Ananthashayan Puvanenthirarasan

Gravity Maps

Gravity Maps are a newly discovered class of integer mappings that generalise the well-known Collatz function. Defined through simple modular rules, these mappings extend beyond a single base and exhibit consistent collapse of trajectories to unity. While no formal proofs are att...

Circles through Natural Numbers

This paper introduces Prime-Diameter Circles (PDCs)—a geometric framework that unifies prime generation, distribution, and classical number-theoretic conjectures. By defining circles whose diameters are bounded by prime coordinates, PDCs reveal profound symmetries: primality refl...

Restricted Partitions

This paper introduces Sivanendran’s Restricted Partition Function (SRPF), a novel framework for constructing and enumerating restricted partitions of natural numbers. Unlike contemporary approaches, SRPF relies on simple floor functions and integer division, making it computation...

Treatise on Digit Strings

This treatise develops a structural theory of digit strings in positional notation, introducing repunits, corepunits, replimits, and coreplimits as palindromic constructs whose dualities and product identities reveal profound symmetries in arithmetic. These digit structures show...

Treatise on Restricted Partitions

This paper introduces Sivanendran’s Restricted Partition Function (SRPF), a novel framework for constructing and enumerating restricted partitions of natural numbers. Unlike contemporary approaches, SRPF relies on simple floor functions and integer division, making it computation...

Treatise on Digit Strings

This treatise develops a structural theory of digit strings in positional notation, introducing repunits, corepunits, replimits, and coreplimits as palindromic constructs whose dualities and product identities reveal profound symmetries in arithmetic. These digit structures show...

Treatise on Restricted Partitions

This paper introduces Sivanendran’s Restricted Partition Function (SRPF), a novel framework for constructing and enumerating restricted partitions of natural numbers. Unlike contemporary approaches, SRPF relies on simple floor functions and integer division, making it computation...

Treatise on Prime-Diameter Circles

Jeyananth’s Circles, also called Prime-Diameter Circles (PDCs), are a geometric framework that connects prime numbers to circle constructions on the 2-D plane. Defined through prime endpoints of diameters aligned with the axes, PDCs introduce notions such as floor and ceiling coo...