Gravity from entanglement equilibrium on a finite quantum network: assumptions, known obstacles and quantum tests

General relativity describes how spacetime curves, but not what the curved thing is made of. This paper pursues one possible answer: spacetime emerges from a finite, unitary quantum network, and the Einstein equation is, as in Jacobson's work, an equilibrium condition on the entanglement of small balls. The aim is not to defend this picture. The aim is to separate cleanly what in it is assumed, what is derived and what is only shown on small toy models (Table 1). Four results are central. First, I place the model relative to the known obstacles to emergent gravity, namely Marolf's argument on local kinematics, the Weinberg–Witten theorem and the failure of gravitational observables to factorise, and state which premise the model gives up in each case or what remains to be shown. Second, giving each branch of a superposition its own geometry turns out to be a separate assumption. It is fulfilled automatically if the long-wavelength degrees of freedom of the network form a quantum mediator. A toy model illustrates the known alternative: a network that responds only to the mean value of the source does not entangle and permits either superluminal signalling or communication between branches. Third, the first layer of the model predicts the same gravity-mediated entanglement as perturbative quantum gravity: entanglement with the Newtonian phase, no decoherence beyond that known there, and no collapse. In the laboratory the weak second layer is suppressed by a factor of about 2·10⁻¹¹; if it is classical, consistency requires an irreversible coupling with decoherence of its own, whose size I do not quantify. For tabletop experiments the model therefore makes no new prediction, but tabletop experiments can refute it. Fourth, I treat finite cores of black holes and the fate of information. Both rest on explicitly stated assumptions and illustrate known results. Distinguishing predictions of the model lie in the second layer and in cosmology; they are the subject of Papers A2, B and C. Files: IVW_A1_foundations_en.pdf (English) and IVW_A1_foundations_de.pdf (German) contain the same text and the same numbers. ivw_a1_calculation_en.py (English output) and ivw_a1_calculation_de.py (German output) recompute every number of the paper in eleven sections and check it at the end (runtime about five seconds; libraries in REQUIREMENTS_en.txt). The original individual scripts, the computation plans frozen with SHA-256 checksums before the computation, the reports and the register of the author's own errors are available from the author on request. This is Paper A1 of a series on the Informational Vector World Model (IVW). Papers A2 (covariant action for the weak second layer), B (pre-registered test of the quenching-time relation on 51 dwarf galaxies), C (numerical conjecture for the density of cold matter) and a combined paper follow as separate records.