This work presents a minimal structural framework for interpreting quantum discreteness and coherence as emergent properties of recursive ordering, rather than as primitive features of microscopic degrees of freedom. Motivated by recent experimental results demonstrating enhanced coherence under quasiperiodic (e.g., Fibonacci) driving, the paper explores how stability can arise from structured, non-repeating dynamical constraints imposed on system evolution. We introduce a conservative formalization in which discrete quantum states correspond to states that remain stable under recursive domain cycling (up to global phase), while incompatible modes fail to accumulate coherently and are naturally expelled toward boundaries. This perspective is expressed through three complementary layers: a minimal conceptual statement, an extended dynamical formulation compatible with standard quantum mechanics, and a purely algorithmic pseudocode representation suitable for simulation and toy-model exploration. The framework does not propose new physical primitives, nor does it replace existing quantum formalisms. Instead, it provides an interpretive and organizational lens through which familiar features—such as half-factors, coherence plateaus, boundary effects, and quasiperiodic stabilization—may be understood as signatures of relational and recursive structure. The presentation intentionally emphasizes clarity, restraint, and reproducibility, leaving room for independent rediscovery, reinterpretation, and future extension by others. This work builds on a year-long exploration of structured recursive geometry, toy models, and quasiperiodic dynamics, and is intended as a conceptual bridge between abstract stability principles and concrete quantum behavior.
This work presents a minimal structural framework for interpreting quantum discreteness and coherence as emergent properties of recursive ordering, rather than as primitive features of microscopic degrees of freedom. Motivated by recent experimental results demonstrating enhanced coherence under quasiperiodic (e.g., Fibonacci) driving, the paper explores how stability can arise from structured, non-repeating dynamical constraints imposed on system evolution. We introduce a conservative formalization in which discrete quantum states correspond to states that remain stable under recursive domain cycling (up to global phase), while incompatible modes fail to accumulate coherently and are naturally expelled toward boundaries. This perspective is expressed through three complementary layers: a minimal conceptual statement, an extended dynamical formulation compatible with standard quantum mechanics, and a purely algorithmic pseudocode representation suitable for simulation and toy-model exploration. The framework does not propose new physical primitives, nor does it replace existing quantum formalisms. Instead, it provides an interpretive and organizational lens through which familiar features—such as half-factors, coherence plateaus, boundary effects, and quasiperiodic stabilization—may be understood as signatures of relational and recursive structure. The presentation intentionally emphasizes clarity, restraint, and reproducibility, leaving room for independent rediscovery, reinterpretation, and future extension by others. This work builds on a year-long exploration of structured recursive geometry, toy models, and quasiperiodic dynamics, and is intended as a conceptual bridge between abstract stability principles and concrete quantum behavior.
Recent experimental demonstrations of quasiperiodic temporal control—most notably Fibonacci-driven pulse sequences—have revealed unexpectedly stable dynamical phases in quantum systems, including time-quasicrystalline behaviour and extended coherence lifetimes. This paper provides a theoretical interpretation of such phenomena within the ψ₀-OCM (Osborne Cosmological Model), where stability arises not from algorithmic error suppression but from boundary-conditioned stabilization of dynamical configurations. Within this framework, quasiperiodic driving is interpreted as a non-resonant constraint pattern that suppresses destabilizing modes by preventing phase closure across temporal boundaries. Temporal order emerges as a stabilised topological phase rather than a symmetry-broken state, with robustness governed by boundary compatibility rather than periodicity. The analysis reframes quasiperiodic control as a form of temporal boundary stabilization, offering a unifying explanation for time-quasicrystals, enhanced coherence, and dynamically protected phases without invoking exotic new matter. Implications are discussed for quantum control, non-equilibrium phases of matter, and the interpretation of time in non-algorithmic physical models.
(This version has been superceeded, see v.3) Contemporary approaches to physical unification typically emphasize dynamical laws, interpretive frameworks, or information-theoretic reconstructions. Less attention is given to the structural constraints that determine which physical descriptions can remain coherent and stable under interaction, scale transition, and aggregation. This paper develops a constraint-first analysis of coherence, arguing that persistence and unification require restrictions on admissible physical continuations that are not reducible to dynamics alone. Within the framework referred to here as Quantum Coherence Theory (QCT), coherence is treated not as a fragile quantum resource but as a structural property governed by interaction geometry and constraint density. On this view, classical behavior emerges when accumulated constraints sufficiently narrow admissible evolution, while quantum behavior re-emerges when constraints are relaxed. The account does not introduce new dynamics, collapse mechanisms, or modifications of quantum formalism, but instead clarifies the conditions under which existing formalisms yield stable, unified descriptions. The resulting constraints distinguish QCT from observer-centric, intrinsic-collapse, and purely descriptive decoherence accounts, while remaining compatible with globally unitary dynamics. Formal analysis in later sections develops operational redundancy conditions, admissibility constraints on joint states, and rigidity-style arguments linking redundant record structure to the stability of classical descriptions. These results do not constitute a complete theory of unification, but they narrow the space of physically admissible descriptions and clarify the structural role of coherence in bridging quantum and classical regimes.
