Search Results (1,090)

In the Selection-Stitch Model (SSM), baryonic matter is a $K=4$ remnant trapped in a tetrahedral void of the $K=12$ FCC vacuum lattice. We examine the second interstitial site, the octahedral void, as a candidate dark matter trap. Its bonded subgraph is the complete tripartite graph $K_{2,2,2}$. Four structural properties follow from its symmetry. Two are exact: the defect is self-conjugate, and it has no first-order electric dipole. Two are weaker and are stated as such: the electromagnetic coupling is suppressed at dipole order rather than at all orders, and the mechanism that generates SU(3) color for the tetrahedral baryon has no counterpart here. A closed inclusion–exclusion expansion on $K_{2,2,2}$ gives the structural count $C_{\mathrm{DM}}=25·144-30·10+8·8=3364$. It terminates at third order because the octahedron’s six vertices forbid a four-matching. Under one stated assumption, the standing-information postulate, this corresponds to $m_{\mathrm{DM}}=(3364/1836)\times m_p=1.719$ GeV with the proton mass as the sole calibration input and no cosmological fitting.The same geometry fixes the annihilation channel. Two octahedral defects can meet only along a shared octahedron edge, and of the four cages their interface admits, only the two tetrahedra are products of the merger. The residual therefore has mass $m_p$, and the only channel producing a line gives $E_{\gamma }=1.591$ GeV. A recently reported $1.5$–$1.6$ GeV gamma-ray line has weighted centroid $1.578\pm 0.048$ GeV, which is $0.3\sigma$ away. No observational input enters the derivation. Full article

In this paper, we investigate the antiholomorphic counterpart of bicomplex quadratic dynamics by introducing bicomplex Mandelbar sets associated with the three natural involutive conjugations of the bicomplex algebra. For each conjugation ${†}_m$, $m\in \{1,2,3\}$, we study the iteration ${\left(F_m\right)}_C\left(\eta \right)={\left({\eta }^{{†}_m}\right)}^2+C$ on $\mathbb{BC}$ and define the associated parameter set via the boundedness of the orbit of the origin. Using the idempotent decomposition, we obtain a conjugation-dependent classification of the dynamics: ${†}_3$ yields the idempotent product of two classical Mandelbar sets, whereas ${†}_2$ and ${†}_1$ generate cross-coupled quadratic systems, holomorphic and antiholomorphic in one step, respectively. We further prove that the ${†}_1$- and ${†}_2$-dynamics are equivalent up to complex conjugation of an idempotent parameter; consequently, the principal three-dimensional slices of the corresponding Mandelbar sets are congruent, mirror-symmetric copies of one another, although neither possesses this diagonal symmetry individually. We visualize these slices and rigorously establish their reflection symmetries. The results clarify the role of bicomplex conjugations in antiholomorphic dynamics and reveal structural phenomena absent from the holomorphic bicomplex Mandelbrot setting. Full article

When a lithium-ion cell’s series resistance is underestimated, the pre-update terminal-voltage innovation contains the first-order term $e_k\approx -I_k{R}_{0,k}\delta b$. This term breaks conditional sign symmetry and creates an odd response under current reversal. We test that mechanism before using it as an activation rule. The operational null is a near-zero conditional innovation centre with weak innovation–current coupling; declared falsifiers are comparable coupling under the nominal model, the wrong correlation sign under positive resistance error, failure of charge/discharge polarity reversal, or negative-control activation approaching ohmic-mismatch activation. A persistence-confirmed gate combines normalised-innovation-squared exceedances, innovation–current compatibility, a positive local resistance correction, and five consecutive qualifying windows. Sixty settings were ranked on 10 calibration seeds and frozen before disjoint holdouts. From 1.0× to 2.0× R₀, the sign-imbalance index increased from 0.0040 to 0.0786, and |$corr\left(e,I\right)$| increased from 0.0658 to 0.7777. The 30-seed static holdout produced 0/30 nominal activations, 27/30 detections at 1.5×, and 30/30 detections at 2.0–3.0×. A disjoint linear-drift audit yielded 0/30 pre-ramp activations and 30/30 detections at a median 1.71× multiplier, reducing late-drift SOC RMSE from 3.129% to 0.895%. A signed-current audit confirmed the predicted polarity reversal. An estimator-unseen audit gave 30/30 ohmic detections but retained 2/30 current-linked non-ohmic and 1/30 current-bias triggers, so the rule is not a unique fault classifier. NASA and LG records remain diagnostics of fixed versus always-on adaptation; they do not validate the gate or independent absolute SOC. The contribution is a falsifiable residual-symmetry mechanism with an explicit evidence boundary, rather than a post hoc symmetry label or hardware claim. Full article

