Ernesto Cisneros Cino
Musician · Digital Artist · Writer
Ernesto Cisneros Cino
COSMOLOGY & PHYSICS
The search for structure (for the hidden architectures beneath experience) has followed me since childhood. Long before I understood equations, I sensed that memory, rhythm, intuition, fear, and beauty were all part of a larger system, connected by patterns we rarely stop to observe. Years later, that intuition evolved into a formal exploration of cosmology, physics, and mathematical modeling.
These writings and models are not the product of an academic institution, but of a lifelong fascination with how complexity organizes itself: how systems oscillate, stabilize, drift, collapse, or return to equilibrium. Music, networks, human behavior, and the universe itself seem to share a common grammar, one made of cycles, limits, noise, and the persistence of memory.
This section brings together the core of that exploration: conceptual frameworks, speculative physics, and mathematical structures such as the Finite Memory Law, stochastic cosmology models, and other attempts to describe how information, entropy, and perception shape the world we inhabit.
Some texts are technical, others reflective. Together, they form a single path: the search for meaning in the patterns of the universe, and in the fragile traces that consciousness leaves behind.
This section presents the essential ideas behind my independent research in Finite-Memory Stochastic Cosmology, including all materials up to Version 3.2 (DOI: 10.5281/zenodo.17686852).
The core model explores small, log-oscillatory deviations in dark energy produced by a finite-memory stochastic process. It is an effective, testable alternative to ΛCDM, accompanied by a reproducible validation protocol based on Pantheon+ supernova data.
Additionally, the archive includes the Finite Memory Law (FML), an intuitive, speculative extension of a stability parameter that emerged from the model. It is not a universal law, but a conceptual exploration preserved here for transparency.
This page functions as the historical record of the research’s evolution up to v3.2, before external evaluation.
The Resilience Windows (RW)
The Resilience Windows proposes that every stable system (physical, biological, cognitive or social) emerges from the interplay between memory and oscillation. When the product of these forces remains within a narrow range, equilibrium is possible. When memory fades too quickly or oscillation becomes too intense, systems drift into instability. This model began as a conceptual bridge between physics, networks and human experience, and later evolved into a mathematical framework.
Stochastic Cosmology
This work explores the universe as a system governed not only by deterministic laws, but by stochastic behavior embedded in its fabric. Instead of viewing noise as an error, the model treats randomness as a structural feature of cosmology, shaping trajectories, equilibria and the long-term evolution of the universe. The full paper and its appendix present the foundations of this approach in Spanish
Version dated November 23, 2025, Finite-Memory Stochastic Cosmology 3.2 (https://doi.org/10.5281/zenodo.17686852) in revision...
Finite-Memory Stochastic Cosmology:
A Log-Oscillatory Dark Energy Model with Geometric Noise
Cutoff
You can also check out my repositories on GitHub
Mathematical & Structural Models
Alongside the main papers, several auxiliary models explore related ideas: recurrence, pseudo-Hermitian structures, oscillatory stability, memory decay, phase transitions in complex systems, and parallels with Krein-space intuition. These notes form an evolving toolkit rather than a closed theory open to refinement, reinterpretation and future mathematical formalization.
Interact with the models below to see how simple equations capture key ideas from Stochastic Cosmology and the Resilience Window.
By adjusting the parameters, you can observe how memory, oscillations, or decay shape the behavior of a system, just as these mechanisms influence stability and evolution in the cosmological framework described on this page.
Explore how a noisy system can still behave in an ordered way.
With a larger τ the fluctuations become smoother and more persistent; with a smaller τ they become fast and uncorrelated.
This is the core idea behind the memory structure of the stochastic cosmology model.
This model shows how the geometric cutoff 𝑆 ( 𝑧 ) S(z) regulates the strength of stochastic effects at different redshifts. By adjusting the parameters 𝑧 𝑐 z c and Δ 𝑧 Δz, you can see where the transition occurs and how sharply it switches. This function controls the temperature of the horizon in the stochastic cosmology described on this page.
This model illustrates a small oscillating deviation from a pure cosmological constant. By adjusting the amplitude A, the decay scale z<sub>τ</sub>, the frequency ω and the phase φ, you can see how w(z) moves around −1 while remaining tightly constrained. This structure is directly related to the effective equation of state used in the stochastic cosmology model on this page, where oscillations are allowed but strongly bounded by observations.
This interactive model shows a simplified expansion history of the universe. By changing the matter density Ω<sub>m</sub> and the effective equation–of–state parameter w, you can see how the normalized expansion rate E(z) = H(z)/H<sub>0</sub> evolves with redshift. This toy version reflects the same structure used in the stochastic cosmology framework on this page, where small deviations from w = −1 and the balance between matter and dark energy shape the global dynamics.
This final model combines the main ingredients of the stochastic cosmology framework on this page. The background w₀(z) represents a smooth, oscillating equation of state, while the term ζ(z) adds stochastic fluctuations with memory, modulated by the geometric cutoff S(z). By adjusting σ₀, τ<sub>z</sub>, z<sub>c</sub> and Δz, you can explore how different levels of noise, correlation and cutoff shape possible histories for w(z), providing an intuitive glimpse into how stochastic effects and resilience emerge in the cosmological model.
This interactive model shows how the dark energy equation of state can gently deviate from a pure cosmological constant. The curve compares an oscillating model
Personal Reflection: The Receding Limit
Behind every model lies a personal story: the fears, curiosities and intuitions that shape a way of thinking. The Receding Limit is an autobiographical reflection that traces the origins of these ideas, from childhood observations to the experience of exile, from music to mathematics, from uncertainty to discovery. It is the most intimate bridge between lived experience and speculative cosmology.