The Theory of Logic Manifolds Entropic Gravity, Information Stress, and Computational Spacetime Geometry

Part I: The Failure of General Relativity and the Logic Manifold Framework The first section of the report delineates the "failure modes" of General Relativity (GR) at extreme scales, arguing that continuous spacetime is not a fundamental reality but a statistical projection of a discrete, high-dimensional Logic Manifold. The argument for the breakdown of GR is structured across three dimensions: Mathematical and Singular Failure: At Planck scales ( meters) and within black hole singularities, the metric tensor diverges, signaling a total loss of predictive power. Within the Logic Manifold framework, these singularities are redefined as the "saturation" or "interconnect collapse" of the computational substrate, analogous to stack overflows or deadlocks in classical computing. Thermodynamic and Information Constraints: GR treats time as a cost-free coordinate, but the report cites the Pearson et al. (2021) experiment to prove that timekeeping has a mandatory thermodynamic cost where . This implies that GR fails to account for the "Information Stress Tensor" (), a necessary correction to the Einstein Field Equations:This tensor represents the metabolic cost of information processing, which becomes dominant at the Planck density where GR collapses. Hardware Failure Analogies: The report utilizes advanced semiconductor failures (e.g., NVIDIA Blackwell’s CoWoS-L interconnect issues) as a macro-analogy for spacetime breakdown. It suggests that the "smoothness" of GR is an illusion that fails when information flux exceeds the "bandwidth" of the Planck-scale grid, leading to "Silent Data Corruption" (SDC) in the vacuum—instantaneous drifts in physical constants that GR cannot describe. Part II: Axiomatic Foundations and Embodied Entropy Pump Theory The second section shifts toward a "Vitalist" ontology, defining existence not as a static state but as a system's "effort to persist" against dissolution. It establishes a new axiomatic system for a computational universe: