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Coherence-Geometric Encoder/Decoder: A Multi-Phase Framework for Analog Storage and Transmission

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Internal ID: CGI-RSR-000037
Author(s): Barry L. Petersen
Document Type: Research Paper
Publication Date: Septemeber 12, 2026
Original Creation Date: January 28, 2026
Revised Document Date: September 12, 2026
Status: Public
Domains: Information, Signal Processing
Sub-Domain: Information Transmission, Storage, and Reconstruction
Research Topics: Coherence Geometry, Geometric Encoding and Decoding, Analog Communication, Continuous Information Processing, Latent-State Recovery, Multi-Phase Representation, Signal Reconstruction, Audio, Imaging

Abstract

We introduce a general encoder–decoder architecture based on Coherence Geometry (CG) in which continuous signals are mapped into structured multi-phase latent states (\(\mu\)-space) governed by shared-amplitude constraints and an explicit coherence energy. Channel or storage perturbations act directly on this information-bearing latent state. Recovery is then performed by coherence-driven relaxation toward a coherence-compatible low-energy configuration before the recovered latent is decoded and mapped back into the source or target domain.

The distinguishing feature of the architecture is the operational role assigned to the latent geometry. The coherence constraints do not merely define admissible transmitted states; they participate dynamically in restoring a perturbed representation prior to source reconstruction. Thus, latent-state recovery and source reconstruction are treated as distinct stages, with part of the recovery process internalized into the geometry and dynamics of the transmitted representation itself.

The same framework can support analog, digital, and hybrid implementations. Finite-dimensional CG latents, together with the parameters defining their coherence dynamics, may be serialized, transmitted or stored, and subsequently reconstituted for relaxation and reconstruction. We demonstrate the architecture experimentally using spectral audio and image embodiments based on paired constant-modulus \(\mu\)-states and develop a corresponding conceptual extension to spatiotemporal video. The results show that continuous signals can be represented in noisy CG latents, subjected to coherence-based recovery, and reconstructed in the source domain. These demonstrations establish a practical basis for further investigation of coherence-geometric communication, storage, reconstruction, sensing, and continuous information processing.

Available Document

DOI: 10.5281/zenodo.22722018

Citation:
Petersen, B. L. (2026). Coherence-Geometric Encoder/Decoder: A Multi-Phase Framework for Analog Storage and Transmission (Version 1.0). Zenodo.
https://doi.org/10.5281/zenodo.22722018

Source Code and Supporting Materials

The Zenodo record includes the frozen HorizonSource v0.9 research package used to generate, verify, and reproduce the numerical results reported in Version 1.0.

The package contains the core HorizonSource implementation, automated tests, verification and convergence scripts, stored numerical outputs, example programs, and the figure-generation materials used in the paper. These materials are provided for inspection, transparency, reproducibility, modification, and independent testing. They are not packaged as maintained general-purpose software.

Files included:

  1. Coherence_Geometry_Encoder_Decoder_260912.pdf
    • Version 1.0 research paper.
  2. CG_Encoder_Decoder_Reproducibility_Package_v1.0.zipArchival reproducibility package containing:
    • audio test input and reconstructed output files;
    • image test input and reconstructed output files;
    • the reference audio Jupyter notebook;
    • the Version 2 image Jupyter notebook; and
    • stored numerical output from the audio experiments.

The notebooks expose the numerical implementations underlying the reported experiments and allow the audio and image constructions to be inspected and reproduced directly.

No public technical support or continuing software maintenance is implied.

Summary and Notes

Scope:

The paper develops a general coherence-geometric information pipeline:

source input → source-dependent analysis → \(\mu\)-state encoding → latent perturbation → coherence-directed latent recovery → \(\mu\)-state decoding → source reconstruction.

The central distinction is between recovery of the transmitted information-bearing latent and reconstruction of the original source. The CG latent is therefore not treated merely as a passive encoded representation: its coherence geometry participates dynamically in recovery following perturbation.

The reported audio implementation uses windowed rFFT analysis, paired constant-modulus \(\mu\)-encoding of complex spectral coefficients, latent-space perturbation, coherence-directed recovery, \(\mu\)-decoding, inverse rFFT, and overlap-add waveform reconstruction.

The image embodiment applies the corresponding construction to two-dimensional spectral image data using overlapping patches and rFFT2 analysis.

The experiments also investigate redundant coherent observations by averaging independently perturbed \(\mu\)-space representations prior to relaxation. In the audio experiments, output SNR follows the expected approximately \(10\log_{10}R\) improvement associated with averaging independent noise realizations.

A spatiotemporal video construction is developed conceptually as an extension of the same architecture. No separate video experiment is reported in this release.

The work is intended as a concrete continuous transmission and reconstruction embodiment of coherence-geometric information processing rather than as a replacement for conventional channel theory or symbolic communication methods.

Related Work

Related research and informational framework:

Petersen, B. L. (2026). A Coherence-Geometric Substrate for Information, Modulation, and Inference (Version 1.0). Zenodo.
https://doi.org/10.5281/zenodo.20120903

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). Geometric Encoding and Decoding in Coherence Geometry: A Unified Framework for Transmission, Storage, Inference, Learning, and Control (Version 1.0). Coherence Geometry Institute. Zenodo.
https://doi.org/10.5281/zenodo.22725172

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

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