Physical Sciences

Abstract: The paper explores the provenance of the fundamental physical units in a physical universe defined over a finite relational arithmetic substrate. The units are identified as the four horizons of the substrate: the Planck length, momentum, time, and energy, one per representation domain of the framed shell. The four physical constants \( c \), \( \hbar \), \( G \), \( k_B \) follow uniquely from this quartet, over declared identifications whose epistemic status is tagged throughout. The speed of light is the ratio across the two Fourier pairs of the domain square. The Planck constant is the product within each conjugate pair. The Boltzmann constant is the mixed product. The gravitational constant is the normalisation of the quartet to the totality. The quartet admits exactly one internal cancellation identity. No further algebraically independent relation exists within its lattice. On an admissible substrate the four constants instantiate as exact residues; their unit-face magnitudes are their observer-facing manifestation. Beneath the quartet, dimensional analysis is developed as a graded modular domain algebra over the framed shell. Classical dimensional analysis is recovered exactly inside the sub-capacity window. The domain of the Planck constant is the unit flag: the generator of the unique order-four torsion subgroup that the domain lattice itself carries. The flag marks the crossing between the observer's counts and the substrate-anchored measures. Its torsion-free surrogate is the classical mass dimension. Temperature inherits the acceleration domain. The flag cancels in every count-valued comparison.

Abstract: Dark Matter and Dark Energy compose most of the universe. Yet, there is no understanding of their nature despite decades of intensive research. Here, we propose a new force that explains, without any further assumptions, Dark Matter and Dark Energy and their related observations. This force is similar to Gravity, but it is coupled to the angular momentum tensor instead of the stress-energy tensor. This force appears to be negligible at small distances and increases with distance until it dominates over the. Hence, a force of the large-scale structures. The coupling constant calculated from the observed galactic parameters of this force appears to be so small that it cannot be detected in any laboratory, which may explain why Dark matter has not been found despite extensive research. Dark Matter and Energy are shown to be two distinct aspects of a single force. This paper includes the theoretical framework and empirical calculations proving the above-mentioned arguments.

Abstract: The measurand considered in this work is the Planck length, \( \ell_{\mathrm P} \). The circularity objection surrounding the Planck units has a long history: Bridgman argued in 1922 that no physical significance should be attached to their particular magnitudes until an essential connection among gravitation, the velocity of light, and the quantum had been established; Cohen stated the circularity explicitly in 1987 by noting that a Planck mass calculated from G cannot then be used to determine G independently. Variants of this objection have persisted to the present day. This paper claims that the circle can now be broken. We develop a measurement model in which \( \ell_{\mathrm P} \) is inferred directly from the response of a torsion balance and from a non-gravitational determination of the inertial content of an isotopically enriched \( {}^{28}\mathrm{Si} \) source body. The source mass is represented by an aggregate reduced Compton wavelength constructed from measured photon wavelengths, cyclotron-frequency ratios, silicon lattice spacing, crystal volume, isotope composition, and material corrections. The resulting measurement equation contains neither G nor \( \hbar \) as independent input quantities. We specify the measurand, traceability routes, sensitivity coefficients, covariance terms, and principal systematic corrections. The proposed procedure is not intended to improve upon the numerical uncertainty of the CODATA value of \( \ell_{\mathrm P} \), conventionally inferred from G, \( \hbar \), and c; its significance is operational and methodological, because it provides an independent realization of the Planck length and thereby resolves the long-standing circularity objection.

