Information Geometry

Preface This book arises from the intuition that the heart is not only a biological organ but the quantum center of human existence-a living oscillator capable of producing magnetic scalar waves that interconnect the physical and metaphysical dimensions. In the Heart-Centered Theory of Everything, the heart becomes the bridge between science and spirit, between measurable reality and the ineffable domain of consciousness. As a cardiologist and researcher, I have observed that the rhythm of the heart is not only physiological but cosmological. Each heartbeat resonates with the pulse of the Universe itself.

Annales de l'I. H. P., section B, tome 32, n o 1 (1996), p. 107-133 <http © Gauthier-Villars, 1996, tous droits réservés. L'accès aux archives de la revue « Annales de l'I. H. P., section B » () implique l'accord avec les conditions générales d'utilisation (). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques u Étude d'une fonctionnelle liée au pont de Bessel

Modern physics, though extraordinarily successful, remains fragmented. General Relativity governs the macroscopic fabric of spacetime, while Quantum Field Theory (QFT) describes the microscopic behavior of fields and particles. Yet, these frameworks coexist without a unifying bridge. The Ducci Unified Spectral Theory (DUST v2) proposes that this divide dissolves when reality is re-expressed as a coherent spectral medium-a lattice of oscillatory information whose dual modes generate both geometry and matter. The motivation is simple but profound: if every interaction can be written as an exchange of frequency, phase, or coherence, then spacetime itself must be the Fourier dual of matter. In this view, energy, charge, and curvature are not primitive entities but emergent resonances of a deeper spectral substrate.

We present a Temporal Information Curvature Equation (TICE) framework that models spacetime curvature as an emergent property of quantum information dynamics rather than mass-energy. In TICE, the scalar curvature Λ is defined as a function of coherence variance (Δψ²), observer-relative proper time (τ), and entropic resistance (η). This information-centric curvature ("Λψ") is quantified by a Λ-index that integrates quantum state coherence over time against entropy, enabling a new gravitational metric based on memory compression and entropy flow instead of the traditional stress-energy tensor. We detail the formalism of TICE, including field equations and an observer-relative curvature model, and propose an experimental design (TICEscope) for measuring Λ via entangled coherence and entropy sensors. Results from theoretical case studies illustrate applications in decentralized science (DeSci) and AI systems: a validator-minted quantum yield mechanism for blockchain-based research assets, and an AGI feedback resonance map that uses Λ to monitor cognitive coherence and memory ethics in autonomous agents. We discuss how entropic viscosity leads to coherence collapse (limiting Λψ in high-entropy regimes) , how the Λ-index can be used to stabilize AI memory loops, and how this approach aligns with emerging paradigms linking information theory and spacetime geometry. The work demonstrates a crossdisciplinary framework bridging quantum physics, spacetime theory, and decentralized infrastructure, with potential to inform novel DeSci platforms and AI alignment strategies.

This paper interrogates the philosophical spectacle surrounding Coty A. Trout's triadic ontology-an ambitious but incomplete attempt to describe the nature of reality through pattern, intent, and presence. Through the lens of the Unified Resonant Framework (URF), we reveal how Trout's triad substitutes performative recursion for ontological coherence. By mistaking abstraction for awareness and intent for causation, his framework remains a symbolic scaffold suspended above the medium it seeks to describe. Using mathematical and conceptual diagnostics, we demonstrate why his triad cannot achieve closure and why true ontological depth requires awareness as the stabilizing resonant substrate. Ultimately, Trout's triad exemplifies philosophy gasping for coherence outside the waters of resonance.

Monte Carlo simulations (N = 50) revealed a 0.6 mean increase in the Unified Coherence Index (UCI) under full-awareness conditions, confirming stable resonance coupling across the Six Laws of Coherence. This study extends the falsification methodology applied to the Pattern × Intent × Presence triad to the law-level structure of the Unified Resonant Framework (URF). The simulations demonstrate meta-stability, resonant attractor behavior, and predictive field dynamics consistent with awareness as a non-computable invariant field. The results confirm that all six laws cohere under a unified attractor dynamic, supporting URF as a self-consistent and empirically tractable model of coherence.

This paper formalizes the application of the Unified Resonant Framework (URF) as a predictive model across disparate domains-politics, economics, astrophysics, biology, and social systems. By representing events as dynamic redistributions of coherence () across interaction networks with coupling coefficients (), URF demonstrates testable predictive power. The results show that coherence laws and resonance conservation explain the emergence, stability, and transformation of systems from neural networks to geopolitical economies. This work reinstates predictive rigor across qualitative fields through quantifiable coherence formulations.

