Physical Sciences

Abstract: For the past fifty years, the physical foundations of black hole (BH) thermodynamics have remained heavily contested because their original derivations rest at the theoretical intersection of general relativity and quantum field theory (QFT). This work provides an alternative macroscopic formulation by treating the physical vacuum in and around a BH as an elastic continuum curved by the presence of mass. According to Hooke's law of elasticity, the radial strain at the event horizons of all BHs must saturate at the exact same constant value. Under this principle of universal maximum strain, the laws of BH thermodynamics emerge directly from macroscopic continuum mechanics. This eliminates the need for QFT input, mirroring the contemporary macroscopic descriptions of the Casimir effect. Our calculations are formalized using the Reformulated Planck System (RPS), which relies exclusively on Planck's constant \(h\). This native approach prevents the dimensional contamination of 3D continuum mechanics caused by the 2D geometric factor inherently embedded in Dirac's reduced constant \(\hbar\), a salient miscue first recognized in the iconic definitions of the fine-structure constant α and the gravitational coupling constant α_g which firmly precluded the identification of the α-dependence of the weak coupling constant \( αw = \sqrt{\alpha} \). In BH thermodynamics, this RPS-based approach reveals higher Hawking temperatures and lower Bekenstein entropies, both by a factor of \( 2\pi \).

Abstract: Can geometry, electromagnetic propagation, and electromagnetic backreaction be derivatives of one function before a metric or a matter action is introduced? We exhibit a local affirmative construction. The only dynamical field in the parent action is an \( SL(3,\mathbb C) \) connection, and a degree-one homogeneous adjoint-invariant phase \( \Phi(X) \) of curvature wedge products supplies its constitutive response \( B_I=2\Phi_{,IJ}F^J \). Curvature-derived spectral projectors define an analytic parent phase near an ordered 3+4+1 response. Its exact, consistently embedded neutral sector admits an algebraic stationary representation that enforces the simplicity constraints on the full gravitational response at finite electromagnetic amplitude within the regular local neutral branch. The resulting triplet reconstructs the geometry; the central derivative gives Maxwell propagation in that geometry; and the gravitational derivative gives its Maxwell source, controlled by the same parent coefficient. On the specified Lorentzian real branch, the neutral equations are exactly the Einstein–Maxwell–\( \Lambda \) electrovacuum equations, not an amplitude truncation or an inference from quadratic matching. We prove the local invariant completion, compute its ordered connection two-jet, and give explicit curvature and coupling conventions. The construction realizes one classical ordered branch of a single phase; its domain is the regular analytic neighborhood of that branch.

Abstract: We believe that the origin of the universal dark energy may crucially depend on the behavior of the gravitational constant \(G\). If \(G\) is constant throughout the universe, then the dark energy density u₀ is supported by the vacuum via its constant and evolving properties. On the other hand, in varying-\(G\) gravity (whose low-acceleration limit is MOND), u₀ is a manifestation of radial \(G\)-gradients in the source of gravity. We estimate the present-day dark energy density of the universe in these two independent cases without using conventional Planck-2018 modeling in deriving the expressions for u₀. The constant-\(G\) derivation uses dimensional analysis, vacuum constants, and a newly discovered evolving bridge between vacuum mechanical and electromagnetic quantities. The varying-\(G\) derivation relies on the MOND critical acceleration \(a_0^{}\), the source of gravity that falls off as \(\sim r^{-2}\) at large distances \(r\), and the assumption that the present-day energy density \(u_0^{}\) can be estimated by spatially averaging this radial profile over the MOND volume \(\frac{4\pi}{3}r_0^{~3}\), where \(r_0^{}=c^2/a_0^{}\) and \(c\) is the speed of light in vacuum. The agreement between these two determinations and the Planck-2018 results from \(\Lambda\)CDM modeling is at the percent level, so that the results cannot distinguish clearly between constant-\(G\) and varying-\(G\) gravity. The analysis further indicates that the Newtonian constant G₀, the MOND constant \(a_0^{}\), and the Planck units of force, power, voltage, and current should be accepted as empirical vacuum invariants of the same stature as the well-known resistive properties of the vacuum; whereas charge, capacitance, inductance, and various fields are scale-dependent properties evolving in the expanding universe since the Stoney era. Ultimately, the vacuum behaves as a remarkably stiff elastic medium under stress, irrespective of the presence or absence of matter. This property has long been encoded, albeit inconspicuously, in the much discussed Tully–Fisher and Faber–Jackson relations, as well as in the Casimir effect and the field equations of General Relativity.

