Abstract: In a series of recent papers, Haug and Tatum have suggested a way to resolve the Hubbletension within RH = ct cosmology. Based on the full distance ladder of Type Ia supernovae(SNe Ia), they find that the Hubble constant must be H0 = 66.8943±0.0287 km/s/Mpc. Thisvalue is close to the Planck Collaboration’s CMB-based estimate of 67.4 ±0.5 km/s/Mpc,except that their solution yields a much smaller uncertainty in the Hubble constant. TheSH0ES study by Riess et al., based on SNe Ia observations, gives a significantly higher value:H0 = 73.04 ±1.04 km/s/Mpc. The Hubble tension refers to the large discrepancy betweenthe H0 estimates obtained from the CMB method and those from SNe Ia data. Interestingly,recent JWST observations, when tied to SNe Ia, find H0 = 68.81 ±1.79. Thus, the JWSTresults lower the Hubble constant relative to the Riess study and appear to support the Haugand Tatum solution to the Hubble tension, a topic we discuss in this short note.

Abstract:

This paper proposes a unified theoretical framework based on discrete space element dynamics. The core concept posits the existence of a conserved "spatial raw material" through which quantum virtual processes continuously generate new spatial elements, forming localized density gradients that manifest as spacetime curvature. This mechanism inherently excludes superlative effects, remains compatible with general relativity under covariance constraints, and provides a unified explanation for challenges such as dark matter, dark energy, and black hole singularities. The paper first elucidates the fundamental principle of "global covariant symmetry" and then offers an ultimate interpretation of symmetry breaking: symmetry is not "broken" but rather a local cost paid for global covariance. The core dynamics of this framework are systematically developed, with rigorous derivations of Newtonian gravitational limits, mass-energy equations, the principle of the constancy of the speed of light, the fundamental form of Maxwell's equations, and Newton's three laws from basic assumptions. Furthermore, by strictly defining k-body stable entanglement classes on discrete spacetime graphs, the symmetry group is proven to be SU(k), and the gauge group of the Standard Model—SU(3)×SU(2)×U(1)—is uniquely derived. Under the continuous limit, the Yang-Mills action, chiral fermions, Higgs field, and Einstein's gravity are obtained. The theory predicts all 28 independent parameters of the Standard Model—including gauge coupling constants, fermion mass spectra, CKM matrices, PMNS matrices, Higgs parameters, strong CP parameters, and neutrino mass squared differences—with deviations from experimental values generally below 10⁻⁴ to 10⁻⁸. These predictions constitute the "geometric periodic table" of physical constants, signifying that the 28 free parameters of the Standard Model are completely nullified. The article concludes with multiple quantitative predictions verifiable by future experiments, providing a self-consistent, comprehensive, and experimentally testable new pathway for the unification of quantum gravity and particle physics.

Abstract: This paper investigates the seasonal and daily responses of the zonal‑mean O₃ mass‑mixing ratio to polar‑vortex disturbances during the boreal winter of 2023/2024, using MERRA‑2 data for the period 1 October 2023–30 April 2024. In addition to the expected latitudinal coupling during SSW events, the seasonal ozone field exhibited a pronounced zonally asymmetric distribution, referred to as the zonally asymmetric ozone oscillation (ZAOO), most evident in the lower stratosphere throughout the winter months. The seasonal behaviour of the ozone tendency was also investigated. To provide a plausible explanation for the observed features, a combination of the Quasi-biennial oscillation (QBO), dynamical transport, and photochemical processes was considered. For the first time, TEM diagnostics were applied to individual winter seasons and specific SSW events, enabling detailed examination of ozone‑tendency variability across latitude and altitude. The results provide clear quantification of the dynamical and net chemical contributions to both the seasonal (October–April) and specific SSW event ozone tendencies. These findings support systematic assessments of each intriguing winter and SSW event, offering new opportunities to identify links between SSW type and the dominant mechanisms shaping the ozone‑tendency response.

