Koma Notation Specification

Abstract

As the first stage in formalizing Koma Notation / Koma Language, as announced in the Dualbind Declaration 2026, this specification defines how to describe information structure from an information distribution and establishes the formal boundary required for connection to an effective geometry. Koma Notation v0.20 retains the density kernel \(\rho\), observation domain \(\Omega\), structural gradient, and Fisher-information-type structure used in v0.10. At the same time, the integral quantity denoted \(g_{ij}\) in v0.10 is no longer treated, without qualification, as a local metric on the observation domain. This version separates the local information tensor obtained from the density kernel from the global information matrix obtained by its integral, and does not automatically identify either with a physical spacetime metric. Connection to a physical or effective geometry is retained as a separate problem, to be addressed by an independently defined effective-metric map. This version revises the scope of the geometric connection defined in Koma Notation v0.10. The correction history and differences are addressed in a separate document, the Koma Notation v0.20 Correction Note. Japanese and English versions are included in this record. Note on Scope This specification defines a formal notation system for describing information structure and the boundary of connection to an effective geometry. It does not, on its own, complete a physical theory or establish a physical spacetime metric. For correspondence: laboratory@dualbind.comLicense: Creative Commons Attribution 4.0 International (CC BY 4.0)