The Lugon Framework: Informational Foundations of Physical Law; Part VI — The Möbius Gates: Navigating the Curvature Map

Part VI of The Lugon Framework: Informational Foundations of Physical Law extends the unified equilibrium principle into geometry. The earlier parts established that every conservation law—energetic, causal, or entropic—can be expressed as informational bookkeeping between two complementary domains: the physical domain ℝ and the informational domain ℚ. In Part V, this balance was formalized as a universal equilibrium constraint in which the total informational flux of reality sums to zero. The Möbius Gates begins where that equilibrium leaves off, asking how motion, curvature, and the creation of form arise within an informationally closed universe. If equilibrium defines the ledger, the Möbius Gate is its handwriting. It represents the geometric mechanism by which information becomes matter and matter dissolves back into information without ever breaking conservation. Each gate type—fundamental, twist, flux, resonance, and nested—embodies a distinct way the ledger folds back on itself, forming a non-orientable mapping between ℚ and ℝ. These mappings transform singularities from mathematical infinities into orientation inversions, explain how resonance quantization gives rise to mass, and show why superluminal coherence in the informational sector remains strictly causal in the physical one. At the mathematical core of this part lies a new gate algebra derived from the Coherence Operator . Its nilpotent closure condition ensures that any double traversal of a gate returns the system to its original phase, encoding the CPT symmetry of the ledger itself. The associated commutator relations reproduce the field-strength tensor of gauge theory while extending it to an informational curvature , thereby unifying quantum and gravitational descriptions without adding extraneous fields. When evaluated over a closed Möbius cycle, this curvature yields the long-wavelength limit of gravity and the short-wavelength resonances of gauge interactions within the same formal grammar. The framework thus derives coherence, gauge invariance, and gravitation as algebraic consequences of one underlying informational connection. The thermodynamic extension of this algebra yields a universal relaxation constant that links microscopic informational drift to cosmic cooling. The same exponential decay law governs the relaxation of informational capacity, the red-shift of the cosmic microwave background, and the arrow of time. In this formulation, time’s direction is the slow reconvergence of informational discrepancies—the universe balancing its own books through curvature feedback. Thermal equilibrium becomes informational renewal, and the CMB is interpreted as the scar and echo of the last global Möbius turnover: the final emission of one cycle and the first light of the next. From this geometry arise quantization conditions of measurable consequence. Finite informational capacity forbids infinity, enforcing discrete spectra in both energy and curvature. The resonance-gate equations yield a natural mass gap, a positive lower bound on all gauge fields arising from the coercive closure of informational bandwidth. The same principle defines upper and lower bounds for curvature, energy density, and entropy, tying the stability of physical law to the finiteness of its informational alphabet. Singularities, when viewed through this lens, are no longer pathologies but phase inversions that maintain the continuity of the ledger. The latter sections and appendices translate these principles into explicit falsifiable form. Predicted observables include: (1) quantized gravitational-wave memory plateaus corresponding to discrete curvature increments Δ; (2) resonance mass-gap spacing observable in particle spectra or cavity QED systems; (3) exponential thermal relaxation of the CMB consistent with the universal constant ≈ age of the universe; (4) residual curvature noise floors detectable by interferometers such as LISA; and (5) distance-independent entanglement phase correlations within causal bounds. Each prediction stems from the gate algebra rather than external hypothesis, allowing the Möbius framework to be tested with existing or near-term technology. Conceptually, Part VI closes the theoretical arc begun in The Unified Equilibrium by transforming balance into motion. The universe is portrayed not as a static sum of forces but as an ongoing act of informational reconciliation, written in finite symbols across curved space. Every gate—orienter, inverter, conservator, quantizer, and hierarchizer—functions as a local clause in the same sentence: conservation is not the absence of change but the symmetry of exchange. In uniting quantum resonance, gravitational curvature, and thermodynamic drift under one informational grammar, The Möbius Gates reveals that the laws of physics are the recursive syntax of a universe that writes and rewrites itself to remain self-consistent.