Physical Sciences

Abstract: We propose that the quantum vacuum is a dynamic superfluid that is dragged by the rotating Sun, forming a large-scale vortex. The Sun and the vortex constitute an open system in which total angular momentum is conserved. A single partial slip parameter, fixed solely from the anomalous precession of Mercury, determines the coupling between solar rotation and vacuum entrainment. Over the age of the Solar System, the Sun has progressively entrained outer vacuum layers. The effective circulation of the vortex therefore grows linearly with distance, producing a constant orbital velocity. This naturally yields a distance-independent inward acceleration in the outer Solar System, consistent with the Pioneer anomaly observed between twenty and seventy astronomical units, and, at larger scales, flat galactic rotation curves without invoking dark matter. The model connects, with no additional free parameters, Solar System tests of gravity to galactic dynamics and provides a falsifiable, unified origin for three phenomena that have been treated as separate for more than a century.

Abstract: We determine the minimal strong generators of the orthogonal invariant subalgebra of the chiral algebra of n free bosons. For every n ≥ 1, there is one generator in each even conformal weight from 2 to n² + 3n, resolving Linshaw's conjecture. The free-boson result also gives an independent derivation of the known generic minimal types of the corresponding affine orthogonal coset orbifolds. For n ≥ 2, we identify the Heisenberg orbifold as the simple quotient of the universal even-spin vertex algebra Wᵉᵛ(c, λ) at central charge n and parameter (3n + 2)/[7(n − 1)(5n + 22)]. A Cauchy determinant formula evaluates the diagonal scalar remainders in the decoupling recursion. For consecutive indices, an integral inverse formula makes the relevant trace factor positive. A 2-adic argument proves nonvanishing for every strictly increasing diagonal list and determines its valuation. We also obtain a formula for pairs of lists differing in one entry and an asymptotic expansion of the minimal remainders through the constant term, with error O(n⁻¹).

Abstract: This paper formulates an axiomatic spectral-geometric framework, called the Primacohedron, and proves a conditional theorem: if the Primacohedron axioms hold and the associated zeta spectral operator exists with the stated self-adjointness and spectral correspondenceproperties, then the Riemann Hypothesis follows. The argument is deliberately conditional. It does not claim an unconditional proof of the Riemann Hypothesis, which remains an open Millennium Prize Problem. Rather, it gives a precise Hilbert–Pólya-type route: a self-adjoint operator whose spectrum is exactly the set of imaginary parts of non-trivial zeros forces all corresponding zeros to lie on the critical line. The contribution is to organize the proposed Primacohedron framework into geometric, spectral, arithmetic, and analytic axioms, to derive the conditional Riemann Hypothesis theorem from these axioms, and to identify exactly what remains to be proved in order to convert the conditional implication into an unconditional proof. Connections with the explicit formula, random matrix statistics, quantum chaos, adeles, noncommutative geometry, and the Langlands program are discussed.

Abstract: We derive Lorentzian space-time on a finite holographic substrate: a finite, timeless totality whose capacity bounds the state count of every embedded observer. The observer is a prime shell \( Fp \), \( p=4k+1 \), embedded in the Carrier \( F_\Omega \) with \( p^2 < \Omega \), and its clock is the drive \( x\mapsto gx \) of its frame. Three cycles build the geometry: the additive register \( C_{p} \), the drive \( C_{p-1} \), and the norm-one group \( C_{p+1} \) of the temporal plane \( -g t^{2}+x^{2} \), anisotropic because a generator is a nonsquare. They close the frame moves to \( \mathrm{PGL}_2(Fp) \) and are its only cyclic symmetries. The register square of Hermitian matrices over \( K=Fp(\sqrt{g}) \) is the elliptic one of the two four-dimensional quadratic spaces over \( Fp \), the class the continuum reads as the signature \( (+++-) \). The stabiliser of the time vector is \( \mathrm{SL}_2(Fp) \), which fibres over the \( p(p-1) \) causal rays with fibre \( C_{p+1} \): the exact Hopf fibration. The arrow comes from the Carrier. The chart count of an embedded shell is one-directional, since a registered duration has at most \( p^2 < \Omega - 1 \) chronons, and it advances at one rate for every observer. The time reversal is not a Lorentz move. Time is the drive then follows as a theorem, and causal order between stations is the count read through the cone chart. The record of an embedded observer obeys the second law on every registrable duration, read through the realisation that entropy is the registration count. Every exact statement has a machine check in finite-field or cyclotomic arithmetic and a proof in Lean, the counting theorems in an axiom-free core; the continuum enters only as a labelled degenerate idealisation.