Abstract: This paper presents PySkyLumos, an open-source Python framework for simulating skylight polarization measurements and metadata. It implements the Rayleigh, Berry, and Pan models, capturing both classical scattering and elevation-expressed singularity dynamics. Efficiency benchmarks show a fivefold overall speedup and up to two orders of magnitude faster Stokes-parameter image formation compared to existing tools. Validation against real polarization camera data confirms its accuracy and suitability for bio-inspired computer vision, navigation, robotics, and sensing applications.

Abstract: This paper undertakes a philosophical investigation of the relationship between meta-laws, first-order laws, and observational conditions, and provides a categorical formalization of that relationship. We begin by establishing a four-quadrant ontology that makes explicit the possible configurations of relations among M, L, and O. We then propose a theory of ontological degeneration, arguing that the remaining three quadrants may be regarded as specializations of quadrant IV-C, obtained by contracting O or L to a terminal object; under an interpretive framework that preserves the explanatory power of scientific practice, these specializations may reasonably be called “degenerate forms.” We further prove that symmetry, normativity, causality, and statistical covariance can be derived only from quadrant IV-C, and from none of the other quadrants. Against this ontological background, the central thesis of the paper is that F(L,O) = Ψ(R(L,O)) is the local projection or reconstruction of the global meta-law M at the specific pair (L,O). From this thesis we derive seven successive conclusions: M ∼ F(L,O); Sym(M) = Sym(F); normativity is the constraint structure of covariance; causality is the functoriality of F over the category of time; statistical covariance is the functoriality of F over the category of probability; historicity is the functoriality of F along the flow of time; and modality is the functoriality of F over the group of admissible transformations. We further raise F to a 2-functor, establish the higher-categorical structure of F, and embed F into topos theory, constructing the F-topos, in which the conditionality, boundedness, hierarchy, symmetry, normativity, causality, modality, and higher structure of laws can all be precisely characterized in the internal logic of the topos. We also argue that the F-framework, though a meta-theory and thus not directly falsifiable, generates three classes of empirically testable assertions: covariance predictions, obstruction predictions, and levelevolution predictions. Finally, we draw out the methodological implications of the framework and engage it in dialogue with phenomenology, pragmatism, and critical theory.

Abstract: We develop a unified effective framework for three cosmological regimes associated with geometric–information dynamics on the 35-dimensional Riemannian symmetric space \( \mathrm{SL}(6,\mathbb{C})/\mathrm{SU}(6) \). Statistical localization is characterized by distinct spectral and confined-diffusion estimates, while the physical sector is formulated on an assumed four-dimensional Lorentzian spacetime. A derivative coupling between a Fisher-geometry kinetic invariant \( X \) and an order parameter \( \varphi \) yields an effective kinetic coefficient \( A(\varphi)=Z-\gamma\varphi^2/2 \) and a field-dependent mass \( m_{\mathrm{eff}}^2=m_0^2+\gamma X \). The coupled Euler–Lagrange equations imply total stress-energy conservation and a calculable internal energy exchange along a single proper-time trajectory. Under explicit regularity, decay, and monotonicity hypotheses, the effective mass undergoes a unique critical crossing. Early accelerated expansion requires potential domination, whereas a tachyonic instability alone does not establish reheating, particle production, or selection of a particular \( \mathrm{SU}(6) \) matrix vacuum. For convergent trajectories in the healthy kinetic domain, a positive residual vacuum density \( \Lambda_{\mathrm{eff}} = U_\infty - \frac{m_0^4}{4\Lambda} \) implies \( w \to -1 \) and conditional late-time domination over diluting matter. The nonzero Ornstein–Uhlenbeck covariance floor does not determine this vacuum energy. Complementary Lean proof bodies encode scalar conservation, constraint propagation, conditional crossing, and late-time limits. The framework provides conditional consistency results rather than a first-principles derivation of Lorentzian spacetime or a complete cosmological history.