Abstract: We had previously shown [T. Yarman et al., Results Phys. 10 (2018) 818–821] that the classical adiabatic relation pV ^5/3=Constant for an ideal monatomic gas admits a direct quantum-mechanical formulation in terms of Planck’s constant and confinement-dependent quantum-state indices. This result suggests that macroscopic thermodynamic scaling laws reflect an underlying quantum-state structure. In the present work, we revisit this quantum-state scaling framework and discuss how it may provide a complementary language for thermodynamic accessibility and macroscopic irreversibility. In particular, we emphasize the conceptual distinction between microscopic reversibility, the arrow of time, and operational macroscopic irreversibility. Within this perspective, irreversibility may be interpreted in terms of asymmetries in accessible quantum-state configurations under changing confinement and energy conditions, while the underlying microscopic equations remain formally time-reversal symmetric. At the same time, the concept of operationally inaccessible microscopic quantum reconstruction, such as that with regards to fission, naturally emerges. Still, we do not claim to replace Boltzmannian, correlation-based, or information-theoretic approaches. Rather, the present study proposes a complementary quantum-state scaling perspective for discussing thermodynamic accessibility and the macroscopic evolution of complex systems. Even so, within the present framework, these practical limitations on thermodynamic accessibility do not necessitate a breakdown of formal microscopic reversibility; rather, they align with the Boltzmannian view that macroscopic reversals remain formally possible yet are rendered overwhelmingly inaccessible in practice.

Abstract: A filtered self-reconstruction framework is developed in which finite descriptions are retained through protected interfaces fixed before reduction. Presentation data whose removal preserves the interface and all downstream maps are eliminated, while induced normal and Schur penalties remain in the reduced operator. Finite-core minimality, witness descent, and no-phantom reduction are thereby placed in one ordered residual system. At the state level, the trace-preserving conditional expectation defines a completely positive reconstruction semigroup with monotone subalgebra entropy. For a codimension-three timelike Codazzi defect, atomicity fixes the positive line \(\mathcal O(1)\) over the projective link \(\mathbb{CP}^1_\Gamma\). Under exact degree fidelity, the order-one current moment and order-two trace-free Codazzi moment occupy distinct Borel-Weil levels and select the multiplicity-free carrier \(E_3\oplus E_2\). Selection-witness descent leaves the split grading and determinant line, whose unitary automorphism group is $S(U(3)\times U(2))$; the centered grading determines the hypercharge direction and the even exterior package. The finite cocharacter shadow is \(\mathbb Z_6\), and parity reduction gives a three-dimensional induced module with a torsor Hodge complex. An Alena-Codazzi collar provides a conditional realization of the graded charges and their boundary transport. Exact covariance and a Callias-Schur gap are required for attachment to an isolated low bundle. Mass, mixing, Majorana, scalar, and contact data are assigned by the \(B-L\)-filtered Schur completion, with masses encoded as spectral penalties of the reconstructed defect. Numerical values are reported only for a specified completed branch.

Abstract: Research on exceptional points (EPs) as singularities, where eigenvalues and eigenvectors coalesce, has sparked a revolution in non-Hermitian physics [1–7], offering unprecedented sensitivity and wave manipulation. Previous studies have predominantly focused on isolated points in the complex plane [8–12], often relying on nonphysical complex parameters or active gain–loss modulation. However, such approaches introduce significant system complexity and hinder scalability, leaving the realization of continuous EP structures in purely passive, real-world systems an open challenge [13–18]. To address this challenge, this study reports the discovery of an EP surface within a purely passive, real-parameter, canonical two-degree-of-freedom (2DOF) damped system. A hidden physical landscape was unveiled, termed the L-surface, representing clusters of loci of innumerable EPs. Leveraging the L-surface derived from exact analytical solutions, this study identified and validated fundamental topological phenomena, including topological jump, imprint, and nucleation, all of which were previously obscured by numerical noise [19–23]. The comprehensive analysis and precise identification of this manifold required a physical parameter precision of 100 decimal places. This regime has been conventionally dismissed as mere numerical artifacts in standard 64-bit double-precision floating-point formats. The L-surface provides a robust foundation for next-generation ultrasensitive sensing and energy dissipation across frontiers, ranging from quantum computing [24–26] to advanced biosensing [27, 28], extending its transformative impact to the broader realms of electronics [29, 30] and optics [31–33].