Abstract: Bell tests and Bell's theorem used to interpret the test results opened the door to quantum information processing, such as quantum computation and quantum communication. Based on the erroneous interpretation of the test results, quantum information processing contradicts a well-established mathematical fact in point-set topology. In this study, the feasibility of quantum computation and quantum communication is investigated. The findings are as follows. (a) Experimentally confirmed statistical predictions of quantum mechanics are not evidence of experimentally realized quantum information processing systems. (b) Physical carriers of quantum information coded by quantum bits (qubits) do not exist in the real world. (c) Einstein's ensemble interpretation of wave-function not only will eliminate inexplicable weirdness in quantum physics but also can help us see clearly none of quantum objects in the real world carry quantum information. The findings lead to an inevitable conclusion: Without carriers representing quantum information, physical implementations of quantum information processing systems are merely an unrealizable myth. Examples are given for illustrating the reported results. For readers who are unfamiliar with point-set topology, the examples may alleviate difficulty in understanding the results.

Abstract: We investigate the mechanisms by which natural systems encode data across multi-dimensional spaces. Integrating principles from information theory, probability, and geometry, we propose that certain Lie Groups govern these encoding processes. We first demonstrate that evenly distributed information becomes computationally unsolvable in higher dimensions. If we do not notice the "curse of dimensionality," it is because nature likely uses geometric positional notation at a rudimentary level. By extending the definition of representational cost to m dimensions using Benford’s Law, we identify a cost minimum at powers of Euler’s number (е^m). We introduce the "Lie Squad" (B3, F4, G2, A2, A1, and E6), a set of six compact simple Lie groups whose irreducible representations coincide with this ideal cost when m matches the group’s algebraic rank. These irreps facilitate a fundamental, rank-invariant number system based on balanced ternary, uniquely encoding integers as the difference of two natural numbers in bijective notation. Finally, we examine the Weyl orders of the Lie Squad members to show that Weyl divisors yield a logarithmic scale consistent with Benford’s Law and the universal number system proposed.

Abstract: Understanding pathological processes remains challenging because clinical descriptions primarily rely on phenotypic observations, while the underlying dynamical mechanisms that generate and stabilize disease states often remain implicit. This article introduces forms dynamics as an applied physics framework aimed at interpreting pathology as the dynamical evolution of structured configurations sustained by continuous exchanges of energy, matter and information with the environment. The approach integrates concepts from non-equilibrium thermodynamics, complex systems modelling and Gestalt-inspired structural reasoning. Within this perspective, pathological systems are represented through physically meaningful variables and fluxes whose interactions can be expressed through coupled balance equations or equivalent graphical schematizations. Empirical data, including clinical observations, diagnostic measurements and network-based analyses of biological interactions, inform the identification of relevant variables and pathways. Model calibration constrains parameters using physiological ranges, characteristic timescales and observed trajectories, while validation relies on the consistency of the resulting dynamical regimes with clinical phenotypes and responses to perturbations. Within this framework, physiological conditions correspond to stable attractors in the system’s dynamical landscape, whereas pathological states emerge from altered coupling between variables and fluxes, leading to alternative stable or metastable regimes. By providing a physically grounded representation of pathological dynamics, forms dynamics offers a unifying modelling strategy for complex diseases and may support translational research, physics-informed digital twins and more interpretable computational tools for clinical decision support.

Abstract: We quantize the exterior region of a Schwarzschild-AdS black hole using our model of quantum gravity. The resulting hyperbolic equation is solved by products of temporal eigenfunctions w_i, the eigenvalues of which all have multiplicity one, and spatial eigendistributions v_ij having the same eigenvalues but with multiplicities 1 ≤ m_i, where the m_i could in principle be arbitrarily large. Regarding only the exterior region, there was no guidance how to determine the values of the m_i. However, considering also the quantization of the interior region, where the same question did not arise since the m_i could be chosen by maximizing the value, it seemed logical to choose the same values, too, in the exterior case. Since the eigenvalues in the interior are the same because the temporal Hamiltonian is the same in both cases, this choice defined a unitary equivalence between the respective Hilbert spaces and the respective Hamiltonians. Hence, there is no information paradox on a quantum level.

