This paper extends the Ontological Totality Functional (OTF) programme into the domain of quantum causal structure. Its central claim is that physical admissibility cannot be exhausted by state-level consistency or dynamical stability alone. It must also constrain the admissibility of causal organization itself. The paper introduces a causal defect functional for higher-order quantum processes and argues that definite causal order can emerge as a limiting case of admissible structure. Working in a finite-dimensional process-matrix setting, the paper defines the causal defect as the trace-norm distance to the set of valid causally separable processes with fixed normalization. It proves that this defect is non-negative, vanishes exactly on the causally separable set, and is convex. A free class of admissible supermaps is then identified: linear maps on processes that preserve validity, preserve causal separability, and are contractive in trace norm. Under these maps, the causal defect is monotone. An exact dual operational characterization is established: the causal defect equals the maximal bounded-test advantage over the causally separable set for Hermitian tests of bounded operator norm. In this sense, bounded causal witnesses arise as certified lower-bound functionals for admissibility. To connect the formalism to concrete physical scenarios, the paper studies a dephased-switch family W_eta = W_diag + eta X, where W_diag is causally separable and X encodes interference between orders. For this family, the defect is bounded above linearly in |eta|, while a witness with positive overlap on X yields a matching linear lower bound. As eta tends to zero, the process approaches definite-order admissibility. Within the OTF series, this paper functions as a frontier extension. Paper I introduced physical admissibility mathematically, Paper II studied admissibility in a tensor-cosmology channel, and Paper III interpreted admissibility ontologically. Paper IV shows that the same programme can be pushed into higher-order causal structure, where admissibility constrains not only which states and channels are physically stable but also which causal architectures can count as physically realized. Companion records in the OTF series:OTF I — DOI: 10.5281/zenodo.19068375OTF II — DOI: 10.5281/zenodo.19075284OTF Master Edition — DOI: 10.5281/zenodo.19077303
This paper extends the Ontological Totality Functional (OTF) programme into the domain of quantum causal structure. Its central claim is that physical admissibility cannot be exhausted by state-level consistency or dynamical stability alone. It must also constrain the admissibility of causal organization itself. The paper introduces a causal defect functional for higher-order quantum processes and argues that definite causal order can emerge as a limiting case of admissible structure. Working in a finite-dimensional process-matrix setting, the paper defines the causal defect as the trace-norm distance to the set of valid causally separable processes with fixed normalization. It proves that this defect is non-negative, vanishes exactly on the causally separable set, and is convex. A free class of admissible supermaps is then identified: linear maps on processes that preserve validity, preserve causal separability, and are contractive in trace norm. Under these maps, the causal defect is monotone. An exact dual operational characterization is established: the causal defect equals the maximal bounded-test advantage over the causally separable set for Hermitian tests of bounded operator norm. In this sense, bounded causal witnesses arise as certified lower-bound functionals for admissibility. To connect the formalism to concrete physical scenarios, the paper studies a dephased-switch family W_eta = W_diag + eta X, where W_diag is causally separable and X encodes interference between orders. For this family, the defect is bounded above linearly in |eta|, while a witness with positive overlap on X yields a matching linear lower bound. As eta tends to zero, the process approaches definite-order admissibility. Within the OTF series, this paper functions as a frontier extension. Paper I introduced physical admissibility mathematically, Paper II studied admissibility in a tensor-cosmology channel, and Paper III interpreted admissibility ontologically. Paper IV shows that the same programme can be pushed into higher-order causal structure, where admissibility constrains not only which states and channels are physically stable but also which causal architectures can count as physically realized. Companion records in the OTF series:OTF I — DOI: 10.5281/zenodo.19068375OTF II — DOI: 10.5281/zenodo.19075284OTF Master Edition — DOI: 10.5281/zenodo.19077303