Grid-based density clustering methods—FlowGrid, FLOPTICS, and grid-accelerated DBSCAN and OPTICS—partition a $d$-dimensional feature space into an $m^{\hspace{0.17em}d}$ array of bins and group the non-empty bins by density reachability. They leave a symmetry unexploited: relabelling and reflecting the feature axes permutes the bins while preserving density. We formalise this as an action of the hyperoctahedral group $B_d=C_2\wr S_d$ of order $2^{\hspace{0.17em}d}d!$ on bin-occupancy functions. We prove that the action preserves the Chebyshev bin-adjacency underlying grid reachability (Theorem 1); that grid density clustering is $B_d$-equivariant (Theorem 2); that configurations up to symmetry are counted by a Burnside average over $B_d$ (Theorem 3), with an explicit parity-split closed form for the octahedral case at every resolution, which we have not found recorded elsewhere (Theorem 4 and Corollary 2); and that a canonical-form algorithm computes a unique representative per orbit in $O\left(2^{\hspace{0.17em}d}d!\hspace{0.17em}{m}^{\hspace{0.17em}d}\right)$ time (Theorem 5). We are explicit about scope: a generic dataset has a trivial stabiliser, so there is no per-run gain; the benefit is canonical indexing, deduplication of symmetry-closed libraries, and caching when the same measurement recurs under a different axis convention. The group specialises to the $D_4$ and $O_h$ symmetries of the DR Code. Symmetry enters twice: as the group acting on the grid, and as the line between symmetric instances and the generic asymmetric ones. The finite instances and enumeration formulae are confirmed computationally; the general statements are established by proof. Full article

This paper presents a symmetry-centered analysis of the vertical and yaw dynamics of a low-cost miniature underwater vehicle. Rather than treating the platform only as a control problem, the study formulates the vehicle behavior as a consequence of geometric, hydrostatic and actuation symmetry, as well as of controlled symmetry-breaking effects. A six degrees of freedom (DOF) model is used as the general dynamic description, and reduced subsystems for heave–pitch, yaw and surge are discussed. The proposed contribution is an asymmetry-aware framework that relates ballast imbalance, center-of-gravity displacement, pump mismatch and thruster imbalance to measurable quantities such as vertical positioning error, pitch deviation and yaw drift during immersion. A quantitative geometric-dynamic asymmetry index is proposed to compare nominal symmetric and asymmetric configurations. Experimental information available from the ballast characterization is incorporated. The proposed framework is evaluated through preliminary numerical simulations comparing one nominal symmetric configuration and four controlled symmetry-breaking scenarios. Numerical results demonstrate that structural mass offsets ($C_1$, $C_2$) induce a steady-state attitude error of $\mathrm{\Delta }\theta ={4.2}^{\circ }$ and a parasitic yaw drift of $\mathrm{\Delta }\psi ={2.8}^{\circ }$. Furthermore, transient fluidic ballast imbalances $C_3$ generate a peak asymmetry index of $\mathcal{A}\left(t\right)=0.42$, triggering maximum transient tracking deviations up to ${8.5}^{\circ }$. These quantitative findings demonstrate that the proposed index provides a highly sensitive and reliable diagnostic indicator. The proposed framework can support symmetry-aware design, calibration and control of small underwater robotic vehicles. Full article

Pixel-level annotation of bi-temporal high-resolution imagery is costly because annotators must distinguish genuine changes from pseudo-changes caused by illumination, seasonality, shadows, and residual misregistration. From a temporal-symmetry perspective, unchanged regions approximately preserve cross-temporal semantic correspondence, whereas genuine building changes introduce localized symmetry breaking between the two acquisition times. This paper presents BSCNet, a semi-supervised framework for binary building change detection that jointly models boundary-sensitive differences and scene-dependent scale preferences. A shared-weight MixTransformer extracts multi-level bi-temporal features. The Edge-Aware Optimization Module suppresses spatially invariant channel responses, enhances residual spatial cues, and predicts a Sobel-supervised edge map. The Parallel Selective Context Module aggregates depthwise-separable branches with different receptive fields and produces an image-level scale distribution. The Multi-scale Edge-Consistent Mean Teacher framework aligns the final prediction, intermediate edge representation, and scale-selection distribution between an exponential-moving-average teacher and the student. Experiments on WHU-CD and LEVIR-CD under 5%, 10%, and 20% labeled-data settings show consistent improvements over RCL, C2F-SemiCD, and CutMix-CD. With 5% labeled data, BSCNet achieves F1/IoU scores of 88.57%/79.49% on WHU-CD and 88.88%/79.98% on LEVIR-CD. An additional UAV-CD evaluation examines transfer to 0.06 m low-altitude UAV imagery containing both building and land changes; under 5% supervision, BSCNet obtains an F1/IoU of 68.07%/51.60%. Progressive ablations confirm complementary gains from the boundary, scale, and consistency components. Full article

