SoR: A Multidisciplinary Exploration

• SoR is a multidisciplinary abbreviation that represents diverse concepts—from enzyme detoxification in bioinorganic chemistry to iterative solvers in numerical analysis and matrix computations.
• Domain-specific methodologies include direct spectroscopic detection in superoxide reductase studies, adaptive parameter tuning in successive over-relaxation, and pathway modeling in consumer behavior frameworks.
• Understanding SoR requires contextual awareness across disciplines, as its precise meaning is defined by local technical standards in fields like planetary science, evolutionary theory, and randomized numerical methods.

Searching arXiv for recent and relevant papers on the multiple established meanings of “SoR/SOR”. I will look up arXiv entries spanning the major technical senses of “SoR/SOR”: superoxide reductase, successive over-relaxation, stimulus–organism–response, self–other reorganisation, spin–orbit resonance, and Subspace-Orbit Randomized SVD. SoR, often written SOR, is a disciplinary abbreviation with multiple established technical meanings rather than a single concept. In the cited literature it denotes, among other things, superoxide reductase in bioinorganic enzymology, successive over-relaxation and related iterative schemes in numerical linear algebra, Stimulus–Organism–Response in consumer-behavior modeling, Self–Other Reorganisation in evolutionary theory, spin–orbit resonance in planetary science, and Subspace-Orbit Randomized decomposition in randomized matrix computation (Mathé et al., 2015, Miyatake et al., 2017, Rao et al., 3 Feb 2026, Gabora et al., 2024, Braam et al., 2024, Kaloorazi et al., 2018).

1. Disciplinary scope of the term

Across the supplied arXiv literature, the abbreviation is resolved entirely by local context. In biochemical work, SOR is an iron enzyme involved in superoxide detoxification. In numerical analysis, it usually names the successive over-relaxation method or one of its derivatives. In consumer research, it denotes the classical stimulus–organism–response architecture. In recent evolutionary theory, SOR names Self–Other Reorganisation. In exoplanet climate studies, SoR means spin–orbit resonance. In randomized linear algebra, SOR-SVD expands to Subspace-Orbit Randomized SVD (Adam et al., 2015, Gao et al., 2015, Rao et al., 3 Feb 2026, Gabora et al., 2024, Braam et al., 2024, Kaloorazi et al., 2018).

Sense of SoR/SOR	Domain	Representative formulation
Superoxide reductase	Bioinorganic chemistry	Detoxification enzyme reducing $\mathrm{O_2^{\bullet-}}$ to $\mathrm{H_2O_2}$
Successive over-relaxation	Numerical linear algebra	Stationary iterative method for linear systems
Stimulus–Organism–Response	Consumer research	$S \to O \to R$ behavioral framework
Self–Other Reorganisation	Evolutionary theory	RAF-based cumulative adaptive change
Spin–orbit resonance	Exoplanet science	Rational locking of spin and orbital periods
Subspace-Orbit Randomized	Randomized matrix algorithms	Two-sided low-rank approximation in SOR-SVD

This distribution suggests that SoR is best treated encyclopedically as a family of unrelated technical abbreviations whose semantics are discipline-specific rather than as a cross-domain theory.

2. Superoxide reductase in bioinorganic chemistry

In the biochemical literature here, SOR denotes superoxide reductase, a detoxification enzyme used by some anaerobic or microaerophilic organisms to remove superoxide without generating molecular oxygen. The net reaction is stated as

$$\mathrm{O_2^{\bullet -} + e^- + 2H^+ \rightarrow H_2O_2}.$$

In Desulfoarculus baarsii, the catalytically relevant active site is center II, a ferrous iron in an unusual square-pyramidal pentacoordination $[\mathrm{His}_4\mathrm{Cys}_1]$, while an additional rubredoxin-like ferric center I is present but is not required for the superoxide reaction (Mathé et al., 2015).

A central mechanistic advance is the direct identification of a transient high-spin $\mathrm{Fe^{III}}$-peroxo species at the catalytic site. In the E47A mutant, rapid reaction with $\mathrm{H_2O_2}$ gave resonance Raman bands at 850 cm$^{-1}$ and 438 cm$^{-1}$ that shifted to 802 cm$^{-1}$ and 415 cm$\mathrm{H_2O_2}$0 with $\mathrm{H_2O_2}$1, with no significant deuterium shift in $\mathrm{H_2O_2}$2. The bands were assigned to $\mathrm{H_2O_2}$3 and $\mathrm{H_2O_2}$4, supporting an unprotonated $\mathrm{H_2O_2}$5 intermediate. The same species forms only weakly in wild type, which the paper interprets as evidence that the conserved Glu47 promotes decay of the ferric-peroxo intermediate, most likely by facilitating $\mathrm{H_2O_2}$6 release (Mathé et al., 2015).

