ZHAI XINGYUN

FBT02B: Affine Heisenberg Prequantisation of the Relative–Phase Torus

FBT02A introduces a basic-normalised affine Kac–Moody central extension with integer level kaff = k ∈ Z>0. FBT02C shows that this affine level cannot be identified directly with the two-dimensional Berry–Chern number of the FBT0B relative-phase fibre by equating the rank-one fini...

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...

FBT02B: Affine Heisenberg Prequantisation of the Relative–Phase Torus

FBT02A introduces a basic-normalised affine Kac–Moody central extension with integer level kaff = k ∈ Z>0. FBT02C shows that this affine level cannot be identified directly with the two-dimensional Berry–Chern number of the FBT0B relative-phase fibre by equating the rank-one fini...

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...

FN04: Arithmetic Readout and Multiplicative Generation

The purpose of the present note is not to derive arithmetic from the Generative Comparability Principle developed in Paper–Π.Instead, it identifies a classical mathematical system that naturally realizes the same structural architecture. Prime factorization provides irreducible m...

FN05: The Arithmetic Realisation of Persistent Interfaces

Foundational Note 01 introduces an undivided whole together with the primitive operations of bifurcation and reconstruction. Every admissible bifurcation generates a persistent shared interface, while reconstruction recovers the original structure through that interface.The prese...

FBT08E: Abstract Clock–Sliced Localisation and Worldline Interfaces

This paper isolates the abstract mathematical interface by which a physical configuration acquires a position on a clock slice and, under an additional transport estimate, a causal worldline. It replaces the earlier attempt to manufacture a base localisation functional from an in...

FBT08E: Abstract Clock–Sliced Localisation and Worldline Interfaces

This paper isolates the abstract mathematical interface by which a physical configuration acquires a position on a clock slice and, under an additional transport estimate, a causal worldline. It replaces the earlier attempt to manufacture a base localisation functional from an in...

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...

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...

DCQ4: The Six-Dimensional Symplectic Core of the DCQ Correspondence

This paper extracts and reformulates the geometric core underlying the early papers of the Discrete–Continuous–Quantum (DCQ) correspondence. Its main claim is that the natural continuous completion of the phase-encoded binary construction is not merely a three-torus of phase angl...

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(...

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...

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...

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-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...