The Causal Quantum Spacetime Theory (CQST) treats spacetime as emergent from a discrete causal substrate, the quantum spacetime regenerating (QSR) lattice, assembling its geometric, holographic, quantum-foundational and phenomenological strands. The framework identifies the QSR lattice with Fuller’s Isotropic Vector Matrix and adopts holographic scaling together with the Bekenstein–Hawking one-quarter factor. The vacuum causal density, the squared ratio of the Planck length to the de Sitter radius fixed by Λ, is a constant of spacetime; its logarithmic relation to the fine-structure constant α is a one-parameter calibration predicting no drift. The reduced Planck constant is reinterpreted as the action of one causal tick. The empirical content lies in the photon sector: the discrete electromagnetic action on the face-centred cubic lattice is built over its twelve nearest-neighbour vectors and the propagator obtained within the Brillouin zone. The linear coefficient vanishes identically and helicity-odd birefringence is excluded by inversion. In the twelve-fold FCC formulation, the leading quadratic correction is subluminal in every direction, with isotropic part 1/20 in units of the squared nearest-neighbour separation and an octahedral modulation of 5/18. The quadratic sector lies far below current sensitivity; the first two predictions are exact falsification tests of the assumed lattice symmetries.
Synchronization in networks of conductance-based neurons depends on the external stimulus, coupling architecture, coupling strength, and initial state of the constituent cells. In this work, we numerically investigate a finite all-to-all network of identical Hodgkin–Huxley (HH) neurons coupled through a normalized diffusive membrane-voltage term. The purpose is not to introduce a new neuronal model but to provide a joint finite-time characterization of the membrane voltage and the three ionic gating variables during the development of collective activity. Synchronization is quantified from pairwise state differences using matrix norms, whereas the short-time Fourier transform (STFT) and continuous wavelet transform (CWT) representations are used to describe the time-localized spectral content of the simulated trajectories. For the investigated parameter values and initial conditions, the coupled network exhibits convergence toward a common resting state, a transient single-spike response, sustained oscillatory responses, and transient intervals of reduced coherence followed by more coordinated firing. Increasing the applied current changes the observed response regime and dominant spectral component. Within the finite simulation windows considered here, the frequency estimates obtained from both time–frequency methods also show a small decreasing trend with an increase in coupling strength. This trend is reported as a numerical observation rather than as a universal asymptotic property because its magnitude may depend on the observation window, initial conditions, network size, and frequency-estimation procedure. The results illustrate how voltage coupling affects both the convergence of neuronal trajectories and the finite-time spectral characteristics of the membrane and gating-variable responses.
This paper presents a hybrid search algorithm for Zermelo’s navigation problem in complex vector fields. The method combines local analytical navigation with A*-based graph search to compute high-quality trajectories in scenarios with multiple local optima. Its key idea is to use the optimal navigation law for uniform vector fields as a local propagation rule to generate new nodes. By defining multiple target points and linking them through locally optimal analytical trajectories, the algorithm encourages structured global exploration beyond purely local methods. The resulting framework integrates analytical local navigation with the robustness of heuristic search to integrate global exploration properties. It also adapts automatically to different spatial scales, making it suitable for both local and large-domain problems. Numerical validation under execution-time constraints demonstrates its effectiveness in time-limited settings, with experiments showing strong global exploration and high-quality trajectories under strict computational budgets.
This paper examines how different physical modelling frameworks represent structural change and asks when the organisation through which physical interactions occur should itself form part of the model state. The literature spans classical continuum mechanics and internal-variable theories, configurational mechanics, phase-field and cohesive fracture, enriched and unfitted methods, nonlocal and particle descriptions, quasicontinuum strategies, adaptive and higher-order networks, graph-based learning, and discrete differential and combinatorial formulations. These approaches provide different mechanisms for accommodating evolving geometry, interfaces, interactions, and topology and therefore reveal that the central issue cannot be reduced to a continuum-discrete distinction. The comparison is organised around the objects that carry physical quantities, the relations that determine admissible interactions, the transformations included in the state evolution, and the information about history retained after structural change. From this review, a relational synthesis is developed in which physical entities, their attributed relations, and the quantities carried by both may enter the state of an evolving system. Four concepts are introduced to make this synthesis operational: accumulative and reorganisational change, representational closure, structural memory, and representational transition. A minimal event-map formulation is proposed to identify the requirements for transferring physical quantities, constitutive information, and history when structural carriers change. Fatigue, environment-assisted degradation, transport, plasticity, and fracture are used as comparative tests of representational adequacy. The resulting framework does not prescribe a universal modelling formalism. It provides criteria for determining when structural information can be reduced to effective fields and internal variables, when explicit organisation becomes consequential, and how relational and continuum descriptions might be connected in a controlled manner.
The classical mass–spring–damper and inductor–capacitor–resistor analogy is extended from constant to state-dependent parameters and connected to an experimentally realized coupled Metglas AMCC-1000 resonant magnetic system. The formulation distinguishes externally varying inductance from intrinsic magnetic nonlinearity through secant and differential inductance and incorporates reversible, dissipative, and externally driven dynamics. The experimental study combines coupled-mode design with synchronized voltage and RF-current measurements. Measured component values establish a 32.016/16.461 kHz resonant pair with a frequency ratio of 1.9449, while calibrated RF-probe analysis quantifies the corresponding current components and broadband measurements reveal higher harmonic structure. A complementary 11–13 kHz controlled frequency sweep was performed at fixed 22 V, 388 mA supply conditions and 18% duty cycle. Coherent least-squares analysis identifies a common maximum of the second-order component at an 11.5 kHz drive frequency in two voltage channels and the RF-current channel, with A(2fd)/A(fd) ratios of 0.809, 0.870, and 3.665, respectively. The associated trigger-origin-invariant harmonic phase relation provides complementary phase-domain evidence of an organized frequency-selective nonlinear response. The results establish a reproducible connection between state-dependent oscillator theory, coupled-resonator design, and experimentally measurable harmonic dynamics.