This paper is the mathematical core of a three-paper programme around the Ontological Totality Functional (OTF). Its claim is not that physics needs one more totalizing action, but that it lacks a rigorous language for physical admissibility: the conditions under which a configuration can count as physically stable rather than merely mathematically specifiable. The paper recasts the OTF accordingly. The backbone is a local-to-global construction on a finite 2-complex of contexts. Local states, pointer subalgebras, and quantum channels are assigned to vertices and edges. Two defect terms measure admissibility: the gluing defect, defined from failures of triangular composition of channels in the diamond norm, and the noetic defect, defined from distance to a pointer subalgebra via conditional expectations. Together with a sector-dependent effective action, they define an admissibility functional whose minimizers form the admissible set at cutoff Lambda. Four controlled results are proved in finite-dimensional truncations: existence of minimizers, a zero-defect criterion for the noetic sector, an observable bound implying approximate classicality when the noetic defect is small, and a global path-consistency theorem showing that local triangle defects bound route dependence across any filled disk in the context complex. A continuum scalar surrogate for coarse-grained coherence defects is also introduced, and its effective stress tensor is shown to be conserved on shell. Finally, the paper defines the central target of the programme: mixed category-algebra-scale fixed points, namely compatible families of admissible minimizers across cutoffs. This record is part of the Ontological Totality Functional (OTF) series. Companion works include OTF II, OTF III, OTF IV, and the OTF Master Edition. Companion records in the OTF series:OTF II — DOI: 10.5281/zenodo.19075284OTF IV — DOI: 10.5281/zenodo.19076867OTF Master Edition — DOI: 10.5281/zenodo.19077303
Paper I argued that the Ontological Totality Functional (OTF) should be read not as a new totalizing theory, but as a theory of physically admissible structures. Paper II provides the first dedicated physical realization of that claim. It focuses on one channel only: the classicalization of primordial tensor modes. The central thesis is that a tensor mode does not become physically real merely by being mathematically definable or dynamically squeezed. It becomes physically admissible when two conditions are met simultaneously: local-to-global closure across effective descriptions and sufficiently small noetic defect relative to a pointer subalgebra. The paper formulates a reduced tensor-sector OTF in quasi-de Sitter space, drawing on the language of open quantum systems and recent work on primordial graviton decoherence and primordial-gravitational-wave phenomenology. A tensor gluing defect G_T(k,a) measures inconsistency between competing coarse-grained propagators or channels across scale windows, while a tensor noetic defect N_T(k,a) measures the trace-norm distance of the reduced state to a preferred pointer algebra. These defects define a mode-wise admissibility rate. Gamma_OTF(k,a) = alpha G_T(k,a) + beta N_T(k,a), which enters a defect-dependent Lindblad evolution for the reduced tensor density matrix. The resulting decoherence factor defines suppression of off-diagonal tensor coherences and a scale-dependent classicalization epoch. Three main results are obtained. First, positivity of the defect rates implies monotonic decay of off-diagonal coherences in the pointer basis. Second, if the integrated admissibility rate crosses a finite threshold, then classicalization occurs at a finite epoch for that mode. Third, the OTF channel induces a clean phenomenological parameterization in the tensor sector: a coherence-suppression window and an effective modification of the primordial tensor signal that can be bounded with future B-mode searches. This record is part of the Ontological Totality Functional (OTF) series. Companion works include OTF I, OTF III, OTF IV, and the OTF Master Edition. Companion records in the OTF series:OTF I — DOI: 10.5281/zenodo.19068375OTF IV — DOI: 10.5281/zenodo.19076867OTF Master Edition — DOI: 10.5281/zenodo.19077303
This paper is the thirty-fourth in a sequence developing an interpretive framework that redescribes physical reality as a causally consistent history of information updates rather than as a collection of independently existing objects. It is the capstone (third panel) of the ninth grouping — the quantum-mechanics–gravity interface trilogy (32 Quantum Geometry → 33 Records Backreacting on Geometry → 34 Causal Structure Without a Global Order) — and closes that trilogy. Its core physics is the process-matrix framework (Oreshkov, Costa, & Brukner, 2012), with the quantum switch (Chiribella et al., 2013) as the worked instance and causal (non)separability as the central classification. When the order of operations is quantum-controlled — and, at the interface, when geometry is superposed so different branches carry different causal graphs — the temptation is to posit a hidden definite global total order behind the indefiniteness. The thesis is that there is no Global Causal Sequencer; P1 