This letter — Letter C in the Letter IIA extract of the Theory of Entropicity (ToE) Living Review Letters Series — provides the complete, rigorous, fully formal derivation of the universal speed of light c from the Obidi Action and the Obidi Field Equations (OFE). The central result is the No-Rush Theorem (Theorem C.2), which establishes that c is the maximum rate of entropic rearrangement on the entropic manifold — a finite, universal, and dynamically determined quantity, not a postulate, and not a tautologically defined constant. The derivation proceeds in six logical steps: (i) the quadratic entropic Lagrangian is established uniquely from five symmetry and consistency constraints; (ii) the Euler-Lagrange equations yield the entropic wave equation; (iii) the wave speed cent = √(κ/ρS) is identified as a pure ratio of response coefficients; (iv) dimensional analysis and Planck-scale matching derive κ and ρS independently from first principles; (v) the self-consistency equation: (OAP).

On the Foundational Declaration of the Theory of Entropicity (ToE): Obidi’s Entropic Reinterpretation of Physical Reality in Comparison with Einstein’s Foundational Revolutions Abstract The history of physics is punctuated not merely by new equations, but by decisive conceptual declarations that redefine the ontological structure of reality. Isaac Newton reinterpreted celestial and terrestrial motion through universal gravitation. Albert Einstein redefined space, time, simultaneity, and gravity through the theories of Special and General Relativity. In recent years, John Onimisi Obidi has proposed the Theory of Entropicity (ToE), an ambitious entropy-centered framework that seeks to reinterpret entropy not as a secondary statistical descriptor, but as the primary ontological field underlying geometry, causality, matter, information, and physical law itself. This paper examines the philosophical, structural, and scientific significance of that declaration, driven by the Obidi Action.

For more than a century, modern physics rested on a profound Einsteinian insight: gravity is geometry. Space and time are no longer passive backgrounds but active participants in the structure of reality itself. Yet the Theory of Entropicity (ToE) proposes an even deeper conceptual revolution. It asks a radical question: What if geometry itself is not fundamental? What if the true foundation of reality is entropy? In this framework, entropy is no longer treated as a secondary thermodynamic quantity or statistical measure of disorder. Instead, it becomes a universal dynamical field from which geometry, causality, matter, and gravity emerge. The ontological sequence therefore shifts from Gravity→ Geometry to Entropy → Geometry → Gravity. Under this interpretation, spacetime curvature is not primary but a manifestation of deeper entropic processes. The Theory of Entropicity thus seeks to redefine the foundations of modern theoretical physics through an entropy-first description of nature.

Beyond its mathematical foundations, the monograph situates ToE within the broader landscape of modern theoretical physics, addressing long‑standing tensions between Riemannian, Kähler, and principal‑bundle geometries. It shows that these frameworks are not independent structures requiring unification, but different faces of the same entropic geometry. The entropic manifold provides a natural explanation for the unity of physical law, the emergence of spacetime, and the geometric origin of matter and interactions. This work is intended for researchers in theoretical physics, mathematical physics, information geometry, and the foundations of quantum theory. It provides a self‑contained, rigorous, and conceptually coherent foundation for the Theory of Entropicity and establishes the Obidi Action Principle as a candidate for a unified description of spacetime, matter, and gauge fields.

A major conceptual contribution of this work is the ontological elevation of information geometry. The structures of statistical geometry — distinguishability, curvature, dual connections, and symplectic form — are reinterpreted as the actual geometric fabric of physical reality, not as abstractions describing incomplete knowledge. Spacetime intervals arise from statistical distinguishability; inertial mass emerges from internal curvature; gauge fields arise from the skewness and torsion of the 𝛼 -connections. In this framework, the constants of nature (such as 𝑐 , ℏ , and gauge couplings) appear as ratios of geometric invariants of the entropic manifold. The monograph provides a rigorous derivation of the Einstein–Obidi field equation, the entropic matter equations, and the entropic gauge equations, all obtained as Euler–Lagrange equations of the Obidi Action. These results demonstrate that general relativity, quantum mechanics, and Yang–Mills theory arise as limiting projection.