The universal operator-growth hypothesis (OGH) states that, in a closed chaotic system, the Lanczos coefficients grow linearly, $b_n\simeq \alpha n$. We ask how this structure is modified when the system is coupled to a Markovian environment, so that the generator becomes non-Hermitian. Applying the Arnoldi recursion to the vectorized Lindbladian in the infinite-temperature Wightman inner product, we organize the resulting pair of growth rates ${\alpha }_{\mathbb{C}}\equiv {\alpha }_R+i{\alpha }_I$—defined as effective slopes of the sub-diagonal and diagonal Arnoldi coefficients over a pre-registered fit window—around two statements whose logical status we delimit precisely. First, whenever the dissipator acts as $\mathcal{D}=-2\gamma \widehat{G}$ with $\widehat{G}$, a Hermitian grading (all dephasing-type baths), the diagonal obeys the identity $\mathrm{Re}{a}_n=-2\gamma {⟨\widehat{G}⟩}_n$: the imaginary rate measures how fast the growing operator accumulates weight in the dissipation channels. Second, we prove a conditional parity theorem: if the Hamiltonian, jump operators, and seeds can be made simultaneously real in some basis (an antiunitary condition), then $b_n$ is even, and $\mathrm{Re}{a}_n$ is odd in $\gamma$ exactly, so ${\alpha }_R$ is renormalized only at $O\left({\gamma }^2\right)$, and ${\alpha }_I=2{\kappa }_0\gamma$ follows from closed-system data alone. We exhibit a one-qubit Lindbladian that satisfies the often-assumed generator symmetry ${\mathcal{G}}^{†}\left(\gamma \right)=-\mathcal{G}(-\gamma )$ yet violates parity ($b_1=|1-\gamma |$), showing that the extra condition is essential; all models studied here satisfy it bit-exactly. For large-q SYK, these ingredients predict ${\alpha }_{\mathbb{C}}=\mathcal{J}-2i(q-2)\gamma$, whose imaginary part is fixed solely by the interaction range; the first ladder step is exact, and the multi-step increments approach $q-2$ with system size ($1.92\pm 0.04$ at $N=12$, $q=4$). Under a common fit protocol, the closed-system rates saturate by $N=10$ (${\alpha }_R\left(0\right)\to 0.437$, $2{\kappa }_0\to 0.224$). The imaginary rate is not an independent observable at leading order—its content is its sign, which resolves how the growing operator meets its environment (opposite for spin chains and SYK). Full article

The piezocatalytic activity of metal–organic frameworks (MOFs) is generally hampered by an insufficient intrinsic piezoelectric response, which largely restricts their application in energy catalytic conversion. Herein, MIL-125-NH₂(Ti) (denoted NM) was chosen as a prototypical model to demonstrate that defect engineering serves as an efficient strategy to simultaneously reinforce the piezoelectric characteristics and piezocatalytic hydrogen evolution performance of MOFs. Multiple comprehensive characterizations verify that thermally treated NM-250 (NM thermally treated at 250 °C under flowing N₂ atmosphere) contains abundant in situ-generated oxygen vacancies. These defects disrupt the high intrinsic structural symmetry of pristine NM and promote the establishment of polarized electric fields upon mechanical excitation. Electrochemical measurements further reveal that the introduced oxygen vacancies effectively suppress charge carrier recombination and accelerate interfacial charge transfer, thereby facilitating the piezocatalytic hydrogen evolution reaction. Benefiting from the optimized piezoelectric polarization and improved charge separation efficiency, NM-250 delivers a piezocatalytic H₂ production rate of 413.5 μmol g⁻¹ h⁻¹, exceeding the value of pristine NM (180.9 μmol g⁻¹ h⁻¹) by 2.28 times. This work elucidates the underlying mechanism by which oxygen vacancy defects modulate piezoelectric polarization and catalytic kinetics and validates defect engineering as a promising route to construct high-performance MOFs-based piezocatalysts. Full article

