PaTeX: Pentaract 5D LaTeX Specification and Deterministic Haiku Worker Harness

Abstract

## Overview This technical specification release establishes two machine-first operational primitives for machine-driven document compilation and deterministic LLM execution: 1. **PaTeX (Pentaract 5D LaTeX Specification)**: A multi-dimensional markup extension embedding LaTeX documents into a bounded $N^5$ hypercube grid[cite: 3].2. **Haiku Worker Harness**: A deterministic, zero-temperature execution wrapper for itemized JSON chunk classification[cite: 4]. --- ## 1. PaTeX: Pentaract 5D LaTeX Specification PaTeX projects documents into 5D space across discrete coordinates $(x, y, z, k, w)$[cite: 3]:* **Spatial Extent $(x, y, z)$**: 3D document spatial layout[cite: 3].* **Girih Angle $(k)$**: Rotational perspective (e.g., technical, user-facing, or architecture viewpoints)[cite: 3].* **World Layer $(w)$**: Temporal and versioning axis[cite: 3]. ### Structural Invariants* **Grid Density**: At $N=3$, the pentaract forms a dense $3^5 = 243$ cell lattice[cite: 3].* **Memory Footprint**: $243 \times 8\text{ bytes} = 1,944\text{ bytes}$ total footprint[cite: 3]. Cells use a 32-bit content-address offset pointing to external string heaps rather than storing raw prose inline[cite: 3].* **Linear Address Mapping**: For 0-indexed coordinates $i_j \in \{0, 1, 2\}$, the memory offset is evaluated via $\text{idx}(i_x, i_y, i_z, i_k, i_w) = i_x + 3 \cdot i_y + 9 \cdot i_z + 27 \cdot i_k + 81 \cdot i_w$[cite: 3]. The origin cell (all trits $= 0$) sits at index $121$[cite: 3].* **Lossless Slicing**: Pinning Girih angle $k$ and world layer $w$ extracts a conventional 3D LaTeX document with $O(1)$ metadata overhead[cite: 3]. --- ## 2. Haiku Worker Harness The generic worker harness provides a stateless execution driver for classification pipelines[cite: 4]:* **Deterministic Sampling**: Enforces temperature $0.0$ greedy sampling to eliminate non-deterministic output drift[cite: 4].* **Stateless Dispatch**: Executes independent worker loops over JSON input chunks with worker attribution (`worker_id`)[cite: 4].* **Fail-Loud Logging**: Isolates item-level errors and logs failure reasons directly into output JSON payloads without crashing worker threads[cite: 4].