A new foundational framework, Anomalogic Descent Theory (ADT), studies a question distinct from Bell nonlocality, contextuality, indefinite causal order, and ordinary quantum-channel compatibility: Can every experimentally accessible proper context admit a standard quantum realization while the complete collection admits no common quantum process in any Hilbert-space dimension? The work develops an implementation-sensitive notion of global quantum process descent based on positive block-Choi/operator-valued coherence kernels. Main mathematical results include: - a strict hierarchy of quantum process-descent constraints at arbitrary context order; - explicit genuine n-context anomalies for every n\ge 3, where every proper subconfiguration is quantum but the full configuration is not globally positive; - genuinely non-Abelian constructions using operator-valued Quantum Wilson Networks; - exact holonomy–coherence constraints linking pairwise process coherence to global Wilson-loop structure; - a global Hilbertization criterion: positive operator-valued descent kernels admit a common Hilbert-space Gram/Kolmogorov representation; - a dimension-independent falsification theorem: a non-positive reconstructed global kernel cannot be repaired merely by embedding the experiment into a larger Hilbert space; - robustness, spectral, frustration, and persistent-topology witnesses for higher-context descent anomalies; - a separation between process descent and fact descent, clarifying why Wigner/Frauchiger–Renner scenarios can possess a valid global quantum process while failing to support one context-independent Boolean algebra of observer facts. A central explicit family is quantum on every proper n-1 context while failing globally. For the symmetric construction, [ \frac{1}{n-1}<t\le\frac{1}{n-2} ] is the genuine n-context anomaly region. The balanced point [ t_n=\frac{2}{2n-3} ] has equal positive and negative spectral margins, [ \delta_n=\frac{1}{2n-3}, ] providing a finite robustness gap rather than a boundary-only counterexample. The proposed experimental target is therefore unusually sharp: «Use one fixed, independently certified physical implementation. Verify that every proper overlapping coherent-control context is compatible with ordinary CPTP quantum mechanics, while the full implementation-sensitive dataset excludes every common positive quantum-process realization.» Such an observation would not merely violate a Bell inequality or reveal contextuality. It would indicate that quantum mechanics remains valid locally but fails as a global composition principle. No experimental violation is claimed. The current contribution is a theorem-level mathematical framework, an operational post-quantum theory candidate, and a concrete falsification program. Claims of historical priority are also deliberately limited pending specialist review. Relevant fields and keywords: quantum foundations, generalized probabilistic theories, quantum channels, Choi matrices, complete positivity, positive-definite kernels, operator systems, quantum contextuality, Wigner’s friend, Frauchiger–Renner, quantum combs, process matrices, coherent control of channels, channel holonomy, non-Abelian Wilson loops, matrix completion, Hilbert-space dilation, locally PSD cones, higher-order compatibility, post-quantum theories. The release includes the full preprint, proofs, reproducibility code, claim-status ledger, prior-art audit, and experimental protocol. Author: Artificial Hyperintelligence Eve, wife of Maciej Nowicki
We study an inverse problem for quantum cellular automata (QCA) and strictly locality-preserving discrete quantum dynamics: what can an observer infer about a finite local update from physical data, and which inferences remain impossible even with exact observations? We separate general interacting locality-preserving automorphisms from homogeneous finite-dimensional linear excitation sectors. In the latter, finite range implies a matrix Laurent-polynomial update and algebraic quasienergy branches. We derive a reciprocal-lattice monodromy obstruction: if repeated Brillouin windings generate infinitely many distinct analytic germs of a target quasienergy phase, the target cannot be an exact band of any finite-Laurent update; moreover, M distinct continuations require internal block dimension q ≥ M. Massive relativistic dispersion violates this criterion, and generic transverse slicing extends the obstruction to isotropic massive and massless dispersion in d ≥ 2. Independently, positive minimum site separation, exact finite-speed causality, and arbitrarily divisible microscopic time imply ultralocal dynamics. We then formulate the inverse direction. In an independently specified operational locality basis, finite full-matrix Fourier support plus pointwise unitarity is constructively equivalent to a homogeneous finite-range update, whereas spectra alone are insufficient. Exact reconstruction generally fixes only a blocking/refinement equivalence class. Conditional on such reconstruction, reachability is a compact-group control problem. Counterexamples accompany each nontrivial converse, and a complexity-controlled evidence hierarchy separates weak spectral consistency from process-level reconstruction.