Abstract: The fine-structure constant is an empirical boundary datum of quantum electrodynamics, not a value derived by the Standard Model. We formulate a conditional reconstruction model in which its inverse is the invariant capacity of a neutral codimension-two holonomy defect. The Indefinite Reconstruction Stability Principle requires a persistent neutral parent to remain complement-readable under arbitrarily continued finite reconstruction; with the punctured-normal-fiber theorem, this selects codimension two and an internal winding group Z. In the premetric domain, automorphism-related alternatives receive equal structural weight without invoking distance, energy, or probability. Readout of unit phase and spin-frame channels produces a canonical three-stratum U(1)–SU(2) exposure object with normalized valuation Ω=4π³+π²+π. Four necessary read-out roles together with a protected identity select the first faithful cyclic interface Z/5Z; its reciprocal outgoing–returning incidence space has one protected zero and a transitive orbit of 24 exposed states, fixing the first reciprocal correction. The saturated family of later cyclic resolutions and odd interface grading then determine an absolutely convergent tower with an exact logarithmic resummation. Identifying this response with the Thomson-limit electromagnetic coupling gives α⁻¹=137.035999176142, approximately 0.041 standard deviations below the 2022 CODATA value. The result is parameter-free within the declared axioms and separately falsifiable at its normalization, quotient, incidence, and physical-correspondence steps.

Abstract: We analyze the centrality (⟨N_part⟩) dependencies of midrapidity transverse momentum (p_T) spectra for identified light-flavor hadrons (charged pions and kaons, protons and antiprotons) in asymmetric p+Pb collisions at √s_nn = 5.02 TeV at the LHC. Using the new two-component Tsallis-Hagedorn Model with Transverse Flow (THMTF), we describe the ALICE experimental data up to p_T = 20 GeV/c across seven multiplicity classes. To reveal potential system-size dependencies, these results are systematically compared with symmetric Pb+Pb collisions at √s_nn = 2.76 and 5.02 TeV. It is estimated that collective radial flow emerges at ⟨N_part⟩ ≈ 4.0 ± 0.5 along with simultaneous transitioning of kinetic freeze-out temperature (T₀) to a nearly plateau region in p+Pb collisions. The kinetic freeze-out temperature (T₀) appears to demonstrate distinct centrality dependencies in small and large collision systems before reaching a stable plateau. In p+Pb collisions, T₀ initially rises up to its threshold value before stabilizing, suggesting that high energy densities in central p+Pb events might cause the compact system to decouple rapidly before undergoing significant expansion. Conversely, in Pb+Pb collisions, T₀ steadily decreases up to a larger threshold ⟨N_part⟩ value before reaching a plateau. This initial downward trend of T₀ in Pb+Pb collisions is consistent with the larger volume of heavy-ion fireballs, which may undergo more prolonged hydrodynamic expansion and extensive cooling before reaching the low-density decoupling limit. In both p+Pb and Pb+Pb collision environments, central collisions point toward enhanced thermalization, as deduced from decreasing-with-centrality trend of non-extensivity parameter q. Parameter q hierarchy (q (mesons) > q (baryons)) suggests that baryons may form predominantly in the highly thermalized core. In both p+Pb and Pb+Pb systems, the momentum scale parameter (P₀) rises steadily with centrality and correlates strongly positively with the average flow velocity (< β_T >), suggesting that larger pressure gradients may simultaneously drive collective flow and high-p_T particle production. However, at high p_T, the power-index n points to potentially different dynamics between the two systems. While large-scale Pb+Pb collisions exhibit spectral flattening likely related to strong hydrodynamic pressure, the p+Pb system shows a stable n for mesons (consistent with vacuum-like jet fragmentation), but a rising-with-centrality trend of n for protons and antiprotons. This rise of power-index n may indicate intermediate-p_T baryon enhancement via parton recombination/coalescence. These different physical trends are supported by Pearson correlation analyses of extracted model parameters in p+Pb and Pb+Pb collision systems. The results of present work establish critical benchmarks for theoretical models describing the transition from microscopic interactions to collective behavior in high-energy collisions.

