Physical Sciences

Abstract: We present the Lucron Model, a physical framework in which fundamental reality is a network of identical units called Lucrons. Each Lucron possesses intrinsic minimal properties---length, time, mass, charge, and action---that are the smallest non-zero values in every metric. The apparent absence of intrinsic properties at ordinary scales is an effect of scale, not a metaphysical absence. We show that a single-scale Lucron with scale \( \ell_L \) and coupling \( g_* \), together with the permutation symmetry \( S_3 \) of the bound-state ``candado,'' reproduces the following without fine-tuning: (i) the Planck scale, \( G = \ell_L^2 \); (ii) gauge unification with \( \alpha_{\rm GUT} = g_*^2/(4\pi) \approx 1/24 \); (iii) the Weinberg angle \( \sin^2\theta_W = 3/8 \) at the GUT scale; (iv) the electroweak hierarchy \( v/m_P = e^{-2\pi^2/g_*^2} \); (v) the electron hierarchy \( m_e/v = e^{-7/g_*^2} \); (vi) the Koide formula with \( \theta = 2/9 \) rad; (vii) the Cabibbo angle \( \sin\theta_C = \sqrt{m_d/m_s} \); (viii) the PMNS angles \( \theta_{23} \approx 45° \) and \( \theta_{13} \approx 8.5° \); (ix) the cosmological constant \( \Lambda \ell_P^2 = N^{-2/3} \approx 10^{-122} \) for \( N \sim 10^{183} \). We also identify where the model fails quantitatively: the CKM angle \( \theta_{23} \) (factor \( 1.4 \)), the CP phase \( \delta_{\rm CP} \) (factor \( 2.4 \)), and the PMNS angle \( \theta_{12} \) (factor \( 1.25 \)). These failures point to unresolved geometric details of the candado. We further show that the volume law \( V = v_0 \sum_i 1/c_i \) reproduces \( \Lambda \)CDM at the cosmological level, yielding \( \chi^2 = 12.8 \) against DESI DR2 BAO, identical to \( \Lambda \)CDM. With two fundamental parameters \( (\ell_L, g_*) \) and one symmetry (\( S_3 \)), the model accounts for approximately twenty dimensionless constants, a significant reduction over the Standard Model's nineteen free parameters.

Abstract: A lattice of locally coupled quantum oscillators is proposed as a candidate microscopic substrate for emergent spacetime. Each oscillator is treated as an elementary substrate unit (ESU): a minimal quantum degree of freedom whose local dynamics, correlations, and collective organization may underlie higher-level physical structure. For the minimal fixed cubic-lattice realization, the exact collective-mode dispersion relation is derived and shown to approach relativistic propagation at long wavelength, with limiting speed c_eff = a√(K/M). The leading lattice correction is anisotropic and quadratic in momentum, providing both a direct Lorentz-violation signature and an intrinsic ultraviolet cutoff. For a Planck-scale lattice spacing, the corresponding Lorentz-violation scale is E_LV ≈ ħc/ℓ_P ≈ 1.22×10^19 GeV, roughly eight orders of magnitude above the conservative quadratic-order lower bound inferred from GRB 090510 for the bosonic collective sector constructed here. Comparison with strings and matrix models, spin networks, causal sets, causal dynamical triangulations, and quantum graphity shows that the oscillator substrate trades background independence at this stage for calculability, explicit microscopic dynamics, and quantitative falsifiability. The framework further treats possible chains, loops, defects, networks, fields, and particles as structures to be generated—or excluded—by the substrate dynamics rather than inserted independently. Thus the model supplies a concrete first-stage substrate hypothesis and a dynamical selection principle. The calculation establishes kinematic continuum-like emergence on a fixed lattice; dynamical connectivity, a universal causal structure, a massless spin-2 gravitational sector with the required gauge structure, and viable chiral matter remain decisive tests of the broader hypothesis.