Abstract: The Topological Relational Field Theory (TRFT) series [1–3] previously elevated the finite observation window to a thermodynamic coordinate and, in TRFT III, proposed a candidate fourth law based on the time-conjugate field \( Φ \). In this paper, within the frameworks of standard quantum estimation and open-system theory, we perform a rigorous independent test and boundary delimitation of this candidate law, and complete three substantive developments of cross-scale significance. The core conclusions are fully testable independently of the framework (dual-track independence). First, we establish the precise domains of kinematics and thermodynamics. By introducing the Scaled Reference Point Relation (SRPR) and the quantum Cramér–Rao bound (CRB), we prove that in the macroscopic reality regime (\( r \) > 1), the CRB strictly takes over statistical precision, and the candidate law degenerates into a conditional constraint on bandwidth; whereas in the extremely short, few-body attosecond limit (\( r \) ≪ 1), the original law again becomes an absolutely tight upper bound, thereby precisely delimiting the valid territory of the law. Second, we reveal the "third class of irreversibility" of the arrow of time (the cosmic resource barrier). The derivation shows that the number of independent measurements required for reverse recovery of decoherence explodes exponentially as \( e^{2\varGamma t} \). Combined with the upper bound on baryonic matter in the observable universe, this gives a resource barrier \( Γt≈91.8 \). Even approaching the Bremermann limit, the barrier is delayed only logarithmically to about 139. This establishes an extremely hard physical limit based on the total capacity of the universe, opening a new paradigm independent of statistical probability and local energy consumption. Third, we reveal the microscopic origin of topological decoherence and the prerequisite for an engineering breakthrough. Within the SSH + Lindblad model, we rigorously prove that uniform environment coupling (\( P=I \)) locks the loss rate due to wavefunction normalization; only by "screening the edges and coupling solely to the bulk region" (\( P ≠ I \)) can the topological decoherence rate be exponentially suppressed by wavefunction overlap (\( {\varGamma }_{\mathrm{topo}}\propto e^{-cN} \)). This mechanism connects with the macroscopic barrier and establishes the core spatial-geometric prerequisite that must be satisfied for topological quantum device design in the NISQ era.

Abstract: The experimental test of the CHSH inequality confirms the quantum-mechanically predicted perfect correlations between spatially separated photons in single pairs. This paper considers two representative explanations of the correlations, Bell's theorem and Einstein's explanation. By explaining the correlations non-locally as the so-called entanglement, Bell's theorem denies the existence of definite polarizations possessed by photons in the absence of measurement. The denial amounts to refuting Einstein's argument for defending his local-realist world view in the Einstein-Bohr debate on the conceptual foundations of quantum mechanics. As shown in this paper, Bell's theorem is an erroneous explanation of the experimental results obtained by testing the CHSH inequality. It conceals the origin of the randomness exhibited in the experimental test. Einstein's explanation is based on his separability principle and his ensemble interpretation of ψ-functions. It is supported by a formal analysis. In contrast to Bell's erroneous explanation, Einstein's explanation reveals the deterministic nature of the correlations and explains the correlations reasonably.