Parkinson’s disease (PD) is associated with alterations in gait symmetry and plantar loading that can be examined using vertical ground reaction force (VGRF) recordings. This study presents a confidence-stratified, physiology-anchored multiple-instance learning framework with concept-bottleneck-inspired pathways (implementation identifier: DRO-PAS-MIL-CBM; hereafter, PAS-MIL) for retrospective session-level PD-versus-control classification. Each gait session is represented as a bag of temporal windows. Eight predefined bilateral signal descriptors are combined with eight learned latent temporal dimensions, aggregated through attention-based pooling, and processed by concept-guided, prototype, anchor-only, and static-feature expert pathways. The evaluation used five-fold person-grouped cross-validation on 306 sessions from 165 participants in the PhysioNet Gait in Parkinson’s Disease database.Inner person-grouped out-of-fold ExtraTrees probabilities were used to construct the confidence strata and distillation targets. PAS-MIL achieved a pooled session-level area under the receiver operating characteristic curve of 0.771, average precision of 0.890, and a mean fold AUC of $0.826\pm 0.041$. Relevance analysis identified C05 (asymmetry variability) and C08 (bilateral change mismatch) as the highest-weighted predefined physiological anchor descriptors. Protocol-stratified sensitivity analysis showed variation across the three source sub-studies, with AUCs ranging from 0.740 to 0.790. Probability calibration remained suboptimal after temperature scaling (mean per-fold ECE, $0.291\pm 0.042$). The results demonstrate the feasibility of integrating physiology-informed descriptors, temporal representation learning, and session-level aggregation. The study is a retrospective proof of concept and does not establish external robustness or clinical deployment readiness. Full article

Product concept images combine symmetry, closure, balance, and repeated components. Existing shape analysis and computational aesthetic methods can quantify these properties; however, when evidence is reduced to global descriptors or aggregate scores, image-layer provenance and sensitivity to rasterization or heuristic settings may be obscured. This paper presents a traceable image-processing pipeline based on scenario framing, alternative specification, geometry-informed computation, evidence synthesis, and design embodiment (SAGE-D), evaluated on four controlled smart-speaker alternatives using separate body, light-band, and aperture masks. Seven dimensionless descriptors measure silhouette reflection, centroid balance, light-band closure, aperture regularity and gradient, component-scale retention, and contour compactness. Resolution resampling, one-pixel morphology, parameter perturbation, and synthetic controls assess sensitivity. At $512\times 512$ pixels, A, B, and R showed exact bilateral silhouette consistency; B and R showed complete light-band occupancy; and C and R showed strong downward aperture-radius gradients. Conventional same-mask measures gave concordant geometric readings, while leave-one-gate-out analysis showed that screening depended mainly on predefined closed-ring and linear-gradient requirements. Only R passed all six case gates. SAGE-D is used here as an auditable organization of layer-specific measurements and bounded screening rules, not as a superior descriptor set. The conclusions are limited to the supplied two-dimensional (2D) representations and do not establish population-level generalizability, preference, or engineering performance. Full article

Digital innovation platform ecosystems can scale rapidly without becoming durable because broad participation does not ensure sustained value circulation. Existing models homogenize complementors, obscuring horizontal coopetition among distinct groups and its interaction with vertical governance. We examine how vertical and horizontal relations shape value-flow architecture and sustainability. Drawing on ecological symbiosis theory, we distinguish a platform orchestrator, technology-extending complementors, and service-integrating complementors. We construct an extended three-actor Lotka–Volterra model and use the Global Value-Flow Symmetry (GV) index and the continuous directional indicator ${\delta }_c$ to assess symmetry and direction. Designed for theory building rather than empirical calibration or testing, the analysis uses no empirical data and compares 35 vertical–horizontal configurations through deterministic simulation and sensitivity analysis. Results show the following: (1) Greater symmetry is associated with higher aggregate maintained output, but vertical backflow direction shapes its distribution; $\mathrm{G}\mathrm{V}$ must therefore be interpreted with ${\delta }_c$. (2) Under complementor-favoring vertical parasitism, horizontal mutualism expands complementor output but intensifies negative vertical backflow, simultaneously increasing aggregate output and reducing platform equilibrium—a cooperation paradox. (3) The same horizontal mutualism yields three focal outcomes across the examined vertical structures: Negative complementor-to-platform effects produce the cooperation paradox, absent effects produce value decoupling, and mutually positive vertical exchange produces systemic resonance. Thus, horizontal cooperation does not necessarily enhance sustainability; its effect depends on whether complementor gains feed back to support platform capability. This study advances platform-ecosystem sustainability research and offers theoretical guidance for optimizing value backflow and cooperative governance. Full article