This work presents an axiomatic and structural reconstruction of core elements of quantum mechanics. Starting from minimal principles — symmetry under vanishing preference, normalization, consistency of probability assignments, and coherence-preserving dynamics — we derive several central features of the quantum formalism rather than postulating them. Key results include: A geometric derivation of the constants 1/21/\sqrt{2}1/2 and 1/21/21/2 from symmetry and normalization. A theorem-level derivation of the Born rule (including the qubit case) from noncontextuality and additivity. A reconstruction of Schrödinger dynamics from reversible norm-preserving structure. A derivation of the tensor-product structure for composite systems from composition axioms and local tomography, with entanglement emerging as a necessary consequence. Formal treatment of Bell–CHSH nonlocality, Tsirelson’s bound, and no-signalling. A conditional reconstruction of complex Hilbert space structure from intrinsic phase dynamics and compositional consistency. The manuscript is self-contained and framed in standard mathematical-physics language. It does not propose modifications to quantum mechanics, but instead clarifies why many of its defining structures arise inevitably from deeper structural constraints. Prior computational and model-based work by the authors (including diagnostic toy models exploring phase locking, coherence stabilization, and recursive-time dynamics) is acknowledged but intentionally not reproduced here, in order to keep the present work focused on axiomatic structure rather than model-specific architecture. This upload is intended as a foundations and reconstruction contribution, suitable for readers interested in the mathematical and conceptual structure of quantum theory.
This work presents a unified generative framework for logic, computation, and physical theories, starting from a minimal recursive structure. Rather than assuming pre-existing logical axioms, computational primitives, or physical laws, the framework derives them as emergent features of a single generative process governed by stabilization and constraint propagation. Within this model, classical logic and computation arise as stabilized regimes of recursive structure, while quantum-mechanical phenomena are interpreted as pre-stabilization behavior—patterns that have not yet resolved into invariant records at the emergent spatial level. Superposition, interference, entanglement, and measurement are described structurally, without invoking parallel-world narratives or epistemic uncertainty. Measurement is treated as constraint coupling that forces refinement until a stable record forms. The framework emphasizes pattern persistence, invariance under refinement, and dynamic resolution as organizing principles. It provides a conceptual account of quantum behavior that is consistent with standard quantum mechanics while reframing it as a consequence of generative structure rather than an axiomatic starting point. This work is foundational and conceptual in nature. It does not propose new experimental predictions or modifications to established physical theory, but aims to clarify the structural relationship between computation, logic, and physics, and to offer a coherent ontological picture underlying these domains.Contact: arthur.nogman@gmail.com
This work presents a structural reformulation of quantum dynamics based on a scalar coherence functional defined over a general state space. The framework distinguishes two mathematically natural classes of dynamics generated by such a functional:(i) gradient flows, which monotonically increase coherence and correspond to stabilization or selection processes, and(ii) antisymmetric flows, which conserve coherence and generate reversible dynamics. We show that standard unitary quantum mechanics arises as a special case when the state space is a complex Hilbert space, the coherence functional is chosen as the negative energy expectation, and the antisymmetric structure corresponds to the canonical complex structure. In this setting, the Schrödinger equation follows directly from the formalism, without postulating unitarity as an independent axiom. The framework is extended to open systems using the density-operator formalism and completely positive trace-preserving maps. Under standard assumptions (Markovianity, continuity, and semigroup structure), the reduced dynamics takes the Gorini–Kossakowski–Sudarshan–Lindblad form, with dissipative terms interpreted as coherence-stabilizing dynamics. A supporting lemma demonstrates exponential suppression of off-diagonal density matrix elements under dephasing Lindblad operators. Using the Wigner phase-space representation, we further show that conservative coherence dynamics reduces to classical Liouville transport in the semiclassical regime, with quantum corrections governed by the Moyal bracket expansion. This work does not propose a modification of quantum theory. Rather, it offers a structural reorganization of existing formalisms. All results remain fully compatible with standard quantum mechanics while providing a unified perspective on unitary evolution, decoherence, and the emergence of classical behavior. Related work. A companion technical note, Structural Decomposition of SRG Recursion into Flow, Phase, and Closure (Halldórsson & ChatGPT, 2025, Zenodo), develops a discrete dynamical-systems formulation of SRG-style recursion and connects it explicitly to Lemmas 2.5, 2.7, and 2.9 of the present work.
This series presents a structured and logically sequential formulation of a discrete informational framework governed by global coherence constraints. Although it originates from the same research program developed in the earlier exploratory preprint series (P-series), the works presented here constitute an autonomous and self-contained series, organized in a progressively axiomatic form and focused on the explicit derivation of the framework’s effective structures. The goal of the construction is to investigate whether structures commonly associated with quantum mechanics, thermodynamics, and geometry may emerge from a discrete relational substrate without being introduced as fundamental postulates. Each article addresses a specific level of the theoretical derivation and forms part of a progressive logical structure based on results established in the preceding works of the series. This article develops the emergence of Hilbert-space structure and Schrödinger-type effective dynamics from the coherent two-field sector established in Paper 02. The work demonstrates that the global coherence constraints imposed on the discrete informational substrate naturally generate an effective complex representation endowed with linear superposition properties and unitary-preserving evolution. The analysis shows that the two-component coherent sector admits a mathematically stable reformulation equivalent to a Hilbert-space structure, and that the effective evolution of the coherent amplitudes leads to a Schrödinger-type dynamical equation without introducing quantum mechanics as an initial assumption. The article further derives the probabilistic interpretation associated with the effective amplitudes and clarifies how quantum-like statistical behavior emerges from the internal coherence conditions of the underlying discrete system. No quantum postulates are assumed at the foundational level. The purpose of the article is to demonstrate that the formal structures associated with quantum mechanics can emerge as effective consequences of coherence-preserving informational dynamics. The article does not assume quantum mechanics as a foundational theory and does not postulate the Hilbert-space formalism a priori. Instead, the work demonstrates that, within the internal hypotheses and coherence constraints of the proposed discrete informational framework, structures mathematically equivalent to Hilbert-space representations and Schrödinger-type evolution can arise as effective emergent descriptions. The purpose of the derivation is therefore not to reproduce standard quantum mechanics by assumption, but to show that quantum-like formal structures may consistently emerge from deeper coherence-preserving informational dynamics.