ZHAI Xingyun

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

We formulate the residual S-sector of the Fracture–Berry–Tension framework as a strict affine central sector while keeping the geometric, Hamiltonian, loop-algebraic, prequantum, Berry, and representation-theoretic layers mathematically distinct. The regular geometric input disti...

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

This bridge note formulates a balanced tension-shell condition linking three logically distinct structures in the Fracture–Berry–Tension framework: the non-central gate Casimir of FBT01B, the positive affine level introduced by FBT02A, its first-harmonic prequantum realisation in...

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 architecture of the Fracture–Berry–Tension framework. This revision gives a conditional geometric realisation of that algebra on the single-carrier regular relative-phase architecture of FBT0B and the mixed s...

FBT02C: An S-Sector Maintenance Self-Energy Model of Effective Mass

This paper develops a conditional coarse-grained maintenance self-energy model for stable internal configurations in the Fracture–Berry–Tension framework, updated to the current single-carrier geometry of FBT0B and the affine-prequantum closure of FBT02A–FBT02B. The regular six-d...

DCQ5: Spectral–Chern Closure of the Determinant-Twisted Tautological Carrier

The DCQ framework begins from a six-bit configuration space H6 = {±1}6 and its continuous phase-orbit completion N = (CP1)3. The repeated appearance of the number 6 in this setting raises a structural question: is 6 merely the input dimension of the construction, or can it be rec...

FBT07A: Three Ambient Semiclassical Thimble Branches on the Relative–Phase Complexification

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...

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

This paper establishes the minimal geometric backbone of the Fracture–Berry–Tension (FBT) framework. The construction begins from two structural postulates. FP1 introduces a minimal noncommutative triadic tension core whose cyclic commutation relations have the local algebraic fo...

PAPER-Γ: Dialectical Generative Algebra: A Novel Algebraic Framework for Generation

This paper introduces the Dialectical Generative Algebra (DGA), a purely algebraic framework designed to formalize generation rather than static symmetry. A DGA consists of a vector space equipped with two bilinear operations, ⊲ (thesis action) and ⊳ (antithesis action), together...

DCQ6: From the DCQ Symplectic Core to FBT Relative-Torus Geometry

In earlier papers of the Discrete–Continuous–Quantum (DCQ) programme, the phaseencoded embedding of the six-bit configuration space into the Grassmannian Gr(3, 6) led to a compact six-dimensional symplectic manifold (N, ω) ≃ (CP1)3 equipped with a Hamiltonian T3 action. In the Fr...

FBT0E: The Block-Grassmannian Ambient Geometry of the DCQ Carrier

DCQ1 assigns the six-bit polarity space H6 = {±1}6 to three fourth-root phase labels and then to block-decomposable three-planes in C6. FBT0A independently selects the coherent six-real-dimensional carrier Ncoh = (CP1)3. The purpose of FBT0E is to prove that these two constructio...

FBT0D: Singular Fibres and Readout Transformations of the Relative–Phase Torus

FBT0D studies singular completions of the single active relative–phase bundle fixed by FBT0B v4.4, Krel ,→ X(6)Regπ −→ B(4)Reg, and keeps the strict principal branch distinct from affine torus families with nontrivial integral cycle monodromy. Generic codimension–two discriminant...

DCQ3: The Double Readout Space and Categorical Statistics in the Discrete–Continuous–Quantum Correspondence

Papers DCQ1 and DCQ2 established the kinematic and phase-geometric foundations of the Discrete–Continuous–Quantum correspondence. DCQ1 introduced an isometric phaseencodedembedding H6 = {±1}6 ↩→ Gr(3, 6), together with its natural Plucker/Fock carrier Λ3(C6), dimΛ3(C6) = 20. In i...

DCQ1: A Discrete-Continuous-Quantum Correspondence

We construct a kinematic correspondence between a finite binary configuration space, a continuous Grassmannian geometry, and associated quantum-geometric carrier spaces. The core construction starts from the six-bit spaceH6 = {±1}6,with 64 configurations, and embeds it into the c...

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...

FBT08D: From Pre-Causal Propagation to Measurable Space and Time

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...

FBT07B: Berry Curvature–Flux Classes on the Relative–Phase Fibre

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...

FBT07C: Action-Depth and Finite-Readout Pushforward Measures

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...

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...

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(...

FBT08C: Pre-Spacetime QGT Propagation and Action-Parametrised Spatial Emergence

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...