Abstract: Metabolism in living things is the combination of enzyme-catalyzed biochemical reactions that drive biological work in the form of energy capture and release, molecule synthesis, cell replication and other functions. It is constrained by many factors, including resources, enzyme characteristics, and temperature under the requirement that organisms persist through time. Here, the biochemical foundation for metabolism is viewed from a thermodynamic perspective that explores three different metabolic currencies: (1) entropy production, which reflects the ability to persist at or near steady state through time by the rate at which entropy of surroundings is increased relative to that inside a system, (2) reaction rate or the rate of formation of products, and (3) power, the rate at which “free” (Gibbs) energy available for doing work is generated. Rate-temperature relationships for each objective are derived from a reaction-displacement model of a metabolic reaction for near-steady-state conditions, which are presumed to be required for organisms to persist over time. Reaction rate, entropy production and Gibbs energy production are maximized at different optimal temperatures, T_opt, all at barely distinguishable near-maximum reaction rates. These theoretical predictions nevertheless provide distinct, testable hypotheses for organism response to temperature under maximizing each of the three metabolic currencies. The framework also suggests that there exists a maximum temperature for life, T_max, at which entropy generated near reaction sites by reaction activation becomes greater than that generated away from reaction sites by the dissipation of heat and products. The framework predicts shifts in Topt and T_max that differ among types of reactions, enzyme concentrations, organism element concentration and varying body size. Overall, the framework provides a greatly expanded set of hypotheses and explanations for temperature performance relationships for life, including variation in both T_opt and T_max, for growth versus locomotion and respiration, “fast” versus “slow” life histories, resource-rich versus resource-poor environments, and intra- and interspecific variation in body size.

Abstract: Temporal effects associated with surface plasmon polaritons (SPP) in a quantum slab of a plasma material, such as a thin film of metal, semiconductor or a graphene plate, where the quantum dispersion effects, and in particular exchanges effects, are retained.

Abstract: If the invariance of light speed is absolutely universal in covariant space rather than contra variant space, the following researches and conclusions on general covariance would be so far as to catch up with very high probabilities and reliabilities. As has been verified, it is. General covariance is tested controversial after the investigations on gravitational redshift and acceleration. Further inspections on differential geometry indicate the opportunities of inequality of mixed derivatives of bases for the transformations between Riemannian spaces that will then lead to the inequality of Christoffel symbols of alternative sub-index and then the failure of the classical equations of Christoffel symbols. That is one of the reasons that causes controversies on general covariance. Even the negative form of time metric could be proved to be a false setting in that space transformations do nothing with the negative sign inherited from that of Minkowski space. Nevertheless, after discussions on transformations between original spherical space, distance expressed spherical space and Cartesian space, it has been seen that the distance factors for angular coordinates of a spherical space are improper to be employed the metrics in general relativity, instead of that, the concept of gravitational metrics were suggested. In fact, Christoffel symbols and base derivatives both are valid methodologies for analysis in a non-Euclidean space. The concept of trajectory derivatives was carried out to define the derivations on trajectory of matter motions that could help to revise those equations and calculations. Measurable experiments on gravitational redshifts and accelerations have been carried out to support the theoretical results. Conclusions have been drawn that light speed keeps general covariance in gravitational fields but light energy momentum would not, may as well, the motions of massive matters in gravitational fields do not perform general covariance thoroughly. It is impossible to geometrize the gravity effects of massive matters with position depending metrics in that the variable velocities cannot be eliminated thoroughly. Consequently, inferences on kinematics and relativistic release were carried out, which might have been forcefully verified in applications. With the concept of gravitational metrics, the so-called geodesic equations have been falsified to be kinematic equations anymore. Velocities, mass energy and momentum all should have their conservative forms. To seek for these conservative forms is the critical route to create kinematic or dynamic equations of motions of light rays and massive matters. The conservativeness of light angular momentum has been discovered in most surprising form. Renovated solutions for light rays as well as massive matters have been carried out that forcefully impact the traditional methodologies on kinematics of trajectory and time delay because they are the correct interpretations of the realities. It should be highlighted that the renovated mass equation, the general mass equation for free motions, could completely demonstrate energy variations, especially the variations in gravitational fields, that help to create more general dynamic equations, so as to cause an irrelativistic solution of planet perihelion precession. As a proof by contradictions, the traditional solution of that must be involved with errors. Newtonian ballistic method was put forward to make numerical analyses on close-to-light-speed motions, and the invalidity of that method on light propagation could be seen as another support to the conclusions and inferences. Another forceful falsification on energy momentum conservativeness carried out in the discussions on the traditional treatment of time delay of close-to-light-speed particles, has thoroughly exposed the essential mistakes in the way of methodologies. Dynamic models of fluid planet rings were founded to interpret the evolutions of accretions of quasars and active galactic nuclei and the mechanism of relativistic release. It is predicted that the peak release of an inflow is at 1.5 of gravitational radius and the peak luminosity of an accretion may locate at the position of about 1.33 of gravitational radius. Relativistic frequency shift interprets the mechanism of giant redshifts that predict the probability of observational redshifts might be up to a particularly higher level with respect to that have been observed in the past years. The width equations of emission and absorption lines indicate the mechanism and the positions of broad line regions and narrow line regions. It could be imagined that the relativistic emissions and relativistic absorptions with relativistic redshifts would have been involved with fantastic mystery of intrinsic structures of matters that we know less.

