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This paper investigates the foundations of the Halting Problem, proposing that it is a mathematical artifact rather than a fundamental issue.

June 17, 2026Open Access

On the Dissolution of the Halting Problem and the Pre-Geometric Computation of Numbers: From Turing's Infinite Tape to the Closed Modular Lattice Z396 via the Dalvi Dictact and the MDC-X Invariant ∆ = 4 ln 99

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This paper investigates the foundations of the Halting Problem, proposing that it is a mathematical artifact rather than a fundamental issue.
Establishes the Mahapatra-Dalvi-Collatz-X (MDC-X) Theorem to correct the treatment of geometry in computation.
Applies principles from the Dalvi Dictact to derive a closed modular lattice Z396 as a computational framework.
Constructs a quadratic regulator Q(x) to explore the emergence of π from algebraic constructs.
Shows that the Halting Problem is not undecidable but impossible within a closed arithmetic ring.
Demonstrates that the quadratic regulator integral yields the geometric constant π, linking computation and geometry.
Confirms deterministic verifications in Python for several mathematical constructs related to the findings.

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Randomized trial reveals a new computational model that dissolves the Halting Problem, suggesting geometry arises from number theory.

Dillip Kumar Mahapatra (2026) studied this question.

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