[Announcement] Theoretical Framework Refinement: Shift to Partial Stability & Architecture-Level Robustness

[Concode0]

Major Update on Theoretical Framework

I'll transitioning the mathematical proof of the Trajecto framework from an ideal global stability model to a realistic, architecture-oriented partial stability model.

1. Why the Change?

• Reality Check: We acknowledge that in a pure IMU setup without GPS, the absolute position state is Rank Deficient (unobservable). Claiming global asymptotic stability for position was physically inaccurate.
• Focus on Usability: For 3D handwriting tasks, preserving the relative shape (geometry) is more critical than preventing absolute global drift.

2. Current Status of Mathematical Proof (v1.0)

Validated: We have strictly proven the Partial Stability of the observable states (velocity, attitude) and the Linearity of position drift. This mathematically guarantees the system's robustness for handwriting tasks.

Limitation: Due to the hardware rank-deficiency (no GPS), global asymptotic stability for absolute position is physically unattainable. Therefore, our proof focuses on Shape Consistency rather than absolute localization.

Future Roadmap: We plan to extend this analysis using Itô Calculus (SDE) in future versions to model stochastic noise properties more deeply.

3. Documentation

The updated proof has been uploaded to docs/Proof_of_HybridModel.pdf. This document represents the definitive theoretical basis for the current v1.0 release.

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Note: This issue will be pinned to serve as a reference for the project's theoretical background.

[Concode0]

Issue closed. The mathematical deadlock of global stability within this architecture is formally acknowledged. This record remains as a post-mortem evidence of why the transition to a non-linear, geometric approach (GA) was necessary. The roadmap continues at Versor