Independent Research
Sharp Variance Bounds for Random Greedy Independent Sets in Split Graphs and Cographs
Arya Somu · Proposition · Draft
Determines the exact largest variance of random-order greedy independent-set size among split graphs, and separately among cographs, with the unique extremizer in each class. Includes a stability result and an explicit 336-vertex counterexample to extending the bound to all graphs. The draft contains complete proofs and reproducible exact-arithmetic checks; independent proof review and a broader prior-art assessment remain open.
Choosing Experiments for Causal Prediction
Arya Somu · 2026
An exact Bayes-risk benchmark asks whether language models can choose the experiment that best improves a future causal prediction. Locked studies find that unaided 32B, 72B, and 235B conditions did not meet their registered better-than-random rules. A 32B agent improved with an exact-risk calculator, though its tool use was incomplete. The registered v5 235B comparison was not run.
Reward Variation Without Demonstrated Token Savings: Audited Fixed-Reward Studies
Arya Somu · 2026
Two audited fixed-reward studies, including nine Qwen3-4B runs across three paired seeds and 96 untouched final tasks. The full penalty changes update support but misses the registered practical token-saving criterion. Includes complete scientific records, uncertainty, training details, and CPU reproduction.
Climate Information and Wheat Futures: A Filtered-Information Theory of Forecast Value, Equilibrium Response, and Trading Feasibility
Arya Somu · 2025
Develops a mathematical theory of climate information in wheat futures, with proofs for physical forecast value, equilibrium price sensitivity, the nonidentification of trading alpha, and cost-aware abstention. Includes full derivations and a point-in-time testing protocol; no completed backtest or profitability claim.
An Investigation Regarding Pseudorandom Number Generation with Xor Shifting
Arya Somu · 2024
Explores xorshift pseudorandom number generation through a mathematical model and a 20,000-number sample. This was my Internal Assessment for IB Mathematics HL 2.