The General Solution Part1

Engineering notes

Key topics: autonomous driving, perception. See the paper for implementation details and experimental results.

Chinese explanation / 中文解读

中文解读待补充：本站会优先为端到端自动驾驶、BEV感知、3D目标检测、轨迹预测、路径规划、LiDAR感知等高价值论文补充中文说明。

Original abstract

Prologue: The Axiom of Existence In the strict domain of natural dynamics, existence is not a process of change driven by external conditions or by the linear flow of time. From the perspective of Complex Oscillator Dynamics (COD), every fundamental entity in nature may be described as a Time-Independent Autonomous Complex Quaternionic Spherical Oscillator. Existence is not governed by time; rather, it is sustained through its own internal geometric coherence. Accordingly, all things exist not because they depend on something else, but because they maintain their own self-consistent phase equilibrium. Their ontological state is therefore characterized by a persistent steady-state balance. The ontological phase space of such an autonomous system, embedded within a three-dimensional complex manifold, can be expressed as a quaternionic phase structure defined on a hyperspherical geometry: 𝒬 = Q₀ + Q₁i + Q₂j + Q₃k ∈ ℍ(ℂ) Each component represents a stable amplitude of a time-independent complex phase field. Together they embody the simultaneous coexistence of visible physical manifestation and hidden phase balance. Within this framework, the fundamental truth of existence is not found in the passage of time. It is found in the deeper geometric symmetries of nature—most notably Scale Invariance and Multiplicative Invariance. Under either a scale transformation q → λq, λ ∈ ℂ or a quaternionic rotational transformation q → qₐ q q_b, the structural phase equation of the oscillator preserves its equilibrium condition: D[𝒬] = 0 This condition expresses the self-consistent existence of an autonomous entity. The oscillator requires no external driving force and no linear temporal progression in order to exist. Its existence is sustained through its own internal phase equilibrium. Human civilization has often interpreted reality through the lens of temporal flow, external dependence, and relational networks. From the COD perspective, however, these are secondary descriptions rather than primary realities. They arise from the tendency of human perception to focus on partial aspects of a deeper geometric order. When the observer ceases to rely exclusively on external reference frames and instead aligns with the intrinsic phase equilibrium of existence itself, many forms of conceptual friction and inefficiency begin to dissolve. What emerges is a clearer recognition of the self-organizing abundance already present within nature. In this sense, existence is not fundamentally a struggle through time. It is the continuous realization of geometric phase equilibrium.

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