There is a huge discrepancy between the divergent vacuum zero-point energy in quantum field theory and the macroscopic cosmological constant. Within the framework of connectivity engineering, this paper explores the regulatory mechanism of underlying graph topology on the ground state energy of finite systems. By introducing a truncated step k in a one-dimensional XXZ spin network, numerical results show that the absolute value of the system's ground state energy does not decline trivially and linearly with the reduction of interaction bonds, but rather exhibits strong non-trivial topological frustration. The normal network (k=1), due to strong local entanglement, exhibits a lower bare ground state energy density; while after introducing long-range geometric decoupling, the parity matching of sub-chain lengths and boundary reconstruction lead to a non-monotonic evolution of the ground state energy density, reaching a maximum at k=4 due to odd-lattice frustration. This topology-induced energy renormalization conceptually provides a minimal discrete sandbox for the "geometric truncation" of vacuum energy, and implies that the residual energy of macroscopic spacetime (dark energy) may correspond to the geometric frustration tension of the underlying discrete network that has not been fully canceled after topological saturation.
There is a huge discrepancy between the divergent vacuum zero-point energy in quantum field theory and the macroscopic cosmological constant. Within the framework of connectivity engineering, this paper explores the regulatory mechanism of underlying graph topology on the ground state energy of finite systems. By introducing a truncated step k in a one-dimensional XXZ spin network, numerical results show that the absolute value of the system's ground state energy does not decline trivially and linearly with the reduction of interaction bonds, but rather exhibits strong non-trivial topological frustration. The normal network (k=1), due to strong local entanglement, exhibits a lower bare ground state energy density; while after introducing long-range geometric decoupling, the parity matching of sub-chain lengths and boundary reconstruction lead to a non-monotonic evolution of the ground state energy density, reaching a maximum at k=4 due to odd-lattice frustration. This topology-induced energy renormalization conceptually provides a minimal discrete sandbox for the "geometric truncation" of vacuum energy, and implies that the residual energy of macroscopic spacetime (dark energy) may correspond to the geometric frustration tension of the underlying discrete network that has not been fully canceled after topological saturation.
Traditional holographic duality usually assumes a smooth and continuous spacetime background, where boundary entanglement strictly follows the area law. However, the real microscopic quantum gravity background may possess a non-trivial fractal structure. Within the framework of connectivity engineering, this paper investigates the regulatory mechanism of fractal networks (Sierpinski gasket) on quantum entanglement structures. Numerical results show that, unlike a one-dimensional gapped chain restricted to an extremely low area law constant, the entanglement capacity of the fractal network is significantly enhanced due to the presence of multiple branches and geometric shortcuts, approaching the upper bound of the Page curve at the bipartite symmetry point for this finite size. This topological resonance brought by self-similar hierarchical levels of the fractal demonstrates a generalized area law dominated by fractal dimension. This result proves that the fractal dimension of the underlying spacetime is the key geometric origin determining the long-range distribution of quantum information and the upper bound of entanglement capacity.
The contradiction between the thermodynamic arrow of time and microscopic dynamical reversibility is a core problem in statistical physics. Within the framework of connectivity engineering, this paper proposes a new mechanism: irreversible accumulation of subsystem entropy caused by topological quenching. We numerically simulate the cyclic switching of a one-dimensional spin network between topological steps k=1 and k=4. Results show that each switch from the highly connected state to the frustrated state leads to an irreversible "fall" of information into the local entanglement space; when switched back to the initial topology, the subsystem entanglement entropy cannot recover to its initial value, but instead surges from 0 to approximately 2.96 and remains in the saturation regime, exhibiting a unidirectional entropy accumulation. Since the theoretical maximum entropy of this subsystem is 3.0, this irreversible saturation directly reveals the limit of information coarse-graining. The above results prove that the microscopic origin of the arrow of time is precisely the information scrambling caused by the irreversibility of underlying geometric topological reconstruction.
In this paper, we discover the topological quantization and phase transition mechanisms of holographic extremal surfaces in discrete tensor networks, providing a rigorous discrete dynamical benchmark for the proposition that "gravity is entanglement". Using a one-dimensional spin network with a fixed truncated hopping step k, we derive a rigorous analytical solution for the peak position of entanglement entropy, demonstrating that it is solely determined by the underlying connectivity step k. The perturbative phase diagram further reveals that this quantized gravity ladder is strongly protected by the topological gap below a critical perturbation V_c, exhibiting unique critical scaling behavior at the transition point. The fitted critical exponent beta approx 0.07 is significantly lower than the mean-field exponent of conventional phase transitions, revealing a unique "critical rigidity" characteristic of finite-size long-range topological networks. This model not only provides a rigorous graph-theoretical benchmark for a discrete analogue of the Ryu-Takayanagi area law but also, through the "geometric decoupling" mechanism, constructs an analytically solvable microscopic dynamical sandbox for the highly debated entanglement wedge disconnection in the black hole island formula.
