Computational mathematics and
algorithmic systems.

High-precision number theory • Dynamics • Algorithms at scale

Featured Work

Highest Impact
View Discrete Descent Hybrid Algorithm

Discrete Descent Hybrid Algorithm

2025
Under Review
O(log n) descent via Gram points instead of O(n) search.
Proves RH holds at heights where classical methods fail computationally.

Numerical zero verification for the Riemann zeta function up to T = 10¹⁶ using hybrid descent methods and topological interlacing.

Progress95%
Number TheoryC++HPC
View Non-Ergodic Random Walks

Non-Ergodic Random Walks

2026
Negative Theorem
Extreme events dominate the history, preventing statistical stabilization.
Standard financial risk models (using Gaussian assumptions) fundamentally fail here.

Studying ergodicity breaking in Lévy flights with α=1. Exploring the failure of time-average convergence in heavy-tailed systems.

Progress90%
Probability TheoryStochastic Processes
View NeuroOS Kernel

NeuroOS Kernel

2025
Experimental
Memory pages decay over time and must be maintained by frequent usage, mimicking synaptic reinforcement.
An operating system that naturally forgets unused data, freeing resources like a biological brain.

Experimental biomimetic kernel exploring memory persistence models inspired by neural reinforcement mechanics.

Progress60%
SystemsBio-inspiredC

Other Projects

2025 - 2026
View ℂ-Space Engine

ℂ-Space Engine

2025

A generalized 2D physics engine simulating a universe where physical constants are Complex Numbers.

Progress75%
Physics SimC++20Complex Analysis
View Kolakoski Sequence Analysis

Kolakoski Sequence Analysis

2026

Investigating structural properties of the Kolakoski sequence density using graph-theoretic approaches on a 34-state manifold.

Progress90%
CombinatoricsGraph TheoryPython
View Kimberling Expulsion Conjecture

Kimberling Expulsion Conjecture

2025

Analyzing the Kimberling expulsion process using an O(1) state recurrence. Discovered a record-breaking survivor lasting 67 billion steps.

Progress85%
DynamicsProbabilityC++
View Twin Prime Cluster

Twin Prime Cluster

2025

Distributed computing architecture for validating twin prime candidates at scale. Concurrently validating over 400 candidates across the cluster.

Progress80%
Distributed SystemsCloudPython

Akshit Sivaraman

Shiv Nadar Institute of Eminence