Abstract: The Earth’s gravitational field undergoes systematic periodic modulation arising from interference between the Sun and Moon shadow cone zones. We present evidence for the Dx-Factor vortex— a previously unknown gravitational phenomenon with 29.53-day lunar synodic periodicity confirmed across six globally distributed superconducting gravimeter stations spanning 83° of latitude (60.2°N to 32.4°S). Analysis of 25+ years of IGETS Level 3 residual data yields 544 detected gravitational peaks across three primary validation stations on three continents. All three stations independently confirm the 29.53-day periodicity at extraordinary statistical confidence: Membach (50.6°N, Belgium) p ≈ 10⁻¹¹⁵; Medicina (44.5°N, Italy) p = 2.8×10⁻¹²⁴; Sutherland (32.4°S, South Africa) p = 3.0×10⁻⁶¹; combined p ≈ 10⁻³⁰⁰. The vortex arises from geometric interference between the Sun and Moon shadow cones, whose apices sit at Earth’s centre and whose bases expand across Earth’s surface. The gravitational anomaly is governed by: Δg(φ,Ψ) = A₀ × W(φ) × cos²(Ψ), where A₀ ≈ 300 nGal is the intrinsic amplitude, W(φ) is the dimensionless 1-minute measurement efficiency factor of IGETS instruments (not an intrinsic vortex property), and cos²(Ψ) is the cone-rim interference term (Ψ = lunar phase angle), producing equal peaks at New Moon and Full Moon (Ψ = 0° and 180°) and negative troughs at quadrature (Ψ = 90° and 270°). The vortex ring radius follows R(Ψ) = R₀ × sin(2Ψ) with R₀ ≈ 80°, reaching maximum size at Ψ = 45°. Epoch-folded analysis of 773 lunar cycles across four stations reveals that the ascending rim-crossing phase angle scales linearly with vortex core diameter at 0.56°/km (r² = 0.9985), confirming the ring expansion geometry. Metsahovi (60.2°N) exhibits a bimodal timing distribution with peaks at Ψ ≈ 24° (ascending) and Ψ ≈ 65° (descending), predicted by the ring model to within 0.6°. A universal gravitational energy diffusion coefficient K₀ = (2.816 ± 0.165) × 10⁷ m²/s is confirmed across all six stations to within 5.85%, with no station-specific fitting parameters. The Cibinong station (6.49°S, Indonesia) is predicted to show δg = 308.7 nGal as an immediate, falsifiable test from the existing IGETS archive. The discovery establishes: (1) the first observational evidence for gravitational shadow cone interference at Earth’s surface; (2) a complete predictive model explaining timing, amplitude, and sign at all six stations; (3) a new planetary habitability criterion — the Moon-Sun angular diameter ratio of 0.971 (within 3% of unity) is unique in the solar system; and (4) five falsifiable predictions for community validation, including single-event detection at equatorial stations using 1-second gravimeter data.

Abstract: Enhanced radiation during flares increases ionisation in the Earth's ionosphere, yet different ionospheric layers absorb different emissions because they differ in composition and plasma characteristics. To investigate the relative timings of the responses at different altitudes, we analyse 66 X-class flares from 2024–2025 using EUV and X-ray irradiance with simultaneous GNSS vertical total electron content (VTEC), very-low-frequency (VLF) phase measurements and magnetometer observations of the horizontal geomagnetic perturbation (\(\Delta B_{\mathrm{h}}\)). Response lags were measured by cross-correlating time derivatives and feature matching. Against the same EUV drivers, \(\Delta B_{\mathrm{h}}\) response lags by \(\approx\)13 s and VTEC by \(\approx\)33 s, consistent with slower electron loss in the F region than the E region. \(\Delta B_{\mathrm{h}}\) responses reproduce unique EUV and X-ray features, indicating the influence of both wavelength ranges on E-region ionisation. In the D region, VLF phase lags the X-ray rise by +51, +30 and +12 s relative to progressively softer channels, and phase maxima precede softer X-ray peaks, indicating that recombination begins to prevail over ionisation before flux reaches its maximum. These results, for the first time, empirically demonstrate the altitude difference in recombination rates of the ionosphere and the noticeable contribution of both EUV and X-ray emission to E-region dynamics during flares.