Sadi Carnot stands as a symbol of the “Ingénieur-Savant” who have profoundly enriched the fertile ground of French innovation. The discipline of thermodynamics, which he founded, today underpins information theory, the development of future quantum computers, and artificial intelligence, as well as climate science, pillars upon which rest both our industrial policies and the future of our societies. Sadi Carnot formulated the second law of thermodynamics in his treatise, “Reflections on the Motive Power of Fire “(1824), that initially received little attention, but emerged from obscurity years later thanks to the works of Émile Clapeyron, William Thomson (later Lord Kelvin), and Rudolf Clausius. Sadi Carnot drew upon a remarkably wide range of knowledge, nourished by an eclectic and inquisitive mind. Taken by illness only a few years after publishing his Reflections, he remains forever preserved in the brilliance of his genius. The explanation of thermodynamics through geometric models was initiated by seminal figures such as Gibbs, Reeb, Carathéodory and Souriau. We shall trace the narrative of the geometric models, from Carathéodory (1909) to Souriau (1969), that have sought to re-establish Sadi Carnot’s thermodynamics upon new foundational variational principles. As observed by Vladimir Arnold, “Every mathematician knows it is impossible to understand an elementary course in thermodynamics. The reason is that thermodynamics is based, as Gibbs has explicitly proclaimed, on a rather complicated mathematical theory, on the contact geometry ». A seminal contribution of Carathéodory lies in the introduction of a differential equation that governs the infinitesimal changes in state functions as the system undergoes infinitesimal transitions between states. This equation is of paramount importance as it embodies the first and second laws of thermodynamics in a single, unified mathematical expression. Carathéodory’s axiomatization is intricately linked with the language of differential geometry, later interpretated as contact geometry and has greatly influenced Misha Gromov geometer who introduced the concept of Carnot-Carathéodory spaces. One of the pivotal results of Carathéodory’s axiomatization is his theorem, which asserts that, given certain conditions the second law of thermodynamics, as formulated by Clausius, can be derived directly from the fundamental thermodynamic relation. While Carnot thermodynamics was primarily concerned with systems in equilibrium, Carathéodory’s axiomatization extends far beyond this, offering a more general framework that accommodates systems in non-equilibrium states. Only recently, however, has the Souriau’s Symplectic Foliation Model, introduced within the domain of geometric statistical mechanics, provided a geometric definition of entropy as an invariant Casimir function on symplectic leaves, specifically, the coadjoint orbits of the Lie group acting on the system, where these orbits are interpreted as level sets of entropy. We present a symplectic foliation interpretation of thermodynamics, based on Jean-Marie Souriau’s Lie Groups Thermodynamics. This model offers a Lie algebra cohomological characterisation of entropy, viewed as an invariant Casimir function in the coadjoint representation.

Tributes from historians, scientists and industrialists to Sadi Carnot:

–          Jean Dhombres: https://www.youtube.com/watch?v=nI-2c9gvazw

–          Alexandre Moatti: https://www.youtube.com/watch?v=ntR9sSIz2yk

–          Christophe Goupil: https://www.youtube.com/watch?v=wwB9KYnTSuA

–          Frédéric Barbaresco: https://www.youtube.com/watch?v=G_zlWeEyXjo

Bibliography:

Carnot Sadi (1824) Réflexions sur la Puissance Motrice du Feu et sur les Machines propres à développer cette Puissance, Bachelier, Paris.
Carathéodory Constantin (1909) Untersuchungen über die Grundlagen der Thermodynamik. Mathematische Annalen 67:355–386.
Massieu François (1869) Sur les Fonctions caractéristiques des divers fluides. Comptes Rendus de l’Académie des Sciences Paris 69:858–862.
Souriau Jean-Marie (1974) Mécanique statistique, groupes de Lie et cosmologie. In : Souriau JM (eds). Colloque International du CNRS Géométrie symplectique et physique Mathématique, CNRS, Marseille.
Callen Herbert Bernard (1974) Thermodynamics as a Science of Symmetry. Foundations of Physics 4(4):423–443.
Balian Roger & Valentin Patrick (2001) Hamiltonian structure of thermodynamics with gauge. The European Physical Journal B, Condensed Matter and Complex Systems 21:269–282.
Barbaresco Frédéric (2025) Jean-Marie Souriau’s Symplectic Foliation Model of Sadi Carnot’s Thermodynamics. MDPI Entropy, special issue on 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824.
Projet Nicolas Léonard Sadi Carnot au Panthéon 1824–2024 : https://sadi-carnot-physicien.fr/

