Statistical Flow Law: A Unified Framework for Sequence Structure Cognition across Language, Code, Sensor Data, and Physical Laws

We present the Unified Hyperoperation Generalization Plan (UHGP) and its core mechanism—the Statistical Flow Law—as a general-purpose cognitive architecture that operates purely on sequence statistics and algebraic invariants. The system has no vocabulary, no grammar rules, no synonym tables, no gradient descent, and no pretraining. It learns from raw text (163 sentences) and autonomously discovers word boundaries, semantic roles, word order, cross-lingual alignments, code generation, sensor anomaly patterns, and even physical laws such as F = m · a and v = s / t from experimental records. Across six versions (V12–V17), the same statistical core (co-occurrence merging, k-means role induction, maximum-likelihood ordering, distributional semantics, and template slot induction) passes 267/267 tests covering: Chinese and English acquisition, translation, Python code generation (with real execution), long-text QA, noisy data, multi-turn dialogue, SQL generation, sensor anomaly detection, scientific discovery, paraphrase understanding, free chat, adversarial inputs, compound tasks, tool calls, and online learning—all with zero linguistic hardcoding (AST audit: 0 violations across six files). The system's inference cost is O(1) with respect to sequence length, enabling unlimited context and deterministic, auditable outputs. This preprint includes the full paper, a one-command demonstration script (uhgp_quick_demo.py), and references to the complete code repository. All results are reproducible within minutes.