Abstract: Cold-atom experiments now control the exchange phase of strongly interacting one-dimensional gases and resolve the asymmetric momentum distribution of a driven impurity together with its relaxation after trap release. We introduce a finite-memory closure from Viscous Time Theory (VTT) for the preparation-history dependence of this observable. The prepared exchange phase remains the experimental control variable; a causal reduced coordinate follows it with a finite response time, and the mismatch between the two is the VTT state variable. Under an odd-response condition on the impurity momentum distribution, the momentum skewness acquires a linear, history-resolved correction. We test the closure in a microscopic reference model, a spinful Bose–Hubbard ring with exact time evolution, using protocols that end at the same exchange phase and differ only in their history. Interacting systems develop a history-dependent skewness that is small and oscillatory for slow preparation and of order one for fast preparation. An oscillatory generalization of the closure, calibrated on monotonic ramps alone and then frozen, predicts the held-out reversal protocols and reduces the mean-square error of the memoryless adiabatic baseline in the slow regime by 30 to 45% at fixed interaction strength and by 12% after averaging over a 20% spread of interaction strength. The response persists at a larger system size, where its frequency follows the lower level spacing of the system. The results define a quantitative experimental programme: calibrate on monotonic pulses, predict reversal pulses, and compare with a full microscopic baseline supplied with the same pulse history.

Abstract: The performance of photonic integrated circuits (PICs) is governed by the extent to which intrinsic material properties are realized in fabricated device geometries and in the associated optical, electrical, and thermal interfaces. This tutorial traces this materials-to-manufacturing translation from platform selection and electromagnetic design through layout generation, nanofabrication, metrology and characterization, and ultimately packaging. It analyzes how dimensional bias, sidewall and surface roughness, redeposition, thin-film stress, contamination, cladding choice, and facet preparation influence key figures of merit, including propagation loss, phase fidelity, coupling efficiency, modulation performance, and nonlinear frequency conversion. Established and emerging PIC platforms are compared in terms of functional capability, process limitations, and measurement context, with explicit separation of intrinsic material attributes from isolated device demonstrations and from evidence of manufacturability. Design and simulation workflows are linked to process variability, design-rule verification, and experimentally measured geometry. Fabrication pathways based on lithography and laser writing, including the integration of tuning elements, are discussed with emphasis on interdependencies among sequential process steps. Within-study attenuation contrasts and a residual-loss analysis are used to quantify how remaining loss channels constrain the net benefit of specific interventions. Case studies then apply these concepts to low-loss routing, electro-optic functionality, programmable photonic circuits, and thin-film ferroelectric poling. Collectively, the presented framework supports informed selection of compatible platforms and process flows, identification of diagnostically relevant measurements, and rigorous assessment of proposed improvements against circuit-level performance requirements.

Abstract: Prigogine's theory of dissipative structures explains how order appears far from equilibrium, but not what it means for such order to persist well. We distinguish passive dissipative systems, whose order is imposed by boundary conditions, from active ones, which defend an internal reference by spending free energy conditionally, reactively or predictively. We introduce Regulatory Solvency, the margin between harvestable free energy and the cost of regulation and of maintaining accumulated structure, with a reserve and a stochastic viability kernel restricted to affordable controls. On these we define health, for any substrate, as five conditions over a horizon (viability, solvency, autonomy, plasticity, calibration), graded by a Health Profile and distinct from capacity. We classify pathologies by mechanism and give a rule that identifies them from the profile and the budget. For one disturbance episode, the delay of a feedback loop sets a threshold that a stronger effector cannot move but prediction can, and in a minimal model anticipation is selected where it is cheaper than standing fast capacity. In that model, on perturbations run after the rule and evaluation code were frozen, which re-use known mechanisms at new magnitudes and are not a blind test, the rule named the induced cause in 87% of the runs it flagged (against 24% for always naming the most common cause), or 65% of all perturbed runs, and raised no alarm in 200 control runs, of which 14 nevertheless failed a survival-based challenge test; it did not detect a loss of sensing, which was not part of the test.

