Algebraic Merkle Mountain Ranges (AMMR)

Merkle trees provide cryptographic integrity for collections of data but discard the algebraic structure of the processes that generate that data. This limits their usefulness in settings requiring aggregation, composability, and verification of structured computation. This work introduces Algebraic Merkle Mountain Ranges (AMMR), a generalization of Merkle-style structures in which each node carries both a cryptographic hash and an algebraically composable summary. These summaries obey a merge law compatible with a binary operator, enabling the structure to function as a committed evaluation tree over an algebra. AMMR enables compact, verifiable representations of computation histories while preserving both integrity and structure. The framework supports applications in consensus verification, distributed computation, optimization pipelines, and proof-carrying execution. This document represents Version 0.1 of a conceptual framework and is intended as a foundational abstraction for further development and refinement. --- Authorship and Tooling Transparency: This document was developed with the assistance of large language models (LLMs) as part of the writing and structuring process. The underlying concepts, system design, and direction of the work originate from the authoring entity. LLM tools were used to assist in organization, articulation, and formatting. All technical claims and interpretations were reviewed and directed by the author.