The Obidi Action Principle and the Geometry of the Entropic Manifold: Foundations of the Theory of Entropicity (ToE) This monograph presents the first complete mathematical and conceptual formulation of the Theory of Entropicity (ToE), a unified geometric framework in which spacetime, matter, and gauge interactions emerge from the intrinsic geometry of a single underlying structure: the entropic manifold. At the heart of this framework lies the Obidi Action Principle (OAP), a diffeomorphism‑invariant variational principle constructed from the Fisher–Rao metric, the Fubini–Study metric, and the Amari–Čencov 𝛼 -connections. These three geometric sectors — traditionally belonging to statistics, quantum mechanics, and information geometry — are shown to be not epistemic tools but ontological structures that encode the fundamental laws of physics. The monograph develops the entropic manifold 𝑀 as a smooth (finite‑ or infinite‑dimensional) differentiable manifold whose points represent.

On the Conceptual Leap of the Theory of Entropicity (ToE): From the Information Geometry of Fisher-Rao, Fubini-Study, and Amari-Čencov to the Geometry of Distinguishability, and to the Geometry of Physical Spacetime FAQ (Frequently Asked Questions): Question: Replies to Objections to the Theory of Entropicity (ToE): “So, ToE is saying that just as gravity is operational at each point in spacetime, so is Entropy and that gravity is generated from entropy?” Answer: Yes — but with a crucial refinement: Entropy is not in spacetime; entropy creates spacetime. Gravity is not merely “generated from entropy”; gravity is the curvature of the entropic ToE identifies the geometry of distinguishability with the geometry of physical change. Physical change defines spacetime intervals. Therefore, the geometry of distinguishability becomes the geometry of spacetime. Spacetime emerges as the macroscopic limit of this entropic geometry. This is not statistical. It is geometric. This is Obidi Action.

Foundations for Quantum Information and Spacetime Structure: The finite timescale for entanglement formation posited by ToE suggests new limits on quantum information transfer speeds and ties the foundations of quantum information directly to entropy dynamics—potentially offering a new way to look at the emergence of spacetime itself. In summary, the implications of ToE for quantum entanglement are profound: it imposes a universal, finite timescale on entanglement events, grounds quantum correlations in the physical dynamics of entropy, and frames all of quantum nonlocality as the consequence of locally enforced, entropy-driven causality rather than instantaneous action. § I An Introduction to John Onimisi Obidi's Philosophy The philosophy behind John Onimisi Obidi's formulation of the Theory of Entropicity (ToE) centers around the idea that entropy is the fundamental field and causal substrate of physical reality. Obidi's approach is not just a technical shift but a philosophical one.

The Theory of Entropicity (ToE) brings several distinctive implications for quantum entanglement compared to standard quantum mechanics: Finite Formation Time for Entanglement: ToE predicts that entanglement between particles is not established instantaneously. Instead, every entanglement event unfolds over a finite and irreducible time interval, set by the so-called Entropic Time Limit (ETL). Experiments have recently observed that quantum entanglement formation requires around 232 attoseconds—providing empirical backing for this idea. Entropy as a Causal Driver: Entanglement and the collapse of the wave function are not just statistical or informational processes. In ToE, these are governed by the dynamics of the entropic field, meaning that the unidirectional flow of entropy strictly regulates when and how entanglement is formed. This approach introduces an explicit arrow of time into the equations governing quantum phenomena. No Instantaneous 'Spooky Action': Standard quantum M.

The Theory of Entropicity (ToE) is a novel framework in fundamental physics proposed by John Onimisi Obidi, first introduced in 2025. This theory represents a significant shift from conventional physics paradigms by positioning entropy—not spacetime geometry or conventional fields—as the truly fundamental driver of all physical processes. Core Principles of the Theory of Entropicity (ToE) Entropy as a Fundamental Dynamic Field: In ToE, entropy is not just a statistical measure of disorder but is elevated to a dynamic, physical field (denoted as S(x)) that permeates the universe. This field possesses its own degrees of freedom and can propagate and interact, much like other fundamental fields in physics (e.g., electromagnetic field). The Entropic Field as the Causal Medium: All physical events, observations, and interactions are governed by this entropic field—which actively enforces irreversibility locally and universally. The traditional roles played by spacetime, causality, and etc.