Abstract: Pickup acceleration, sprinting from a moving start, is common in team sports. Purpose: This study compared video-derived step-to-step kinematic changes between faster and slower athletes at walking (1.5 m/s) and jogging (3.0 m/s) entry velocities. Subjects: Twenty-eight male athletes (19.1 ± 5.1 years; 1.83 ± 0.07 m; 80.1 ± 16.6 kg) were classified as fast or slow by their maximum acceleration (amax). Methods: Two trials per entry velocity were completed, with kinematics measured via position encoder and 2D markerless video. Between-group differences were assessed using independent-samples t-tests (p < 0.05) and Hedges' g (Bonferroni corrected at p < 0.01). Results: At 1.5 m/s, faster athletes achieved greater amax (3.38 ± 0.18 vs. 2.99 ± 0.18 m/s²; p < 0.001, ES = 2.18), with shorter Transition step length (−7%; ES = -0.47), longer Pickup 1 anterior touchdown distance (~38%; ES = 0.68), longer flight time (~25%; ES = -0.46), higher step acceleration (~16%; ES = 0.50), and shorter Pickup 2 ground contact time (−20%; ES = -0.70). At 3.0 m/s, faster athletes ( amax = 2.56 ± 0.15 vs. 2.14 ± 0.16 m/s²; p < 0.001, ES = 2.74), were characterized by shorter anterior touchdown distance (−28%; ES = -1.03; p = 0.004–0.005), greater step acceleration (~22%; ES = 0.90; p = 0.004) across all steps, shorter ground contact time on Transition (−12%; ES = -0.56) and Pickup 1 (−5%; ES = -0.78), and smaller shin angle at touchdown (−10%; ES = -1.28; p = 0.01 to <0.001). Conclusion: Faster athletes exhibited distinct kinematic profiles; these findings enable a better understanding of the technical determinants of pickup acceleration, which may inform coaching strategies aimed at improving this ability.

Abstract: How does the loss of rotational energy shape the spin evolution of a neutron star? Combining conservation of angular momentum and energy with electromagnetic and gravitational-wave torques, we derive analytic models of the rotation period in terms of the magnetic field \( B_{p} \), radius \( R \), moment of inertia \( I \), inclination \( α \) and ellipticity \( ε \). For a force-free dipole, \( P^{2}=P_{0}^{2}+2{\pi }^{2}B_{p}^{2}R^{6}\left(1+\sin^{2}\alpha \right)t/\left(Ic^{3}\right) \). For any torque coefficient \( K\left(t\right) \) the braking index obeys \( n=n_{0}-2{\tau }_{c}\,dlnK/dt \), so field decay gives \( n=3+4{\tau }_{c}/{\tau }_{D} \) and a finite asymptotic period. Combined dipole and gravitational-wave braking is solved exactly; a measured n between 3 and 5 gives the torque ratio \( \eta =\left(n-3\right)/\left(5-n\right) \), and the lifetime gravitational-wave energy fraction is \( 1-\ln\left(1+{\eta }_{0}\right)/{\eta }_{0} \). The coupled spin–inclination evolution conserves \( Ωcosα \) in vacuum and \( \varOmega \cos^{2}\alpha /\sin\alpha \) in force-free magnetospheres, where alignment raises the braking index by at most 1/4. Applied to observed pulsars, the models give an initial period of 19 ms for the Crab and show that braking indices below 3 require torques that grow with time.

