Self-reported theory claims extending Shannon coding theorems to the action level via isoteleia maps

Readers can now learn of a self-reported mathematical theory of pragmatic information: an isoteleia mapping treats different semantic paths leading to the same optimal action as equivalent, and the authors claim to have proved counterparts of Shannon's source, channel and rate-distortion theorems at the action level, aimed at task-oriented communication, networked control and embodied AI.

Previously, Shannon's source, channel and rate-distortion theorems stayed at the level of information transmission and, by the authors' account, did not cover semantic equivalence at the action level.

The theory is self-reported by Kai Niu and Ping Zhang; the text runs 151 pages, with v3 updated on September 17 and the first version submitted to arXiv on September 10 (arXiv:2609.10986).

These are the authors' theoretical claims, without peer review or independent verification, and no third-party replication yet.