Constraint Propagation and Gauge Nature of the Lapse in Projection-Origin Geometry (Projection-Origin Gravity 6)

⚠️ 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 study investigates the temporal behavior of the discrete Bianchi structure within a projection-origin geometric framework under controlled lapse reparameterization. Previous works demonstrated that projection-origin geometry admits a weak-field embedding in which the discrete four-dimensional Bianchi residual can be strongly suppressed by an appropriate choice of the lapse parameter. The closure was shown to persist under both shift-free and shift-enabled static ADM configurations. The present work extends this analysis into the time domain. The spatial geometry is fixed to the projection-origin weak-field configuration while time dependence is introduced solely through lapse modulation.Using a unified discrete operator framework, geometric quantities are reconstructed at each time step and a quasi-dynamical constraint diagnostic is evaluated. The results show that lapse modulation produces a coherent, phase-locked response of the constraint residual. A stability phase diagram reveals a sharply defined tolerance boundary in modulation amplitude, while frequency dependence remains comparatively weak within the explored parameter range. Arrival-time diagnostics further demonstrate that lapse reparameterization coherently deforms causal propagation while leaving the spatial curvature kernel unchanged. These findings indicate that within projection-origin geometry the lapse acts as a slicing gauge parameter governing the temporal stability of the conservation structure. The analysis therefore provides a structural bridge between static geometric consistency and future dynamical formulations without assuming Einstein’s equations or introducing propagating gravitational-wave modes. 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.