Abstract: Foundational tensions between special relativity and quantum mechanics, together with conflicts between general relativity and quantum gravity, and unresolved cosmogonical and cosmological anomalies, block theoretical unification and limit explanatory depth. Based on ontological first principles rather than mathematical constructs, this analysis integrates a “discrete,” background-independent, relativistic 4D spacetime with a physically co-located Planck Domain. Through a one-to-one identity, the Planck Domain mirrors the discrete spatial elements of 4D spacetime, enabling a single, unified set of physical laws across quantum and classical regimes. Under this framework, ontic single- and N-body quantum states evolve deterministically in 4D spacetime and collapse instantaneously in the Planck Domain. Current theoretical tensions between special relativity and quantum mechanics, including nonlocality, separability, time, simultaneity, total energy scaling, and probability conservation, are reappraised by replacing the Hilbert-space wavefunction with an ontic energy field and a single energy-based operator that governs both motion and gravitational response. The identical ontological framework and dynamical laws apply unchanged across general relativity and quantum gravity, recasting gravity as the relational dynamics of discrete energy rather than the coupling of the stress-energy and metric tensors and reappraising the equivalence principle and the black hole information paradox. Cosmogonically, the same model re-examines the origin of 4D spacetime, accounting for near-homogeneity, isotropy, and low gravitational entropy without ad hoc assumptions, fine-tuning, or perturbative techniques, and provides ontological foundations for the cosmological constant and global energy conservation. Eight descriptive mathematical validations, derived from a unified evolution law, Planck Domain collapse rule, and the relational gravity law, support (but do not govern) the analysis: (i) the low-ℓ CMB TT shape generated from a field with one global amplitude on power; (ii) CHSH correlations at Tsirelson’s bound from collapse; and (iii–viii) hard-mass relational dynamics, highlighted by a tilted Earth–Moon orbit, a tilted hierarchical three-body system, and a high-energy Mercury–Sun analog, all sustained for 1000 orbits or inner orbits.

Abstract: Since its establishment, quantum mechanics has developed for a century and has a very large theoretical system, but the phenomenon of quantum mechanics still lacks a generally accepted explanation, which undoubtedly shows that the existing theoretical system is incomplete. Inspired by ancient Chinese philosophy, we propose a theoretical framework in this paper, which provides a new perspective for explaining quantum mechanical phenomena including superposition and entanglement. In addition, the proposed framework contributes to a profound understanding of the law of conservation of energy. We show through examples how basic superposition states and entangled states are constructed. Our work can inspire people to think deeply about the mysteries of nature, especially quantum mechanical phenomena.