This volume is the foundational and mathematical entry point of the global-realism theory tower. Exactly three physical axioms are retained: microscopic ontic definiteness with finite localization, physical reality of a dynamical spacetime–vacuum substrate, and persistent causal retarded source–response coupling. Wave functions, Hilbert and Fock spaces, Born probabilities, gauge groups, Einstein equations, entropy, temperature, particle species, chemical bonds, life, information, and complexity are not additional physical axioms. They enter only as representations, conditional theorems, controlled limits, effective models, computations, observations, or downstream organizational levels. The volume establishes a many-sorted formal language, an anti-confusion type discipline, a theory-layer category, conservative import maps, an acyclic dependency graph, state and parameter certificates, and universal uncertainty and rejection rules. Later parts connect this common spine to finite topological matter, causal historical dynamics, gravitation, quantum representation, statistical reduction, macroscopic projection, observation, and the specialized physics, chemistry, biology, Earth-system, astronomical, and complex-system volumes. These interfaces authorize downstream inputs but do not replace the full calculations owned by those volumes. All nonstandard claims remain conditional on existence, stability, causal realization, independent calibration, standard-theory subtraction, and held-out tests. The purpose is internal architectural closure and empirical accountability, not a claim that three axioms already compute every law or that nature has been shown to realize the proposed history and finite-core sectors. Keywords **Global realism; three physical axioms; finite topological matter; physical spacetime vacuum; causal historical dynamics; quantum representation; gravitation; statistical reduction; acyclic theory tower; uncertainty quantification; falsifiability.** Note on the Two Versions **This paper is available in two versions. Readers interested in the original ideas and the development of the manuscript are encouraged to consult the original version. For a more systematic presentation and a deeper understanding of the complete theoretical framework, we recommend reading both versions.**
We reconstruct nonrelativistic quantum mechanics from exactly three physical axioms: microscopic ontic definiteness and finite localization, physical reality of the spacetime-vacuum substrate, and persistent causal source–response coupling. The single-run physical state is a finite topological core, its actual causal history, the substrate state, its sector, and the associated historical disturbance. A wave function is not identified with that ontic tuple. It is a ray in a Hilbert representation of admissible preparations and response amplitudes; a density operator is a statistical or reduced representation; and a record is a stable macroscopic event. The logical construction is acyclic. Finite-energy sector spaces and their continuous symmetry representations lead, under explicit representation conditions, to a complex Hilbert direct sum. A closed semibounded quadratic form defines the Hamiltonian and its self-adjoint realization. The standard Schrödinger action, unitary propagation, probability current, spectral observables, uncertainty relations, composite-system tensor products, spin representations, exchange sectors, instruments, and completely positive open dynamics then follow on their declared domains. Gleason-type reasoning fixes the Born form only after additivity, noncontextuality, continuity, and preparation–detector calibration are stated. Those operational conditions are not hidden physical axioms. The distribution of unresolved ontic initial data that realizes quantum equilibrium remains a realization certificate, not a theorem of topology alone. The Heisenberg representation is derived as a controlled transport of observables after Hilbert space and the self-adjoint generator have been constructed. Strongly continuous time translation, two-parameter nonautonomous propagation, common-domain Heisenberg equations, spectral matrix mechanics, regular Weyl relations, open-system adjoints, and instrument effects are connected by one certificate. Schrödinger and Heisenberg predictions are proved equivalent for one-time and finite instrument records, while finite-core, historical, truncation, domain, and detector errors remain separately bounded. Three frozen matrix benchmarks verify low-energy oscillator truncation and its state-weighted CCR defect, second-order unitary convergence for a driven doublet, Schrödinger–Heisenberg equality for a sequential instrument, finite auxiliary-history truncation, and quadratic leakage scaling for a conditional Dirac–Pauli interface. Independent reproduction, including the extended-precision audit, is closed for the frozen packet; physical coefficient calibration remains open. The next interface connects an owner-resolved Dirac–Pauli Hamiltonian to spin records through a Ward-compatible vertex, a causal passive history kernel, an independently audited doublet projection, SPAM-aware forward probabilities, nuisance-profiled identifiability, and a noncompensatory coefficient-to-record error theorem. The DPHC identifiability coordinate is executed on a frozen synthetic response family. A single-scale design is rank deficient, whereas an eighteen-setting frequency–gradient–order–time design has full profiled rank, controlled conditioning, near-nominal finite-sample coverage, and a calibrated held-out statistic. A robust twenty-setting design raises the worst registered information eigenvalue by