Abstract: Scalar magnetic descriptors are useful only when omitted information does not change the selected response beyond the required accuracy. We combine a literature audit with one-dimensional and three-dimensional tests. In an eight-material historical ledger, room-temperature labels coincide with magnetic-order eligibility, preventing identification of an additional descriptor effect. A published boundary benchmark resolves size dependence at fixed material descriptor. In a finite chiral-spin model with complete dipolar interactions, four near-matched-radius pairs at the same initial field and pairwise equal thickness have different field-step responses. First-order source-state susceptibility fails its declared twofold-improvement criterion. A disclosed second-order extension, derived from equilibrium response, is tested on eight new settings. Its root-mean-square radius error is 0.000259 lattice spacings, compared with 0.006649 for the best tested scalar normalization and 0.002221 for a multivariable baseline. Independent dipole calculations, stationarity refinement, contour checks and isolated prediction replay establish the numerical scope. The method requires the complete source configuration and Hamiltonian derivatives. The results demonstrate a target-specific audit and mechanistic restoration within declared finite geometries; they do not establish a low-cost material-only descriptor, calibrated lifetime or universal material optimum.

Abstract: This article presents the authors’ proposed theory on the formation of cavitation voids in the false vacuum during the inflationary phase of the Big Bang. It examines the structure of, and the physical processes occurring in, the transition region at the boundary between the false and physical vacuums. It has been demonstrated that, during the formation of physical vacuum voids (regions in which the Λ-term, a constant in the equations of general relativity, goes to zero), conditions arise in the transition region between the false vacuum and the physical vacuum that allow for the formation of a narrow layer of matter. This layer may be the precursor to the bridges observed in the large-scale lattice structure of the universe. The mechanism of bubble expansion during the inflationary phase of the universe is examined. It has been demonstrated that the inflationary phase of expansion passes into the standard Big Bang model due to the conversion of the false vacuum into matter at the boundaries of the bubbles. This model does not require the universe to undergo an extremely rapid expansion to explain the quasi-homogeneous and isotropic distribution of matter and the cosmic microwave background. Furthermore, it can account for the formation of the large-scale lattice structure of the universe. The estimated radii of cosmic voids are consistent with observational data.

Abstract: A recent similarity solution of the two-dimensional unsteady laminar boundary-layer equations [B. H. Sun, Phys. Fluids 36, 083616 (2024)], expressed in terms of Kummer functions, was proposed as the solution for a semi-infinite flat plate impulsively set into motion, but its boundary conditions cannot be satisfied at any finite time. We show that the solution is, in fact, a Burgers–Townsend strained shear layer superposed on the decaying, zero-pressure-gradient straining flow u = x/t, v = −y/t. For this class the nonlinear terms cancel identically, and the shear component obeys a linear equation that a Lundgren-type change of variables reduces to the heat equation; the Kummer functions are the fractional repeated-integral error functions i^2/3 erfc. The two forms of the published solution are copies of a single flat-wall solution related by Prandtl’s transposition theorem, and the flat-wall representative is an exact solution of the full Navier–Stokes equations, not merely of the boundary-layer equations. The correct physical setting is a sheet stretching at the decaying rate 1/(t + t₀), the S = −1 point of the Wang–Andersson family of unsteady stretching-sheet flows. Within this setting we solve three well-posed initial–boundary-value problems in closed form: (1) impulsive translation of the stretching sheet, whose wall shear stress crosses over from the Rayleigh law to −1.370 ρU_s√ν/t; (2) the decay of a pre-existing shear layer, governed by the exact invariant \( $s^3\!\int_0^\infty Y u'\ \)dY and (3) arbitrary wall histories, including power-law ramps with wall-shear factor √3 Γ(p + 1)/Γ(p + 1/2) and an oscillating sheet that relaxes to the classical Stokes layer. All three problems are two-dimensional – both velocity components are nonzero and the field depends on x – in contrast to Stokes’ first and second problems, which are one-dimensional and are recovered only as limits. The published Kummer solution is identified as the self-similar late-time attractor of problem (1). The unsteady Blasius problem for a finite plate remains open.

