WCM Bridge Paper P: Wave Function Collapse as Geometric Collapse in Photosynthesis — D₂→0 in 24-Cell Probability Current Space

We apply the Watabe-Claude Method (WCM) — a 4D geometric framework based on the 24-cell regular polytope (F₄ symmetry) — to the quantum biology of photosynthesis. Using a 7-site Lindblad master equation for the Fenna-Matthews-Olson (FMO) light-harvesting complex, we compute the probability current J (t) and project it onto the 24-cell vertex distribution to obtain the cosine distance D₂ (t). Three core findings are established: (PS-1) The quantum energy transfer efficiency reaches η=99. 1% from BChl7 (reaction-center-proximal site), within 1. 1% of the experimental value of ~98%, correlating with D₂→0 collapse dynamics — establishing that FMO's 98% quantum efficiency is a consequence of 24-cell geometric optimization. (PS-2) A 4-directional OEC water model reflecting Mn₄Ca C₄v symmetry yields D₂OEC < D₂bulk for all tested parameters, providing the first geometric account of OEC-proximal water's unique character. (PP-N1) Instantaneous D₂ (t) oscillates at twice the quantum beat frequency (TD2 = 77. 6 fs ≈ Tbeat/4 = 74. 75 fs; difference 3. 8%), representing geometric second-harmonic generation (SHG) in 24-cell F₄ space. Five engineering guidelines for artificial photosynthesis are proposed: D₂-optimized antenna design, OEC-mimetic C₄v catalyst geometry, Site4-type energy hub molecule design, quantum-classical boundary exploitation, and D₂-based real-time monitoring. Numerical code: bridgeₚaperₚᵥ3. py (Python 3, numpy/scipy). Runtime: 1. 23 s (Mac mini M2). Related WCM Bridge Papers: - Bridge Paper C: https: //doi. org/10. 5281/zenodo. 20783868- Bridge Paper F: https: //doi. org/10. 5281/zenodo. 20826265- Bridge Paper H: https: //doi. org/10. 5281/zenodo. 20826791- Bridge Paper S: https: //doi. org/10. 5281/zenodo. 20838559