ZHAI XINGYUN

FN03: Symmetric Bifurcation from an Undivided Whole

Symmetry is usually introduced as a primitive principle in modern physics. The purpose of the present note is to investigate two questions that are more primitivethan symmetry itself. Why should symmetry exist at all? And where does motion reside? Starting from the concept of an...

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-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-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-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-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-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-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-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-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-Π: Generative Comparability and the Origin of Geometry

Geometry is conventionally founded upon an already available space, manifold, metric, topology, or differentiable structure. The present paper proposes that these structures are not logically primitive. The analysis may be carried one level further. Before distinguishable objects...