Abstract: Lithium filaments penetrate solid electrolytes by wedging open pre-existing flaws, and the field has consequently treated the problem as one of fracture mechanics: raise the toughness, close the crack, and penetration is delayed. Here we show that mechanical stress acts on filament growth through a second channel that has been overlooked, and that this channel is exponential rather than linear. Because ion migration in a solid requires a local dilation of the lattice, the ionic conductivity of every solid electrolyte depends on stress through an activation volume ΔV∗, a quantity measured to span 0.6–25 cm³ mol⁻¹ across sulfide and polymer conductors, and never measured at all for the oxide garnets. The stress field of a pressurised filament therefore reshapes the conductivity of the electrolyte that feeds it. Using coupled finite-element simulations of a sharp, Li-filled edge flaw we find that the sign of this feedback is set by the near-tip stress state, and that in an unstressed electrolyte it is adverse: the crack tip sits in tension, transport there is enhanced, and the supply of lithium to the tip rises by 12–22% at the activation volumes measured for sulfide argyrodites (0.58–1.08 cm³ mol⁻¹) and by a factor of 6.6 at the value measured for PEO–LiTFSI (25 cm³ mol⁻¹), even as the supply to the crack flanks falls. We derive a two-constant scaling law, σ ^tip_h = κ (p − λσr) with κ =3.00 and λ = 1.195, which locates a narrow but real operating window, σ_r < p < λσ_r, in which the flaw is open yet its tip remains compressed. Inside that window the feedback reverses sign, giving a predicted 3.6-fold gain in critical current density of which about half is fracture-mechanical in origin. Because the exponent scales with ΔV∗, the effect is a 10–35% correction for stiff inorganic conductors but the dominant term for polymer and polymer-in-ceramic electrolytes, where Γ ≈ 7at crack-tip stresses. The framework predicts that critical current density should correlate negatively with ΔV∗ in unstressed cells, and identifies a concrete architecture—a compressively prestressed gating skin—that converts a known linear benefit into an exponential one.

Abstract: Planck units are fundamental constants of physics. Time, mass, and gravitational force can be expressed in terms of Planck units. Planck time constitutes the fundamental unit of the numerical order of events unfolding in time-invariant space. There is neither a physical past nor a physical future. Time as duration is an emergent physical quantity that arises only in the process of measurement. Every physical object is an energetic structure of space itself. Gravity is mediated by variations in the energy density of space.

Abstract: Regional WRF-Chem dust simulations may require continuous integrations when state continuity is scientifically important, yet extended limited-area runs can depart dynamically from the driving analysis. We use a two-tier controlled design that separates dynamical attribution from aerosol transport response: a continuous chemistry-free FREE-FDDA pair spanning 104 days (15 March-27 June 2024) isolates the meteorological response to spectral nudging of the horizontal wind, and paired event-scale WRF-Chem simulations of two Saharan outbreaks test whether that response propagates into dust prediction skill. The meteorological response is variable-selective and strongly non-monotonic. Sea-level pressure improves most (mean daily RMSE 2.08 to 1.53 hPa) as an indirect response of the mass field, 10 m wind speed improves coherently but less (2.50 to 2.20 m s-1), and 2 m temperature does not improve (2.05 to 2.15 °C); the benefit recurs episodically as synoptic regimes evolve rather than following a universal lead-time threshold. Aerosol transport, evaluated against AERONET Version 3 Level 2.0 AOD550 with Level 1.0 as a coverage-sensitivity check, is conditional. In the weakly forced June case all seven sites improve simultaneously in RMSE, correlation and variability amplitude (station-mean RMSE 0.457 to 0.235; correlation 0.778 to 0.881). In March, RMSE decreases at all eight sites but mean correlation is unchanged, indicating amplitude correction without uniform improvement of plume timing. Spectral nudging therefore acts as a process-targeted constraint on circulation and transport consistency whose aerosol benefit is greatest when transport error dominates; it does not replace constraints on dust emission, optical properties or removal.

