Mycelium Networks as Biophilic Oracles: Integrating RECSM Torsion Geometry, IIT 4.0, and TSP Optimization via the 0.72 Topological Threshold

We propose a theoretical framework linking fungal mycelium network dynamics to NP-hard optimization through the Recursive Einstein-Cartan-Suresh Resonant Metric (RECSM) and Integrated Information Theory (IIT) 4.0. Drawing on Suresh et al.'s (2026) torsion-driven consciousness geometry and recent work by Schumann et al. (2024) on fungi as Turing automata with oracles, we hypothesize that mycelial networks exhibit topologically protected information integration at the critical persistence threshold p = 0.72, enabling oracle-like behavior for certain NP-complete problems. We developed a computational model incorporating RECSM's golden-ratio modulation (φ = 1.618) and tested it on Traveling Salesman Problem (TSP) instances from n=5 to n=1800. Benchmark results from controlled experiments on AlmaLinux 8.10 server (April 2, 2026) show 0-2% approximation error on small instances with polynomial O(n²) scaling. Performance is competitive with classical TSP heuristics (Christofides, Lin-Kernighan) but does not constitute a computational breakthrough. Critically, we identify three convergence points: (1) our β = 0.72 causal power parameter matches Suresh's topological mass gap threshold, (2) our iterative algorithm exhibits recursive breath-like dynamics predicted by RECSM, and (3) performance correlates with predicted IIT φ-density. We integrate Schumann et al.'s oracle automata framework, showing how hybridization of behavior maps to integrated information density (κ), oracle modifications map to causal power (p), and diagonalization parallels the Extended Causal Structure (Φ_ECS). This work does NOT claim fungal consciousness is proven or true NP-oracle computation achieved. Rather, we present a theoretical mapping between three complementary frameworks (RECSM, fungi as oracles, IIT 4.0) with preliminary computational evidence suggesting the synthesis merits empirical investigation. We outline validation pathways using Suresh's proposed 10 GHz cryo-biotic protocol with multi-electrode array recordings of actual mycelial networks. Version 3 includes: (1) Schumann et al. (2024) citation as requested by Prof. Andrew Adamatzky, (2) integration of fungal oracle theory subsection, (3) complete benchmark data with honest O(n²) complexity acknowledgment, (4) comprehensive limitations section, (5) proper theoretical framing without overclaiming.