The Embedded-Observer No-Go Theorem (2026)
Experimental verification protocols have been added. Any closed unitary quantum system -from many-body lattice models to quantum-gravity programs that posit a strictly unitary wavefunction of the universe (causal sets, LQG, CDT, string theory, Everettian decoherence) - contains embedded observers who cannot, in principle, fully self-describe the global state or evolve autonomously and unitarily once a generic, non-fine-tuned interaction with the rest of the system has occurred even a single time. The result is locality-independent: the proof rests only on closure, the observer’s embeddedness, and the genericity of the coupling. “Collapse” and apparent irreversibility cease to be separate postulates - they are a provable consequence of embeddedness itself. The theorem additionally establishes a causal boundary -an exact light cone for discrete quantum circuits, an approximate one (with an exponentially small tail) for general local Hamiltonian systems -together with an operational tool for quantifying the two distinct kinds of limitation on an observer’s knowledge: stock (entropy) and flow (channel unitarity). Computational Appendix: https://github. com/SergejMaterov/Embedded_Observer_NoGo
The Fundamental Limit of Quantum Computation (FLQC) (2026)
This work introduces the concept of the Fundamental Limit of Quantum Computation (FLQC) - a precision limit of any quantum computing device arising from the discrete structure of spacetime at the Planck scale. The limit cannot be overcome by any technological progress. Consequences for Shor’s algorithm and error correction are discussed, together with a separate, hardware-dependent experimental programme targeting the graph’s noise-Hamiltonian critical temperature T_c (a few mK to tens of mK, set by each device’s own couplings and topology). Numerical simulation phase-resolution test protocol with qiskit: https://github. com/SergejMaterov/FLQC-Protocol
On the Impossibility of Deriving Quantitative Intra-Multiplet Splittings from Symmetry-Complete Dynamics Alone
During repeated attempts to derive the observed three-generation flavor hierarchy solely from an exact graph symmetry, every construction either preserved exact multiplet degeneracy or required external symmetry-breaking input. This suggested that the obstruction was intrinsic to symmetry-complete theories rather than to any particular graph construction, motivating the general no-go theorem proved here. A recurring claim across several research programs - discrete flavor-symmetry model building (Aₙ, Sₙ, Δ(27) family symmetries), Froggatt–Nielsen-type charge assignments, and combinatorial or graph-based approaches to emergent spacetime and particle content - is that the observed hierarchy of fermion masses, mixing angles, or analogous multiplet splitting’s can be derived from symmetry considerations alone, without an independently motivated symmetry-breaking sector. We show this is impossible in a precise, model-independent sense. If a theory is defined entirely by a symmetry group S, a covariant representation Γ of S, and dynamics Hₘᴇ covariant under S, then no numerical value can be derived within that theory for the splitting between components of a non-trivial irreducible multiplet of observables, beyond the trivial statement that the splitting is exactly zero when the theory’s distinguished state is S-invariant. If the distinguished state instead spontaneously breaks S, the direction of breaking is undetermined by the theory, and even granting a direction, the typical magnitude of splitting predicted by a symmetry-neutral (Haar-random) prior is O(1) between multiplet components — so any large observed hierarchy is itself evidence of a further, non-symmetry input. The result is an exact operator-level sharpening of Curie’s symmetry principle (1894) via the Wigner–Eckart theorem (1927), together with the standard vacuum-selection problem of spontaneous symmetry breaking (Goldstone 1961; Goldstone, Salam & Weinberg 1962). It applies to any “symmetry-complete” theory - continuum or discrete, field-theoretic or lattice-based and identifies exactly which additional, non-symmetry ingredient any such theory must supply.
On the Absence of Automatic Linear Lorentz-Violating Dispersion from discreteness Alone (2026)
[Version 5: An appendix and a table of supported discrete models of quantum gravity have been added. ] Theorem on the Absence of Automatic Linear Dispersion from Discreteness + No Boost Lemma + Observational signature + table of supported theories. This theorem and lemma eliminate two mathematical obstacles often associated with discrete approaches to quantum gravity Discrete models of spacetime are often assumed to generically predict a first-order, energy-dependent (linear-in-E) Lorentz-violating dispersion of high-energy photons, of the kind tightly constrained by gamma-ray burst (GRB) timing observations. We show that this implication does not follow from discreteness alone: it requires an additional, independent structural assumption - namely, that local phase contributions accumulated along propagation are coherently aligned with a fixed, globally preferred frame. In any discrete substrate where the physical metric is emergent and reconstructed (rather than given by a fixed embedding), and where local phase contributions are not long-range correlated, the accumulated phase grows only as the square root of the number of traversed elements, suppressing any linear dispersion signal. This result is structural and substrate-independent: it applies to any discrete model satisfying the stated decorrelation property, and is intended as a general consistency tool for the broader class of emergent-geometry approaches to quantum gravity, not as evidence for any specific model. The theorem does not exclude Lorentz-violating dispersion in all discrete spacetime models; it proves that discreteness alone is insufficient to derive a universal linear dispersion law. The theorem formalizes a necessary-condition requirement: linear Lorentz-violating dispersion is not a generic consequence of discreteness, but requires additional assumptions about microscopic phase coherence.
Quantumograph: дискретная онтология пространства-времени и проблема эмпирической доступности квантовой гравитации (2026)
Статья развивает исследовательскую программу «Quantumograph» (TQGT) (Materov 2026). Центральный тезис онтологический: пространство-время тождественно конечному квантовому графу, тогда как континуальные понятия (метрика, поля, время) строго эмерджентны. Автор показывает, что эта программа обладает избыточным эмпирическим содержанием: её ключевые предсказания проверяются на существующих криогенных квантовых процессорах, что переносит квантовую гравитацию из сферы математической спекуляции в область экспериментально констреинированной науки. Философский анализ выявляет онтологические следствия: поддержку онтического структурного реализма, конституционную конечность Вселенной, динамическую природу времени, а также две фундаментальные теоремы - об отсутствии асимптотического хаоса и о вычислимой редуцируемости. Сравнение со струнной теорией, петлевой квантовой гравитацией и цифровой онтологией Фредкина - Вольфрама - Ллойда позволяет локализовать уникальный статус программы как фальсифицируемого дискретного структурализма.