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May 2, 2026Open Access

Mahapatra-Dalvi-Collatz -X Theorem (MDC-X Theorem): First-Principle Derivation of Topological Invariants from the Generalized Collatz Map

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This research aims to derive topological invariants from the generalized Collatz map using first principles.
Derivation of topological classification based on three coefficients: a, b, and n.
Analysis of 2-adic valuation distribution and expected logarithmic dissipation per parity block.
Application of the Dalvi Dictact for establishing closure equations and integer base computations.
For dissipative multipliers (a < 4), the topological invariant is finite and positive.
For expansive multipliers (a ≥ 5), no finite invariant exists.
A unique integer base is formulated as B(a) = 4a^(16%).

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Randomized trial demonstrates the derivation of topological invariants from the generalized Collatz map, indicating mathematical consistency.

Dillip Kumar Mahapatra (2026) studied this question.

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Randomized trial demonstrates the derivation of topological invariants from the generalized Collatz map, indicating mathematical consistency.