Abstract: Physical--observation dual-axis (PODA) Theory holds that physical reality is realized jointly through physical state and observation state. A change of observation state can therefore change the realized physical fact even when the physical state is held fixed. We develop the phase law of this PODA structure. A coherent readout of the joint observation law gives a smooth scalar complex response \( g \). Wherever this response is nonzero, differentiating its polar decomposition gives the observed phase rate and the one-form \( A_g=\operatorname{Im}(\mathrm d g/g) \). A transported phase with the same increments differs from the observed phase by a constant reference factor. We derive its differential equation and unique initial-value solution, and show that the equation is horizontal lifting for the unique response-compatible connection on the trivial principal \( \mathrm U(1) \) phase bundle. We call the resulting equation \( \widetilde c^{\,*}\Omega_g=0 \), the Phase Transport Fundamental Equation (PTFE), the first fundamental equation of observation space in PODA Theory. Its group-valued, covariant-derivative and continuous real-phase forms express one transport law: a path and an initial phase determine a unique horizontal lift. Integration gives finite phase comparison, composition along successive paths, and inverse transport between two observation states of the same physical source. Positive amplitude rescaling leaves the law unchanged; synchronized changes of response and fiber coordinates preserve its covariant form. The induced connection is flat and has trivial circular holonomy, although a continuously unwrapped phase may wind. We distinguish the full response \( \mathsf G_0, \) the phase-transport structure \( \mathsf G_1 \), and the task quotient \( \mathsf G_2 \). At the last level, maximal invariants describe the quotient, and a target can be recovered exactly when it is constant on each fiber of the quotient observation. Phase transport and the information retained after a task reduction thus follow from the same joint observation law.

Abstract: This paper formulates a thermodynamically consistent finite-strain Maxwell-Glen model for glaciological applications in a Lagrangian setting. A multiplicative decomposition of the deformation gradient separates the elastic and viscous mappings, while a trace-free material velocity gradient describes isochoric creep. The elastic state is represented by a logarithmic strain, and its associated material stress drives a temperature-dependent Glen law. Under the isotropic constitutive assumptions, commutation reduces the multiplicative metric update to an additive elastic-viscous corrector. The exponential map is evaluated by a Cayley-Hamilton reduction for generally nonsymmetric arguments, and a consistent linearisation supplies the material tangent. Homogeneous simple shear verifies agreement with spatial Glen flow under non-coaxial deformation. A self-weighted plane-strain column confirms preservation of the incremental viscous Jacobian to the solver tolerance. For a floating shelf, depth-dependent viscous resistance reverses the shelf-edge bending relative to uniform viscosity.

Abstract: We propose a fast mapped spectral method for a class of variable-order fractional partial differential equations posed on the real line. The main difficulty arises from the spatially dependent fractional order of the operator, which prevents the direct diagonalisation techniques available for constant-order fractional Laplacians and leads, in general, to expensive nonlocal discretisations. To overcome this limitation, we introduce an operator-interpolation strategy in which the variable-order fractional Laplacian is approximated by a finite combination of constant-order fractional operators evaluated at suitably chosen interpolation nodes in the fractional-order variable. Each constant-order contribution is treated through a Fourier-like mapped Chebyshev representation on R, allowing the corresponding nonlocal operator to be evaluated efficiently in spectral space. Chebyshev interpolation with respect to the fractional order is employed to obtain an accurate approximation over a prescribed interval s(x) ∈ [s_min, s_max]. This construction separates the difficulties associated with spatial unboundedness and variable nonlocality, and leads to an implementation whose cost is governed by a small number of fast constant-order operator evaluations. The spatial discretisation is combined with a pseudospectral treatment of nonlinear terms, avoiding the explicit construction of dense high-order interaction tensors. Approximation properties are analysed by separating the error due to interpolation in the fractional order from the mapped spectral discretisation error in space. The proposed approach is first validated on variable-order fractional problems with prescribed or manufactured solutions. It is then applied to stationary variable-order fractional Allen–Cahn equations in heterogeneous media, with particular attention to the influence of spatial variations of the fractional order on interface profiles, asymmetry, and far-field decay. Numerical experiments are designed to assess accuracy, convergence, computational complexity, and robustness with respect to both the spectral resolution and the variation of the fractional order.