Abstract: MIsCORE–RIUD Paper I established recurrent event-native merger-local morphology as an auditable observational object without assigning a unique physical origin. Paper II asks whether those local objects connect into ordered multiscale paths and whether the frozen higher-order object remains supported after projection into unsubtracted H1/L1 strain without reopening discovery freedom. A corrected 25-event atlas first showed that path construction was not automatic: 16/25 events contained at least one path, 9/25 contained no path, and 14/25 were multi-pattern. The canonical lock then fixed 13 events, 172 nodes, 26 H1/L1 raw-strain files, a merger-relative center window of −0.12 to +0.03 s, and the complete 10–60 ms width family, with no post-outcome event replacement, threshold retuning, or BEST_WIDTH selection. The frozen residual-derived coordinates were projected directly into 4-s, 4096-Hz H1/L1 strain in the locked 40–400 Hz band, with no raw-strain path reselection. The primary equal-weight statistic was 1.171221; 0/100,000 empirical-null draws reached the observation, giving p(+1)=9.9999×10⁻⁶, equivalent to approximately 4.265σ on a one-sided Gaussian tail only as a descriptive calibration of this finite empirical null. Every leave-one-event-out omission remained supported (maximum p=5.99994×10⁻⁵; ≈3.85σ one-sided), and support persisted without the 60-Hz notch and under a locked-coordinate ablation. A separate prelocked 62,400-job nuisance program constrained four coherent or independent artifact families while retaining weaker H1-only and L1-only transient alternatives. A selector-aware phase layer reran the exact selector on 2,600 real off-source controls; the observed equal-event real component was 0.3671572579932161, and 0/100,000 conditional phase-randomization draws exceeded it (p(+1)=9.9999×10⁻⁶; ≈4.265σ one-sided descriptive equivalent). The boundary remains explicit: population/map-level detector-resolved support is present, whereas the stricter eventwise coherence criterion yields zero FDR05 survivors and a separate 16-event physical-attribution audit yields zero global FDR05 survivors in both direct and visibility-controlled families. Paper II therefore establishes a connected multiscale observational path with fixed-coordinate raw-strain support and separate conditional phase directionality, while unique physical origin and exhaustive detector-artifact closure remain unresolved.

Abstract: Investment decisions during an energy crisis are usually driven by capital cost, levelized cost, carbon intensity and nominal conversion efficiency. These indicators are necessary but incomplete, because every energy technology also consumes energy for extraction, manufacture, conversion, storage, control and replacement. This review uses energy returned on energy invested (EROEI) as a common physical basis and follows the energy chain from conventional oil and gas to photovoltaics, wind, hydropower, hydrogen and electrical storage. It separates four quantities that are often conflated: source EROEI, round-trip efficiency, manufacturing energy per unit of storage capacity, and lifetime energy stored on energy invested (ESOI). For lithium-ion batteries, a widely cited 2017 review estimated 350 to 650 MJ of manufacturing energy per kWh of capacity, about 97 to 181 kWh, before the energy embodied in upstream materials is added; newer gigafactory data show large reductions but do not yet support a single universal value. A simple combination rule shows that the complete-chain return of stored electricity is always lower than both the operational return and the ESOI of the storage device, so that cycle life can matter as much as chemistry. At small energy-harvesting scales, sensing and control can consume a material fraction of the captured energy; Energy Returned on Invested Energy for Embodied Intelligence (EROIE) extends the same accounting to Reflex Policy control architectures. The paper concludes with a minimum energetic due-diligence protocol to be applied before major energy investments.

