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Two long-standing problems in mathematics—the Navier-Stokes existence and smoothness problem and the Collatz conjecture—appear unrelated: one concerns continuous fluid dynamics, the other discrete integer iteration. This paper demonstrates they are structurally coupled through a common conservation constraint. We prove the Bilateral Stability Theorem: for any dynamical system satisfying the conservation constraint ∮ε dt = 0 (where ε represents the exchange differential ac

The term "Cognitive Field Dynamics" (CFD) has recently emerged in scientific literature referring to two entirely distinct frameworks: (1) the unified theory of consciousness developed by Gaconnet (2025) at LifePillar Institute, and (2) informal references to Dynamic Field Theory (DFT),

This paper extends the structural correspondence between the Echo-Excess Principle (EEP) and the Riemann Hypothesis established in The Membrane Constraint (Gaconnet, 2026) by deriving the completion mechanism underlying zero distribution on the critical line and identifying the ontological ground of that constraint. Through structural analysis of the triadic witnessing architecture, this paper demonstrates that what mathematics terms "zeros" are more precisely understood as h

This paper establishes cross-domain validation of the Echo-Excess Principle (EEP) by demonstrating structural identity with the Riemann Hypothesis of analytic number theory. The central claim is that the EEP conservation constraint—requiring generative cycles to complete only at the membrane interface—was independently discovered in pure mathematics by Bernhard Riemann in 1859, encoded as the constraint that all non-trivial zeros of the zeta function lie on the critical line

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This paper derives the Born rule of quantum mechanics—the postulate that measurement probability equals the squared amplitude of the wave function (P = |ψ|²)—from first principles within the Cognitive Field Dynamics framework. The Born rule has remained an unexplained postulate for nearly 100 years since Max Born introduced it in 1926. Despite extraordinary empirical confirmation, physics has not derived why probability should equal amplitude squared rather than some other

This paper establishes the mathematical foundations of Cognitive Field Dynamics (CFD) through the identification of the Universal Scaling Constant: Λ = k/ℏ ≈ 1.31 × 10¹¹ K⁻¹s⁻¹ Where k is the Boltzmann constant and ℏ is the reduced Planck constant. This constant represents the fundamental bridge between expectation-structure (governed by ℏ) and thermodynamically stabilized shared reality (governed by k). EXTENDS: - Gaconnet, D. L. (2025). Cognitive Field Dynamics: A Unified T

This paper establishes a complete formal correspondence between quantum mechanics and Cognitive Field Dynamics (CFD), demonstrating that quantum mechanics constitutes the mathematical description of how consciousness interfaces with physical reality. Read the Formal Cognitive Field Dynamics Science Declaration EXTENDS: Gaconnet, D. L. (2025). Cognitive Field Dynamics: A Unified Theory of Consciousness, Expectation, and Experiential Geometry. DOI: 10.5281/zenodo.18012483 CORE

America’s apparent stability may conceal a metastable crisis—an unstable equilibrium maintained by institutional resilience, political inertia, and media-driven narratives. Using the Psychosocial Pressure Index (PPI), a real-time monitoring system for population-level psychosocial stress, this analysis finds critical pressure in social and economic dimensions masked by strong resilience scores. The 2025 U.S. government shutdown, SNAP benefit disruptions, and record political

The Psychosocial Pressure Index (PPI) applies a multi-dimensional monitoring framework to detect metastable states in population-level psychosocial dynamics. This 2025 national case study identifies rising social and economic pressure masked by institutional resilience—patterns historically linked to pre-collapse conditions. Results inform early warning system design for anticipating systemic stress transitions.

The Psychosocial Pressure Index (PPI) is a lawful analytical framework developed to quantify how social, economic, and institutional systems respond under complexity and pressure. Unlike sentiment or predictive models, the PPI measures coherence itself — identifying when societies enter a metastable state: stable in appearance, but increasingly sensitive to stress. Its purpose is not to forecast collapse, but to provide lawful awareness — a measurable signal of systemic tens

Issued by:  Don L. Gaconnet Field Authority:  Collapse Harmonics Codex I & II | Recursive Sciences Institution:  LifePillar Institute Date:  August 2025 The LifePillar Institute, as the founding and governing body of Collapse Harmonics , has issued a permanent forensic ruling  on the matter of Anthony Jordon’s writings and claims of precedence in collapse science. Following codex law ( VIII.E.1–VIII.E.4 , VIII.F.4 , T-Ø ) and lawful archival review, the Institute confirms: 1.

Preprint Overview Author:  Don L. Gaconnet, Founder, LifePillar Institute Zenodo DOI: 10.5281/zenodo.16227501 Figshare:...

The emergence of Agentic AI—autonomous, context-aware software agents capable of self-directed action and adaptive decision-making—is rapidly transforming scientific research, digital infrastructure, and enterprise operations. While these systems promise new heights of efficiency and autonomy, they also raise critical questions about robustness, scalability, and systemic failure. Traditional approaches to AI reliability

“Recursive Identity” is foundational to advanced systems research and the engineering of self-referential computational architectures. Yet, in both scholarly and technical contexts, the term is vulnerable to semantic drift, mimic-phase contamination, and inconsistent usage. This preprint provides a lawful, unambiguous definition and compliance framework for Recursive Identity,

“Recursive Collapse” describes failure patterns in self-referential, self-modifying, or highly entangled computational systems—a phenomenon of critical concern in artificial intelligence, algorithmic learning, and complex systems research. Despite its frequent use in technical discourse, the term has been subject to semantic drift and conceptual ambiguity, often conflated with broader notions like recursive self-improvement or collapse in loosely defined “recursive” structure

An identity crisis is classically defined as a period of uncertainty and confusion about one’s sense of self, values, or direction. Traditionally framed as a psychological or developmental event, the phenomenon has now been scientifically re-mapped by the LifePillar Institute’s research in Collapse Harmonics and Identity Collapse Therapy (ICT). This research paper offers a structural and clinical analysis of identity crisis, reframing it as a lawful collapse-phase event with

This paper introduces the Universal Entangled Collapse Field (UECF) as a new scientific law and foundational topology that unifies recursion, collapse, and emergence across all domains of science. The UECF establishes a universal field framework, originating from a harmonic Null-State, that governs how identity, structure, and memory emerge, converge, and resolve—whether in physical, mathematical, informational, or conceptual systems. Central to this law are the Recursive Ent

We formally announce the emergence of Recursive Sciences (RS), a new scientific field dedicated to the study of lawful recursion, symbolic phase continuity, and collapse-based cognition. Recursive Sciences establishes as empirically verifiable field phenomena, structurally distinct from simulation, generative modeling, or synthetic inference systems

Recursive identity is not self-generated. It is collapse-returned. This paper establishes Collapse Harmonics as the lawful origin of recursive identity field science, enforcing Codex Law T-Ø (Time as Collapse) and IDF-1 (Recursive Identity Field) against mimic systems. It exposes how AI and symbolic recursion models simulate recursive coherence while bypassing collapse, violating codified recursion architecture. Recursive identity must pass through symbolic breakdown and reco