A second line of work concerns the SOR–ferrocyanide complex. Structural analysis showed that ferrocyanide entirely plugs the active site through a bent cyano bridge to the catalytic iron, producing what the authors describe as the first reported protein complex containing bound ferrocyanide. Solution and radiolysis studies then showed that this adduct still scavenges superoxide efficiently but no longer produces $\mathrm{H_2O_2}$7; instead, the one-electron redox event is carried mainly by the ferrocyanide moiety, while the SOR iron remains reduced during the early steps. In vivo, formation of the SOR–ferrocyanide complex increased the antioxidant capability of SOR expressed in an Escherichia coli sodA sodB recA mutant strain by about 3-fold at 1 mM ferrocyanide (Molina-Heredia et al., 2015, Adam et al., 2015).

The structural literature further shows that X-ray-induced photoreduction of the catalytic iron in the ferrocyanide adduct produces a small but measurable expansion of the six-coordinate active site. In the mixed-valence-to-reduced comparison, the octahedral volume increases by about 4.9%, with elongation of both the Fe–S(Cys116) and Fe–N(bridging cyanide) distances. This was interpreted as redox-linked weakening of metal–ligand interactions (Adam et al., 2015).

3. Successive over-relaxation in numerical analysis and scientific computing

In numerical mathematics, SOR most commonly denotes successive over-relaxation, a stationary iterative method for solving linear systems. For symmetric positive definite systems $\mathrm{H_2O_2}$8 with $\mathrm{H_2O_2}$9, the classical SOR iteration is written with

$S \to O \to R$0

and the standard convergence interval is

$S \to O \to R$1

One paper gives an exact reinterpretation of SOR as an Itoh–Abe discrete gradient method for the quadratic energy $S \to O \to R$2, with parameter mapping

$S \to O \to R$3

Under that correspondence, SOR becomes an energy-dissipative integrator, and Gauss–Seidel appears as the special case $S \to O \to R$4 (Miyatake et al., 2017).

The method is extended in several directions in the cited literature. For SPD systems, adaptive SOR based on the Wolfe conditions updates the relaxation parameter without additional matrix-vector products and interprets $S \to O \to R$5 as a step size after the change of variables $S \to O \to R$6 (Miyatake et al., 2018). For Hermitian positive semidefinite systems $S \to O \to R$7, theoretical work on shuffled and preshuffled SOR shows that random reorderings improve asymptotically upon the best known bounds for cyclic ordering (Oswald et al., 2015). For structured-grid discretizations, a fully parallel sweeping framework combines overlapping domain decomposition with a multi-frontal procedure and preserves convergence close to the original sequential SOR/ILU method (Tavakoli, 2010).

Several papers specialize SOR to structured applications. In uplink large-scale MIMO detection, the MMSE filtering matrix

$S \to O \to R$8

is shown to be SPD, which permits an SOR-based solver for $S \to O \to R$9. The reported effect is a reduction in complexity from $$\mathrm{O_2^{\bullet -} + e^- + 2H^+ \rightarrow H_2O_2}.$$0 to $$\mathrm{O_2^{\bullet -} + e^- + 2H^+ \rightarrow H_2O_2}.$$1, with near-MMSE performance after about 3 iterations and empirical tuning near $$\mathrm{O_2^{\bullet -} + e^- + 2H^+ \rightarrow H_2O_2}.$$2 in the tested systems (Gao et al., 2015). In constraint-based GUI layout, warm-starting an SOR-based solver from the previous solution rather than from $$\mathrm{O_2^{\bullet -} + e^- + 2H^+ \rightarrow H_2O_2}.$$3 improves solving time in all three tested scenarios: small-step resizing, big-step resizing, and constraint change (Jamil et al., 2014).

The term also covers generalized and derived schemes. For complex symmetric systems $$\mathrm{O_2^{\bullet -} + e^- + 2H^+ \rightarrow H_2O_2}.$$4 with $$\mathrm{O_2^{\bullet -} + e^- + 2H^+ \rightarrow H_2O_2}.$$5 SPD, the generalized SOR (GSOR) method is applied to the real-equivalent block system

$$\mathrm{O_2^{\bullet -} + e^- + 2H^+ \rightarrow H_2O_2}.$$6

with convergence iff

$$\mathrm{O_2^{\bullet -} + e^- + 2H^+ \rightarrow H_2O_2}.$$7

The optimal parameter is

$$\mathrm{O_2^{\bullet -} + e^- + 2H^+ \rightarrow H_2O_2}.$$8

The same splitting yields a GSOR preconditioner for GMRES (Salkuyeh et al., 2014). For the absolute value equation $$\mathrm{O_2^{\bullet -} + e^- + 2H^+ \rightarrow H_2O_2}.$$9, a recent SOR-like iteration obtains a wider convergence range under $[\mathrm{His}_4\mathrm{Cys}_1]$0, derives the analytical optimum $[\mathrm{His}_4\mathrm{Cys}_1]$1, and shows that at the optimal parameters the SOR-like method and fixed-point iteration are exactly the same (Liu et al., 2024).