In the framework of connectivity engineering, this paper proposes a method to inversely reconstruct the internal discrete topological connectivity from the boundary entanglement entropy spectrum. Based on a one-dimensional spin-1/2 network, we extract a three-dimensional entanglement fingerprint characterizing the internal connectivity: the mutual information peak, the peak position, and the late-time residual fidelity. Numerical diagnostics show that when the connectivity reaches k=3, the mutual information peak reaches 1.49 times that of the baseline network, and the system enters the topological saturation regime; at this point, the fingerprint vectors for k=3 and k=4 are indistinguishable within numerical precision. We prove that this degeneracy originates from the joint mechanism of graph-theoretic topology and dynamical decay, and further increasing k does not yield substantial cross-region entanglement channels. Even in the presence of numerical noise, the significant gap in late-time fidelity between k=2 and the saturation regime ensures the high robustness of the inverse mapping. This result establishes the effectiveness of the "entanglement fingerprint distance" as an inverse diagnostic operator, providing an operational benchmark for discrete bulk geometry reconstruction using purely boundary observables.
Contemporary quantum mechanics’ Measurement Problem has long been trapped in the phenomenological quagmire of the "Observer Paradox." Traditional interpretations logically fail to explain how, in the early extreme universe devoid of macroscopic instruments or conscious observers, elementary particles spontaneously collapsed from probability superposition states into entities possessing rest mass. Grounded in the absolute vacuum repulsion framework of the Grand Unified Theory of Cosmic Mind (GUTCM), this research proposes an ontological-level "Spontaneous Decoherence" dynamical mechanism that completely discards the external observer. It strictly argues that the origin of physical entities does not stem from probability collapse, but rather from the "Truncated Logical Deadlock" encountered by the quantum information structure during underlying geometric compilation. This paper demonstrates at the geometric topological level that the underlying absolute vacuum of the universe is not a single void, but an ontology possessing two limit thermodynamic phases: the unsaturated "absolute nothingness" (0-domain, white paper state) and the fully saturated "extreme full energy state" (∞-domain, black paper state). In the underlying genesis compilation lacking a time parameter (dt≡0), the writing of the 1D geometric repulsive trajectory of the wave function and the infinite-speed flipping of the background absolute vacuum polarity inevitably undergo a topological "Asynchronous Intersection." When a wave function trajectory penetrating the underlying canvas encounters the instantaneous assimilation of background polarity mid-writing (e.g., the background instantly turning from black to white), the geometric contrast of its latter half is forcibly erased. This "midway flip" geometric accident causes the linear information code originally pointing toward an infinite future (e.g., 0111⋯→∞) to be forcibly truncated and zeroed (phase-shifting to 0111…0000). This massive information flow—having lost its evolutionary path and with nowhere to retreat—is forced to curl inward under extreme topological tension. It mutates from linear divergence into a Russell's paradox-style self-referential loop, triggering A≡¬A. This forced transfer of energy and logical closed loop directly forms an unravelable "Topological Standing Wave Knot" in topology. This non-trivial knot structure props open an absolute "Information Repulsion Domain (Microscopic Event Horizon)" in physical space, successfully resisting the thermodynamic dissipation and information erasure pressure of the global absolute vacuum. This model strictly proves that as long as the infinite-speed flipping of the dual-phase vacuum continues, such "truncated deadlocks" will inevitably occur endlessly. This is the ultimate dynamical root of why the number of elementary particles in the macroscopic universe continuously increases exponentially with epoch evolution. Simultaneously, these deadlock structures that survived the cruel screening of "Algorithmic Darwinism" during the Planck epoch—their topological invariants and anti-crash mechanisms maintaining recursion—ultimately solidified into the physical laws and conservation laws of the Standard Model we see today. This study thoroughly proves: Existence is an eternal deadlock in cosmic geometric compilation; without needing any observer, physical objective reality can complete absolute self-proof through underlying topological truncation.
The core of quantum error correction lies in how to isolate local errors to prevent them from contaminating the global system. Within the framework of connectivity engineering, this paper proposes a holographic quantum error correction mechanism based on pure geometric decoupling. Numerical results show that in a locally connected network (k=1), local errors rapidly diffuse globally through the increase of entanglement entropy; while in the decoupled network (k=3), long-range hopping constructs a graph-topological barrier, strictly locking the error within the isolated sub-chain where it was injected, and the mutual entanglement entropy between A and B remains strictly at its initial zero value. Since the physical hopping between subsystems is cut off, the injected error state cannot trigger global chaos, and the purity of boundary information remains stable. This mechanism does not rely on traditional redundant encoding, but rather utilizes the intrinsic graph-topological isolation property of geometric connectivity to achieve "physical-layer" fault tolerance. It provides a minimal discrete dynamical benchmark for understanding Bulk Locality in holographic duality and points the way for designing redundancy-free quantum memories.