Abstract: The galaxy rotation-curve discrepancy is one of the most persistent empirical tensions in modern astrophysics. This study binds the tension to a prior question: does the discrepancy itself contain predictable information? Therefore, using 175 individual SPARC galaxy files containing 3,391 radial measurements, we calculate the direct signed discrepancy between the observed and baryonic contributions, retaining its positive and negative branches, and concentrate on the positive branch. A primary population of 166 galaxies (3,214 measurements) is represented by ΔV²(r)=B+Cr. The coefficients show substantial radial organization. The main empirical result is that measurable population information can be used to predict the known discrepancy in any galaxy (i.e., being excluded) using information that was not used to construct the population relationship (from that excluded galaxy). The analysis begins with the complete 175-galaxy SPARC dataset and proceeds in two tracks. The empirical track follows along: observation → baryonic contribution → signed discrepancy → radial structure → population prediction → blind reconstruction. The interpretive track then injects fundamental inquiry and asks what it means if the discrepancy contains organized information not explicitly represented in the observable baryonic description. The observations that encompass the dataset capture a deeply consistent and diverse range of galactic information. Nine structurally distinct systems, identified as anomalous by quantitative criteria and visual inspection, remain part of the observational dataset but are screened from the primary population representation; they are not treated as erroneous measurements, they are simply sequestered.The present paper explicitly separates empirical predictability from physical interpretation. The strict LOGO result is the primary benchmark, and the modified LOGO (grouped hold-out) analysis tests whether that result depends on the informational content of the blindly selected inquiry galaxies.

Abstract: We study a minimal active Brownian ratchet in which the internal motility state is resolved as a three–state Markov chain—forward run, non–propelled pause, and reverse run—with every reversal passing through the pause. Coupled to a three–-site, two–temperature ratchet potential, this construction yields an exactly solvable nine—state network in which the trichotomous drive is an internal degree of freedom carrying its own entropy production, rather than a prescribed external fluctuating force. Pause kinetics renormalize the bare propulsion \( v_{0} \) to the dwell–weighted drift \( v_{\mathrm{eff}}=v_{0}(\Pi_{+}-\Pi_{-}) \), which shifts the stall force and can reverse the current at fixed potential and fixed temperatures through residence times alone. At the exact stall force the dissipation remains positive and grows as \( c\,v_{0}^{2} \); we derive this scaling, decompose it into spatial and internal switching channels, and trace it to a general projected–current mechanism valid for any finite Markov network with a projected observable. In the fast–pause limit the model reduces to the two–orientation direct–flip theory with explicit swap rates, and the passive limit recovers the Carnot bounds for heat–engine and refrigerator operation.

Abstract: The rate at which quantum fluctuations of observables can change provides a useful characterization of the dynamical behavior of quantum systems. For closed quantum systems undergoing unitary evolution, previous work has established a general upper bound on the growth rate of the uncertainty of an observable in terms of the standard deviation of its dynamical velocity. This result is closely related to quantum acceleration limits and provides a compact constraint on fluctuation growth. In this work, we will briefly review the closed system results and extend this perspective to open quantum systems, where the state evolves nonunitarily as a consequence of interactions with an environment. The central result is an upper bound on the rate of growth of the uncertainty of an observable that remains valid for general density-matrix dynamics. We develop two complementary derivations. The first introduces a Hermitian pseudo-Hamiltonian describing the local unitary evolution of the eigenvectors of the density matrix. The second, and more general, derivation proceeds directly from the density-matrix derivative and therefore does not require knowledge of the generator of the dynamics. Both approaches lead to the same fluctuation-growth bound. An important practical advantage is that the bound can be evaluated from the observable, the state, and its time derivative without requiring reconstruction of the complete dynamical generator.