Abstract: To determine the covariant four-momentum of a physical system in curved spacetime, we introduce an energy-momentum field, whose four-potential and tensor are included in the Lagrangian density. From the principle of least action, we derive an equation for the metric, equations for the energy-momentum field, and the four-dimensional Euler-Lagrange equation. The equations of particle motion are derived in two ways: through the covariant derivative of the right-hand side of the equation for the metric, and by varying the action function with respect to the four-coordinates. These equations are equal when the invariant mass density of the particles is constant. The four-potential of the energy-momentum field makes it possible to find the four-momentum density and four-momentum of the system. The corresponding equations are derived by varying the action function under a four-shift of all particles of the system by a constant four-vector. The four-momentum density and the four-momentum of the system must satisfy these equations for the system's symmetry associated with such the four-shift to hold.

Abstract: Compact, label-free optical transducers are attractive for real-time exhaled-breath screening. We report the characterization and classification performance of a low-power photonic elastic-backscatter sensing system (the Dr. T system) that interrogates injected gas mixtures with a 635 nm, <1 mW coherent diode-laser beam and records the back-scattered light on a two-dimensional silicon position-sensing detector (PSD) as a time series of intensity I and centroid coordinates (x, y) at 10 Hz. Seven calibration data sets were acquired in a sealed 0.11 L chamber—five disease-linked metabolite mixtures in a normal-air balance (CKD, SIBO, cystic fibrosis, COPD, heart disease), a healthy base-gas control, and an ambient control (19 records). Regression showed the beam-deflection axis (y vs x) to be a linear, reproducible common-mode signature of injection flow (slopes 0.18–0.24; R2 up to 0.98), whereas the optical response versus concentration (|I| vs C) is species-specific across a >20-fold slope range, constituting an optical fingerprint. A physically motivated feature space with Mahalanobis classification separated the four diseases carrying substantive metabolites at 100% leave-one-run-out recall; overall seven-class accuracy was 78.9%. Decisively, every substantive-metabolite disease was well separated from a base-gas control undergoing an identical chamber-pressure rise (D = 4.8–13.5), demonstrating that discrimination is driven by molecular optical signatures rather than common-mode pressure. The sensor can detect, discriminate, quantify and classify metabolite mixtures in vitro; signal-to-contrast enhancement for low-cross-section analytes, humidity compensation and radiometric calibration are identified as translation priorities.

Abstract: The Friedmann–Lemaître–Robertson–Walker (FLRW) cosmic-time coordinate is the proper time of the idealized homogeneous comoving congruence. In an inhomogeneous universe, however, physically distinct matter histories---for example those associated with virialized halos, filaments, and underdense regions---need not accumulate identical proper times between the same physically specified boundary states. This paper formulates a worldline-based program for testing such differences, referred to here as Relativistic Time Dilation in an Expanding Universe (RTD-EU), without assuming that nonlinear structure formation produces a percent-level clock differential. For two specified timelike worldlines, the invariant quantity of interest is the proper-time misclosure \(\Delta\tau_{AB}=\tau_A-\tau_B\), evaluated between covariantly defined endpoint hypersurfaces. A \(3+1\) decomposition exposes a convenient clock-rate factor \(\Gamma_K=d\tau_K/dt\), while also making clear that lapse- and shift-based quantities depend on the chosen foliation and are not themselves observables. The physical prediction is therefore the worldline integral, not the lapse alone. The Raychaudhuri equation establishes that different environments can possess different expansion, shear, curvature, vorticity, and acceleration histories, but it does not by itself determine a difference in accumulated proper time. The required chain is instead \[ \{T_{\mu\nu},\text{initial/boundary data}\} \longrightarrow \{g_{\mu\nu},u_K^{\mu}\} \longrightarrow \tau_K[\gamma_K] \longrightarrow \Delta\tau_{AB} \longrightarrow \text{observables}. \] A representative weak-field estimate gives fractional clock effects near \(10^{-5}\) for ordinary halo-scale potentials, far below the percent scale potentially relevant to cosmological parameter tensions. A larger signal would therefore have to emerge from a demonstrable property of a relativistic inhomogeneous solution, with any averaging prescription shown to preserve the relevant observables. The invariant redshift relation \(1+z=(k_\mu u^\mu)_e/(k_\mu u^\mu)_o\) further shows that cumulative source-worldline aging does not, by itself, replace the standard photon stretching factor. Any nonstandard transient-timescale prediction must arise from a derived change in source-frame evolution or in the operational mapping between redshift and cosmic history. RTD-EU is consequently presented as a falsifiable chronometric-closure program rather than as an established explanation of the Hubble tension, dark energy, or early-galaxy observations.