Abstract: The Spiral Structure Model (SSM) is a phenomenological model in Bohr’s tradition: restricted to kinematics and geometry, it trades dynamical depth for ontological clarity and experimental exposure. Three postulates suffice: (I) the photon is a pointlike energy quantum in uniform helical motion, axial and circulation speeds both equal to c; (II) physical space is an elastic, relativistically covariant medium sustaining vortex excitations; (III) the electron is a stable topological vortex defect of that medium. These yield, every step labeled: the photon’s circulation angular momentum mcr_γ = ℏ as a consistency theorem identified with its spin; logarithmic vortex confinement with zero free parameters; the two polarization states and no longitudinal mode; orbital angular momentum as an ensemble property; the electron’s 720-degree periodicity and spin ℏ/2 from π1(SO(3)) = Z₂; the fine-structure constant as a ratio of structural scales; the free radiation field as an ensemble statistical moment; a phase-coupling account of two-slit interference; and a double-helix ontology of entangled pairs reproducing the CHSH value 2√2. Three falsifiable discriminants are stated with kill criteria: a wavelength-locked on-axis detection void, a spin-dependent electron form-factor window near Q = mc, and a circulation-periodic component in entangled-pair coincidence timing.

Abstract: Most post-model analyses begin with a named target: a waveform error, detector artifact, unmodeled transient, or parameterized departure from an established model. RIUD Paper I asks an earlier question: can recurrent merger-local structure be converted into a stable scientific object before its physical identity is known? The audited Paper-I development record comprises 612 preserved executions spanning successful, negative, unresolved, and technical branches. Development began with fixed physical phase-deformation models and reversed direction after those models failed to yield a stable population result. A residual-first reference in GW190521_074359 produced a two-stage merger-local morphology that survived synthetic-null, real off-source, waveform, posterior, and intrinsic-parameter-refit attacks, while a competing ringdown representation prevented the original basis from being treated as unique. The search was then generalized from fixed coordinates to an event-native family over local time, frequency, temporal width, inter-detector lag, and detector relation. In locked matched-background development tests, GW190521_074359, GW150914, and GW170104 each produced 0/1000 exceedances (p+1 = 0.000999); GW170814 entered as a non-blind catalog extension and also produced 0/1000 under its fixed-candidate validation. A later rigid temporal interpretation failed, separating the observational morphology from a stronger temporal story. The observation/scoring machinery itself was then audited. In a 227-row morphology/scorer audit, metadata-only leave-one-out classification reached 0.404, width-only classification reached 0.762, and frequency-width association gave Cramér’s V = 0.752, while direct mass dependence was negligible. Physical-sign posterior subtraction removed or weakened a stronger interpretation in 79/150 samples, whereas wrong-sign controls removed 0/12. An attractive 310.4-Hz branch failed an independent raw-FFT placebo in 3/3 target events and was discarded. The mature event-native score was deployed across a frozen 374-event native-strain universe, explicitly as a deployment census rather than 374 detections; the frozen score distribution comprised 31 FAIL, 162 PASS, 150 STRONG, and 31 VERY STRONG events. A later audit retained 374/374 finite scores, 343 H1/L1-ready events, 327 QC-valid events, and 300 prospective-eligible events after excluding 27 outcome-seen cases; the selection score was not retuned. Subsequent physical-identity tests rejected or bounded simple ppE-like, single-wavepacket, rigid common-center, and universal fixed-GR interpretations. A 29-event held-out cross-detector audit supported detector-related coordinate localization, but a conservative matched-SNR waveform-mismatch bank remained statistically compatible with the observed residual distribution. The surviving result is therefore deliberately bounded: RIUD Paper I establishes a recurrent event-native merger-local morphology as an auditable observational object, while leaving its unique physical cause unresolved.

