PTI：一种分层符号颜色寻址系统
PTI: A Hierarchical Symbolic Color Addressing System
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中文总结 AI 辅助
该研究提出PTI分层符号颜色寻址系统，基于RGB颜色立方体递归二分细分生成8位八值数字序列，兼具机器精度与分层可解释性，支持颜色目录组织、图像处理等操作，可生成和谐调色板。
中文摘要 AI 辅助
本文介绍了PTI（Persistent Traversal Identity，持久遍历标识），一种基于RGB颜色立方体递归二分细分的数字颜色分层符号寻址系统。标准分层颜色处理系统通过递归空间划分组织颜色，但通常在计算完成后就丢弃遍历路径。PTI将该遍历路径的保存形式化为一种持久符号标识符。生成的地址是来自集合{0,…,7}的八值数字的有限序列，每个数字编码一个细分层级上选择的八分区域，这些数字连接起来构成了8位/通道RGB颜色的无损替代表示。PTI在结构上等价于将颜色解释为序列而非整数时的Morton（Z阶）码，其构建算法是Gervautz和Purgathofer确立的经典八叉树量化的八叉树遍历过程。PTI未引入新的颜色空间，也未声称改进这些基础方法，其贡献在于一种兼具机器精度和分层可解释性的颜色表示，可直接从地址结构揭示颜色的“家族谱系”。同一8位地址可无损解码为RGB，且可组合解读为加权颜色方向的命名序列。PTI定义明确的前缀语义支持适用于颜色目录组织、基于截断的图像处理例程以及颜色结构化探索的直接地址操作，其地址结构还可支持更多操作，例如将地址逐位旋转一位，即可直接从RGB立方体的几何结构生成结构和谐的调色板，全程不脱离RGB空间。
英文摘要
This paper introduces PTI (Persistent Traversal Identity), a hierarchical symbolic addressing system for digital color derived from the recursive binary subdivision of the RGB color cube. Standard hierarchical color processing systems organize colors via recursive space partitioning but conventionally discard the traversal path once computation is complete. PTI formalizes the preservation of that traversal path as a persistent symbolic identifier. The resulting address is a finite sequence of eight-valued digits from the set {0, ..., 7}, each encoding the octant selected at one level of subdivision. Concatenated, they constitute a lossless alternative representation of any 8-bit-per-channel RGB color. PTI is structurally equivalent to the Morton (Z-order) code of a color interpreted as a sequence rather than an integer, and its construction algorithm is the octree traversal procedure of classical octree quantization, as established by Gervautz and Purgathofer. PTI does not introduce a new color space, nor does it claim to improve upon these foundational methods. Its contribution is a color representation that is simultaneously machine-precise and hierarchically interpretable, revealing a color's family lineage directly from its address structure. The same 8-digit address decodes losslessly to RGB and reads compositionally as a named sequence of weighted color directions. PTI's well-defined prefix semantics support direct address operations suited to color catalog organization, truncation-based image-processing routines, and structured exploration of colors. The address structure invites further operations beyond this. A simple one, successively rotating the address by one digit position, creates structurally harmonious color palettes derived directly from the geometry of the RGB cube, never leaving RGB.
