arXiv subjects

Vivek Kumar Singh

Publications and source records attributed to Vivek Kumar Singh.

At least 19 recordsLinked to original sources

arXiv2026

Worldsheet skeins and block decomposition of quivers

Following the knot-quiver correspondence, we investigate quiver counterparts of the HOMFLYPT skein relations by interpreting link invariants in terms of holomorphic worldsheets and their multicover contributions. Extending this framework to more general worldsheet geometries, we conjecture that, up to quiver equivalence, the adjacency matrix of the quiver associated with any link in a skein triple admits a block decomposition whose diagonal blocks are quiver adjacency matrices associated with the other two links. We verify this conjecture in numerous examples.

hep-th↗

arXiv2026

Planner-as-Router: Joint Plan-Time Model Routing for Cost-Efficient Multi-Agent Workflows

Running large language model (LLM) agents in production gets expensive fast. A frontier model (the largest, most capable tier) is accurate but can cost 25 times what a small model costs per token, and the gap compounds once a workflow chains several calls together. Planner-as-Router (PaR) attacks this from a different angle. Instead of leaving model-tier selection to some component downstream, it folds the choice into planning itself. As the planner breaks a query into subtasks, it also assigns each one a model size tier (small, mid, or frontier, ordered by capability and price), so the dependencies between subtasks are visible before any specialist runs. Unlike per-call routers such as cascade routing, which look at one node at a time, PaR sees the whole workflow up front and needs no separate router model or training data. We evaluate PaR with EntBench, a benchmark of 54 enterprise agentic tasks across seven classes, graded by actually running the generated Structured Query Language (SQL) and MongoDB queries against live databases. Over 1,157 evaluations spanning eight routers and three seeds, PaR stays on the observed cost-accuracy frontier. It matches a sink-frontier heuristic (frontier model on terminal nodes only) in accuracy at comparable cost and a faithful FrugalGPT cascade at lower cost, and cuts cost 44% against all-frontier routing while giving up 2.9 points of accuracy. Several accuracy gaps fall inside the plus-or-minus six-point confidence interval of a 54-task study, so we frame PaR's advantage as frontier position rather than a clean accuracy win. We also report a preliminary observation, not a validated result: a small pilot hints that cheap routing may carry a hidden compounding penalty on compositional workflows, which we frame as a hypothesis for future measurement. PaR, EntBench, and all evaluation code are open source.

cs.AI↗

arXiv2026

Governing the Edge: Automating Commercial Property and Casualty Insurance Underwriting via a Hybrid Local-Cloud Multi-Agent Framework

Underwriters in commercial Property and Casualty (P&C) insurance spend 30 to 40% of their time on administrative work rather than risk judgment, and a single submission takes about 40 minutes by hand. We present Governing the Edge, a multi-agent framework for that layer, organized around a data-residency constraint: sensitive submission data must not leave the perimeter. Eleven agents and two deterministic control nodes, one a human-escalation interrupt, form a 13-node LangGraph workflow across two tiers. Agents touching raw submissions run locally on Gemma 2, each bound through a tool interface logging every invocation (synthetic stubs in the current prototype); only anonymized scores and non-identifying fields cross to Claude Sonnet in the cloud. Compliance rules are encoded as conditions on graph edges, so a non-compliant submission never reaches pricing. We walk through one full scenario end to end, a commercial auto submission whose principal driver carries serious violations, showing every agent call, every tool invocation, and the resulting routing decision. The framework processes a 40-minute manual submission in a few minutes on a single edge device, dominated by serialized on-device inference. On the hard-stop violation tier the framework enforces every rule correctly and reproducibly, since hard stops are deterministic predicates over fields extracted at temperature 0; overall compliance accuracy across the 20-scenario benchmark is 70%, with the remaining gap concentrated in softer, judgment-based tiers. It keeps a complete audit trail and respects the privacy boundary throughout. We release all code, compliance rules, tool stubs, and synthetic datasets.

cs.AI↗

arXiv2026

ChurnBench: A Drift-Aware Benchmark Demonstrating That Refresh Scheduling, Not Cache Age, Governs Staleness in Agentic AI

