ZHAI Xingyun

PAPER-FBT21: An Effective Sink-Field Extension of the DCQ Morse Network

This paper develops an effective bridge layer between the affine-central S-sector of the FBT framework, the thermodynamic Morse-network structure of DCQ10, and the fourth temporal layer of PAPER-Ω. The first input is the affine-central picture of FBT02A, where the residual S-sect...

PAPER-FBT02A: The S-Gate as a Strict Affine Central Charge

We formulate the residual S-sector in the Fracture–Berry–Tension (FBT) framework as a strict affine central-charge sector. The central point is that the physically relevant S-direction is not merely a finite-dimensional commuting u(1) factor, but the genuine onedimensional center...

PAPER-FBT10B: The Scalar Response Mode as an Emergent Higgs-like Sector in the FBT Framework

In the Fracture–Berry–Tension (FBT) framework, the effective four-dimensional spacetime metric is interpreted as a coarse-grained response to quantised dual-phase curvature rather than as a fundamental field. Once a symmetric response tensor is introduced on the emergent Lorentzi...

PAPER-FBT0B: Moment–Map Reduction and Global Torus Structure of the Dual–Phase Sector

FBT0A establishes the first-principle and coherent-state origin of the minimal six-dimensional readout geometry of the Fracture–Berry–Tension framework. In its canonical compact realization, the readout isMcoh6 = (CP1)3, equipped with a product Fubini–Study symplectic form and a...

PAPER-FBT10C: The Traceless Response Mode as the Spin-2 Gravitational Wave Sector in the FBT Framework

The Fracture–Berry–Tension (FBT) framework interprets the effective four-dimensional spacetime metric as a macroscopic response geometry built from coarse-grained quantised dual-phase curvature. In FBT10A, the metric was written schematically as gμν = g(0)μν + Ngrav 〈Sμν〉, wher...

PAPER-FBT08D: Asymptotic Null-Shear Readout of the QGT Propagation Layer

This paper develops an asymptotic boundary representation of the QGT propagation layer introduced in FBT08C. The main text of FBT08C defines a local pre-spacetime velocity ratio νQ(u, v) =|Ωread(u, v)| / √︁gread(u, u)√︁gread(v, v), which satisfies 0 ≤ νQ ≤ 1 on a K¨ahler-compatib...

PAPER-FBT08C: QGT Velocity Ratio and the Pre-Spacetime Origin of Propagation

This bridge paper develops a pre-spacetime interpretation of velocity inside the Fracture–Berry–Tension framework. The guiding idea is that velocity is more primitive than the later separation between space and time: before an effective Lorentzian spacetime has been reconstructed...

PAPER-FBT08B: Finite Readable Phase Capacity and the Structural Origin of the Vacuum Propagation Bound

This paper studies a possible structural origin of the finite vacuum propagation bound c∗ used in the Lorentzian bridge paper FBT08A. The aim is deliberately limited. We do not derive the numerical value of the physical speed of light, nor do we claim a complete microscopic trans...

PAPER-FBT08A: A Geometric Bridge from Berry Locked Symplectic Structure to Lorentzian Kinematics

This paper isolates the geometric bridge from the six-dimensional FractureBerryTension (FBT) carrier to four-dimensional Lorentzian kinematics. In the updated foundational formulation, the upstream carrier is the coherent-state symplectic readout B6 ≃ (CP1)3, ΩB = λ1Ω(1)FS + λ2Ω(...

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 th...

PAPER-FBT07A: Three Semiclassical Sector Classes on the Dual–Phase Torus

A central structural question of the Standard Model is why matter appears in exactly three generations. In this paper we give a mathematically sharpened flavour-sector formulation of the Fracture–Berry–Tension (FBT) programme. The starting point is the reduced dual-phase sector o...

PAPER-FBT07C: Fibrewise Hermitian Depth Statistics and Laplace-Novikov Readout

FBT07B established that thimble depth on the compact dual-phase sector is naturally a curvature-flux class defined only modulo the period lattice of the phase curvature. The present paper develops the next layer: once a capping lift and a dimensionless normalization have been cho...

PAPER-FBT07B: Thimble Depth as a Curvature–Flux Readout on the Dual–Phase Sector

This paper isolates a single geometric question in the Fracture–Berry–Tension (FBT) framework: how should the depth of a semiclassical thimble on the dual-phase sector be read directly from the underlying curvature data? Working on the compact dual-phase sector Σ2 ∼= T2, equipped...

PAPER-FBT05A: Effective Berry Geometry on the Relative-Phase Fibre

This paper clarifies the Berry–Chern quantization mechanism associated with the relative dual-phase torus in the Fracture–Berry–Tension framework. The upstream geometric input comes from FBT0A and FBT0B. FBT0A constructs the canonical coherent-state readout B6 = (CP1)3 with its H...

PAPER-FBT0A: First Principles of the Fracture–Berry–Tension Framework

This paper establishes the minimal geometric backbone of the Fracture–Berry–Tension (FBT) framework. The starting point consists of two structural postulates. The first postulate, FP1, introduces a minimal noncommutative triadic tension core whose cyclic commutation relations hav...

PAPER-FBT01A: Symplectic Pairing, Connection Curvature, and Dual-Phase Readout

This paper revises the curvature analysis of the Fracture–Berry–Tension (FBT) carrier geometry in light of the updated foundational structure established in FBT0A and FBT0B. In the current formulation, the minimal six-dimensional carrier is the coherent-state symplectic readout B...

PAPER-FBT02B: An S-Sector Maintenance Self-Energy Model of Effective Mass

We propose a dissipative coarse-grained model of inertial mass built on the strict affine S-sector established in FBT02A. The starting point is the geometrically normalized central generator S, whose microscopic level is fixed by Berry flux in the parent dual-phase sector. After...

PAPER-FBT01D: Balanced Tension Shell and the Central S-Gate

This bridge note formulates a balanced tension-shell condition linking the non-central gate Casimir of FBT01B with the central S-gate normalisation of FBT02A and the dualphase Morse-negative sign of FBT15A. FBT01B establishes the four-gate algebra ggate ∼= su(2) ⊕ u(1), where the...

PAPER-FBT01B: The Four Tension Gates: Structural Origin, Gate Algebra, and Geometric Roles

The four tension gates{X, Y, Z, S}provide the minimal generator-level skeleton of the Fracture–Berry–Tension (FBT) framework. Their role is not to replace later curvature, scalar-readout, gauge, or dynamical constructions, but to furnish a common structural layer from which later...

PAPER-FBT0D: Singular Fibres and Readout Transformations of the Dual–Phase Torus

FBT0B studies the regular moment-map reduction and global torus-fibration structure of the dual-phase sector of the Fracture–Berry–Tension framework. Its main object is the regular relative torus fibration T2 ↪→ XRegπ −→ BReg, together with connection, Chern, holonomy, and monodr...