PAPER-FBT0C: Structural Correspondence Principle - A Hierarchical Reading of Symplectic Invariants in the Fracture–Berry–Tension

This paper proposes a Structural Correspondence Principle for the Fracture–Berry–Tension (FBT) framework. Within the six-dimensional coherent-state symplectic readout established in FBT0A, B6 ≃ (CP1)3, Ω = λ1Ω(1)FS + λ2Ω(2)FS + λ3Ω(3)FS , λk > 0, the natural wedge hierarchy of the symplectic form, Ω, Ω2, Ω3, defines three distinct invariant orders. The central claim of the present work is that these invariant orders are not merely mathematical strata, but admit a natural physical reading: first-order invariants govern internal phase-sensitive structure, second-order invariants govern effective four-dimensional response, and third-order invariants govern global information balance. This principle is compatible with the moment-map and reduction-theoretic analysis of FBT0B, where the four-dimensional effective carrier is obtained through diagonal Marsden–Weinstein reduction, Mred4,c = μ−1Δ (c)/ΔU(1). The purpose of the paper is not to present a complete dynamical derivation of quantum theory, gravitation, and information conservation from first principles. Rather, it formulates a structural correspondence principle explaining why distinct physical frameworks may arise as different effective readings of one and the same six-dimensional coherent-state symplectic geometry. More precisely, the paper argues that: (1) the six-dimensional FBT readout carries a finite ladder of natural invariant orders; (2) this ladder is mathematically consistent with the classical Poincar´e–Cartan viewpointon integral invariants; (3) the dual-phase sector is primarily sensitive to first-order symplectic area; (4) effective four-dimensional response is naturally tied to second-order symplectic fourvolume; (5) global normalization and information balance are naturally tied to the total Liouville volume 󰁕Ω3. Thus, what appear as distinct physical frameworks may be interpreted as different invariant-order projections of a single underlying six-dimensional symplectic readout. The Structural Correspondence Principle is proposed as a conceptual bridge between the foundational geometry of FBT and its later physical applications.