Constraint-Induced Spectral Selection in Projection-Origin Geometry: Exponential Instability from Conservation Violation (Projection-Origin Gravity 8)

⚠️ CORRECTION NOTICE (added 2026): The author has since identified serious errors in this work through a systematic adversarial audit. The central claims of this record should not be relied upon. Specific issues found across this research program include implementation errors (e.g., conflation of signed cosine with cos²), circular definitions, proof gaps, results that reduce to known theorems, and effects that vanish under proper null models and direct-influence correction. This record is left online for transparency and as a documented case, not as a valid result. For the author's current, audited methodology, see the later work on classical-baseline auditing of quantum-like contextuality claims: https://doi.org/10.5281/zenodo.20680607 — A. Ogasawara This work investigates the dynamical consequences of violating theconstraint structure in projection-origin geometry. Previous studies established that discrete Bianchi closure can beachieved by selecting an appropriate lapse slicing and that weak-fieldperturbations propagate as stable transverse–traceless modes under thesame unified discrete operator. The present work introduces a constraint-cleaning parameter thatcontrols the strength of restoration of the conservation structure.By analyzing the minimal growth rate of perturbations across theparameter space of the lapse and cleaning amplitude, we identify aspectral stability manifold associated with constraint-compatibleslicings. The results show that the minimal growth rate scales approximatelylinearly with the cleaning amplitude, producing a stabilizing shiftof the spectrum. In the absence of sufficient restoration, thedynamical system becomes exponentially unstable due to perturbationsof the underlying conservation structure. These findings indicate that the lapse slicing is not arbitrary butis dynamically selected through spectral stability requirements.The analysis provides a dynamical interpretation of gauge selectionwithin projection-origin geometry without invoking Einstein fieldequations. Note: Parts of the manuscript were linguistically and structurally refined with the assistance of AI-based tools.All scientific content, analysis, and conclusions are the author's own. Note: This work represents Version 1.0 of an ongoing research program on the Order-Projection Principle (OPP). Minor typographical corrections and clarifications may appear in later versions. The core conceptual claims remain unchanged.