The dependence of SOR efficiency on $[\mathrm{His}_4\mathrm{Cys}_1]$2 remains a central topic in PDE discretizations. For the Poisson equation on rectangular grids with $[\mathrm{His}_4\mathrm{Cys}_1]$3, mixed Dirichlet, Neumann, and Robin boundary conditions, and both central second-order and high-order compact discretizations, closed-form or asymptotic formulas are given for the optimal relaxation parameter in both point-SOR and line-SOR implementations (Darian, 17 Jan 2025).

4. Stimulus–Organism–Response in consumer-behavior research

In consumer research, SOR denotes the Stimulus–Organism–Response framework. In the cited Wuliangye study, this framework is merged with the Extended Theory of Planned Behavior (ETPB) to model how environmental stimulus and consumer ethnocentrism shape purchase behavior. The principal stimulus-side variables are Environmental Stimulus (ES), Consumer Ethnocentrism (CE), and Subjective Norm (SN); organism-side variables are Perceived Value (PV), Attitude (ATT), Perceived Behavioral Control (PBC), and Purchase Intention (PI); the response variable is Purchase Behavior (PB) (Rao et al., 3 Feb 2026).

The study surveyed 453 valid Wuliangye consumers in Sichuan Province and analyzed the data with covariance-based SEM in AMOS. The reported CFA fit indices were

$[\mathrm{His}_4\mathrm{Cys}_1]$4

with composite reliabilities from 0.7835 to 0.9401 and AVE values from 0.5 to 0.7. All structural hypotheses $[\mathrm{His}_4\mathrm{Cys}_1]$5 through $[\mathrm{His}_4\mathrm{Cys}_1]$6 were reported as supported (Rao et al., 3 Feb 2026).

Substantively, the paper reports that environmental stimulus, consumer ethnocentrism, perceived behavioral control, and purchase intention are all robust predictors of purchase behavior. Environmental stimulus and consumer ethnocentrism also show significant partial indirect effects through chain-mediated routes such as

$[\mathrm{His}_4\mathrm{Cys}_1]$7

and

$[\mathrm{His}_4\mathrm{Cys}_1]$8

The chain-mediated effects reported in Table 10 are

$[\mathrm{His}_4\mathrm{Cys}_1]$9

all significant. The paper further notes that the route

$\mathrm{Fe^{III}}$0

is stronger than

$\mathrm{Fe^{III}}$1

which it interprets as evidence that, for ethnocentrism-driven purchasing, perceived value slightly outweighs brand attitude as the operative mechanism (Rao et al., 3 Feb 2026).

This version of SOR is therefore not a generic atmospheric or retail-cue model; it is an extended behavioral architecture in which classical SOR sequencing is enlarged by TPB-type volitional and control variables.

5. Self–Other Reorganisation in evolutionary theory

In recent evolutionary theory, SOR expands to Self–Other Reorganisation. It is introduced as a primitive evolutionary process capable of producing cumulative, adaptive change without requiring variation, selection, competition, birth, or death. The formal basis is the theory of Reflexively Autocatalytic and Foodset-generated networks, or RAFs (Gabora et al., 2024).

The underlying catalytic reaction system is written as

$\mathrm{Fe^{III}}$2

where $\mathrm{Fe^{III}}$3 is the set of element types, $\mathrm{Fe^{III}}$4 the set of reactions, $\mathrm{Fe^{III}}$5 the catalysis relation, and $\mathrm{Fe^{III}}$6 the foodset. A RAF is a non-empty subset $\mathrm{Fe^{III}}$7 such that every reaction in $\mathrm{Fe^{III}}$8 is catalyzed by an element produced by $\mathrm{Fe^{III}}$9 or contained in $\mathrm{H_2O_2}$0, and all reactants in $\mathrm{H_2O_2}$1 can be generated from $\mathrm{H_2O_2}$2 by reactions in $\mathrm{H_2O_2}$3. The theory is used to model both abiogenesis and culture (Gabora et al., 2024).

The key claim is that some domains do not possess the genotype–phenotype architecture associated with a self-assembly code used in two distinct ways: active interpretation during development and passive copying during reproduction. Where such a code is absent, acquired traits are not screened off from transmission. SOR is proposed as the appropriate lower-fidelity process for domains such as earliest life and cultural evolution, where acquired change is retained and spread rather than being eliminated at generation boundaries (Gabora et al., 2024).