Abstract:

We develop an information-theoretic route from microscopic conserved-charge dynamics to an infrared mass prediction in the minimal Z₂ singlet-scalar Higgs-portal dark-matter model. We define an operational quantum information copy time \( \tau_{\mathrm{copy}}(Q)\ \) for a conserved charge Q and introduce a Liouvillian-squared information susceptibility \( \chi^{(2)} \) based on the Kubo--Mori metric. Empirically, across several decades in \( \chi^{(2)} \) we find the robust scaling \( \tau_{\mathrm{copy}}(Q)\propto (\chi^{(2)}_{Q})^{-1/2}\ \) (Table 1 and Figure 1). Analytically, a general linear-response/Cauchy-Schwarz inequality bounds the growth rate of any receiver-optimised overlap by \( \sqrt{\chi^{(2)}_Q}\ \); for a fixed operational threshold \( \eta\ \) and normalised sender/receiver operators this implies the conditional lower bound \( \tau_{\mathrm{copy}}\gtrsim \eta/\sqrt{\chi^{(2)}_Q}\ \) under mild regularity/monotonicity assumptions (Closure Supplement, Section "Copy-time bound''). We also provide stabiliser-code diffusion benchmarks that illustrate the scaling and help calibrate normalisations in the diffusive universality class. We then argue that spatially varying copy times naturally define an ``optical'' geometry for coarse-grained information propagation: a local information speed \( v_{\mathrm{info}}(x)\propto \tau_{\mathrm{copy}}(x)^{-1}\ \)induces an effective metric, and diffeomorphism invariance in the long-wavelength description implies that the Einstein--Hilbert term is the leading infrared operator, with higher-derivative corrections controlled by gradients of \( \tau_{\mathrm{copy}}\ \). In this perspective, we define the scalar dressing parameter \( \kappa_{\text{eff}} \) intrinsically from microscopic QICT susceptibilities in the electroweak-symmetric regime; asymptotic-safety FRG results, when invoked, serve only as an external cross-check rather than as a foundational assumption. Within a gauge-coded QCA realising a Standard-Model-like generation, anomaly cancellation singles out hypercharge Y Yas the unique non-trivial anomaly-free Abelian factor coupling to both quarks and leptons; we also provide a self-contained anomaly calculation (see the Closure Supplement, "Hypercharge from anomaly constraints'') and emphasise that this selects a one-dimensional anomaly-free direction; it does not exclude embeddings or additional hidden sectors. This is a minimal-factor selection under stated assumptions and does not exclude embeddings, additional hidden sectors, or discrete quotients. Matching to a thermal Standard Model plasma at a reference temperature \( T_\star\ \)in the electroweak-symmetric regime \( T_\star\gtrsim T_{\rm EW} \), and adopting benchmark inputs (with an explicit operational construction of \( T_\star\ \) given in the Closure Supplement (Point~(6)) and an explicit interacting thermal-QCA susceptibility protocol given in the Closure Supplement (Copy-time bound / Point~(6))), \( \frac{\chi_Y}{T_\star^2} = 0.145 \pm 0.010,\qquad \) \( \kappa_{\mathrm{eff}} = 0.1356 \pm 0.0714,\qquad \) \( C_\Lambda = 1.606 \pm 0.044 \), we obtain the Golden Relation \( m_S = C_\Lambda \sqrt{\kappa_{\mathrm{eff}}\,\chi_Y} \) and the prediction \( m_S = 58.5 \pm 15.6~\text{GeV},\qquad \) \( m_S \in [43,74]~\text{GeV}\ \text{(conservative)} \). We provide a minimal, fully analytic phenomenological consistency check of the Higgs-portal model in the vicinity of the Higgs resonance, using closed-form expressions for the Higgs invisible width and the spin-independent nucleon cross section. The mass prediction is conditional on the explicit benchmark intervals and on the stated matching assumptions; the copy--susceptibility exponent is universal in the variational sense above, while the overall normalisation entering the benchmark closure is calibrated using a diffusive benchmark class (a separate step, not used in the unconditional bound).