In production, agentic systems answer questions over data that lives in several places and keeps changing: licenses are reassigned, users offboarded, prices changed, contracts renewed. Existing retrieval benchmarks freeze the data, so they cannot ask whether an agent's answer is still true, only whether it found the right passage. We present ChurnBench, an open-source benchmark that generates a four-source enterprise data fabric as a timeline rather than a snapshot. Every change is written to an append-only ground-truth ledger, and gold answers are computed from that ledger, never from the live stores. An answer that was correct when its data was retrieved but wrong when evaluated is therefore detected and labeled a freshness error, distinct from a reasoning error; we validate this by resolving ground truth at both timestamps for every case reported. Using the instrument, we find that when a system refreshes on a schedule, cache age does not predict staleness. Across cache ages of 1, 14, and 28 days, freshness errors were 7, 4, and 4, because scheduled refresh bounds staleness by time-to-live, and no TTL lapse was observed in any window. A controlled ablation confirms the mechanism: disabling tiered refresh raises freshness errors from 4 to 45 at 28 days and leaves them identical at one day. The variable a drift benchmark should sweep is therefore TTL configuration against each entity's rate of change, not drift-window length. ChurnBench, the evaluation harness, and all per-error data are released open source.

cs.SE↗

arXiv2026

Total Cost of Agency: Exact Attribution of Memory Injection Cost in Multi-Agent LLM Workflows

Every node in a multi-agent large language model (LLM) workflow retrieves context from memory and injects it into its prompt, where those injected tokens are billed as input tokens at the same per-token price as the system prompt and the user query. Production observability tools report total token cost but do not separate the tokens a node generates from the tokens it is handed, so this component of the bill is invisible to the teams paying it. We introduce the Total Cost of Agency (TCA), a decomposition of multi-agent workflow cost into base prompt, inference, memory injection, miss penalty and context-accumulation components, and an exact attribution method: a two-pass, non-billable token count that measures injected tokens directly rather than estimating them from word-count proxies. On a 200-task enterprise benchmark executed against real model APIs, memory injection accounts for 13.6 percent of the variable cost a compile-time optimizer can act on, about 12 percent of the full billed cost, and its share rises from a structural zero at workflow depth one to 27.6 percent at depth six. Injected tokens grow linearly with depth over the measured range (R^2 = 0.9974, depths two through six); a quadratic fit yields a negative leading coefficient, so the data do not exhibit convex growth at these depths. We show the component is controllable at fixed model tier: reducing the retrieval window capacity from 32 to 2 entries lowers injected tokens by 28.7 percent with an accuracy change within seed-level variation. We report in full that our graph-rewriting transforms are approximately cost-neutral in isolation, that two of the five decomposition terms are zero by construction in this harness, and that total workflow cost is dominated by model tier assignment, which we hold fixed and treat as prior work. Prompt caching is not evaluated; all figures are for the uncached case.

cs.AI↗

arXiv2026

Technical Report on Resilient and Secure Large-Scale Energy Internet Systems

This IEEE PES Task Force report examines the security and resilience of large-scale Energy Internet (EI) systems, in which electricity, information, and market layers are tightly coupled through pervasive digitalization. The report characterizes the EI cyber-physical threat landscape and surveys detection, assurance, and mitigation techniques, presents modeling, control, and decision-making frameworks that capture cyber-physical interdependencies, including storage integration, multi-dimensional resilience, and electricity price forecasting, examines adversarial risks and trustworthy deployment of artificial intelligence, and introduces graph-based, attack-resilient information routing. The report closes with recommendations for research, standardization, and regulatory efforts needed to realize a resilient and secure large-scale EI.

eess.SY↗

arXiv2026

PROSLEX: A Novel Dataset for Expert-Annotated Legal Statute Prediction for Indian Judiciary

Legal Statute Prediction (LSP) involves automatically identifying relevant legal statutes given factual descriptions in legal documents, typically framed as a multi-label classification task within natural language processing and information retrieval research. While recent advances have begun incorporating Large Language Models (LLMs) for statute prediction, current approaches primarily focus on accuracy metrics without addressing the critical need for legal reasoning, a fundamental requirement in judicial contexts where decisions must be explainable and justifiable. To address this research gap, we present PROSLEX (PRediction Of Statutes and LEgal eXplanation), a comprehensive dataset comprising 1,623 expert-annotated legal documents from the Indian context. Each document is paired with statute predictions and detailed explanations, totaling 7,450 explanations, capturing the underlying legal reasoning. Using this dataset, we systematically evaluate various prompting strategies, including zero-shot, few-shot, chain-of-thought, and tree-of-thoughts approaches, to generate both statute predictions and their corresponding legal rationales. Our evaluation framework measures not only predictive performance but also the coherence and legal validity of generated explanations, positioning PROSLEX as a benchmark for developing explainable AI systems that can support legal practitioners while advancing research in interpretable legal NLP. To ensure reproducibility, we have made our PROSLEX dataset and model code available on GitHub: https://github.com/subinay494/Legal_Statute_Prediction_Explanation.