Abstract: We present a simulation with two isolated computers (“Alice” and “Bob”) generating coincident events with independently randomized measurement settings. The underlying model is fully deterministic and yields CHSH violations up to S ≈ 3, despite satisfying the operational requirements of loophole-free Bell experiments. The effect arises from a system of mutually exclusive observables combined with a protocol for handling missing detections. Surprisingly, injecting random values can strengthen rather than suppress observed violations, especially in the case of measurement-induced counter-correlations. Furthermore, we argue that pairwise measurements with alternative settings impose a monogamy-like constraint on quantum event structures. Predicted Bell violations, though natural in such systems, cannot be observed without correcting displaced events.

Abstract: The upcoming COMET and Mu2e experiments aim to search for charged-lepton flavor violation with unprecedented sensitivity, requiring an exact characterization of the muon decay-in-orbit (DIO) spectrum near its kinematic endpoint. Here, we present a testable prediction derived from rest mass dynamics and special relativistic energy conservation. In contrast to standard Quantum Electrodynamics —where the bound muon retains its invariant rest mass— our approach predicts that atomic binding intrinsically rescales the bound particle's internal dynamics. For muonic aluminum (Z=13), this yields two correlated, parameter-free signatures at the DIO endpoint: i) a downward endpoint displacement of approximately 0.95 MeV, and ii) a 0.9% horizontal compression of the spectrum corresponding to an equivalent retardation of the integrated decay rate. The simultaneous observation of these signatures would provide direct empirical evidence for the proposition that atomic binding modifies a bound particle's intrinsic rest mass.

Abstract: We present a unified thermodynamic framework in which the flow of quantum information — described covariantly by the entropy current vector s^μ-- couples to fermionic matter and simultaneously provides the microphysical origin of spacetime geometry. The Dirac equation is modified as (iℏγ^μ ∂_μ-mc+λγ^μ s_μ)ψ=0, where dimensional analysis identifies λ as a coupling constant of mass dimension [λ]=-2, naturally placing the theory as a low-energy effective field theory. The modified dispersion relation E=-λs^0 c±c√(p^2+m^2 c^2 ) shows that uniform entropy flow produces only an overall energy shift, while non-uniform flows induce a complete gauge-like structure in the non-relativistic limit: the spatial entropy current s acts as a vector potential, and its curl generates an effective magnetic field B_eff=(λ/m)∇×s, driving spin precession via ω_entropy=(λ/m)∇×s. Extending the Proca-type dynamics of s^μ to curved spacetime with non-minimal curvature coupling, we quantize the entropy flow field and integrate out its quantum fluctuations. In this framework, the Einstein-Hilbert action emerges as the low-energy effective action, with Newton's constant Gdetermined by the entropy field's vacuum expectation value. The linearized theory yields a massive spin-2 excitation -- the emergent graviton -- with dispersion E^2=p^2+m_s^2, where the entropy field mass m_s is constrained by LIGO/Virgo gravitational-wave observations to m_s≲10^(-20)eV. Using STAR data on Λ hyperon global spin polarization in heavy-ion collisions, we estimate λ∼10^(-7)-10^(-5) GeV^(-2), corresponding to an entropy-flow energy scale Λ_λ∼10^2-10^3GeV. This framework naturally connects to Jacobson's thermodynamic gravity, Verlinde's entropic gravity, and the generalized second law ∇_μ s^μ≥0, providing a quantum-information theoretic foundation for the emergence of spacetime and a concrete, testable realization of gravity as an entropic phenomenon.

