Geometric Encoding and Decoding in Coherence Geometry: A Unified Framework for Transmission, Storage, Inference, Learning, and Control
Internal ID: CGI-RSR-000038
Author(s): Barry L. Petersen
Document Type: Research Paper
Publication Date: September 12, 2026
Original Creation Date: March 26, 2026
Revised Document Date: September 12, 2026
Status: Public
Domains: Information, General
Sub-Domain: Coherence-Geometric Information Processing / Operational Structure
Research Topics: Geometric Encoding and Decoding, CGIS, CDIS, CDIT, CDIR, Coherence-Directed Recovery, Information Storage, Information Transmission, Inference, Learning, Control
Abstract
We introduce Geometric Encoding and Decoding (GED) as a general operational paradigm within the Coherence-Geometric Information Substrate (CGIS). Building on the pre-symbolic treatment of information developed in earlier work, GED distinguishes the preparation of an information-bearing coherence-compatible state, its persistence or propagation under perturbation, and subsequent recovery through coherence-directed dynamics.
In this framework, encoding maps information into a structured configuration within a constrained phase–amplitude state space. Decoding corresponds more generally to coherence recovery: the evolution of a perturbed or incomplete state toward a configuration compatible with the governing coherence geometry. Where the landscape contains distinct stable attractors, this process takes the more specific form of basin recovery; in continuously parameterized regimes, recovery may instead restore coherence constraints while preserving continuous informational degrees of freedom.
Three fundamental informational roles recur within GED: Coherence-Driven Information Storage (CDIS), describing persistence of structured information; Coherence-Driven Information Transmission (CDIT), describing propagation across channels or domains; and Coherence-Driven Inference and Recovery (CDIR), describing recovery of perturbed or incomplete configurations. These roles are informational expressions of the broader triadic organization of coherence-governed systems. Learning may reshape the coherence landscape in which these roles operate, while control may bias or steer the associated dynamics.
Symbolic and statistical representations may be introduced through projection, discretization, or other forms of abstraction, but are not required for the underlying geometric operations. By separating coherence-governed representation and recovery from subsequent projection, GED provides a common operational language linking the CGIS substrate to concrete applications in transmission, storage, inference, learning, and control.
Available Document
Citation:
Petersen, B. L. (2026). Geometric Encoding and Decoding in Coherence Geometry: A Unified Framework for Transmission, Storage, Inference, Learning, and Control (Version 1.0). Zenodo. https://doi.org/10.5281/zenodo.22725172
Source Code and Supporting Materials
No source code is required for this conceptual and structural research paper.
Primary file:Geometric_Encoding_Decoding_260912.pdf
Version 1.0 archival research paper.
A README file accompanying the Zenodo deposit records document provenance, scope, citation information, and archival metadata.
Summary and Notes
Scope:
This paper develops Geometric Encoding and Decoding (GED) as a general operational description for information processes within the Coherence-Geometric Information Substrate (CGIS).
GED organizes three principal informational roles:
- Coherence-Driven Information Storage (CDIS): persistence and maintenance of structured information.
- Coherence-Driven Information Transmission (CDIT): propagation or transfer of structured information across channels, domains, or representations.
- Coherence-Driven Inference and Recovery (CDIR): recovery of perturbed, incomplete, or displaced informational configurations.
These informational roles correspond to the broader triadic organization of coherence-governed systems. Stabilization is expressed informationally through inference and recovery, activation through persistence and storage, and transport through transmission.
Within GED, decoding is treated generally as coherence-directed recovery rather than being restricted to a particular symbolic or discrete decoding procedure. Where a coherence landscape contains distinct stable attractors, recovery may take the more specific form of basin recovery. In continuously parameterized regimes, recovery may instead restore coherence constraints while preserving continuous informational degrees of freedom.
Learning is treated as modification of the coherence landscape in which these operations occur, while control biases or steers the associated dynamics. Symbolic, statistical, and discrete representations may arise through projection or abstraction but are not required for the underlying geometric operations.
The paper therefore serves as an operational synthesis within the informational branch of Coherence Geometry. It connects the foundational CGIS treatment of information, the triadic organization of coherence-governed systems, and concrete coherence-geometric transmission and recovery mechanisms within a common language for storage, transmission, inference, recovery, learning, and control.
Related Work
Foundational informational work:
Petersen, B. L. (2026). A Coherence-Geometric Substrate for Information, Modulation, and Inference (Version 1.0). Zenodo.
https://doi.org/10.5281/zenodo.20120903
Related structural and operational work:
Petersen, B. L. (2026). Triadic Organization of Coherence-Governed Systems: Stabilization, Activation, and Transport as Constraint-Driven Modes (Version 1.0). Coherence Geometry Institute. Zenodo.
https://doi.org/10.5281/zenodo.22721088
Petersen, B. L. (2026). Coherence-Geometric Encoder/Decoder: A Multi-Phase Framework for Analog Storage and Transmission (Version 1.0). Coherence Geometry Institute. Zenodo.
https://doi.org/10.5281/zenodo.22722018
Petersen, B. L. (2026). Emergent Intelligence from Coherence-Driven Dynamics: Archival Submission Packages. Zenodo. https://doi.org/10.5281/zenodo.20191577
Related framework:
Petersen, B. L. (2026). Coherence Geometry Foundations, Part I: Orientation,
Closure, and Algebraic Foundations (Version 0.1). Zenodo.
https://doi.org/10.5281/zenodo.20156531
Petersen, B. L. (2026). Coherence Geometry Foundations, Part II: Physical
Projections (Version 0.2). Zenodo.
https://doi.org/10.5281/zenodo.20156996
Petersen, B. L., Johnson, R. K., & Bruno, A. E. (2026). A Conceptual Overview of the Coherence-Geometric Framework: Organizational Structure, Terminology, and Projection (Version 1.0). Coherence Geometry Institute. Zenodo.
https://doi.org/10.5281/zenodo.22720726