Here I collect theoretical work on mathematics, systems, and structural irreducibility.
The website is in German for context; the mathematical papers are usually in English (PDF/DOI).
In this overview, all scientific papers and preprints are listed by topic area. The titles match the Zenodo titles exactly, and the summaries capture the core content. For each entry, a Zenodo link to the original source is provided.
Mathematics & Computer Science
The Structural Impossibility of P = NP
Type: Paper · Language: EN · Status: Published · Year: 2026
Abstract:
This paper develops a structural re-evaluation of the P vs. NP problem based on irreducible fixed-point processes. It argues that a large class of NP problems should not be understood as search problems, but rather as emergent consistency events whose solutions do not pre-exist but arise exclusively as global fixed points. From this perspective, the classical identification of verifiability with constructibility is shown to rest on an ontologically incomplete assumption of existence.
On this basis, a new structural class is introduced: cNP (Constructive NP) — the class of irreducible fixed-point problems. This class comprises problems whose solutions possess no local precursors, no meaning-bearing intermediate states, and no approximable partial structures. For such problems, construction is fundamentally impossible, while verification remains possible.
The paper demonstrates that NP thereby splits structurally into two domains: reconstructive problems (NP-search) and emergent fixed-point problems (cNP). P, in turn, is characterized as the class of locally reconstructible systems. From this structural incompatibility it follows that local reconstruction processes (P) cannot simulate fixed-point emergence (cNP).
Accordingly, P ≠ NP does not emerge as an algorithmic conjecture, but as a structural necessity derived from the ontology of solution formation itself.
The analysis is further connected to the irreducible structure of prime numbers: primality is identified as a prototypical cNP phenomenon—verifiable, yet structurally non-reconstructible. This establishes a coherent framework unifying prime number theory, complexity theory, emergence, and algorithmic epistemology within a shared fixed-point model.
The paper positions itself as a contribution toward an ontological completion of complexity theory, in which computability is defined not primarily by runtime considerations, but by structural forms of existence, reconstruction, and emergence.
Why Prime Numbers Are Not a Mystery – Human Simplification, Multiplication, and the Emergence of Apparent Chaos
Type: Paper · Language: DE + EN · Status: Published · Year: 2025
Abstract:
This paper argues that prime numbers do not constitute an intrinsic mystery of the numerical world, but arise as a necessary structural consequence of additive growth combined with reconstructive order.
Rather than proposing new proofs or computational methods, the work provides a structural and epistemological clarification of why prime numbers have historically been perceived as chaotic or random. The analysis shows that this perception results from a conflation of generative and reconstructive levels.
By clearly distinguishing addition as a nature-grounded process of emergence from multiplication as a human practice of simplification and ordering, the classical “problem” of prime numbers becomes visible as a misclassification.
The paper positions itself as a conceptual and structural contribution to number theory.
Notes on related work:
The formal mathematical development of the underlying structure can be found in:
https://zenodo.org/records/17649211
An algorithmic and illustrative implementation is available at:
https://github.com/syntaris/primes4everybody
The Irreducible Structure of the Prime Distribution
Type: Paper · Language: EN · Status: Published · Year: 2025
Abstract:
This paper develops a constructive model of the number space in which prime numbers do not appear as properties of already given numbers, but as fixed points of a globally determined and irreducible growth process. Primality is not understood as a local, retrospective test property, but as a generative condition emerging from the entire previously formed multiplicative structure of the number space. Whether an additional additive step is realizable is thus determined below the number under consideration; the property “prime” logically precedes the number to which it refers.
From this perspective, central phenomena of analytic number theory no longer appear as statistical effects, but as consequences of global structural causality. Fixed points occur where the existing structure no longer permits further generability. Within this framework, phenomena such as the sign changes of π(x) − li(x), the Goldbach coupling of two fixed points, and the critical strip of the Riemann zeta function receive a natural structural interpretation. These relations are not formulated as classical proofs, but as structural necessities within the constructive number space.
Finally, the paper shows that any correct method of prime generation must exhibit the same global informational dependency. A corresponding algorithm is formulated as a resonance-guided fixed-point procedure, confirming the irreducibility of the prime distribution: prime numbers are not locally predictable, but can only be detected through the unfolding of the global structure.
The work positions itself as a contribution to a fundamental reconstruction of arithmetic, replacing the static attribution of properties with a generative perspective. While classical number theory describes the topological map of prime numbers, the model developed here investigates the structural foundation from which this map necessarily emerges.
