Form–Cause Processor (FCP): A Structural-Resonance Computational Architecture Governed by the Universal Odd-Parity Mode λ₃*

Overview The Form–Cause Processor (FCP) is a novel computational architecture in which information processing emerges from structural relaxation within a physically defined energy landscape EΦ, q. Unlike digital, neural-network, or quantum-gate paradigms, FCP derives computation from geometric necessity rather than algorithmic rules. Key Discovery A universal odd-parity curvature eigenvalue λ₃* ≈ 0. 152044 governs the slow manifold of structural evolution. This constant is not empirically fitted but follows analytically from Schur–Weyl representation theory of SN-symmetric Hessians. Its universality across system sizes (N = 3, 5, 7, 9,. . . ) establishes it as a geometric invariant of permutation-symmetric energy landscapes. Theoretical Foundations Gradient-flow dynamics: Computation as monotonic convergence toward structural alignment Odd-parity projection: The unique irreducible representation orthogonal to collective modes Symmetry protection: λ₃* is fixed by symmetry rather than device design, enabling scalable analog computation Applications Domain Mechanism Navigation Real-time structural embedding with 0. 7–7 ms adaptation latency Fusion plasma stabilization λ₃* as stabilizing curvature threshold for MHD mode suppression Structural inference Physically realized MAP estimation under GMRF priors Hardware Implementation Three viable platforms are identified: MEMS oscillator networks Electronic LC resonator arrays Optical gradient-potential systems All candidates provide O (1) noise resilience independent of system size, as only odd-parity modes couple to the resonance core. Significance FCP offers a symmetry-protected route to scalable analog computation, suggesting that structurally tuned dissipative dynamics may define a new computational complexity class. This work bridges quantum foundations, information geometry, and statistical physics of computation. Related Works Field–Structural Information–Gravity Framework (doi: 10. 5281/zenodo. 17620967) Structural Stabilization of Helical Fusion Plasmas (doi: 10. 5281/zenodo. 17670783) Even-Odd Vacuum Structure in GHZ Coherence (doi: 10. 5281/zenodo. 17649694) Notes This work introduces the first universal curvature eigenvalue governing dissipative analog computation. Key contributions: (1) Rigorous derivation of λ₃* from SN representation theory (2) Concrete hardware architectures with O (1) noise resilience (3) Applications to navigation, fusion plasma stabilization, and statistical inference.