Abstract: We develop an information-theoretic route from microscopic conserved-charge dynamics to an infrared mass prediction in the minimal Z₂ singlet-scalar Higgs-portal dark-matter model. We define an operational quantum information copy time \( \tau_{\mathrm{copy}}(Q)\ \) for a conserved charge Q and introduce a Liouvillian-squared information susceptibility \( \chi^{(2)}_{\mathrm{micro},Q}\ \) based on the Kubo--Mori metric. Under explicit locality, spectral-gap and hydrodynamic assumptions, we formulate a conditional scaling theorem implying \( \tau_{\mathrm{copy}}(Q)\propto \bigl(\chi^{(2)}_{\mathrm{micro},Q}\bigr)^{-1/2}\ \); we provide numerical evidence for this scaling in stabiliser-code diffusion models (Supplemental Material). We then argue that spatially varying copy times naturally define an "optical'' geometry for coarse-grained information propagation: a local information speed \( v_{\mathrm{info}}(x)\propto \tau_{\mathrm{copy}}(x)^{-1}\ \) induces an effective metric, and diffeomorphism invariance in the long-wavelength description implies that the Einstein-Hilbert term is the leading infrared operator, with higher-derivative corrections controlled by gradients of\( \tau_{\mathrm{copy}}\ \). In this perspective, we define the scalar dressing parameter \( \kappa_{\text{eff}} \) intrinsically from microscopic QICT susceptibilities in the electroweak-symmetric regime; asymptotic-safety FRG results, when invoked, serve only as an external cross-check rather than as a foundational assumption. Within a gauge-coded QCA realising a Standard-Model-like generation, anomaly cancellation singles out hypercharge Y as the unique non-trivial anomaly-free Abelian factor coupling to both quarks and leptons. Matching to a thermal Standard Model plasma at a reference temperature T⋆ in the electroweak-symmetric regime (T⋆≳TEW), and adopting benchmark inputs (with an explicit operational construction of T⋆ given in Supplement~S7), \( \frac{\chi_Y}{T_\star^2} = 0.145 \pm 0.010,\qquad \) \( \kappa_{\mathrm{eff}} = 0.136 \pm 0.019,\qquad \) \( C_\Lambda = 1.6 \pm 0.2 \), we obtain the Golden Relation \( m_S = C_\Lambda \sqrt{\kappa_{\mathrm{eff}}\,\chi_Y} \) and the prediction \( m_S = 58.4 \pm 8.6~\text{GeV},\qquad m_S \in [50,67]~\text{GeV}\ \text{(conservative)} \). We provide a minimal, fully analytic phenomenological consistency check of the Higgs-portal model in the vicinity of the Higgs resonance, using the closed-form expressions for the Higgs invisible width and the spin-independent nucleon cross section. We emphasise that the mass prediction is conditional on the input benchmark intervals and on the diffusive QICT universality class assumptions.

Abstract: Wave–particle duality in interferometric systems is commonly formulated through complementarity relations linking fringe visibility and path distinguishability. In realistic experiments, interference suppression arises not only from unitary which-path marking but also from environment-induced decoherence. We derive an angle-dependent pure-dephasing model from a microscopic system–bath Hamiltonian, obtaining a Lindblad master equation with geometric coupling dependence. Moving beyond the Markovian limit, we utilize a second- order time-convolutionless (TCL2) expansion with a structured spectral density to show that geometric scaling persists in non-Markovian regimes, potentially leading to geometry-dependent coherence revivals. Furthermore, we explicitly derive the entropy production rate, demonstrating that the transition toward classicality is quantitatively governed by directional entropy flow. The framework remains fully within standard quantum mechanics, introducing no modifications to the Schr¨odinger equation. Experimental falsifiability criteria, including early-time scaling and coherence revivals, are presented.

Abstract: We show the Born rule P = |ψ|² is the unique probability rule consistent with thermodynamic constraints on record formation, conditional on the regime where Landauer-type bounds apply. The derivation proceeds from five operational postulates: normalization, phase information loss in record formation, interference consistency, tensor product factorization, and continuity. The key physical insight is that creating a classical measurement record requires that phase information is not retained in the record accessible to observers, a not-reversible operation with entropy flow to the bath and Landauer cost k_B T ln 2 per bit. The squared modulus emerges as the unique probability rule that (i) eliminates phase to produce positive probabilities, (ii) preserves interference effects before measurement, and (iii) satisfies standard probability axioms. This thermodynamically motivated derivation complements Gleason's theorem: where Gleason proves the rule is mathematically necessary (dimension ≥ 3), we show it is the unique rule realizable through record formation under these constraints (all dimensions including d=2). The framework provides a concrete answer to "why squared?": the irreversible formation of a classical record, on a Hilbert space whose norm is preserved by unitary evolution, admits no other consistent probability rule.

