Context: This manuscript provides the rigorous mathematical and information-theoretic toolkit for the DAGI research program at Whytics, bridging abstract mereology with effective field theory and macroscopic observables. Abstract: We extend the Directed Acyclic Graph Informational (DAGI) framework by integrating a rigorous mereological decomposition based on Möbius inversion on partially ordered sets. The central output is a multiscale expansion that decomposes a macroscopic informational observable $g(X)$ on node-sets $X$ into unique, irreducible contributions $f(Y)$ across all sub-configurations $Y \subseteq X$. To bridge this abstract mereology with physical kinematics, we apply the formalism to total correlation (multi-information). Its Möbius inversion isolates order-resolved $k$-body dependency atoms that can be positive (synergy) or negative (redundancy). We introduce the positive-tail truncation $f^+(X) = \max\{f(X),0\}$ to rigorously isolate active, irreducible synergistic constraints; this "$f^+$ tail" yields the exact geometric source terms employed in the companion Emergent Spacetime Geometry (ESG) framework. We also show how the same decomposition can be coupled back into dynamics via a coarse-grained effective field theory (EFT) Lagrangian. Finally, we summarize computational pathways and modern experimental status, including superconducting-qubit demonstrations that extract irreducible 3-body and thresholded high-order synergies from IBM quantum processors using Möbius/HOIC diagnostics. Key Highlights: Order-Resolved Information: Deploys Möbius inversion on subset lattices to cleanly separate multi-partite redundancy from irreducible synergy. Effective Dynamics: Proposes a method to couple higher-order informational constraints back into an effective Lagrangian, providing a concrete mathematical basis for context-dependent dynamics ("downward causation") while avoiding double-counting via connected-cluster normalizations. Hardware Extraction: Details the analytical foundation used to isolate multiscale High-Order Information Content (HOIC) in real quantum circuits (e.g., IBM Torino benchmarks). Companion Toolkit: Serves as the mathematical prerequisite for defining the discrete curvature sources used in the DAGI Emergent Spacetime Geometry (ESG) mapping.
Context: This manuscript provides the rigorous mathematical and information-theoretic toolkit for the DAGI research program at Whytics, bridging abstract mereology with effective field theory and macroscopic observables. Abstract: We extend the Directed Acyclic Graph Informational (DAGI) framework by integrating a rigorous mereological decomposition based on Möbius inversion on partially ordered sets. The central output is a multiscale expansion that decomposes a macroscopic informational observable g(X) on node-sets X into unique, irreducible contributions f(Y) across all sub-configurations Y⊆X. To bridge this abstract mereology with physical kinematics, we apply the formalism to total correlation (multi-information). Its Möbius inversion isolates order-resolved k-body dependency atoms that can be positive (synergy) or negative (redundancy). We introduce the positive-tail truncation f+(X)=max{f(X),0} to rigorously isolate active, irreducible synergistic constraints; this "f+ tail" yields the exact geometric source terms employed in the companion Emergent Spacetime Geometry (ESG) framework. We also show how the same decomposition can be coupled back into dynamics via a coarse-grained effective field theory (EFT) Lagrangian. Finally, we summarize computational pathways and modern experimental status, including superconducting-qubit demonstrations that extract irreducible 3-body and thresholded high-order synergies from IBM quantum processors using Möbius/HOIC diagnostics. Key Highlights: Order-Resolved Information: Deploys Möbius inversion on subset lattices to cleanly separate multi-partite redundancy from irreducible synergy. Effective Dynamics: Proposes a method to couple higher-order informational constraints back into an effective Lagrangian, providing a concrete mathematical basis for context-dependent dynamics ("downward causation") while avoiding double-counting via connected-cluster normalizations. Hardware Extraction: Details the analytical foundation used to isolate multiscale High-Order Information Content (HOIC) in real quantum circuits (e.g., IBM Torino benchmarks). Companion Toolkit: Serves as the mathematical prerequisite for defining the discrete curvature sources used in the DAGI Emergent Spacetime Geometry (ESG) mapping.
