The Planck Boundary: A Structural Limit Between Quantum Potential and Relativistic Geometry

This paper proposes a structural resolution to the persistent failure of quantum mechanics (QM) and general relativity (GR) to unify within a single mathematical framework. Moving beyond technical obstacles, we introduce the Structural Floor Principle: a meta-invariant architecture (n = 1/n) where mature theoretical systems reach stable, self-balancing limits. Key Framework Contributions: The Planck Scale as a Meta-Floor: We demonstrate that the Planck length (sqrt (hbar G / c³) ) is not merely a limit of scale, but a structural balance point between the "Anchor" of quantum uncertainty and the expansion of gravitational collapse. Temporal Complementarity: We frame QM as the description of the Unbounded Future (probabilistic potential) and GR as the Bounded Past (geometric actuality). We argue that these represent opposite temporal directions that cannot be collapsed without loss of information. The Observer as a Normalization Operator: We interpret wavefunction collapse and the measurement problem as Infinite-Depth Root Extraction (where the limit of a^ (1/n) as n approaches infinity is 1). This identifies "Particles" as the identical fixed points of normalized identity. Cosmic Acceleration via Sampling Asymmetry: We suggest a structural explanation for dark energy as the "Gap" between configuration-space growth (N³) and observer-accessible sampling capacity (sqrt (N) ). This work connects foundational paradoxes (Zeno, Gödel, Riemann Hypothesis) to physical limits, suggesting that unity exists at the level of invariant architecture rather than through the merging of equations. It frames the "Present" as a mandatory temporal thickness window where complementary descriptions cohere.