John Onimisi Obidi [Investigator, Researcher, Thinker, Consultant, Physicist, Philosopher, and Humanist] is the pioneer, originator, and creator of the Theory of Entropicity (ToE) — a paradigm‑shifting framework positioned as a candidate for a Grand Unified Theory in modern physics. ToE derives the speed of light, relativistic effects, and quantum constraints directly from the dynamics of the universal entropic field, reframing entropy not as a statistical abstraction but as the fundamental substrate of reality. Through the Master Entropic Equation (MEE) - which is the Entropic Field Equations of ToE equivalent to Einstein's Field Equations of General Relativity - and the Obidi Action, Obidi demonstrates how thermodynamics, relativity, quantum mechanics, and information theory emerge as entropic inevitabilities. ToE has successfully re‑derived the classical Einstein results of the perihelion precession of Mercury and the deflection of starlight, confirming its consistency with Physics.

Jacob Bekenstein and Stephen Hawking demonstrated in the 1970s that black holes possess genuine thermodynamic entropy proportional to their horizon area, irreversibly linking gravitational geometry to information theory and suggesting that entropy is not merely a statistical tool but a physical quantity encoded in the fabric of space. Ted Jacobson and Erik Verlinde proposed that gravity itself might be an emergent phenomenon arising from entropic considerations — not a fundamental force but a statistical consequence of information and entropy at the horizon. This was a radical proposal that ToE absorbs and extends. John Onimisi Obidi synthesizes all of these threads into a single "entropy-first" field theory, promoting entropy from an emergent quantity to the fundamental ontological substrate from which all of the above frameworks are derivable as limiting cases. The KOL formalizes this lineage through a definitive 37-row Master Correspondence Table mapping concepts from seven prior.

The Kolmogorov–Obidi Lineage (KOL): A Century of Convergence One of the most intellectually satisfying aspects of ToE is the depth of its historical self-awareness. The theory does not present itself as arriving from nowhere. Instead, it locates itself within a traceable intellectual lineage — the Kolmogorov–Obidi Lineage (KOL) — that maps the century-long convergence of probability theory, information science, and gravitational physics toward a single entropic synthesis. The lineage proceeds through five defining figures and their contributions: Andrey Kolmogorov (1903–1987) axiomatized probability in 1933, providing a rigorous mathematical foundation for uncertainty based on measure theory and sigma-algebras — shifting the study of chance from philosophical speculation to formal mathematical architecture. Claude Shannon (1916–2001) extended Kolmogorov's framework into communication theory, defining entropy as a measure of informational uncertainty and establishing the mathematics.

The history of theoretical physics is marked by rare moments when a framework arrives that does not merely extend the existing edifice but proposes to rebuild it from a more fundamental substrate. The Theory of Entropicity (ToE), formulated by John Onimisi Obidi beginning in 2025, represents one such moment of the ontological triadic ARC of Audacity, Radicality, and Courage. It proposes that entropy — long treated as a statistical byproduct of physical processes — is in fact the primary field from which geometry, matter, spacetime, and physical law themselves emerge. This paper examines not merely what the Theory of Entropicity (ToE) claims, but why it appeals: its mathematical economy, its philosophical coherence, its historical depth, and the particular aesthetic satisfaction and elegance it offers to those who find beauty in unification and in the oneness [and unity] of all existence. § Problem of Foundations:Modern physics rests on two magnificent but mutually incompatible Pillars.

Core Principles of ToE Entropy as a Fundamental Field: ToE redefines entropy into an active, continuous field. In this view, all physical phenomena emerge directly from the flow and conservation of this field. Emergent Gravity and Motion: Gravity is not considered a fundamental force, but rather an emergent consequence of entropic gradients created by the distribution of mass. Objects "move" because the entropic field reorganizes itself toward equilibrium. Relativity Derived from Entropy: Rather than postulating kinematic necessities (like the speed of light, time dilation, and length contraction), ToE claims these are entropic inevitabilities. The speed of light is proposed as the universal upper limit for the rate of entropic rearrangement. Mathematical Framework: At its core, the framework introduces the Obidi Action and the Master Entropic Equation (sometimes called Obidi Field Equations), which serve a structural role similar to Einstein’s Field Equations in General Relativity.