Geometric Separation of Exponential Growth Spaces
Typ: Paper · Sprache: EN · Status: veröffentlicht · Jahr: 2025
Kurzbeschreibung:
Das Paper stellt einen neuartigen, intuitiven Zugang zu Fermats letztem Satz vor, der vollständig auf strukturellem Denken, geometrischer Anschauung und dem inhärenten Wachstumsverhalten exponentieller Funktionen beruht. Anstelle abstrakter moderner Beweistechniken wird gezeigt, dass die additive Inkompatibilität von Potenztermen in höheren Dimensionen zu einer natürlichen und unvermeidlichen Trennung des Lösungsraums führt.
Die Argumentation entwickelt sich aus drei komplementären Perspektiven: einer geometrischen Betrachtung räumlicher Inkompatibilität, einem strukturellen Modell auf Basis eines Wurzelnetzes exponentieller Beziehungen sowie einer wachstumsbasierten Logik, die den grundlegenden Widerspruch zwischen linearer Addition und exponentieller Ausdehnung herausarbeitet.
Ziel der Arbeit ist es, eine Beweismethode zu formulieren, die prinzipiell bereits mit den konzeptuellen Mitteln der Zeit Fermats denkbar gewesen wäre, dabei jedoch moderne strukturelle Klarheit besitzt. Das resultierende Rahmenwerk bestätigt nicht nur Fermats Behauptung, sondern legt zugleich tiefere Zusammenhänge zwischen Dimensionalität, Resonanz und dem arithmetischen Raum offen.
Structure of Numbers – A New Perspective on Order, Resonance and Emergence
Type: Paper · Language: EN · Status: Published · Year: 2025
Abstract:
This paper develops a fundamentally new perspective on the nature of numbers and explicitly questions the axiomatic foundations of classical mathematics. Instead of set-theoretic constructions or the Peano axioms, it proposes a dynamic, resonance-based approach grounded in structural emergence. Numbers are not treated as static objects or countable units, but as relational nodes within a living, evolving field of tension and differentiation.
Within this framework, prime numbers are not interpreted as irregular exceptions, but as necessary structural events—gaps within an unfolding resonance pattern. The work deliberately refrains from classical proofs and instead formulates a logically coherent interpretative model that understands mathematics not as a formal rule system, but as a refined perception of natural order.
Philosophical references, including Kant and Buber, serve to situate the approach epistemologically. The document is addressed to readers who are open to connecting mathematical structure with systemic and emergent modes of thought.
Formally Justified Proof of the Riemann Hypothesis via Structural Emergence in the Number Space
Type: Paper · Language: EN · Status: Published · Year: 2025
Abstract:
This preprint presents a formally grounded proof of the Riemann Hypothesis based on a structural approach to number theory. The Riemann zeta function is embedded within a two-layer model that connects complex analysis with emergent symmetries in the distribution of prime numbers.
Within this framework, it is shown why all non-trivial zeros of the zeta function necessarily lie on the critical line. The approach combines analytical rigor with structural emergence and does not present the result as an isolated technical achievement, but as part of a broader, independent research program investigating the systemic origins of number-theoretic phenomena.
A Structural-Theoretical Derivation of Goldbach’s Conjecture
Type: Paper · Language: EN · Status: Published · Year: 2025
Abstract:
This preprint develops a structural-theoretical derivation of the Goldbach Conjecture based on a novel model of prime numbers introduced in the earlier work “Prime Numbers as Structural Phenomena – A Two-Layer Model.” The approach is grounded in two fundamental axioms: emergent structural tension (P1) and code independence (P2).
On this basis, a coherent resonance space of structural primes is defined, whose additive superposition completely covers the entire space of even numbers. The Goldbach Conjecture thus no longer appears as an open question, but as a necessary consequence of the internal structure of the number space.
The proof deliberately refrains from classical analytical methods and instead follows from a deeper structural and resonance-based logic.
Prime Numbers as Structural Phenomena – A Two-Layer Model for Their Emergence and Detection
Type: Paper · Language: EN · Status: Published · Year: 2025
Abstract:
This paper presents a new structural theory of prime numbers and develops a two-layer model that explains the emergence and detection of primes from principles of structural independence. As foundational mechanisms, it introduces the concept of “light value” as structural freedom and “code freedom” as modular resonance.
