Resource Dependency and Conditional Reconstruction in Entanglement-Weighted Causal Emergence

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-18
DOI
https://doi.org/10.5281/zenodo.22824925
Primary Topic
Quantum many-body systems
Type
preprint
Controls
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preprint

Resource Dependency and Conditional Reconstruction in Entanglement-Weighted Causal Emergence

Tao Lin
Zenodo (CERN European Organization for Nuclear Research)
Quantum many-body systems
preprint

Resource Dependency and Conditional Reconstruction in Entanglement-Weighted Causal Emergence

Tao Lin
preprint en

Abstract

We study the explicitly defined ECE/TAMN target mechanism below—not a universal class of all entropy- or topology-based emergent-gravity models—in which graph-based gauge kinematics, an entanglement–topology scalar $$\Theta(A) = S(A) + \lambda \chi(A),$$ topological surgery labels, and causal-set continuum reconstruction are intended to arise from one microscopic mechanism. The central result is a resource-dependency theorem. At each microscopic cutoff, kinematics and eligibility do not identify a stochastic dynamics. Even after one optionally adjoins a stationary law and detailed balance on a finite paired control support, symmetric conductance freedom remains. By contrast, a well-posed Markov specification together with an initial law determines its path measure. An intrinsic causet-valued dependency map is then additional data needed to obtain an event-causet law, and a well-defined family of event-causet laws still does not force a four-dimensional manifoldlike scaling phase. At the microscopic level, a symplectic phase space and threshold do not determine a Hamiltonian or stochastic generator; even a Gibbs stationary law with detailed balance leaves an arbitrary symmetric conductance field. External jump chronology is not an intrinsic causal order, and static availability of many independent moves does not imply that the dynamics realizes a large causal antichain. Bounded local rewrite rules likewise do not select a four-dimensional scaling exponent. These results sharpen the source-law obstruction from "missing formula" to genuine dynamical nonidentifiability. Independently, the raw scalar mechanism has two further obstructions: a subextensive leading small-region term makes $\Theta / \operatorname{Vol}$ singular, while a fixed metric-independent topological invariant has zero direct smooth bulk stress within a fixed topological sector. A relative Chern charge can become an additive reversal-odd history variable after the required gauge-cobordism lift, but it is not an irreversible path law. Positive statements survive downstream. On a given Lorentzian continuum, inverse-intensity weighting recovers physical volume. Causal order and uncalibrated nonuniform intensity have the exact degeneracy $$(g, \rho) \sim (\Omega^2 g, \Omega^{-d} \rho),$$ but a regular event measure together with an independent length calibration uniquely selects a metric representative. Under the standard small-ball entanglement-equilibrium hypotheses, the gravitational relation closes only conditionally and perturbatively. The resulting theory is therefore not a completed derivation of spacetime. It is a theorem-level classification of which resources are not determined by the stated upstream data, which proposed identifications are impossible in the scoped mechanism, and which continuum reconstructions become rigorous once their upstream inputs are supplied.

Zenodo (CERN European Organization for Nuclear Research)
Peace, Justice and strong institutions
Quantum many-body systems
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