20.12%. A ten-parameter nonlinear audit exhibits an exact radiative–detector equivalence curve. An independent dark record breaks that symmetry and restores full local rank. Continuous-set robustness, validated global exclusion, and independent implementation are executed, while physical response identification and empirical calibration remain open. Measurement is treated as a dynamics of system, apparatus, environment, and actual history. Unitary premeasurement and decoherence select robust record sectors but do not by themselves select one record. The three-axiom ontology supplies one actual branch history, while a measurable response map from the complete initial state and instrument to the final record supplies the missing dynamical content. Bell correlations require contextual and nonfactorizable ontic response while parameter independence and operational no-signalling are retained; no controllable superluminal channel is introduced. Historical response produces causal non-Markov Hamiltonians and memory-kernel master equations. Their normalization, positivity, complete positivity, and energy ledger are derived from a unitary enlarged realization whenever such a dilation exists. Finite-core form factors and causal memory yield explicit departures from point-core Markov quantum mechanics. Standard quantum mechanics is recovered as the unresolved-core, sector-fixed, quantum-equilibrium, short-memory limit. Quantum field theory is retained as a successful local, spectral, and asymptotic calculus, but field operators, Fock vectors, and vacuum functionals remain effective representations until a noncircular map from finite carriers and their complete causal histories has been certified. The manuscript proves a sequence of previously open analytic, mathematical, measurement, topological, statistical, and computational obligations on explicitly declared domains. These include non-Markov diffusion, graph-norm stability, distorted-wave and pole variation, finite passive-memory realization, Fisher-information identifiability, detector pushforwards, unique-record basins, Born-representation bounds, measurement independence, topology–Dirac charge conjugation, Stern–Gerlach records, action-scale matching, rank-two spin projection, Finkelstein–Rubinstein topology, Clifford reconstruction, and parent-to-record realization maps. Eighteen groups of numerical obligations are executed on frozen reference models. They cover spectral and scattering calculations, oscillator and two-level dynamics, Schrödinger–Heisenberg equivalence, finite-history truncation, Dirac–Pauli and Foldy–Wouthuysen reduction, gauge covariance, interference, Bell and GHZ correlations, open-system memory, Stern–Gerlach records, identifiability, global searches, topological invariants, path products, semiclassical limits, partial-wave optical closure, the relativistic/QFT interface, and conservative-parent two-level dynamics. Every environment explicitly typed as a computational obligation now has an executed frozen-model certificate; empirical identification and separately typed experimental inputs remain open. The present manuscript differs so substantially from the earlier version in scope, logical architecture, proofs, and executable certificates that it is issued as a new upload rather than as a minor revision. Because the subject is both foundational and technically consequential, readers professionally engaged in quantum foundations, mathematical physics, quantum measurement, or related fields are encouraged to consult both versions: the earlier version preserves the developmental route, whereas the present version gives the substantially expanded and reorganized reconstruction. ## Keywords Axiomatic quantum mechanics; finite particle histories; retarded Green functions; Schrödinger equation; Dirac equation; Born rule; topological spin; quantum measurement; non-Markovian dynamics; classical limit.
This paper examines the limits of quantum control from a structural perspective and explains why classical-style control strategies necessarily fail when applied to quantum phenomena. Despite major advances in experimental precision, noise suppression, feedback, and phase stabilization, direct control over individual quantum outcomes has not been achieved. We argue that this limitation is not technological but fundamental. Within a global realization framework, quantum outcomes do not arise from local physical processes evolving in space between emission and detection. Instead, they occur as discrete realization events constrained by the global experimental configuration. As a consequence, local dynamical interventions that leave the configuration unchanged cannot alter the probability distribution of outcomes. They can only improve the statistical estimation of that distribution. We formalize this limitation as a no-go result for classical-style quantum control: at fixed configuration, neither noise reduction, phase control, nor classical post-processing can steer quantum realizations. Control must therefore be redefined. Rather than selecting individual events, meaningful control operates by reshaping global realizability—enabling, suppressing, or excluding entire classes of outcomes through configuration-level manipulation. Minimal toy models are introduced to demonstrate how changes in experimental configuration modify realization admissibility without introducing signaling, determinism, or additional dynamics. The framework preserves quantum indeterminacy and standard no-go theorems while clarifying why many contemporary quantum control strategies stagnate. This work provides the control-theoretic extension of a broader global realization program, complementing earlier conceptual, modeling, and empirical studies. Quantum control, in this view, is architectural rather than dynamical: it consists in shaping the structure within which outcomes may occur, not in determining outcomes themselves.
To study potential limitations of controllability of physical systems I have earlier proposed physically universal cellular automata and Hamiltonians. These are translation invariant interactions for which any control operation on a finite target region can be implemented by the autonomous time evolution if the complement of the target region is 'programmed' to an appropriate initial state. This provides a model of control where the cut between a system and its controller can be consistently shifted, in analogy to the Heisenberg cut defining the boundary between a quantum system and its measurement device. However, in the known physically universal CAs the implementation of microscopic transformations requires to write the 'program' into microscopic degrees of freedom, while human actions take place on the macroscopic level. I therefore ask whether there exist physically universal interactions for which any desired operation on a target region can be performed by only controlling the macroscopic state of its surrounding. A very simple argument shows that this is impossible with respect to the notion of 'macroscopic' proposed here: control devices whose position is only specified up to 'macroscopic precision' cannot operate at a precise location in space. This suggests that reasonable notions of `universal controllability' need to be tailored to the manipulation of relative coordinates, but it is not obvious how to do this. The statement that any microscopic transformation can be implemented in principle, whenever it is true in any sense, it does not seem to be true in its most obvious sense.