Given a positive number $n>1$ and two distinct planar focal points A and B, the locus of all points P such that $\left|AP\right|=n\left|BP\right|$ is a circle of Apollonius of index n Under what conditions is B the center of a hyperbolic circle in the Poincaré disk? In particular, for any circle $\mathcal{E}$ in $\mathbb{C}$ lying within the unit circle, where the Euclidean center u of $\mathcal{E}$ is other than O and its Euclidean radius is $ϵ$, $0<ϵ<1$, there exists another circle $\mathcal{D}$ and a point B in $\mathcal{E}$ where the center of $\mathcal{D}$ is O and its Euclidean radius is $\delta$, $0<\delta <1$, for which $\mathcal{D}$ and $\mathcal{E}$ are hyperbolic translates of one another, as are O and B; by rotation symmetry of $\mathbb{C}$ about O, we may take A, B, and u as real numbers with $v=B$, and $u+ϵn=A$, with $0<u<v<1$, and we conclude that $n\delta v=1$. That is, B is the hyperbolic center of $\mathcal{E}$ as well as the inner Apollonian focus of $\mathcal{E}$ whose Apollonian index is n, and $A=u+ϵn$ is the outer focus of $\mathcal{E}$. Furthermore, if P and Q are distinct points on such a circle of Apollonius with index n we have the cross-ratio of the four points (not necessarily collinear) for which ${\displaystyle \frac{\left|AP\right|\left|BQ\right|}{\left|AQ\right|\left|BP\right|}}=1$; with X being an indeterminate point, this identity in turn means that ${\displaystyle \frac{\left|AP\right|\left|BX\right|}{\left|AQ\right|\left|BX\right|}}={\displaystyle \frac{\left|AP\right|\left|BQ\right|}{\left|AQ\right|\left|BP\right|}}$ is the equation of a circle, demonstrating why this old Apollonian algorithm forms the core idea for a hyperbolic metric. Full article

For the first time, the structure of natural hexacelsian, BaAl₂Si₂O₈, a polymorph of celsian and paracelsian, has been refined. Hexacelsian was found in rankinite-bearing paralava near Mount Ye’elim in the northern part of the large Hatrurim Complex pyrometamorphic rock area (Hatrurim Basin) in the Negev Desert, Israel. It associates with Ba-bearing minerals such as barioferrite, walstromite, gurimite and the potentially new mineral BaCa₂Mg(SiO₄)₂, forming small isolated aggregates between the rock-forming minerals. These rock-forming minerals are represented by gehlenite, rankinite, wollastonite and schorlomite. The structure was refined for a hexacelsian grain measuring 0.039 × 0.026 × 0.016 mm with the composition (Ba_1.01K_0.05Na_0.01Ca_0.01)_Σ1.08(Si_1.96Al_1.91Fe³⁺_0.11)_Σ3.98O₈ to R₁ = 3%. Natural hexacelsian with P6₃/mcm symmetry and unit cell parameters of a = 5.2973(4) Å, c = 15.6068(10) Å, γ = 120°, and V = 379.28(6) ų is an analogue of synthetic low-temperature α-hexacelsian. The hexacelsian structure (polytype 2H) is formed by double layers of tetrahedra linked by their tops and bases, which are parallel to (001). Each layer is built from hexagonal (ditrigonal) rings of tetrahedra. The tetrahedra in rings with a disordered Al/Si distribution are rotated by approximately 14.5° compared to the position of the tetrahedra in ideal hexagonal rings in the high-temperature γ-hexacelsian. Every second layer in the structure of the studied hexacelsian is rotated through 180°. The hexacelsian crystallised at temperatures above 1100 °C as a disordered, metastable γ-hexacelsian (1H). A decrease in temperature leads to the ordering of O2 sites and the formation of partially ordered α-hexacelsian (2H), which preserves the disordered distribution of Al/Si at the tetrahedra. Some of the γ-hexacelsian grains in paralava were replaced by celsian under high-temperature conditions. Under low-temperature conditions, α-hexacelsian is replaced by cymrite during the zeolitisation of pyrometamorphic rocks of the Hatrurim Complex. Full article