Context: This manuscript serves as the empirical Quantum Darwinism validation track for the Directed Acyclic Graph Interpretation (DAGI) framework at Whytics. It bridges Wojciech Zurek's paradigm of decoherence with DAGI's topological mereology, providing the rigorous mathematical derivation of the "Redundancy Plateau" utilized throughout the broader research program. Abstract: Recent advances in quantum experiments allow rigorous tests of how classical reality emerges from quantum systems. Here we present an experimental validation of the Directed Acyclic Graph Interpretation (DAGI) theoretical framework using a multiscale information decomposition applied to a state-of-the-art quantum Darwinism experiment on superconducting circuits (Zhu et al., 2025). We analyze the mutual information between a quantum system and fragments of its environment, decomposing it via a Möbius inversion technique into irreducible k-body informational contributions. Our results confirm a unique prediction of the DAGI framework: we observe a "Redundancy Plateau" where higher-order synergistic information (involving three or more environmental subsystems, k≥3) is strongly suppressed for partial environment fragments. First-order redundant information (f1) heavily dominates, second-order overlaps (f2) are strictly negative, and higher-order terms (k≥3) nearly perfectly cancel out. Synergy becomes significant only when the entire environment is accessed, successfully isolating the system's residual quantum entanglement as an irreducible N-body secret. This pattern cannot be reproduced by standard decoherence models without DAGI’s information-theoretic perspective. The validation of this prediction bolsters the falsifiability of the DAGI framework and provides the exact kinematic mechanism for how objective classical reality emerges from the quantum substrate.
Context: This manuscript belongs to the computational validation track of the DAGI (Directed Acyclic Graph Interpretation) research program at Whytics. It provides a mathematically exact confirmation of holographic entanglement wedge reconstruction using multiscale information theory. Abstract: We validate the entanglement wedge reconstruction property in a holographic stabilizer code using a multiscale information-theoretic approach. In a 16-qubit stabilizer graph code, we identify a bulk qubit whose information can only be recovered from a specific minimum set of five boundary qubits (its "entanglement wedge"). We employ the Directed Acyclic Graph Interpretation (DAGI) framework and a Möbius inversion-based decomposition of mutual information to quantify how information about the bulk is distributed among boundary subsets. Our analysis confirms that no information about the bulk qubit is accessible from any proper subset of its five-qubit wedge or from disjoint outside regions. Only when all five qubits in the entanglement wedge are present does the mutual information rise to its maximum (2 bits), corresponding to a perfect quantum correlation. Moreover, a Möbius decomposition reveals that this 2-bit mutual information is an irreducible five-party correlation: all lower-order contributions (one-body, two-body, etc.) are zero. We thus explicitly confirm that the bulk qubit's information is encoded entirely in a five-body entanglement, providing a quantitative, multiscale verification of entanglement wedge reconstruction in the code. Key Highlights: Exact Holographic Validation: Quantitatively confirms the entanglement wedge threshold in a 16-qubit hyperbolic graph code using exact algebraic rank methods. Synergy Verification: Proves via Möbius inversion that bulk information manifests entirely as an irreducible 5-body synergistic correlation, with strictly zero information present in lower-order marginals. Open Source Framework: The complete Python computational pipeline—including graph-state generation, Möbius inversion, and visualization routines—is included in this release to guarantee reproducibility.
Context: This manuscript belongs to the empirical hardware-validation track of the DAGI (Directed Acyclic Graph Interpretation) research program at Whytics. It provides direct experimental evidence for high-order informational thresholding, a concept central to the framework's treatment of emergent spacetime and black hole information. Abstract: The Directed Acyclic Graph Interpretation (DAGI) framework predicts that certain globally coherent variables are not locally accessible, but instead reside in irreducible high-order information structures (synergy) that become available only when sufficiently many degrees of freedom are jointly accessed. Motivated by Page-time transitions in black-hole information and by entanglement-wedge thresholds in holographic quantum error correction, we design a deliberately minimal "threshold-lock" circuit family whose measurement statistics implement a synergy-only encoding of a binary label K: all 1- and 2-bit marginals of the early radiation are (ideally) independent of K while the 3-bit prefix jointly reveals K. We execute this experiment on IBM Quantum ibm_torino with n=6 measured qubits and 2048 shots per key, alongside a "leaky" control in which low-order information is intentionally present. Using a Möbius/DAGI decomposition of the mutual information over the prefix subset lattice, we observe a sharp Page-like turn-on for the locked variant, with cumulative positive synergy dominated entirely by an intrinsic order-3 term. A bootstrap reliability sweep confirms that the locked order-3 synergy mass is statistically stable, while the leaky order-3 signal remains unstable. These results constitute a compact, falsifiable hardware demonstration that DAGI can detect and distinguish high-order, thresholded information release from low-order leakage in real quantum measurement data, supporting the use of DAGI Möbius diagnostics as experimental probes of Page-like information transitions and as design tools for DAG-inspired QECCs. Key Highlights: Hardware-Verified Thresholds: Demonstrates a distinct Page-curve-like accessibility transition on a superconducting IBM Quantum processor. Synergy vs. Leakage: Proves the efficacy of the DAGI Möbius decomposition in distinguishing true irreducible high-order synergy from low-order hardware leakage. Holographic Analogs: Provides an operational, circuit-level analog for entanglement-wedge reconstruction phenomena utilized in emergent gravity and holographic error correction.