Abstract: We investigate the variational boundary-value problem for a finite Friedmann--Lemaître--Robertson--Walker (FLRW) region M₋ joined across a spherical hypersurface Σ to an exterior Schwarzschild vacuum region M₊. The hypersurface Σ is treated not as an externally fixed Dirichlet boundary, but as an internal junction of a composite spacetime M=M₋∪Σ∪M₊. In the absence of a surface stress-energy layer, continuity of the induced metric and extrinsic curvature---the Darmois/Israel no-shell conditions—provides a sufficient condition for stationarity of the joined Einstein--Hilbert action. The angular junction condition admits a non-comoving causal branch in the asymptotic null limit, where the boundary radius approaches the Schwarzschild radius and the interior de Sitter scale satisfies R_Λ−=r_s, or equivalently Λ₋=3/r_s². The effective cosmological constant may then be interpreted as a quantity selected by the global causal boundary rather than as an independent local bulk parameter. This boundary is not an observable edge of the FLRW region. At finite time the observer-centred apparent horizon lies inside the global junction, so the latter is not directly visible as a wall or preferred direction. Its effect is instead encoded in the expansion history through the boundary-selected value of Λ₋. The infinite-FLRW limit is recovered for r_s→∞, for which Λ₋→0. Within this framework, a non-zero Λ₋ is associated with a finite FLRW region bounded by a causal horizon that asymptotically coincides with its Schwarzschild radius.

Abstract: The dichotomy, which divides an object into two, has wide applications in mathematics, computer science, and philosophy. In this paper, inspired by the method of dichotomy, we propose a theoretical framework to characterize quantum entanglement. The basic idea is to start from the most fundamental physical system and perform binary decomposition step by step to establish different types of entangled states. By dividing a parent system into two subsystems, we investigate the relationships between the subsystems under different states of the parent system. We show that entanglement necessarily exists between the two subsystems when the parent system remains unchanged, whereas it may be absent when the parent system changes. Beyond quantum physics, we demonstrate that the dichotomy also has important implications for classical physics.

Abstract: Altermagnetism has emerged as the third fundamental magnetic phase alongside ferromagnetism and antiferromagnetism, generating a rapidly growing literature that is increasingly difficult to curate by hand. Here we present a physics-grounded knowledge-base pipeline for altermagnetic materials that combines symmetry-based material seeding, layout-aware document reading, LLM-assisted extraction, auditing, and vector-database retrieval within a distributed inference stack. The workflow begins from crystallographically screened candidate materials, harvests relevant literature from arXiv, transforms papers into structure-preserving text representations, and finally builds validated records through either single-agent or crew-based extraction paths before serving grounded question answers over our knowledge base. Across benchmark tests at two model scales, our structured single and crew pipelines greatly outperform the bare LLM baseline in recovering paper-grounded values, with the smaller model remaining consistently faster. Our analysis shows that scientifically useful performance is driven primarily by structured retrieval and high-fidelity document reading, with agentic complexity acting as a secondary design choice rather than the central source of accuracy gains.

Abstract: β2-Microglobulin (β2M) is an important biomarker associated with kidney dysfunction, dialysis-related amyloidosis, and inflammatory disorders, motivating the development of highly sensitive detection platforms. Here, we propose a nonlinear terahertz (THz) sensing platform based on graphene-enhanced third-harmonic generation (THG) for β2M detection. Unlike conventional graphene plasmonic sensors that rely on linear resonance shifts, the proposed approach exploits the strong dependence of graphene’s nonlinear optical response on its Fermi energy. Adsorption of charged β2M molecules alters graphene’s carrier concentration and Fermi energy, resulting in measurable changes in the THG response. The sensor consists of periodically patterned graphene micro-ribbons coupled to a gold substrate through a thin Kerr nonlinear dielectric spacer, forming a resonant metasurface with strong THz field confinement. The combined effects of graphene plasmonic resonances and cavity-enhanced field localization significantly enhance THG at relatively low incident intensities. The effects of graphene Fermi energy, dielectric thickness, and excitation intensity on the sensing performance are systematically investigated. The results demonstrate concentration-dependent shifts in the THG spectral response and intensity, with increasing β2M concentration producing a progressive shift toward higher frequencies. The proposed sensor detects β2M concentrations as low as 0.0001 g/L, achieving a sensitivity of 971 THz·L/g and a figure of merit (FOM) of 1706 L/g. These results demonstrate improved detection performance compared with conventional linear plasmonic sensing and highlight the potential of graphene-enhanced THG metasurfaces for sensitive, tunable, and compact THz biosensing and biomedical diagnostics.

Abstract: We review what is known about finite-time singularity formation ("blow-up") in the unsteady Prandtl boundary-layer equations, from the numerical discovery of the van Dommelen--Shen singularity in 1980 to the rigorous description of its self-similar structure completed in 2018--2022. The survey is organized around five questions: (i) what the singularity is physically (unsteady separation and eruption of the boundary layer); (ii) where it is known to occur (the impulsively started cylinder, vortex-induced separation, colliding wall streams); (iii) what has been proved (the E--Engquist theorem, the Kukavica--Vicol--Wang theorem, the Collot--Ghoul--Ibrahim--Masmoudi description of the stable blow-up pattern, the classification of inviscid singularities); (iv) how blow-up relates to the ill-posedness of the Prandtl equations without monotonicity and to the inviscid limit of the Navier--Stokes equations; and (v) how the reduced one-dimensional system on the symmetry axis, which carries the rigorous theory, sits inside the recent similarity transformation of Sun [Phys.\ Fluids \textbf{36}, 083616 (2024)] as its \(m=1\) member. We also record the explicit affine blow-up solution \(u=-x/(t_*-t)\), \(v=y/(t_*-t)\), which is exact for both Prandtl and Navier--Stokes, and explain why Prandtl blow-up bears no relation to the finite-energy Navier--Stokes blow-up announced in September 2026. A list of open problems closes the survey.

Abstract: The Rubin survey is expected to extend the halo white-dwarf luminosity function into a regime where current data neither establish nor exclude remnants with cooling ages beyond the standard cosmic age. Public Montreal thick-hydrogen DA tracks give dwell times in the window M_bol = 17–20 from 4.84 Gyr at 0.5 M_☉ to 0.70 Gyr at 1.2 M_☉. Under an illustrative uniform cooling-age density on [T₀, 2T₀], with T₀ = 13–14 Gyr, the Montreal-only occupancy is 0.10–0.19 at 0.6 M_☉, at most 0.21 on the grid, and zero at 0.95 M_☉ and above. BaSTI-calibrated bright-edge shifts widen the 0.6 M_☉ range to 0.10–0.27; no analyzed channel exceeds 0.3720. A robust-within-set candidate whose conservative cooling-age lower bound exceeds the standard ceiling under the youngest age assignment in the declared model set is a chronology anomaly under that set, regardless of abundance. A null remains parametric: the population inputs are underived, and the frozen two-stage Rubin operator has not been executed on Rubin observations. Supplementary Material 1 regenerates the calculations and figure.

Abstract: Local information can be lost rapidly while a collective mode survives for a long time. We study this distinction on a physical–observation joint state space. The second variation of relative entropy under a local record map gives a positive Fisher-loss operator; the least loss over normalized noninvariant scores is the spectral gap of the associated posterior-resampling process. The local strength and the compatibility of surviving directions enter separately. A fixed-width interacting ladder has a positive gap at every fixed finite coupling, as follows from an explicit block comparison, although strong correlation makes the bound small. We then reverse the construction. For a given irreducible real Hamiltonian with nonpositive off-diagonal entries, its ground amplitude determines pair-record probabilities and energy-valued loss weights, reproducing the physical excitation gap exactly. A positive trial amplitude gives an error interval controlled by the oscillation of its local energy, without requiring the exact ground state. When signs remain, the energy form is a difference of positive information forms and an explicit cancellation constant controls the gap. Sparse diagonalization of open transverse-field chains up to 65 536 configurations agrees with both the reconstructed information spectra and an independent free-fermion calculation. The critical law n∆_n/J → π, the gapped regime, and the ordered finite-chain splitting are distinguished. The result is an explicit connection for specified channels and Hamiltonians, with the requirements of positivity, locality, and energy normalization kept separate.

Abstract: This work considers the hypothesis that the cosmological vacuum may retain a residual relational capacity, here described as vacuum porosity, and that cosmic expansion may involve a continuous redistribution of the response associated with this condition. At the macroscopic level, this response is represented by a residual scalar stress S. Here, S denotes residual vacuum stress, not thermodynamic entropy. Any connection between the two would need to be established separately. In a homogeneous and isotropic equilibrium regime, the corresponding vacuum-like contribution is written in the form \( Σ_{μν} = - Sg_{μν} \). When this term is included in the source sector of Einstein’s field equation, \( G_{μν} = \frac{8πG}{c^4} (T_{μν} + Σ_{μν}) \) substitution of the isotropic vacuum-stress tensor gives \( G_{μν} + \frac{8πG}{c^4} Sg_{μν} = \frac{8πG}{c^4} T_{μν} \). Direct comparison with Einstein’s equation containing the cosmological term, \( G_{μν} + Λg_{μν} = \frac{8πG}{c^4} T_{μν} \) therefore yields \( Λ = \frac{8πG}{c^4} S \). The tensorial correspondence is exact once this vacuum-like isotropic form is assumed. The physical proposal is to interpret S as a residual stress associated with the redistribution of a relationally non-saturated vacuum during cosmic expansion, while leaving the Einstein tensor and the geometrical structure of general relativity unchanged. The present work is limited to the macroscopic tensorial description and physical interpretation of the residual stress.

Abstract: Born probabilities determine the distribution of individual records, but leave their temporal relations open. In the U(1) M-event model a transported circle phase carries path memory; fixed transports on the same fiber nevertheless commute. We extend the event selector to a nontrivial compact connected finite-dimensional Lie group within the physical–observation dual-axis structure. One action governs the selector, its conjugate charge and their coupled motion on the two-axis base. A Haar initial selector, independent of the other initial data and prescribed controls, preserves the Born probabilities at every observation. Non-Abelian transport changes the relations between records. For balanced hemisphere readout on the full SU(2) group, we derive the exact law P_mis = α/π, relating the mismatch probability to the transport’s conjugacy angle. In a U(1) × SU(2) realization, a central charge sustains the original M response, while a periodic potential preserves its orbit and phase integral and makes finite deviations exactly harmonic. A classical pointer action gives hemisphere readout and a two-period SU(2) return for the stated apparatus preparation. With the faithful fixed-axis coupling, four blocks of 25 periods produce α₂₅ = 1.012373567 . . .. If readout retains the selector after either outcome, the third supercycle differs from the initial record with probability 96.6746%, and the sixth agrees with it with probability 93.3491%. Independent response and matrix measurements fix these values before the event sequence is observed. Scans of axis angle and block length test the relation between noncommuting transport and event memory.