ZHAI Xingyun

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...

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

This paper constructs the projective Berry geometry on the actual relative-phase torus from the positive FBT02B prequantum line. The mixed mother form restricts to zero on a regular fibre, whereas the effective Berry ray line is the dual of the positive prequantum line. At level...

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

The present paper reconstructs the curvature-readout layer of the FBT framework. The reconstruction follows the removal of the primitive physical 4+2 claim from FBT0A and the single-carrier relative-torus architecture of FBT0B v4.x. The foundational coherent carrier remains Bcoh6...

PAPER-FBT0B: Global Relative–Phase Torus Geometry of the Coherent Carrier

FBT0A establishes the coherent six-dimensional carrier Bcoh6 = (CP1)3 and its regular Hamiltonian three-phase frame. FBT0B v4.4 develops the global relative-phase geometry needed by the active four-dimensional FBT architecture. The revision removes the diagonal Marsden–Weinstein...

PAPER–Σ: Symplectic Foundations of Action, Global Structure, and Observable Readout

This paper develops a pre-metric symplectic foundation for action, global structure, and observable readout in the Fracture–Berry–Tension framework. Its central claim is deliberately narrower than a direct derivation of matter, gravity, dark sectors, black holes, or Hawking radia...

PAPER-Ω: Time from Geometry: Multi–Layer Temporality and Phase Locking in a Six–Dimensional Symplectic Framework

We formulate a typed architecture for temporality in a six–dimensional symplectic setting. Time is not inserted as one primitive background coordinate. Three geometric readouts are distinguished—Hamiltonian flow time, internal phase time, and effective Lorentzian time—and a fourt...

PAPER-Θ: Structural Temperature and the Geometric Origin of Thermal Physics: A Four-Layer Foundational Framework

Temperature is not assumed here to be a primitive coordinate of geometry. The paper isolates three logically distinct thermal readouts. A branch structural temperature is an energy–entropy conjugate along a specified admissible one-dimensional family. An equilibrium Gibbs tempera...

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-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-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...