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≥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≈1023) entities.
We report a hardware validation of the DAGI (Directed Acyclic Graph Information) framework on IBM Quantum hardware using a small, controlled experiment whose ideal output distribution is constrained to a low-dimensional modular manifold (a "ridge"). For two n-bit registers (u,v) with n=4 (modulus 16), each key instance k induces an ideal relation v≡k⋅u(mod16), producing a visually distinct ridge in the joint (u,v) distribution. Executed on ibm\_torino in a single Sampler V2 job (8 keys, 1024 shots/key, N=8192 total shots), the ridge persists under hardware noise with ridge-hit probability phit=0.1830 (uniform baseline 1/16), corresponding to a ridge contrast of 2.93× (95\% bootstrap CI [2.80, 3.06]). Key recovery exceeds chance: per-shot accuracy 0.1689 (chance 0.125, 95\% Wilson CI [0.1610, 0.1772]), and per-group dictionary recovery 0.375 (chance 0.125). To test the central DAGI hypothesis -- that recoverable key information is predominantly high-order/synergistic rather than visible in low-order marginals -- we compute a Möbius-based information decomposition of I(K;DS) over detector-bit subsets S via a Möbius inversion pipeline and evaluate targeted positive synergy CPSK at order kmax=3. We observe CPSK(k=3)=0.08788 with significance under label-shuffle permutation tests (accuracy p=0.001996, CPSKp=0.004975). Uniformity diagnostics show near-uniform single-bit marginals while correlation concentrates in specific low-order pairs, and a bootstrap reliability sweep confirms order-3 targeted synergy remains statistically reliable at the full 1024-shot target budget. These results support the claim that DAGI detects and quantifies nontrivial, hardware-resilient, higher-order information structure associated with a known global algebraic constraint.
The DAGI program uses M\"obius inversion on partially ordered sets to decompose an information observable into irreducible contributions. A central methodological question is whether the Boolean powerset is merely a convenient default, or whether the poset should be engineered to match the physical accessibility structure of the experiment. We report a hardware validation of the latter claim on IBM Quantum hardware (\texttt{ibm\_torino}). In repetition-code memory circuits with mid-circuit measurement and reset, we compare two decompositions computed on exactly the same detector-window data: a truncated subset lattice (all detector subsets with ∣S∣≤3) and a reachability-defined causal-cone poset (truncated past cones with rmax=3). Controlled contexts increase two-qubit exposure using barrier-separated canceling two-qubit operations while preserving the ideal logical circuit. Across a single-patch pilot and two multi-patch extensions (P=4 and P=8 far-separated parallel patches), the detector windows contain measurable context signal. The strongest positive result is not raw classification accuracy but \emph{region stability}: top cone-poset regions selected by M\"obius magnitude are highly patch-invariant, whereas subset-lattice top terms are nearly random-like across patches. For P=4 and P=8, normalized top-region Jaccard stability is $\Jnorm_{\cone}=0.505$ and 0.603, while $\Jnorm_{\sub}=0.008$ and −0.001. Out-of-patch classifiers remain only weakly above chance, but multinomial logistic calibration reduces expected calibration error to 0.035--0.079 and removes a large Naive-Bayes calibration artifact. This weak classification is expected: predicting a global two-qubit-load context from one local 12-detector window is a low-SNR domain-generalization task. The mutual information statistic in this experiment is interpreted as an operational proxy for the context-modulated correlated-error footprint, not as a direct measurement of pure topological synergy. We therefore state a conservative conclusion: causal-cone posets expose reusable, patch-invariant macro-region signatures in this repetition-code hardware setting; they are not yet shown to improve logical decoding or to dominate arbitrary subsets in all predictive tasks. The accompanying dataset bundle contains raw detector windows, QPY circuits, explicit poset definitions, fold outputs, and paper-ready tables.