19 papers
Typed Congruences and Quotient-Critical Irreducibility in Complete Ternary -Semirings
Chandrasekhar Gokavarapu, Madhusudhana Rao Dasari
We study congruences and binary reducibility in completely additive ternary -semirings through their two-sorted atomic cores. For an odd , an abelian group of expone…
Barr-Exactness and Congruence-Based Homological Algebra in Ternary -Semimodules
Chandrasekhar Gokavarapu, D Madhusudhana Rao
Let be a ternary --semiring and let be the category of ternary --semimodules with the intrinsic five--ary action $T\times Γ\times M \times Γ\times T…
Central Splitting, Division-Stable Residuals, and Opposite-Ring Transfer for Strongly C4*-Rings
Chandrasekhar Gokavarapu, Naveen Kumar Kakumanu, Sajani Lavanya Madasi +2
The known decomposition theorem for strongly \(\Cfourstar\)-modules gives a semisimple summand and a summand-square-free residual summand, with two-way Hom-orthogonality when the a…
Morita Transport, Marked Projective Loci, and Dedekind Classification for C4-Type Conditionss
Chandrasekhar Gokavarapu, Sekhar Babu Gosala, Sudhakar Gadde +2
Objectwise Morita invariance of $\Cfour$ is known. We prove the corresponding statements for $\Cfourstar$, semi-weak-CS, and strongly $\Cfourstar$, including the chain joins in the…
Certified Reduced-Order Surrogates and Stability Margins in Viscous Incompressible Flow and Fluid--Structure Interaction
Chandrasekhar Gokavarapu, Naveen Kumar Kakumanu, Anjali Datla +1
Let solve the incompressible Navier--Stokes equations in a regime in which an energy inequality is available and each constant in that inequality is computable from declare…
Certified Learning under Distribution Shift: Sound Verification and Identifiable Structure
Chandrasekhar Gokavarapu, Sudhakar Gadde, Y. Rajasekhar +1
Proposition. Let be a predictor trained on a distribution and evaluated on a shifted distribution . Under verifiable regularity and complexity constraints, the excess ri…
Quantitative fixed-point theorems with verifiable hypotheses: rates and stability
Chandrasekhar Gokavarapu, Srinivasulu Ch, D V N S Sriram Murthy +1
Let $(X,\dist)$ be a complete metric space and let be a closed invariant set. We study fixed points of maps governed by a \emph{verifiable} contract…
Finite-sample certification and operating envelopes for spectral clustering and graph centrality
Chandrasekhar Gokavarapu, Sekhar Babu Gosala, Rajeev Muthu +2
Spectral clustering and node rankings are commonly reported from one observed network without a finite-sample statement of what the observation supports. We develop a certification…
The Spectral Topology of Global Imbalances:A Graph-Theoretic Framework for Systemic Risk in the Balance of Payments
Chandrasekhar Gokavarapu, Sanjeev Kumar Chejarla, Balayya Rajana +2
We model global balance-of-payments linkages as a directed weighted exposure network and study systemic fragility through the spectrum of the associated operators. From a signed bi…
The Spectral Geometry of Ternary Gamma Schemes:Sheaf-Theoretic Foundations and Laplacian Clustering
Chandrasekhar Gokavarapu
This article develops a self-contained affine -scheme theory for a class of commutative ternary -semirings. By establishing all geometric and spectral results internally, the…
Asymmetry in Spectral Graph Theory: Harmonic Analysis on Directed Networks via Biorthogonal Bases (Random-Walk Laplacian Formulation)
Chandrasekhar Gokavarapu
The operator-theoretic dichotomy underlying diffusion on directed networks is \emph{symmetry versus non-self-adjointness} of the Markov transition operator. In the reversible (deta…
Unified Geometric, Fuzzy, and Computational Framework for Ternary Gamma Semirings
Chandrasekhar Gokavarapu, D Madhusudhana Rao
Aim. This paper (Paper D) unifies the ideal-theoretic, computational, and homological layers developed in Papers A (Rao 2025), B (Rao 2025), and C (Rao 2025) into a geometric frame…
Fundamental comparison, base-change, and descent theorems in the -theory of non-commutative n-ary Gamma-semirings
Chandrasekhar Gokavarapu, Dasari Madhusudhana Rao
We develop a comparison, base-change, and descent framework for the algebraic -theory of non-commutative -ary -semirings. Working in the Quillen-exact (and Waldhausen) set…
Finite diagonalizable torsors and Kummer cohomology over semiring schemes
Chandrasekhar Gokavarapu, Sajani Lavanya Madasi, Rajeev Muthu +2
Classical descent treats a finite diagonalizable torsor as a higher-rank locally free object. Over semirings that route is incomplete: fpqc-local freeness is not known to imply Zar…
Asymmetry in Spectral Graph Theory: Harmonic Analysis on Directed Networks via Biorthogonal Bases (Adjacency-Operator Formulation)
Chandrasekhar Gokavarapu
Classical spectral graph theory and graph signal processing rely on a symmetry principle: undirected graphs induce symmetric (self-adjoint) adjacency/Laplacian operators, yielding…
Structure and Spectral Theory of Non-Commutative and -ary -Semirings
Chandrasekhar Gokavarapu, D. Madhusudhana Rao
This paper develops the structural and spectral foundations of noncommutative and n-ary Gamma semirings, extending the commutative ternary framework established in earlier studies.…
Derived -Geometry, Sheaf Cohomology, and Homological Functors on the Spectrum of Commutative Ternary -Semirings
Chandrasekhar Gokavarapu, D. Madhusudhana Rao
This paper develops a comprehensive geometric and homological framework for derived Gamma-geometry, extending the theory of commutative ternary Gamma-semirings established in our e…
Axiomatic Foundations of Chemical Systems as Ternary -Semirings
Chandrasekhar Gokavarapu, Venkata Rao Kaviti, Srinivasa Rao Thirunagari +1
Chemical transformations depend not only on the identities of the reacting species but also on the catalytic, environmental, and intermediate conditions under which they occur. Cla…
Computational and Categorical Frameworks of Finite Ternary -Semirings: Foundations, Algorithms, and Industrial Modeling Applications
Chandrasekhar Gokavarapu, Dr D Madhusudhana Rao
Purpose: This study extends the structural theory of finite commutative ternary -semirings into a computational and categorical framework for explicit classification and constru…