Abstract: Similar to electroweak interaction, strong force and electromagnetism can have similar Higgs mechanism mediated interaction. Thus, gluons can acquire mass. And, neural colored gluons have larger mass than colored gluons. Total, we can have eight gluons without red-anti-red gluon. The puzzle of proton or neutron mass can be solved. We can also derive a new SU(5) model to include all the above eight gluons, three W/Z bosons, photon, Higgs boson, three generations of leptons and quarks to make a new 5x5 SU(5) model. Wightman axioms can be fulfilled in this new SU(5) without causing proton decay crisis. !6f matter field construction is used to put all the particles. We can also add the 4x4 four dimensional spacetime tensor integrating mass-energy density, light pressure, electric fields, and magnetic fields as well as four gradients to make a new contravariant SO(10) model. Weyl tensor and Ricci tensor related to the new SO(10) model are also given. Both SO(10) generator matrix and 10x10 complete matrix are given. Thus, grand unified theory or theory of everything can be obtained, that is compatible with four dimensional spacetime without extra-dimension needed in string theories.

Abstract: Consciousness is proposed as a fundamental n-dimensional complex field which is intrinsically lossless, meaning it does not dissipate or lose information like physical systems do. This explains why subjective experience remains stable even when gravitational conditions change dramatically, such as for astronauts moving between Earth and Moon. Mind is defined as the interface between matter and consciousness. It has a physical origin in coherent electromagnetic fields in microtubules, as predicted by Fröhlich in 1968 who showed that biological systems under metabolic energy form Bose-like condensation of coherent vibrations, and by Popp since the 1970s who proved that living cells emit ultra-weak coherent biophotons originating from DNA. The mind part is measurable as terahertz coherence and biophoton emission, while pure consciousness itself remains non-measurable. This model inverts the Orch OR theory: microtubules are not generators but receivers of consciousness.

Abstract: Radiation synthesis differs from known methods in its high rate of energy input. Radiation energy is instantly introduced into the entire volume of the charge, which is 6 to 12 mm thick, depending on the electron energy. The introduced energy is used to create electronic excitations, the relaxation of which results in the formation of a new material, IAG: Ceramics made from Y₂O₃ and Al₂O₃ powders with a Ce₂O₃ activator. The overall ceramic formation process is independent of electron energy in the range of 1.4–2.5 MeV. The efficiency of radiation synthesis of IAG: Ceramics depends on the power density of the electron flux incident on the surface of the treated charge and the duration of radiation treatment. There is a clearly defined threshold for the power density of the electron flux above which synthesis occurs: that is, the density of the generated electronic excitations and radiolysis products upon decay must exceed the threshold values. The morphology of the synthesized ceramic is determined by the irradiation time. When the irradiation time of the feedstock is less than 1 s, the outer surface has time to solidify, resulting in a ceramic with large pores. When the irradiation time of the feedstock exceeds 5 s, the porosity of the resulting ceramic is much lower.

Abstract: We investigate how proposed algebraic relations for particle masses, mixing and gauge couplings can be tested through explicit dynamics. We synthesise nine studies of interacting generalised trace dynamics and its finite matrix extensions, motivated by bosonic exchange between fermionic currents. In a specified physical-current model, two neutral composite condensates appear at a common instability and the global minimum preserves electromagnetism. An exact trace isometry connects a spin-one matrix sector to exceptional Jordan invariants. Vacuum selection places nontrivial restrictions on spectral proposals: one canonical fermion determinant selects commuting equilateral configurations near onset, while a separate polynomial parent favours an associative orientation with a degenerate Jordan doublet rather than equal spacing. In a fixed-charge parent, conserved collective charges produce a calculable difference between relaxed static and closed-system slow spectral response. These results identify dynamical tests for proposed fermion mass relations and the additional physical projection, family frames, kinetic normalisations and matching data needed to obtain masses, mixing and gauge couplings. We also formulate tests of whether the interaction preserves the additive sector's conditional spectral framework at finite coupling. The specified four-dimensional matter representation passes local anomaly tests and, for the stated global group on spin manifolds, the fermionic global test; gauging its family symmetry requires additional dynamical input. The results are established within their declared models; measured fundamental constants and a complete common emergence of spacetime, matter and classical records have not been derived.