Abstract: Local branch selection—a frame-independent postulate under which environmental decoherence einselects a branch structure and a local stochastic process realizes one branch with Born probability—has so far been implemented with continuous spontaneous localization (CSL), whose noise is phenomenological. Here we determine which physical noises can play this role. First we prove a kernel-universality theorem: for any set of commuting Hermitian collapse operators driven by Gaussian noises with an arbitrary positive-semidefinite correlation kernel \( C \), the einselected branch weights are exact martingales, so absorption occurs with Born probability for every kernel; the kernel controls only the selection rate \( \Gamma=\Delta^{T}C\,\Delta \), where \( \Delta \) is the vector of branch eigenvalue differences. For the Diósi–Penrose (DP) kernel \( G/\hbar|\mathbf{x}-\mathbf{x}'| \) acting on mass densities, the rate is \( \Gamma=2EG/\hbar \), with \( EG \) the gravitational self-energy of the branch mass-density difference: Penrose's collapse criterion emerges as the nondegeneracy condition of the Born martingale, and gravitationally induced collapse becomes a parameter-free physical implementation of the selection postulate, with \( \tau_{\rm sel}\sim3\times10^{-16}\, \)s for a milligram pointer. Second, we prove a no-selection theorem: noise coupled as a random Hamiltonian (classical stochastic spacetime fluctuations included) leaves every branch weight exactly constant along every realization while dephasing the ensemble—decoherence without selection—so classical metric-fluctuation dephasing cannot implement the postulate; selection requires measurement-type (norm-changing) noise. Third, for the symmetric EPR configuration we show that gravitational noise cross-correlation between the wings preserves no-signaling exactly (the cross terms of the correlated-kernel Lindblad dissipator vanish under the local partial trace), shifts only the selection rate, and is of relative size \( \sim R\,\delta^{2}/L^{3}\approx4\times10^{-9} \) at one-meter separation; a common-mode stall at perfect correlation is exhibited and verified numerically. Stochastic simulations confirm Born statistics across kernels to sampling precision, machine-zero weight drift for random-unitary noise, and the rate law across the full correlation range. The results upgrade the selection postulate from “CSL-compatible” to “gravitationally implementable,” identify exactly which proposed mechanisms can and cannot supply its randomness, and inherit the active experimental program constraining the DP model.

Abstract: We separate two questions. (Q1, empirical) Do the pole masses satisfy the Koide relation in the polar form \(\sqrt{m_i}=\mu(1+\sqrt2\cos(\varphi_0+2\pi i/3))\) with \(\varphi_0=2\pi/3+2/9\)? No: the same-scheme comparison of \(m_\mu/m_e\) gives 206.77032 vs. 206.7682830(44), i.e. \(\approx460\sigma\), with no theoretical error. (Q2, fundamental) Can a UV theory derive it? The obstruction is scheme dependence and it is large: the common-scale MS ratios differ from the pole ratios by 2.1% (\(m_\mu/m_e\)) and 3.2% (\(m_\tau/m_e\)), moving Q by \( +1.26\times10^{-3}=185\sigma \) and \( \varphi_0 \) by \( -1.19\times10^{-3} \) rad. As the charged-lepton mass anomalous dimension is flavour-universal, there is no continuous scheme dial: only the pole point and the (common-scale) MS point. Hence any UV derivation must explain why the relation holds for pole masses, and no exact \(\varphi_0\) claim is scheme-invariant (\(\Delta\varphi_0=6800\times|\varphi^*-2/9|\)). We also prove an unconditional theorem: for any rational mass triplet, the fitted phase \(\varphi^*\) is a transcendental number of radians — so \(\varphi^*=2/9\), \(1/3\), \(\sqrt2/9\), or any nonzero algebraic radian, is exactly excluded, independently of errors and schemes. Finally the conditional pole-scheme prediction \(m_\tau=1776.969\) MeV (\( 0.85\sigma \)).

Abstract: Molecular shape is routinely explained through bonding language: bonds impose angles, lone pairs repel ligands, steric contacts force torsion, orbital interactions favor conformations, and energy-decomposition components stabilize structures. These useful explanations can reverse the order of the underlying theory. In the full molecular Coulomb problem, a fixed geometry is not an intrinsic label of a stationary eigenstate. Standard quantum chemistry uses clamped-nuclei/Born-Oppenheimer approximation whereby a nuclear configuration, number of electrons, and any additional externally applied potentials, define the electronic Hamiltonian. The quantum state then yields energy and bonding descriptors at each geometry. Repeated calculations at different geometries generate the potential-energy landscape whose stationary structures are identified. We examine VSEPR, steric and Pauli repulsion, biphenyl and cis-2-butene, EDA auxiliary states and path/reference dependence, NCI, orbital representation dependence, QTAIM/IQA, localization-delocalization matrices, stable/metastable metals, nuclear transmutation, and the one-electron Bohm quantum potential. We also separate practical Born-Oppenheimer chemistry from the unresolved full-Coulomb structure problem. Stronger causal claims begin with an independent perturbation of the Hamiltonian, followed by responses of geometry, energy, density, and descriptors. Molecular shape is, therefore, a stationary-state or ensemble property, while bonding descriptors provide higher-level explanations rather than independent microscopic agents. This raises a deeper question: why does quantum matter generate robust, transferable chemical regularities, including recurring hydrogen-bonding patterns?

