Dual Flow Fibonacci: Complete Mathematical, Attribution and Quantum-Extension Record

This standalone record presents the mathematical core, attribution scope, visual provenance, and later quantum-mathematical extension associated with a bilateral dual-flow Fibonacci construction. The mathematical core includes the Fibonacci recurrence, golden-ratio identities, bilateral directional components ±F_n, signed cancellation B_n = 0, total bilateral magnitude S_n = 2F_n, the reflection operator J with J² = I, and the odd-parity relation Jv_n = -v_n. The algebraic conjugate ψ is included together with the identities ψ² = ψ + 1, φ + ψ = 1, and φψ = -1. The former visual panels are replaced by explicit equations and prose descriptions while preserving their conceptual content and provenance labels. The foundational dual-flow Fibonacci geometric symmetry, bilateral two-flow loop structure, and directional infinity framework are attributed to the prior published works and registered models of Marcin Słowik. Subsequent geometric extensions, visual adaptations, and interpretive applications are identified as later developments by Ali Alhawarat. A later quantum-mathematical extension by Ali Alhawarat and Pasquale Camelia is cited separately, involving a two-access projective formulation on CP¹, exact Gudermannian readout laws, Fubini-Study pullbacks, inverse reconstruction, and a conditional pure-state quantum Fisher information corollary. The record does not treat visual Fibonacci forms as empirical evidence of quantum behavior.