Within this framework, prime numbers are interpreted as emergent phenomena that arise precisely where these two dimensions of freedom coincide. The theory reproduces all classical primes up to 100,000 with complete agreement, while simultaneously opening a new algorithmic and philosophical understanding of primality. The present preprint version documents the full conceptual and computational framework of this approach.
Systems & Economics
The Principle of Finite Order – Thermodynamics and the Limits of Economics
Type: Paper · Language: DE + EN · Status: Published · Year: 2025
Abstract:
This paper critiques the traditional description of economic systems as self-referential processes in which capital, labor, and technology operate independently. In contrast, it emphasizes that all economic activity ultimately rests on energy transformation and is therefore subject to the fundamental laws of thermodynamics.
On this basis, the paper develops a theoretical-analytical systems framework that describes economic stability as the result of coupled energy flows: between planetary regeneration, human labor and consciousness energy, and technological efficiency. Drawing on the principles of energy conservation and entropy increase, a formal model is formulated that captures these dynamics in four equations: a capital equation (order as a function of energy input and entropy loss), a human equation (regeneration and depletion of human energy), a cognitive equation (attention as a limited form of energy), and a technological equation (automation as transformer and decoupler).
The resulting system demonstrates that economic instability does not arise randomly, but is thermodynamically necessary when energy flows are consumed more rapidly than they can regenerate at the planetary, human, and cognitive levels. Overexploitation, burnout, information overload, and ecological erosion thus appear as different manifestations of the same entropic process.
From this perspective, economic sustainability is not a moral ideal but a physical condition: a system can endure only if it acknowledges the finitude of the world and understands the human being as an end in itself. The derived principle of finite order marks the fundamental boundary of economic expansion and simultaneously establishes the theoretical framework for an energetically integrated economy of balance.
The AI Consumption Spiral: An Underestimated Systemic Risk for Economy and Society
Type: Paper · Language: EN · Status: Published (Journal) · Year: 2024
Abstract:
This paper examines the hypothesis that the deployment of artificial intelligence may trigger a self-reinforcing consumption spiral that extends beyond previous waves of automation. The point of departure is the assumption that declining incomes weaken purchasing power, reduce demand, and prompt firms to respond to this demand shortfall with further automation. This dynamic may generate a downward spiral that threatens economic stability and social cohesion.
Methodologically, the study combines theoretical modeling with an extensive literature review and draws on official data from international organizations. The findings indicate declining real wages despite rising nominal wages, increasing income inequality, and diverging consumption patterns. Particularly problematic is the loss of purchasing power among lower-income households with a high propensity to consume, while higher-income groups with lower consumption tendencies benefit. As a result, the aggregate demand base of the economy erodes.
The socio-political analysis highlights that this development reinforces inequality, deepens societal polarization, and may impair the functioning of democratic institutions. Recent theoretical approaches emphasizing demand contraction and expectation dynamics confirm the risk of a self-stabilizing AI-driven consumption spiral. According to the analysis, classical instruments such as retraining programs or universal basic income are insufficient to break this cycle. The paper concludes by emphasizing the need for new political-economic strategies to safeguard purchasing power, stabilize expectations, and limit the risk of an AI-induced consumption spiral.
Irreversible Transitions – A Structural Model of Climate Tipping Cascades and Their Systemic Consequences
Type: Paper · Language: EN · Status: Published · Year: 2025
Abstract:
This paper develops a structural framework for analyzing climate tipping points, understood not as isolated events but as interconnected nodes within a system of potential cascading transitions. Rather than presenting a quantitative model, it outlines a qualitative architecture of systemic thresholds, mutual reinforcement, and irreversible shifts. Tipping points are conceptualized as elements of a dynamic resonance structure through which critical transitions can propagate across feedback networks—affecting climate, ecosystems, and socio-economic systems alike.
The aim of the work is not to introduce new empirical data, but to make visible the deeper systemic logic of fragility and nonlinearity within the Earth system. The approach addresses a central gap in current climate discourse: the absence of integrative conceptual models capable of explaining the structural vulnerability of complex systems under stress.
Furthermore, the paper examines the consequences of delayed intervention and demonstrates why classical mitigation strategies may prove insufficient if cascading dynamics and intertwined feedbacks are not adequately taken into account.
Note
For citation and access, I primarily link to DOI/Zenodo.