is a declared architectural commitment, not a theorem, and a rival that posits a deeper definite order underwriting the indefiniteness is acknowledged but declined architecturally. R-A: indefinite operational order is not causal inconsistency or a closed loop — a coherent superposition of order components is causally nonseparable (witness-certifiable; note that witness-based nonseparability and causal-inequality violation are not equivalent, and the quantum switch need not violate a causal inequality) yet a valid, consistent process. R-B (restricted to controlled-order processes such as the quantum switch, or any process with a declared physically recorded order-control observable): recording the order-control does not by itself produce a determinate order — one must distinguish the coherent control, the decohered-but-unconditioned causally separable mixture, and the conditioned record-relative effective order — only the last is determinate, and only relative to a recorded value and the declared parameter chi, whose order-control basis is an admissible decoherence-stable pointer basis/algebra (not an arbitrary rotation). R-C: causal structure is profile-valued, CausalProf = (d_order, d_interv, d_record, d_valid, d_family, d_arrow), with a process-validity (not graph-acyclicity) component and an independent record-arrow component from Paper 9's arrow package. R-D (the novelty witness): effective order is provenance-gradable — a matched pair of histories with identical audited world-side order records but different provenance yields different warranted standing (OrderStandProf). R-E: a conservative-before-radical discipline works indefinite operational order first, then a minimal superposed-causal-graph bridge on Paper 32's identity fibers, separating an identity disposition from an order disposition; full quantization of the causal relation is flagged, not claimed. This retires the Global Causal Sequencer and closes the interface trilogy; no causal loops, no retrocausal signaling, no revived global order, no quantum-gravity completion. Presents no new physics; results are interpretive (L2) on imported physics (L1).
This work develops a graph-theoretic and process-based foundation for indefinite causal order in quantum theory, demonstrating that causal indefiniteness is not an ad hoc or exotic phenomenon but an emergent structural property of quantum dynamics when the primitive unit of evolution is taken to be the П-такт (P-Tact) — a discrete quantum process composed of local unitary superposition and entangling unitary interaction. Building upon a sequence of previously published foundational works, this paper formulates indefinite causal order as a superposition of quantum process graphs, where each graph encodes a definite causal structure, and the quantum state corresponds to a coherent superposition over such graphs. Within this framework, causal order is not fundamental but arises only in coarse-grained or classical limits. We show that: Indefinite causal order naturally emerges from the superposition of process graphs, without invoking external control systems or higher-order operations. The quantum switch is reinterpreted as a special finite realization of a more general graph-superposition principle. Time and causality emerge as effective parameters in the infinite-graph (continuum) limit of discrete П-такт dynamics. The graph-theoretic formulation is fully compatible with — and structurally supports — the Everettian (Many-Worlds) interpretation, where branching corresponds to graph bifurcations rather than wavefunction collapse. Classical spacetime causality appears as a macroscopic ordering imposed on an underlying non-causal quantum substrate. This approach unifies quantum information, indefinite causal order, emergent temporality, and Everettian branching within a single formal framework based on discrete process units and their graph composition. The results close several open conceptual gaps in the interpretation of quantum switches, process matrices, and non-classical causal structures, offering a consistent ontology grounded in quantum dynamics itself. This paper directly builds upon and extends the following foundational works: Pavlov, M. (2026). Quantum Switch as an Emergent Process Structure from Discrete Process Tacts (П-такт). Zenodo.https://doi.org/10.5281/zenodo.18498181 Pavlov, M. (2026). Quantum Switch and Teleportation. Zenodo.https://doi.org/10.5281/zenodo.18509173 Pavlov, M. (2026). Emergence of Causality, Gravity, Time, and Three-Dimensional Space from Discrete P-Tact (П-такт) Dynamics. Zenodo.https://doi.org/10.5281/zenodo.18504244 Pavlov, M. (2026). P-Tact (П-такт) as the Primitive Unit of Quantum Theory. Zenodo.https://doi.org/10.5281/zenodo.18516711 Together, these works establish a coherent program aimed at demonstrating the universality of quantum mechanics, the absence of fundamental collapse, and the emergence of spacetime and causality from discrete quantum process dynamics.