Abstract: Recent lattice studies have revealed that the color flux tube between static quark-antiquark pairs exhibits an excess entanglement entropy (flux tube entanglement entropy, FTE²) that scales linearly with the quark separation L. In this paper, we demonstrate similar behavior in a string-net model based on SU(2)_k fusion categories, where the nontrivial object j=1/2 (analogous to color charge) cannot exist in isolation due to the fusion rules, naturally exhibiting “confinement”. We compute the entanglement entropy of the flux tube connecting two j=1/2objects using the topological definition S(R)=ln⁡(dim⁡(Hom(R))) and find an entropy density σ_k=ln⁡ d_1/2=ln⁡(2cos⁡(π/(k+2))). For k=3, the category reduces to the Fibonacci case, yielding an entropy density σ₃ = ln φ ≈ 0.481 (φ is the golden ratio), which is qualitatively comparable in magnitude to the scale inferred from lattice studies and the entropy-surface mechanism. Minimizing the free energy F=E-TS yields a confinement–deconfinement transition at T_c=J/σ_k.The parameter k offers a tunable knob, making the SU(2)_k family a computable laboratory for entropic confinement. The predicted entropy-density jump and critical scaling can be directly tested in quantum simulator platforms (e.g., Rydberg arrays or superconducting circuits) that realize Fibonacci anyonic models.

Abstract: Whether the universe is a flat or a closed system remains an open question. We derive the reason for the inflationary universe. Furthermore, we discuss why a surface-tension force is required. We present a model of the universe with an equation for its radius that suggests that the universe is infinite and flat. Further, we classically unify all the fundamental forces. Since the universe may have evolved from a point and a closed system to a flat system, our paper may help resolve the cosmological crisis. We provide the theoretical basis of all our findings.

Abstract: Canonical decompositions are among the most powerful organizing principles in mathematics. Prime factorization, Jordan canonical form, spectral decomposition, and Hodge decomposition demonstrate that complicated mathematical objects often admit unique descriptions in terms of elementary structural components. Surprisingly, despite the ubiquity of finite relational systems throughout mathematics, no general decomposition theory appears to exist for finite architectures themselves. Existing approaches typically begin with graphs, operators, Green functions, networks, or application-specific models rather than with architecture as the primitive mathematical object.In this paper we develop a decomposition framework for finite architectures generated by four primitive structural processes: transport, interaction, closure, and hierarchy. Within the free architectural algebra introduced here, every architecture possesses a unique canonical decomposition into these primitive generators. This decomposition induces canonical architectural coordinates and leads to a representation theorem showing that every positive multiplicative structural invariant is uniquely determined by its values on the primitive generators.The framework is formulated independently of any particular realization. Graph theory, Green-function methods, operator theory, and Green-Function Architecture Theory arise naturally as representations of the same underlying structural decomposition. The resulting theory separates structural decomposition from mathematical representation and provides a foundation for studying architectural invariants independently of their realization. The extension of the decomposition theory beyond the free architectural algebra and the determination of distinguished architectural basis constants are formulated as central problems for future research.

Abstract: The report presents the results of broadband dielectric spectroscopy (BDS) studies in bulk nanocolloids: E7 liquid crystalline (LC) mixture plus C₆₀ fullerene nanoparticles. BDS spectra for 260 temperatures from the isotropic liquid (I) phase at ~360K to the nematic (N) phase at the glass temperature T_g~220K was tested. The analysis focused on pretransitional critical-like features and complex glassy dynamics, highlighting their interplay and dominance. This is associated with pretransitional fluctuations, which impact the nematic phase even 90 K below the I-N transition. On approaching T_g, strong previtreous changes detected via dielectric constant and the loss curve maximum appear, starting at T_g+30K. The critical-like behavior on T→T_g appears explicitly also for the parameter describing the distribution of relaxation times. For the 3 main relaxation times in the long-range nematic phase, the optimal portrayal via the new Critical & Activated equation is evidenced. The derivative-based test of coupling/decoupling between translational and orientational processes reveals strong decoupling with the fractional exponent F< 1 below the I-N transition and related to F< 1 above T_g. Notable is the permanent ‘parallel’ orientation of LC molecules by C₆₀ fullerene nanoparticles, which can be significant for applications.