Abstract: We show that the Standard Model of particle physics allows the recently observed 244 EeV ($= 244 \times 10^{18}$ eV) cosmic ray --- the Sun Goddess particle --- to be a proton with the active galaxy 2MASX J16574719+1832247, redshift z = 0.054 as its source. The Standard Model Theory is preferred over conventional theory by a Bayes Factor K = 490, which in Jefferys' Table is a `'decisive'' preference. Further, the Standard Model Theory has now been confirmed by direct observation of the Cosmic Background Radiation (CBR).

Abstract: The thermal drift of microring resonators is one of the key obstacles hindering their practical applications. Employing polymers with negative thermo-optic coefficients to compensate for temperature-induced wavelength shifts represents a common solution. This study utilizes polymethyl methacrylate (PMMA) to compensate silicon nitride microring resonators, achieving thermal drift magnitudes below 2.0 pm/K within the temperature range of 15℃ to 70℃. Furthermore, nonlinear thermal drift characteristics were experimentally observed, and simulations revealed that these nonlinearities primarily originate from the temperature-dependent Young's modulus and Poisson's ratio of PMMA. This research provides design references for waveguide compensation using negative thermo-optic coefficient materials and proposes a conceptual framework for dual-function devices capable of both athermal operation and thermal tuning.

Abstract: The effect of water on the dynamics and ionic conductivity of the ionic liquids 1-ethyl-1-methylpyrrolidinium levulinate ([C₂C₁Pyr]Lev) and 1-butyl-1- methylpyrrolidinium levulinate ([C₄C₁Pyr]Lev) was investigated using differential scanning calorimetry (DSC) and broadband dielectric spectroscopy (BDS) over a wide temperature range. Although both ILs share the same levulinate anion, water induces markedly different dynamical responses depending on cation structure. In both systems, water acts as a plasticizer, lowering the glass transition temperature; however, the extent of plasticization and the resulting relaxation dynamics are cation-dependent. Stronger water–cation interactions are observed in [C₂C₁Pyr]Lev, whereas in [C₄C₁Pyr]Lev, water primarily disrupts alkyl-chain packing, enhancing ionic mobility. Increasing hydration shifts the main relaxation to higher frequencies and increases liquid fragility, while translational ionic motion remains partially decoupled from structural relaxation. These results demonstrate that water plays a cation-specific and mechanistically distinct role in levulinate-based ILs, providing new insights into hydration-controlled glassy dynamics and charge transport relevant for the design of IL-based electrolytes under non-anhydrous conditions.

Abstract: Urban scaling theory establishes that socioeconomic outputs scale superlinearly with city population (β > 1), attributed to social-interaction density, but its applicability to resource-constrained sectors remains untested. We analyse a panel of ∼ 2 , 800 Chinese counties (2000–2023) with GDP decomposed into primary, secondary, and tertiary sectors. Using the urbanization ratio as a continuous moderator in interaction-term regressions, we estimate sector-specific crossover thresholds from sub- to super-linear scaling; a Scale-Adjusted Agricultural Index (SAAI) quantifies each county’s deviation from size-expected output. A robust sectoral spectrum emerges—βpri = 0.87 < βter = 0.96 < βsec = 1.08—whose rank order is preserved across all 24 sample years. The tertiary sector crosses β = 1 at urbanization ratio u∗ = 0.80 (95% CI [0.72, 0.92]), with interaction coefficient β1 = 1.48 (p < 0.001). Province fixed effects confirm the urbanization interaction for secondary and tertiary sectors (p < 0.001) but not primary (p = 0.248), consistent with the crossover being specific to interaction-intensive activities. China’s 832 designated poverty counties exhibit systematically negative SAAI values (Cohen’s d = 0.55–0.87), revealing a persistent scaling deficit that conventional output comparisons obscure. These results show that the scaling exponent is a continuous function of economic structure, identify a quantifiable urbanization threshold for the onset of increasing returns, and supply a boundary condition for Bettencourt’s theory of urban scaling.