This record contains the complete consolidated archive of the Theory of Entropicity (ToE) as published across multiple platforms between Feb. 2025 and Apr. 2026, including all PDFs previously hosted on Figshare. The ZIP file preserves the original versions, publication order, and scientific continuity of the early ToE corpus. The Theory of Entropicity is a developing framework in theoretical physics that places entropy as the ontological primitive of physical reality. Across the Letters and supporting documents, the ToE introduces: the Obidi Action, a variational principle grounded in entropic dynamics the κ–ρₛ entropic field pair, describing the geometry of entropic flow the Entropic Seesaw Model, explaining emergent stability and asymmetry the Least Entropic Resistance Principle, governing natural evolution derivations connecting entropy to electromagnetism, c, mass, and field propagation This archive includes: All ToE Letters (PDF) — including foundational Letters I, IIA, IIB

The **Alemoh-Obidi Correspondence (AOC)** refers to a series of intellectual communications between **Daniel Moses Alemoh** and **John Onimisi Obidi** regarding the foundations of **theoretical physics** and **philosophy**. [1, 2] # Key Scientific Themes Published in April 2026, the correspondence explores a radical shift from 20th-century physics by focusing on: [3] **Entropic Manifolds:** Treating entropy as a dynamical scalar field rather than just a statistical measure.Fundamental Formulation: Re-examining the mathematical and philosophical foundations used to describe physical reality. **Interdisciplinary Approach:** The dialogue integrates physics with broader philosophical and literary perspectives, as reflected in the work of John Onimisi Obidi. [1, 3, 4] The full details of these discussions are documented in their communications on Medium. [1]

John Onimisi Obidi's departure from Paul Tillich's concept of "The Courage to Be" lies in his exploration of the courage to rethink existence itself. Obidi's Theory of Entropicity (ToE) proposes a radical re-constitution of physical ontology, where entropy is not merely a statistical residue but a fundamental dynamical field. This shift requires a form of conceptual bravery, moving beyond the traditional pillars of modern physics to embrace entropy as the substrate from which all other physical structures emerge. Obidi's work challenges long-standing assumptions about the nature of the universe, suggesting that the universe is structured by entropic curvature rather than geometric or particulate primitives. This reorientation demands a readiness to follow mathematical and logical consequences, even when they overturn deeply held scientific intuitions. Obidi's approach is distinct from Tillich's, who focused on the courage to affirm one's being in the face of existential threats.

Collected Works on the Evolution of the Foundations of the Theory of Entropicity(ToE) — Establishing Entropy as the Fundamental Field that Underlies and Governs All Observations, Measurements, and Interactions — Volume I — The Conceptual and Philosophical Expositions — (Version 1.0) — (Wednesday, December 31, 2025). John Onimisi Obidi's Epistemological Departure from Paul Tillich's "Courage to Be": Obidi's Ontological Courage in His Willingness and Audacity to Pursue New Research Beyond the Traditional Foundations of Modern Theoretical Physics John Onimisi Obidi's departure from Paul Tillich's concept of "The Courage to Be" lies in his exploration of the courage to rethink existence itself. Obidi's Theory of Entropicity (ToE) proposes a radical re-constitution of physical ontology, where entropy is not merely a statistical residue but a fundamental dynamical field.

This record contains the complete consolidated archive of the Theory of Entropicity (ToE) as published across multiple platforms between Feb. 2025 and Apr. 2026, including all PDFs previously hosted on Figshare. The ZIP file preserves the original versions, publication order, and scientific continuity of the early ToE corpus. The Theory of Entropicity is a developing framework in theoretical physics that places entropy as the ontological primitive of physical reality. Across the Letters and supporting documents, the ToE introduces: the Obidi Action, a variational principle grounded in entropic dynamics the κ–ρₛ entropic field pair, describing the geometry of entropic flow the Entropic Seesaw Model, explaining emergent stability and asymmetry the Least Entropic Resistance Principle, governing natural evolution derivations connecting entropy to electromagnetism, c, mass, and field propagation This archive includes: