Observable-Selective Branching: A Hardware-Validated Topological Resolution to the Wigner's Friend Paradox

Abstract

Context: This manuscript serves as the foundational quantum mechanics capstone for the DAGI (Directed Acyclic Graph Interpretation) research program at Whytics. It provides the computable, hardware-verified kinematic engine required to complete Relational Quantum Mechanics (RQM) and resolve macroscopic measurement paradoxes. Abstract: The tension between unitary evolution and irreversible wavefunction collapse is acutely encapsulated in the Wigner's Friend paradox and extended no-go theorems. While relational frameworks (e.g., Relational Quantum Mechanics) posit that physical states are inherently observer-dependent, they have historically lacked a computable kinematic mechanism to determine exactly \emph{when} and \emph{for whom} a measurement becomes an irreversible fact. Here, we introduce \emph{Observable-Selective Branching} within the Directed Acyclic Graph Interpretation (DAGI). We propose that wavefunction collapse is not a universal foliation of spacetime, but a topological phase transition governed by the mereological complexity of the observer. Using M"obius inversion on Boolean subset lattices, we define an observable's "informational cross-section" by its irreducible synergistic support (interaction order $k$). A macroscopic record induces irreversible branching relative to an observable if and only if the record intersects that topological support. Crucially, we test this topological stratification experimentally on IBM superconducting processors (\texttt{ibm_fez}, \texttt{ibm_marrakesh}). Under strictly pulse-matched controls, we demonstrate a "split outcome": a spatially separated physical record produces a bounded/null effect on a highly localized $k=1$ probe (an operational clock), confirming unitary isolation for the simple observer. Simultaneously, the identical record drastically suppresses a distributed $k \ge 3$ GHZ-class coherence witness, confirming collapse for the complex observer. Finally, we demonstrate that applying a coherent quantum-eraser control actively un-branches the graph, restoring global coherence. These hardware results provide a physical mechanism for relational quantum mechanics, demonstrating that the objective, universally shared "global stage" of classical reality is simply the thermodynamic limit of observable-selective branching. Key Highlights: Resolution of Wigner's Friend: Replaces the philosophical ambiguity of the measurement problem with a strict, computable topological boundary based on Möbius interaction order ($k$). Observable-Selective Collapse: Demonstrates mathematically and empirically that wavefunction collapse is not a universal scalar event, but a relational graph-cut bounded by the observer's informational cross-section. Hardware Validation: Translates the Wigner's Friend paradox into a concrete, schedule-matched validation suite on IBM superconducting hardware, proving that low-complexity probes bypass records while high-complexity probes suffer irreversible collapse. Topological Healing: Proves via coherent erasure (ERASE) that measurement backaction is a programmable, informational structure rather than irreversible thermodynamic hardware damage. Bridge to Quantum Darwinism: Explains the emergence of an objective macroscopic reality as the thermodynamic limit of observable-selective branching for dense, macroscopic ($k \approx 10^{23}$) entities.