Abstract: We compute the complete relative entropy of a faithful quantum family controlled by spatial translations and Lorentz boosts. The prescribed contrast has a minimal three-dimensional positive Hessian realisation. Finite comparisons determine every minimal single-chart embedding up to an affine transformation and fix the potential's first jet, leaving its normal Hessian free. No positive single-chart realisation on a globally convex domain exists in any finite dimension for the entire control plane, whereas every bounded rapidity strip admits one. An exact dephasing channel preserves the energy-momentum law while reducing the contrast to classical rapidity distinguishability. Calibrating a preparation Hamiltonian gives sharp work-susceptibility and finite-work control-area bounds. Within the specified four-parameter preparation family, intrinsic Bogoliubov-Kubo-Mori (BKM) length bounds entropy change; paths outside that family need not obey this bound, even at the same observable law. A genuine Born lift preserves the commutator form with an exact area remainder independent of normal-potential freedom. These results separate finite-contrast rigidity, calibrated energy response, and geometric compatibility without identifying statistical transport with physical dynamics.

Abstract: The Kraichnan model provides one of the clearest solvable settings for passive-scalar transport in turbulence, but its standard formulations often presuppose familiarity with stochastic-process and field-theoretic methods. Here we develop the model from the passive-scalar advection--diffusion equation upward, emphasizing its physical content while introducing the required formalism as it becomes necessary. Instead of using the full Navier--Stokes velocity, with nonlinear dynamics and multi-scale statistics not known in closed form, the model prescribes the advecting velocity as a Gaussian random field that is white in time, correlated in space, and allowed to have a rough spatial increment covariance. It is therefore not a literal model of Navier--Stokes turbulence, but a controlled idealization designed to isolate scalar transport by a rough random flow. The central simplification is that Gaussianity and temporal delta-correlation allow mixed velocity--scalar averages to be eliminated exactly, producing a closed hierarchy for equal-time scalar correlation functions. The two-point equation becomes a diffusion equation in separation space, with molecular diffusion supplemented by a scale-dependent turbulent diffusivity determined by the velocity-increment covariance. This gives a direct route to Richardson-type dispersion, the scalar variance cascade, the dissipative anomaly, and the inertial-range scaling of the second-order scalar structure function, F²(r) = ⟨[c(x + r) − c(x)]²⟩ ∼ r^2−ξ . Higher-order equations show how a Gaussian advecting velocity can nevertheless generate non-Gaussian scalar statistics, intermittency, and anomalous scaling through zero modes and statistical conservation laws of multi-particle configurations. We also discuss the Lagrangian particle interpretation, smooth versus rough stochastic flows, slow modes and particle-cluster geometry, compressible and anisotropic extensions, and the relation to renormalization-group and operator-product-expansion descriptions. The emphasis throughout is on the physical meaning of closure, roughness, stochastic particle motion, scalar diffusion, and the connection between Kraichnan-type advection and high-Schmidt-number liquid diffusion.

Abstract: We propose a field-quantum framework in which discrete field quanta constitute space (A), attract their neighbours (P1), each carry a two-component complex amplitude whose normalised states carry the Hopf fibration \(S^1\to S^3\to\mathrm{CP}^1\) (P2), and every coherent excitation is one configuration whose energy, orientation and integer counts—action \(\hbar\) per cycle—are attributes of the whole (P3), from which one-quantum wholeness follows as a theorem. The continuum limit is a Lorentz-invariant nonlinear Klein–Gordon theory, and the numerical checks below use lattice simulations of this action. Rest mass is the vacuum-subtracted deformation energy, \(mc^2=\int(T^{00}-T^{00}_{\rm vac})\,d^3x\), verified by 3D decomposition; a boosted soliton recovers \(E=\gamma mc^2\). Velocity and gravitational time dilation issue from one internal light clock: a moving clock's internal signal slants at unchanged transverse size; a static clock's spacing and update rate are each scaled by \(\lambda_g\) (shorter steps, slower steps). The two combine into \(\omega=\omega_0\sqrt{1-v_{\rm eff}^2/c^2}\) (\(v_{\rm eff}=v\) for a moving clock, \(v_{\rm esc}\) for a static one; one rule applied level by level, the factors multiplying when both act), with the conserved product law \(E_\infty=S\,m_{\rm loc}\) verified to 0.65%. The coordinate light speed \(c\lambda_g^2\) gives the $1.751''$ light deflection and the Shapiro delay by Fermat's principle, and the composition law \(\lambda_g=e^{\Phi/c^2}\) yields \(\beta=1\) and the perihelion advance. A finite-energy topological closure principle selects stable structures: a winding line cannot end in vacuum, so it must close. The electron is a localized winding of the orientation field whose charge is the turning sense of its tilt about the vacuum axis—the Gauss charge of the contact-face connection, one half-unit for odd Hopf winding by the Finkelstein--Rubinstein sign—and whose winding is its shape; spin \(\tfrac12\) is the angular momentum of the charge turning through the winding (\(L=-HQ\), at no rotational cost), the magnetic moment the winding current's field. Gravity is the medium's compression response to deformation energy; electromagnetism lives on the contact faces between quanta: with the identification of neighbouring internal frames promoted to a dynamical connection (P1b), Gauss's law is a theorem, Amp\`ere's law is the connection's own dynamics, the Coulomb law with both signs is a lattice result, and light is the connection's free wave—tmassless, two transverse polarisations, helicity \(\pm1\). A wavelength-sized source in this medium radiates an energy per cycle strictly proportional to \(\omega\), so the size of the unit is not obtained. Quantum measurement, interference and entanglement are read through the one-configuration postulate (P3), from which all-or-nothing delivery, the Born weights, the Malus law and the Bell correlations (\(S_{\rm CHSH}=2\sqrt2\)) follow as theorems and numerics, with the origin of the unit itself left open. The fine-structure constant is \(\alpha_e=\kappa_E\tilde\hbar/16\pi\), a product of two lattice numbers left as input; the Sakharov coefficient and absolute particle masses remain open.

Abstract: During the last thirty years, the compelling experimental evidences for oscillations of solar, reactor, atmospheric and accelerator neutrinos imply the existence of 3-neutrino mixing.Since in the Standard Model neutrinos are massless, the mechanism of generation of these small masses is unknown and different according to their nature: Dirac or Majorana? Neutrino oscillations experiments cannot give the answer. In the same way as the mixing of quarks is parametrized by the Cabibbo Kobayashi Maskawa quark mixing matrix - which is a unitary matrix that contains information on the strength of the flavour-changing weak interaction - , neutrino mixing can be parameterized by a 3x3 leptonic mixing matrix,called the Pontecorvo Maki Nakagawa Sakata matrix (PMNS matrix). Neutrino oscillation experiments have improved and stabilised the precision on the measurements of three mixing angles and one CP violating phase, constraining strongly unitarity violation of PMNS matrix. If neutrinos are of Majorana type there are 2 additionnal phases that cannot be accessed by oscillation experiments. In this work, we will use the most recent Nu-Fit of the PMNS parameters at 3σ in normal and inverted neutrino masses hierarchies.We will first discuss the constraints on the sum of neutrino masses and mass hierarchies taking also into account cosmological bounds and KATRIN and DESI experiments. Neutrinoless double beta decay (hereafter denoted 0νββ decay) constrains the effective Majorana mass |m_ee|.Within its experimental limits we will study the sensitivity to the 2 additionnal Majorana phases α and β. We will show that only one phase - α - can be extracted from data. We finally discuss the possibility that neutrino antineutrino oscillations involving muons could be complementary to 0νββ decay to help in finding the nature of neutrinos.