Symmetric electromagnetic sensing architectures induce representation-space decompositions that organize how measured fields respond to rotations, reflections, and programmable configurations. This paper develops a symmetry-resolved framework for analyzing how local parameter sensitivity is distributed across irreducible sectors and how this distribution changes under tensor lifting. Character-weighted Reynolds projectors decompose the derivatives of first-, second-, and fourth-order observables into orthogonal isotypic components, whose relative weights are quantified through normalized entropy, effective-sector occupancy, and dominant-sector concentration. The formulation distinguishes algebraic sector accessibility, determined by induced representations and tensor-product fusion, from the sensitivity profile realized by a specific physical observation model. The framework is validated using a narrowband far-field electromagnetic model of a two-ring $C_4$-symmetric receiving array and is further examined through matched cyclic and dihedral array ensembles. The results reveal a robust redistribution of sensitivity under tensor lifting in the tested cyclic architectures, while the dihedral configurations exhibit a different, order-dependent behavior associated with their richer representation structure. These findings do not imply a universal increase in information or estimation performance; rather, they show that tensorization reorganizes the symmetry channels through which local sensitivity is expressed. The proposed framework provides a diagnostic tool for comparing and designing symmetry-aware antenna arrays, metasurfaces, reconfigurable intelligent surfaces, and related programmable sensing architectures. Full article

Reversible solid oxide cells (ReSOCs) represent one of the most promising electrochemical technologies for sustainable energy conversion and storage, yet their large-scale deployment remains constrained by electrode materials capable of sustaining stable performance under alternating oxidizing and reducing conditions. Reversible solid oxide cells require electrode materials that combine phase stability, chemical compatibility, redox tolerance and a microstructure suitable for gas transport and surface reactions. However, the relationships among cation composition, thermal processing, phase formation and local chemical homogeneity remain insufficiently understood, particularly for compositionally complex perovskite-related oxides. In this work, this problem was addressed through a comparative physicochemical screening of three candidate electrode materials synthesized by a simple co-precipitation route: two co-doped lanthanum ferrites, (La_0.8Sr_1.2) (Fe_0.9Co_0.1)O_6+δ (LSFC) and (La_0.8Ca_1.2) (Fe_0.9Co_0.1)O_6+δ (LCFC), and one high-entropy praseodymium nickelate, Pr(Ba_0.8Ca_0.2)(Fe_0.2Co_0.2Ni_0.2Cu_0.2Zn_0.2)₂O_6+δ (PBC-HEO). DTA–TG analysis was used to determine the thermal decomposition and crystallization ranges of the precipitated precursors. Phase evolution as a function of calcination temperature was investigated by X-ray diffraction, while Raman and FTIR spectroscopy were employed to examine the local metal–oxygen environment and structural disorder. Raman spectroscopy confirmed the formation of perovskite-type metal–oxygen frameworks in all samples and revealed distinct redistributions of spectral weight between apical/equatorial (or symmetry-related) BO₆ stretching sub-modes and bending/tilting modes, reflecting different local defect-chemical mechanisms associated with A-site doping (Sr vs. Ca) in the Ruddlesden–Popper ferrites and B-site multi-cation occupancy in the double-perovskite PBC-HEO. Bulk and local elemental compositions were assessed by ICP-MS and SEM-EDS, respectively, and SEM was used to compare particle morphology and porosity. SEM-EDS analysis showed that PBC-HEO developed the most open and interconnected microstructure among the investigated powders, although accompanied by residual compositional heterogeneity. This morphology may favor gas accessibility; however, its effective impact on electrocatalytic performance requires dedicated surface area, porosimetry, electrical, and electrochemical measurements. LSFC formed a single major Ruddlesden–Popper phase only after high-temperature calcination, whereas LCFC retained calcium-containing secondary phases. PBC-HEO developed a major perovskite-related phase at 700 °C, accompanied by minor Zn-rich segregation. Under the selected processing conditions, PBC-HEO retained the finest and most interconnected porous microstructure, although it also displayed the highest local compositional heterogeneity. These results demonstrate that cation selection and thermal history jointly control phase stability, local disorder and microstructure, providing a basis for the subsequent electrochemical evaluation and optimization of perovskite-related ReSOC electrode materials. Full article