Relational quantum causal processes formulate finite operational contexts as normal positive functionals on local completely positive maps. Response differences generate an influence algebra, and its central projections define jointly readable Boolean events. We develop this starting point through a sequence of exact and controlled models. Fresh-environment unitary collision circuits produce dephasing-exchange kinetics with an exact charge-center fixed algebra, a uniform finite-step limit at fixed response order, and graph-controlled metastable Markov dynamics. An absorbing-state model exhibits a sharp transition between non-Abelian quantum memory and Boolean records. A reversal-covariant defect dynamics generates a locally finite partial order on a restricted graph family without assuming a Lyapunov time. Conditional on a certified order, a positive additive record measure, compactness, and identifiability, we prove subsequential convergence to a Lorentzian metric-measure space, finite reconstruction bounds, and uniqueness of admissible smooth limits. Complementary finite regulators provide controlled tests of modular-to-boost response, null tomography, same-update variational identities, induced quadratic gravity, and compatible common-refinement limits. These results are exact or controlled within their stated models, but they do not yet constitute a single background-independent microscopic law that jointly generates adjacency, time, volume normalization, dimension, signature, nonlinear Einstein constraints, and quantum matter. We therefore present RQCP-QG as a theorem-indexed framework that separates established mechanisms, conditional compositions, and open assumptions.
The idea that events are equipped with a partial causal order is central to our understanding of physics in the tested regimes: given two pointlike events A and B , either A is in the causal past of B , B is in the causal past of A , or A and B are space-like separated. Operationally, the meaning of these order relations corresponds to constraints on the possible correlations between experiments performed in the vicinities of the respective events: if A is in the causal past of B , an experimenter at A could signal to an experimenter at B but not the other way around, while if A and B are space-like separated, no signaling is possible in either direction. In the context of a concrete physical theory, the correlations compatible with a given causal configuration may obey further constraints. For instance, space-like correlations in quantum mechanics arise from local measurements on joint quantum states, while time-like correlations are established via quantum channels. Similarly to other variables, however, the causal order of a set of events could be random, and little is understood about the constraints that causality implies in this case. A main difficulty concerns the fact that the order of events can now generally depend on the operations performed at the locations of these events, since, for instance, an operation at A could influence the order in which B and C occur in A ’s future. So far, no formal theory of causality compatible with such dynamical causal order has been developed. Apart from being of fundamental interest in the context of inferring causal relations, such a theory is imperative for understanding recent suggestions that the causal order of events in quantum mechanics can be indefinite. Here, we develop such a theory in the general multipartite case. Starting from a background-independent definition of causality, we derive an iteratively formulated canonical decomposition of multipartite causal correlations. For a fixed number of settings and outcomes for each party, these correlations form a polytope whose facets define causal inequalities. The case of quantum correlations in this paradigm is captured by the process matrix formalism. We investigate the link between causality and the closely related notion of causal separability of quantum processes, which we here define rigorously in analogy with the link between Bell locality and separability of quantum states. We show that causality and causal separability are not equivalent in general by giving an example of a physically admissible tripartite quantum process that is causal but not causally separable. We also show that there are causally separable quantum processes that become non-causal if extended by supplying the parties with entangled ancillas. This motivates the concepts of extensibly causal and extensibly causally separable (ECS) processes, for which the respective property remains invariant under extension. We characterize the class of ECS quantum processes in the tripartite case via simple conditions on the form of the process matrix. We show that the processes realizable by classically controlled quantum circuits are ECS and conjecture that the reverse also holds.