Relational Complexity, Entropy, and the Emergence of Scale in ZM Cosmology

Short description A conceptual cosmology note within the ZM framework arguing that low primordial entropy, the emergence of effective scale, and temporal asymmetry may be understood as correlated consequences of increasing relational complexity in the PIQ network. The note is structural rather than dynamical and specifies the minimum conditions under which this proposal could mature into a serious cosmological research program. Abstract We present a minimal cosmological note within the ZM framework in which entropy and effective scale are treated not as primitive or independent inputs, but as correlated observables emerging from a deeper property of the underlying PIQ network, namely relational complexity. The central thesis is not that entropy and scale are identical, but that both co-emerge from a common structural transition in a fundamentally discrete and relational substrate. The primordial regime is accordingly described as a state of minimal relational differentiation, with strongly constrained connectivity, low configurational multiplicity, and no developed hierarchy of effective scales. The Big Bang is then interpreted, at the level of principle, as the transition through which this substrate enters a regime of increasing relational complexity. As this complexity grows, three effects arise jointly: the number of admissible microconfigurations increases, which appears macroscopically as entropy growth; the internal organization of the network becomes hierarchically richer, which appears as the emergence of scale; and sufficiently extended coherent relational patterns admit an effective continuum description, which appears as classical spacetime geometry. In this picture, the thermodynamic arrow of time is understood as the large-scale trace of an ordered progression toward increasingly differentiated relational states. The present note is intentionally structural rather than dynamical. Its purpose is to formulate the proposal in a disciplined way, specify its minimum formal requirements, and define the conditions under which it could become a serious cosmological research program. Description (EN) This record presents a conceptual cosmology note within the broader ZM research program. Its aim is to examine whether low primordial entropy, effective scale formation, and temporal asymmetry can be interpreted as parallel consequences of a single deeper process, namely the increase of relational complexity in the PIQ network. The note does not claim a complete cosmological dynamics. It should instead be read as a disciplined structural proposal. It identifies relational complexity, C(G), as a candidate primitive quantity and argues that entropy and effective scale are best treated as derived observables that co-vary with it over the physically relevant regime. The primordial state is accordingly interpreted as a minimally differentiated graph regime with strongly constrained configurational multiplicity and no developed hierarchy of effective scales. The purpose of the present deposit is not to replace standard cosmology, but to isolate a possible explanatory gain: low primordial entropy, scale formation, and temporal asymmetry may share a common structural source in a fundamentally discrete and relational substrate. The note also states the minimum conditions under which this proposal could become scientifically serious, namely a non-arbitrary definition of C(G), a dynamical law for its evolution, and an explicit bridge between graph observables and continuum cosmological quantities. Description complémentaire (FR) Ce dépôt présente une note de cosmologie conceptuelle au sein du programme ZM. Son objectif est d’examiner si la faible entropie primordiale, la formation des échelles effectives et l’asymétrie temporelle peuvent être interprétées comme les conséquences parallèles d’un même processus plus profond, à savoir l’augmentation de la complexité relationnelle du réseau PIQ. Cette note ne revendique pas une dynamique cosmologique complète. Elle doit être lue comme une proposition structurelle disciplinée. Elle identifie la complexité relationnelle, C(G), comme une quantité primitive candidate et soutient que l’entropie et l’échelle effective doivent être traitées comme des observables dérivées qui co-varient avec elle sur le régime physiquement pertinent. L’état primordial est ainsi interprété comme un régime de graphe minimalement différencié, à multiplicité configurationnelle fortement contrainte et sans hiérarchie développée d’échelles effectives. L’objectif du présent dépôt n’est pas de remplacer la cosmologie standard, mais d’isoler un gain explicatif possible : la faible entropie initiale, la formation des échelles et l’asymétrie temporelle pourraient relever d’une même source structurelle dans un substrat fondamentalement discret et relationnel. La note énonce également les conditions minimales sous lesquelles cette proposition pourrait devenir scientifiquement sérieuse, à savoir une définition non arbitraire de C(G), une loi dynamique de son évolution, et un pont explicite entre les observables de graphe et les quantités cosmologiques continues. Scope and disclosure This record is a structural cosmology note within the ZM research program. It does not claim a complete derivation of continuum cosmological equations, nor a quantitative confrontation with observational data at this stage. It introduces no implementation protocol, no algorithmic procedure, and no operational architecture. All claims are formulated at the level of conceptual structure, admissible formal requirements, and theoretical scope.