Abstract: Transmission spectroscopy with the James Webb Space Telescope (JWST) has opened a new regime for the atmospheric characterization of temperate sub-Neptunes and Hycean candidates. However, atmospheric inferences remain sensitive to the methodological assumptions adopted in retrieval frameworks. We perform a multi-framework retrieval analysis of the transmission spectrum of K2-18 b, combining synthetic noise simulations consistent with NIRISS and NIRSpec observations from program GO-2722 with atmospheric retrievals using TauREx 3, petitRADTRANS, and PSG-OEM. We quantify how differences in opacity databases, aerosol parameterizations, and statistical inference methods propagate into retrieved atmospheric properties. All frameworks favor a hydrogen-dominated atmosphere with robust signatures of methane and carbon dioxide, while additional species such as water vapor, ammonia, and hydrogen cyanide remain weakly constrained. We find systematic framework-dependent differences of 0.3–0.7 dex in retrieved molecular abundances, demonstrating that the current JWST transmission spectrum of K2-18 b lies in a regime where retrieval degeneracies remain significant. In particular, we show that the reported evidence for dimethyl sulfide (DMS) is not robust under reasonable variations in retrieval methodology. These results highlight the importance of multi-model retrieval validation for reliable atmospheric interpretation of JWST spectra.

Abstract: The Gassmann–Nur critical-porosity model, as used for amplitude and pore-pressure analysis, assigns a single critical porosity to a mineral — equivalently, it holds the dry-frame Poisson’s ratio constant with porosity. This paper generalizes the model to distinct bulk and shear critical porosities, ϕs ≤ ϕc. Three results follow. First, the Vp–Vs hyperbola which follows when Gassmann is combined with Nur is exact for any constant pair of critical porosities; the equal-porosity condition fixes only the anchor velocity (Vp as Vs approaches zero), not the shape of the curve. Second, a granular frame is physically expected to lose its shear-supporting backbone before its bulk-supporting one, placing ϕs at or below ϕc. Third, the dry sandstone frames of Han (1986) give ϕc = 0.402 and ϕs = 0.350, with the dry-frame Poisson’s ratio rising across the measured porosity range at better than four sigma, rejecting the constant-Poisson idealization within the data. The generalization preserves the hyperbolic form while changing its details — the anchor and the dry-frame Poisson’s ratio — and leaves the single-porosity numerics a close approximation, the separation in critical porosities being small and constant and its effects pronounced only as porosity approaches critical; it identifies where single-porosity pore-pressure prediction carries a systematic bias. It also resolves a standing feature of the published model — the dry- rock residual of its fluid parameter d, which the single-porosity form must carry as an unexplained correction — as the same shear–bulk separation, corroborated independently in dry shale.

Abstract: In guided-wave stimulated Brillouin scattering (SBS), the opto-mechanical coupling strength is determined by the spatial overlap of optical and elastic fields, fundamentally constrained by symmetry. Conventional analyses based on ordinary point groups assume that fields share the waveguide’s symmetry, which is valid for standing-wave modes with zero longitudinal wavenumber. However, in waveguides with longitudinal axis reversing operations, such operations flip the wavenumber sign for traveling wave modes, making the conventional framework insufficient—a limitation not addressed before. Here, we introduce the type III Shubnikov (magnetic) point groups, combining time reversal with axis reversing spatial operations, and establish a co-representation theory for such traveling wave modes. We prove that these modes obey a conjugate symmetry derived from the antiunitary elements of the magnetic point group. From this, we derive a general selection rule for backward SBS: if the waveguide possesses only one nontrivial axis reversing operation (and no other independent symmetry), the conjugate symmetry protects the coupling from being forbidden. Numerical validations on single crystal lithium niobate, fused silica, and single crystal silicon waveguides of a trapezoidal cross section confirm the predicted conjugate symmetry and show that materials with lower intrinsic symmetry more favorably realize such protected backward SBS. This work represents the first systematic introduction of magnetic group theory to nonmagnetic waveguides, offering new insights for material selection and coupling control in guided wave SBS.