cs.AI↗

arXiv2026

Torus Knots in Adjoint Representation

We derive a closed-form expression for the adjoint polynomials of torus knots and investigate their special properties. The results are presented in the very explicit double sum form and provide a deeper insight into the structure of adjoint invariants essential for the Vogel's universality of Chern-Simons theory.

hep-th↗

arXiv2026

A TQFT-based Platform for Efficient Computation of Knot Invariants

We present an interactive web platform that unifies the construction Feynman ribbon diagrams (FRDs), the evaluation of higher-rank Chern--Simons knot invariants, and the identification of FRD-like knots at higher crossing numbers. These tree-structured diagrams naturally represent arborescent knots, which we refer to throughout as FRD-like knots. Within a single visual environment, users can construct an FRD as a tensor network, evaluate its associated Chern--Simons invariants, and use the resulting invariant data to distinguish and identify the corresponding knot. To our knowledge, this is the first platform to combine diagrammatic construction, tensor-network evaluation, invariant computation, and knot identification within a unified workflow.

math.GT↗

arXiv2025

Panhandle polynomials of torus links and geometric applications

We use a decomposition of the tensor of the fundamental representation of the quantum group $U_q(\mathfrak{sl}_N)$ and the Rosso-Jones formula to establish a peculiar ``panhandle'' shape of the HOMFLY-PT polynomial of the reverse parallel of torus knots and links. Due to their panhandle-like intrinsic properties, the HOMFLY-PT polynomial is referred to as a ``panhandle polynomial''. With the help of the $\ell$-invariant, this extends to links the Etnyre-Honda result about the arc index and maximal Thurston-Bennequin invariant of torus knots. It has further geometric consequences, related to the braid index, the existence of minimal string Bennequin surfaces for banded and Whitehead doubled links, the Bennequin sharpness problem, and the equivalence of their quasipositivity and strong quasipositivity. We extend these properties to torus links, which relate to the classification of their component-wise Thurston-Bennequin invariants. Finally, we discuss the definition of the $\ell$-invariant for general links.

math.GT↗

arXiv2025

Clifford Solver for the Tetrahedron Equation and its Variants

The different forms of the tetrahedron equation appear when all possible ways to label the scattering process of infinitely long straight lines are considered in three dimensional spacetime. This is expected to lead to three dimensional integrability, analogous to the Yang-Baxter equation. Among the three possibilities, we consider two of them and their variants. We show that Clifford algebras solve both the constant and the spectral parameter dependent versions of all of them. We also present a scheme for canonically solving higher simplex equations using tetrahedron solutions.

hep-th↗

arXiv2025

Full twists and stability of knots and quivers

We relate the stability of knot invariants under twisting a pair of strands to the stability of symmetric quivers under unlinking (or linking) operation. Starting from the HOMFLY-PT skein relations, we confirm the stable growth of $Sym^r$-coloured HOMFLY-PT polynomials under the addition of a~full twist to the knot. On the other hand, we show that symmetric quivers exhibit analogous stable growth under unlinking or linking of the quiver augmented with the extra node; in some cases this augmented quiver captures the spectrum of motivic Donaldson-Thomas invariants of all quivers in the sequence. Combining these two versions of the stable growth, we conjecture that performing a~full twist on any knot corresponds to appropriate unlinking or linking of the corresponding augmented quiver -- this statement is an important step towards a~direct definition of the knot-quiver correspondence based on the knot diagram. We confirm the conjecture for all twist knots, $(2,2p+1)$ torus knots, and all pretzel knots up to 15 crossings with an~odd number of twists in each twist region.

hep-th↗

arXiv2025

Data to Decisions: A Computational Framework to Identify skill requirements from Advertorial Data

Among the factors of production, human capital or skilled manpower is the one that keeps evolving and adapts to changing conditions and resources. This adaptability makes human capital the most crucial factor in ensuring a sustainable growth of industry/sector. As new technologies are developed and adopted, the new generations are required to acquire skills in newer technologies in order to be employable. At the same time professionals are required to upskill and reskill themselves to remain relevant in the industry. There is however no straightforward method to identify the skill needs of the industry at a given point of time. Therefore, this paper proposes a data to decision framework that can successfully identify the desired skill set in a given area by analysing the advertorial data collected from popular online job portals and supplied as input to the framework. The proposed framework uses techniques of statistical analysis, data mining and natural language processing for the purpose. The applicability of the framework is demonstrated on CS&IT job advertisement data from India. The analytical results not only provide useful insights about current state of skill needs in CS&IT industry but also provide practical implications to prospective job applicants, training agencies, and institutions of higher education & professional training.