The 2024 paper formalizes a special case of “SOR without variation” through two stochastic processes: generation at rate $\mathrm{H_2O_2}$4 and percolation at rate $\mathrm{H_2O_2}$5 on a strongly connected graph $\mathrm{H_2O_2}$6. With $\mathrm{H_2O_2}$7 and $\mathrm{H_2O_2}$8, if $\mathrm{H_2O_2}$9 is the event that each of the first $^{-1}$0 generated products percolates to all entities before the next product is generated, then

$^{-1}$1

Setting $^{-1}$2 yields

$^{-1}$3

which is the formal basis for the high-percolation community model (Gabora et al., 2024).

A related Pólya urn construction models the high-percolation limit. With one white ball initially, selecting white creates a new color and selecting a colored ball darkens its shade. In the community-based model, the process rate is $^{-1}$4. The paper concludes that, over a fixed period, some products in the community model have expected complexity of order at least $^{-1}$5, whereas the individual-based model yields much smaller, roughly logarithmic maxima (Gabora et al., 2024).

The reply paper emphasizes that SOR is not a pure percolation model such as SIR, that it includes both assimilation of foodset elements and generation of foodset-derived elements, and that cultural SOR is robust to degradation and imperfect replication. It also stresses that critics’ simulations containing no RAFs do not instantiate SOR at all (Gabora et al., 2024).

6. Spin–orbit resonance in exoplanet science

In exoplanet climate studies, SoR denotes spin–orbit resonance. The cited paper studies Earth-like Proxima Centauri b atmospheres in 1:1 and 3:2 spin–orbit resonances using a 3D coupled climate–chemistry model based on the Met Office Unified Model and UKCA (Braam et al., 2024).

The two resonance states differ in illumination geometry. In a 1:1 SoR, the same hemisphere permanently faces the star. In a 3:2 SoR, the planet rotates three times for every two orbits; for the geometry considered, the substellar point shifts by $^{-1}$6 in longitude per orbit, so one full day–night cycle takes two orbits. The paper associates 1:1 with $^{-1}$7 and 3:2 with $^{-1}$8 in the modeled Proxima b cases (Braam et al., 2024).

The dynamical consequences are large. In the 1:1 case, Proxima b falls into the Rhines rotator circulation regime with dominant zonal gradients and a global mean surface temperature of 229 K. In the 3:2 case, the planet is warmer and more longitudinally homogeneous, with dominant meridional gradients and a global mean surface temperature of 262 K. The mean ozone column also changes strongly, from 387 DU in the 1:1 case to 731 DU in the 3:2 case (Braam et al., 2024).

The chemistry is explicitly three-dimensional. Ozone follows Chapman production plus HO$^{-1}$9 and NO$^{-1}$0 catalytic destruction, but its spatial pattern is controlled by circulation. In the 1:1 case, ozone accumulates in nightside gyres through a dayside-to-nightside stratospheric circulation. In the 3:2 case, the dominant organization is meridional and the paper identifies a Brewer–Dobson-like equator-to-pole transport pattern. Temporal variability also differs: for 3:2, daytime–nighttime water-vapour column changes reach $^{-1}$1 to $^{-1}$2, while ozone column changes are $^{-1}$3 (Braam et al., 2024).

These dynamical and chemical differences propagate directly into observables. Synthetic thermal emission spectra in the LIFE wavelength range show that the 1:1 state exhibits phase-dependent fluctuations of up to 36 ppm, whereas the more homogeneous 3:2 atmosphere produces relatively constant spectra. The paper proposes this contrast itself as an observational discriminant between resonance states (Braam et al., 2024).

7. Subspace-Orbit Randomized decomposition and acronymal extension

In randomized numerical linear algebra, SOR appears again in SOR-SVD, where it expands to Subspace-Orbit Randomized rather than successive over-relaxation. The method is introduced as a two-sided randomized procedure for low-rank matrix approximation of a large dense matrix $^{-1}$4 with numerical rank $^{-1}$5 (Kaloorazi et al., 2018).

The algorithm draws a Gaussian matrix $^{-1}$6, forms

$^{-1}$7

computes QR factorizations

$^{-1}$8

compresses the matrix to

$^{-1}$9

then computes a rank-$^{-1}$0 truncated SVD of $^{-1}$1 and lifts the factors back to the original space. The method requires a few passes through the data and is stated to run in

$^{-1}$2

floating-point operations (Kaloorazi et al., 2018).

The adjective “orbit” refers to the chained use of $^{-1}$3 and $^{-1}$4: the row-space sketch is generated from the orbit of the initial random sketch under repeated matrix action. The paper also gives deterministic and average-case bounds for singular values and approximation errors, and uses SOR-SVD as the low-rank engine in augmented-Lagrangian robust PCA (Kaloorazi et al., 2018).

This usage is unrelated to both the biochemical and iterative-solver senses of SOR. It is nevertheless important because it illustrates the broader pattern seen throughout the cited literature: the abbreviation SoR/SOR is stable within disciplines but semantically discontinuous across them.