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June 22, 20260 citationsOpen Access

Structural Decomposition of Odd Integers into a Deterministic IK-Surface

Key Points

The aim is to create a structural decomposition of odd integers into a deterministic IK-surface and a chaotic complement.
Defines the conceptual framework and terminology around the IK/CC structure.
Establishes determining rules for mapping odd integers to the IK-surface and chaotic complement.
Introduces the unique relationship between each chaotic complement element and its corresponding IK-surface element through signature mapping.
Establishes the foundational understanding of the IK/CC structure without disclosing specific computational algorithms.

Abstract

This document establishes priority for a structural decomposition of the odd integers into two disjoint sets: a deterministically generated IK‑surface and a chaotic complement (CC). A signature mapping induced by odd‑Collatz dynamics assigns each CC‑element a unique IK‑element. The document defines the conceptual framework, terminology, and hierarchical interpretation of the IK/CC structure. Algorithmic details and computational methods are intentionally omitted to preserve intellectual property while establishing clear prior art.

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