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 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.
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,
CPSK p=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.
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.
Bulk reconstruction is a central problem in AdS/CFT, and entanglement wedge reconstruction is its subregion version. We argue that this subregion statement should be separated from the stronger holographic quantum error correction interpretation, in which one region-independent logical bulk operator has code-preserving representatives in several boundary regions. A simple locality argument shows that such a common reconstruction must commute with the code-preserving local algebras in the complementary regions. This is the mechanism realized in HaPPY-type codes: the erased regions are blind to a protected logical algebra. An ordinary finite
N holographic CFT does not have such a protected invisible sector for supergravity fields. Its low-energy local observables, in particular, suitably smeared stress tensors, detect the physical support and gravitational dressing of ordinary bulk operators, up to possible center or superselection data. Thus, there is no such holographic quantum error correction and the
N=∞ agreement of global and subregion HKLL formulae is a free-theory statement. What remains is entanglement wedge reconstruction without holographic quantum error correction, or subregion complementarity: each boundary region has its own code-preserving low-energy algebra and its own region-adapted bulk interpretation, rather than a shared logical operator.
In the context of quantum theories of spacetime, one overarching question is how quantum information in the bulk spacetime is encoded holographically in boundary degrees of freedom.It is particularly interesting to understand the correspondence between bulk subregions and boundary subregions in order to address the emergence of locality in the bulk quantum spacetime.For the AdS/CFT correspondence, it is known that this bulk information is encoded redundantly on the boundary in the form of an error-correcting code.Having access only to a subregion of the boundary is as if part of the holographic code has been damaged by noise and rendered inaccessible.In quantum-information science, the problem of recovering information from a damaged code is addressed by the theory of universal recovery channels.We apply and extend this theory to address the problem of relating bulk and boundary subregions in AdS/CFT, focusing on a conjecture known as entanglement wedge reconstruction.Existing work relies on the exact equivalence between bulk and boundary relative entropies, but these are only approximately equal in bulk effective field theory, and in similar situations it is known that predictions from exact entropic equalities can be qualitatively incorrect.We show that the framework of universal recovery channels provides a robust demonstration of the entanglement wedge reconstruction conjecture as well as new physical insights.Most notably, we find that a bulk operator acting in a given boundary region's entanglement wedge can be expressed as the response of the boundary region's modular Hamiltonian to a perturbation of the bulk state in the direction of the bulk operator.This formula can be interpreted as a noncommutative version of Bayes's rule that attempts to undo the noise induced by restricting to only a portion of the boundary.To reach these conclusions, we extend the theory of universal recovery channels to finite-dimensional operator algebras and demonstrate that recovery channels approximately preserve the multiplicative structure of the operator algebra.