cs.CY↗

arXiv2025

Colored Jones Polynomials and the Volume Conjecture

Using the vertex model approach for braid representations, we compute polynomials for spin-1 placed on hyperbolic knots up to 15 crossings. These polynomials are referred to as 3-colored Jones polynomials or adjoint Jones polynomials. Training a subset of the data using a fully connected feedforward neural network, we predict the volume of the knot complement of hyperbolic knots from the adjoint Jones polynomial or its evaluations with 99.34% accuracy. A function of the adjoint Jones polynomial evaluated at the phase $q=e^{ 8 πi / 15 }$ predicts the volume with nearly the same accuracy as the neural network. From an analysis of 2-colored and 3-colored Jones polynomials, we conjecture the best phase for $n$-colored Jones polynomials, and use this hypothesis to motivate an improved statement of the volume conjecture. This is tested for knots for which closed form expressions for the $n$-colored Jones polynomial are known, and we show improved convergence to the volume.

math.GT↗

arXiv2025

Non-invertible symmetry breaking in a frustration-free spin chain

A nearest-neighbor, frustration-free spin $\frac{1}{2}$ chain can be constructed {\it via} projectors of various ranks á la Bravyi-Gosset. We show that in the rank 1 case this system is gapped and has two ground states resembling ferromagnetic states. These states spontaneously break the non-invertible symmetry connecting them. The latter is proved using the machinery of algebraic quantum theory. The non-invertible symmetries of this system do not come from a duality.

hep-th↗

arXiv2025

Algebraic classification of Hietarinta's solutions of Yang-Baxter equations~:~invertible $4\times 4$ operators

In order to examine the simulation of integrable quantum systems using quantum computers, it is crucial to first classify Yang-Baxter operators. Hietarinta was among the first to classify constant Yang-Baxter solutions for a two-dimensional local Hilbert space (qubit representation). Including the one produced by the permutation operator, he was able to construct eleven families of invertible solutions. These techniques are effective for 4 by 4 solutions, but they become difficult to use for representations with more dimensions. To get over this limitation, we use algebraic ansätze to generate the constant Yang-Baxter solutions in a representation independent way. We employ four distinct algebraic structures that, depending on the qubit representation, replicate 10 of the 11 Hietarinta families. Among the techniques are partition algebras, Clifford algebras, Temperley-Lieb algebras, and a collection of commuting operators. Using these techniques, we do not obtain the $(2,2)$ Hietarinta class.

hep-th↗

arXiv2024

Institutional Shifts in Contribution to Indian Research Output during the last two decades

In the past few decades, India has emerged as a major knowledge producer, with research output being contributed by a diverse set of institutions ranging from centrally funded to state funded, and from public funded to private funded institutions. A significant change has been witnessed in Indian institutional actors during the last two decades, with various new private universities being set up and several new IITs, NITs, IISERs being established. Therefore, it is important to identify whether the composition of the list of the top 100 research output producing institutions of India has changed significantly during the recent two decades. This study attempted to analyse the changes during the two 10-year periods (2004-13 and 2014-23). The institutions which retain their position within top 100 during both periods are identified, along with the change in their positions. Similarly, institutions that were there in top 100 list during first time period (2004-13) and go out of top 100 list during second time period (2014-23) are also identified. In the same line, the new entrant institutions in the top 100 list during second time period (2014-23) are identified too. The results obtained indicate towards an institutional shift in the contribution to Indian research output.

cs.DL↗

arXiv2024

Who is Funding Indian Research? A look at major funding sources acknowledged in Indian research papers

Science and scientific research activities, in addition to the involvement of the researchers, require resources like research infrastructure, materials and reagents, databases and computational tools, journal subscriptions and publication charges etc. In order to meet these requirements, researchers try to attract research funding from different funding sources, both intramural and extramural. Though some recent reports provide details of the amount of funding provided by different funding agencies in India, it is not known what quantum of research output resulted from such funding. This paper, therefore, attempts to quantify the research output produced with the funding provided by different funding agencies to Indian researchers. The major funding agencies that supported Indian research publications are identified and are further characterized in terms of being national or international, and public or private. The analytical results not only provide a quantitative estimate of funded research from India and the major funding agencies supporting the research, but also discusses the overall context of research funding in India, particularly in the context of upcoming operationalization of Anusandhan National Research Foundation (ANRF).

cs.DL↗