, as Reconstructed from a Mountain Bog in the Harz Mountains (Germany) During the Last 6200 Years.” Geoderma 424 (October): 115991. https://doi.org/10.1016/j.geoderma.2022.115991. Gałka, Mariusz, Adam Hölzer, Angelica Feurdean, Julie Loisel, Henning Teickner, Andrei-Cosmin Diaconu, Marta Szal, Tanja Broder, and Klaus-Holger Knorr. 2022. “Insight into the Factors of Mountain Bog and Forest Development in the Schwarzwald Mts.: Implications for Ecological Restoration.” Ecological Indicators 140 (July): 109039. https://doi.org/10.1016/j.ecolind.2022.109039. Reuter, Hendrik, Julia Gensel, Marcus Elvert, and Dominik Zak. 2019. “FTIR, CuO Lignin, and Bulk Decomposition Data of a 75-Day Anoxic Phragmites Australis Litter Decomposition Experiment in Soil Substrates from Three Northeast German Wetlands.” PANGAEA. https://doi.org/10.1594/PANGAEA.902181.

This dataset contains surface electromyography (sEMG) recordings acquired during the execution of shoulder orthopaedic rehabilitation exercises by healthy subjects while moving a robotic manipulator. …

This dataset contains surface electromyography (sEMG) recordings acquired during the execution of shoulder orthopaedic rehabilitation exercises by healthy subjects while moving a robotic manipulator. Data were collected from 25 healthy participants aged 21–41 years. The exercises were provided by an expert physiotherapist and consisted of shoulder abduction, shoulder flexion, and scapular retraction – the latter also known as “row” or “rower.” During the exercises, subjects received an oral signal indicating when they had to simulate pain-related behaviours. Given that pain-induced abnormal muscle activation occurs during movement [1] and considering the consequent pain-related behaviours that patients usually adopt [2, 3], pain occurrences were simulated by replicating three typical behaviours observed during shoulder rehabilitation, which were agreed upon with the expert physiotherapist.  To the best of the author’s knowledge, the databases most used for automatic pain detection research contain biological data recorded under artificial pain induction, that is, pain elicited by an external source. However, during real orthopaedic rehabilitation sessions, pain is never voluntarily and externally induced. During movement, pain directly affects the muscles and consequently impacts motor capacity [1]. Abnormal muscle activity is the basis for metrics considered among the most objective tools for pain assessment, such as the nociceptive flexion reflex (NFR) [2], and is normally measured using sEMG signals. Therefore, only sEMG signals were collected. The aim of this dataset is to provide a simple yet efficient source for designing machine learning algorithms for pain detection. Moreover, to the best of the author’s knowledge, no currently publicly available dataset contains signals recorded during rehabilitation exercises performed using a robot. sEMG signals were acquired using a Trigno Centro system (Delsys Europe, Greater Manchester, UK) with four wireless, single-channel Avanti EMG sensors. The sensors were placed on the active shoulder of the participants and positioned over muscles commonly addressed during orthopaedic shoulder rehabilitation, as indicated by the expert physiotherapist: the anterior deltoid, rear deltoid, upper trapezius, and lower trapezius.

Anonymous reproducibility artifact for RegimeMamba, an end-to-end framework for probabilistic multi-asset return forecasting. The archive includes the paper-compatible selective state-space implementa…

Anonymous reproducibility artifact for RegimeMamba, an end-to-end framework for probabilistic multi-asset return forecasting. The archive includes the paper-compatible selective state-space implementation, differentiable discrete conditioning module, conditional diffusion decoder, training and evaluation code, controlled architecture ablations, matched Transformer and score-SDE baselines, traditional and univariate controls, conformal calibration procedures, cross-market evaluation scripts, configurations, tests, and lightweight CSV/JSON experimental evidence. Licensed market data and large model checkpoints are not redistributed; data reconstruction and checkpoint requirements are documented in the archive. All author-identifying information, local paths, submission metadata, and reviewer materials have been removed.

The study examines theoretical approaches to defining the economic essence of the concept of FinTech and clarifies its content. The key stages of FinTech development in Ukraine are systematized i…

The study examines theoretical approaches to defining the economic essence of the concept of FinTech and clarifies its content. The key stages of FinTech development in Ukraine are systematized in order to identify the prospects for further integration of innovations into the financial sector. The historical stages of the formation of the FinTech industry are identified, and the distinctive features of its integration into the global financial market are specified in the context of European integration trends. Regulatory approaches and the legal framework governing FinTech are examined, and their effectiveness in fostering market development is assessed. The impact of regulatory and legislative acts on the development of financial technologies is analysed, and an evaluation of their effectiveness is provided. A comprehensive set of measures aimed at improving RegTech development and enhancing the functioning of the National Bank of Ukraine’s regulatory platform is proposed.