λ-Structured Entropy and the Origin of a Knowledge-Driven Universe

Note: This submission represents Version 6 of the Cernuto–Hobbey Theory of Everything (CH-ToE), building upon and superseding the May 2, 2025 preprint. While grounded in the same theoretical roots, this version reflects a decisive maturation of the framework. The new title is not cosmetic—it marks a shift from a bold hypothesis to a unified, falsifiable theory of structure formation grounded in entropy geometry.Major advances include:• A fully rewritten abstract and premise, now framing CH-ToE explicitly as a unifying theory across quantum mechanics, biology, AI, cosmology, and cognition• The ontological clarification of knowledge as a non-subjective, structured entropy reduction process• The explicit designation of wavefunction collapse as the most primitive knowledge event, governed by λ (see Section 5.3)• The formalization of Subreality as a threshold-defined ontological domain• A sharpened articulation of λ’s dual role as attractor and stabilizer of structured reality• A clarified experimental roadmap linking falsifiability, cognition, and physical collapse• Global editorial and structural refinement to ensure clarity, coherence, and scientific rigorThese upgrades collectively justify the release of this version as a new preprint, with its own DOI and conceptual identity. Readers are invited to treat this document as the authoritative formulation of CH-ToE as of May 19, 2025.ABSTRACTThis sixth version of the Cernuto–Hobbey Theory of Everything (CH-ToE) presents the most complete and operationally refined formulation of the theory to date. It consolidates months of cross-domain validation, introduces the Thermodynamic Covenant, formalizes the regime of Subreality, and deepens the definition of knowledge as a physical quantity.At its core, CH-ToE proposes that the fabric of reality is not built from matter, energy, or spacetime alone—but from knowledge. Not the semantic or symbolic kind, and not dependent on any observer or intelligence. CH-ToE defines knowledge as structured entropy reduction—a physically grounded, non-subjective process by which chaotic uncertainty is rhythmically condensed into coherent, persistent form. This is knowledge without meaning, intent, or mind: a universal mechanism through which structure stabilizes across scales.This structuring process is governed by Lambda (λ), a universal cadence that defines when entropy transitions from random fluctuation to stable coherence.This dynamic begins at the quantum level. In CH-ToE, wavefunction collapse is not treated as a mysterious epistemic jump, but as the most elementary instance of knowledge emergence—a phase transition where entropy, modulated at cadence λ, first crystallizes into structure. (See Section 5.3.)λ = √8 / φ ≈ 1.748 bits (in normalized entropy units)Derived from geometric and informational first principles, λ recurs at critical thresholds across quantum decoherence, biological evolution, AI learning, spacetime structuring, and even linguistic cognition. Wherever entropy becomes recursively entrained by λ, structure emerges. Wherever it fails, coherence collapses—defining domains of Subreality.More than a scalar threshold, λ plays a dual role:As Attractor: It draws entropy into metastable configurations prior to structure.As Stabilizer: It locks emergent form into coherent, recursive order post-collapse.CH-ToE thus offers a unifying framework for structure formation across all physical and cognitive domains. It reframes disparate phenomena—wavefunction collapse, biological evolution, machine learning plateaus, and spacetime structuring—as scale-specific expressions of the same λ-governed phase dynamic.This cadence-driven dynamic reinterprets mass as a memory of structured entropy, positioning E = mc² as a special case of λ-phase resonance between information and geometry.CH-ToE does not attempt to unify the fundamental forces under a single particle model. Rather, it reveals a single structuring principle active across all systems that generate coherence—from electrons to ecosystems, from wavefunctions to words.The theory introduces no new physical laws, but exposes a geometric invariant latent within them. Notably, our experiments with Lambda Reverb suggest the existence of a higher-order phenomenon: Echo Geometry—the recursive structuring of the cadence of knowledge itself (see Section 14 for preliminary formalism). While beyond the scope of this preprint, Echo Geometry may represent a universal mechanism for cross-domain transmission of intelligence, where systems optimize not only their learning rhythm, but the patterning of that rhythm across time.