Abstract: We derive a causal law of observer-indexed entropy retrieval: retrieved reference information grows toward the supply available to a finite observer. A recorded admission-and-readout instrument produces orthogonal operational sectors from arbitrary coherent radiation; exact diary fidelity and decoupling give the flagged family, while branch errors bound its approximate realization. An exact quantum transfer channel yields the remaining-gap law and its continuous Lindblad evolution. The channel has an explicit unitary collision realization: admitted reference information moves from radiation to memory, while the capture record remains diary-blind. Its memory marginal is the Choi state of an erasure channel, giving an intrinsic positive-coherent-information boundary at retrieved fraction r = 1/2. A strip-holomorphic modular speed limit bounds how rapidly the channel can activate, with the hyperbolic tangent selected uniquely at extremality. The integrated retrieval dose is invariant under a change of clock, making the Kerr lapse cancellation one geometric instance of a general result. At fixed supply and kinetic rate under an affine clock, the transfer and activation laws compose into a closed proper-time retrieval trajectory on the equality branch, identify that trajectory as the sharp fastest-retrieval envelope, and fix the earliest admissible retrieval horizon. In the continuum formulation, Araki relative entropy defines retrieval on restricted observable algebras, and a split Type-I factor provides the regulated density-operator representation. The experimental program follows the same causal sequence through retrospective analysis and staged intervention. Tier 0A determines whether archived analog-horizon data retain the shot-level, timing, protocol, and processing information needed to ask the retrieval question. Tier 0B then tests whether qualifying data contain observer-, protocol-, readout-, or analysis-operator-indexed correlation structure that standard pooling or filtering suppresses. A positive Tier 0B result identifies retrieval-relevant structure and motivates Tier 1; it does not by itself confirm the complete law. The prospective Tier 1 BEC program targets the held-out g²(t₁,t₂) surface, bandwidth scaling, and protocol dependence. Independent activation readout tests the modular bound and tanh rigidity. Reference-tagged supply and memory test cumulative dose, composite-hazard recovery, degraded-channel ordering, and two-memory allocation. The v2 verification artifact provides synthetic benchmarks and numerical consistency checks at bond dimensions D = 4 and D = 8 for the transfer law, inverse recovery, finite-resolution robustness, and matched adversarial alternatives. Standard RT/HRT geometry and a separate accessibility functional place the retrieval dynamics within holographic language. The retrieval law closes the observer-local path between global encoding and retained access. Information conservation, radiation encoding, causal collection, finite-observer retrieval, formal reconstruction, and comprehension are distinct physical operations. The black-hole information problem contains a proper-time access dynamics that global entropy accounting alone does not determine. Physical complexity enters through encoding, supply, clock, activation, transfer, retention, and observation. Those layers locate each source of retrieval failure instead of idealizing it away. The theory orders the encoding, supply, and retrieval clocks; distinguishes late supply from early supply through their overlap with future transfer dose; and gives an exact finite-lifetime retrieval criterion. Here rᵢ(τ) is the normalized reference information retained by observer i, eᵢ(τ) is the causally available supply, kᵢ(τ) is the composite access hazard, and τ_char is the characteristic activation scale.

Abstract: Rotating traversable wormholes provide a horizonless setting in which to investigate wave dynamics beyond the separable structures familiar from black-hole perturbation theory. We study scalar perturbations in the rotating AdS-Teo wormhole and show that the absence of separability naturally leads to a coupled-channel formulation in which the angular harmonic modes interact through a matrix-valued Sturm-Liouville operator. Imposing regularity at the wormhole throat together with asymptotically anti-de Sitter boundary conditions yields a determinant quantization condition that determines a discrete normal-mode spectrum. A controlled two-channel truncation illustrates how angular-channel mixing produces frequency shifts, spectral repulsion, and collective mode reorganization. From the asymptotic solutions, we construct a matrix-valued boundary response function whose poles coincide with the bulk normal-mode frequencies, while its off-diagonal components provide a direct signature of rotation-induced channel mixing. We further investigate the renormalized vacuum polarization, whose interference terms reveal local quantum signatures of non-separability, and examine semiclassical geodesic correlators as complementary probes of two-boundary connectivity. These results suggest that coupled-channel spectral theory provides a natural organizing principle for rotating, non-separable geometries, replacing conventional mode separability with a framework based on collective normal modes, matrix-valued response functions, and coupled quantum observables.