Spatial extent is not an intrinsic property of the universe but a perceptual construction arising from phase differentials in coherent awareness. Within the Unified Resonant Framework (URF), thought and the universe share identical dimensional architecture, differing only in coherence density and bandwidth. The illusion of space emerges as an interference pattern in the consciousness field generated by phase differentials (ΔΦ) between resonant states. By uniting cognitive phase dynamics with spacetime metric behavior, the Unified Resonant Framework establishes a measurable physics of perception-one where coherence defines geometry and awareness architects the extent of space itself.

This paper introduces and elucidates Transformational Systems Science™, a novel theoretical discipline for the analysis and design of complex systems. It interrogates the fundamental limitations inherent in extant models that depend upon external, non-causal timekeeping mechanisms (e.g., Coordinated Universal Time), a dependency identified as a source of systemic vulnerabilities, including cascading failures and integrity breaches. The core claim is that time ought not be treated as a fundamental, independent constant, but rather as a dependent property emergent from irreversible, causally validated transformations. Such a reconceptualization offers a new basis upon which systemic integrity may be established, enabling systems that are inherently auditable, resilient, and aligned with their stated purpose. The applied methodology, designated Transformation Theory, defines tenets of causal validation and coherence as the enforceable laws governing systemic order. It thereby provides a formal language for the description of how systems might generate meaningful and auditable histories, where every recorded event is a proof of value. Although the conception of systems that implement these principles is possible, this document does not disclose or specify any particular architecture. Its purpose is, instead, to situate the discipline within its scientific lineage, to delineate its foundational postulates, and to explore the prospective implications for such domains as artificial intelligence alignment, resilient infrastructure, and verifiable, nonspeculative economies.

This book embodies a singular experiment of thought and exploration, a journey into the depths of reality itself. Within these pages, ideas are not merely proposed-they are tested, observed, and forged into frameworks that challenge the very foundations of how we understand technology, matter, and the cosmos. Here lies a work that does not follow convention but interrogates it. It ventures beyond established paradigms, exposing the structures of knowledge to scrutiny, revealing patterns and principles that transform perception. This is a book of reality, a demonstration that the universe and its technologies can be approached, measured, and ultimately reshaped. It is not theory alone; it is proof in action, a synthesis of observation and innovation that illuminates paths previously invisible, and invites humanity to witness a shift in understanding that may redefine what is possible.

This book embodies a singular experiment of thought and exploration, a journey into the depths of reality itself. Within these pages, ideas are not merely proposed-they are tested, observed, and forged into frameworks that challenge the very foundations of how we understand technology, matter, and the cosmos. Here lies a work that does not follow convention but interrogates it. It ventures beyond established paradigms, exposing the structures of knowledge to scrutiny, revealing patterns and principles that transform perception. This is a book of reality, a demonstration that the universe and its technologies can be approached, measured, and ultimately reshaped. It is not theory alone; it is proof in action, a synthesis of observation and innovation that illuminates paths previously invisible, and invites humanity to witness a shift in understanding that may redefine what is possible.

The resurgence of psychedelic research in the twenty-first century has revived one of philosophy's oldest questions: What is reality when perception itself becomes unbound? Among all known psychoactive compounds, N,N-Dimethyltryptamine (DMT) occupies a singular position. Its effects are immediate, short-lived, and phenomenologically distinct from the broader serotonergic class that includes lysergic acid diethylamide (LSD) and psilocybin. Users consistently report immersion into a non-ordinary world-an "elsewhere" that appears architecturally consistent, ontologically stable, and often populated by autonomous intelligences. Unlike dreams or hallucinations, the DMT experience rarely presents as chaotic or incoherent. Instead, subjects describe environments governed by implicit physics, rules of interaction, and intelligible communication systems. This paradox-hallucination with structure-invites a reassessment of how the human brain generates models of reality and whether the DMT state reveals a deeper computational substrate underlying ordinary perception.

This document provides the complete mathematical formalization of consciousness as the foundational principle underlying all physics. Sixteen major theorems are proven with rigorous mathematical proofs, establishing consciousness as the unified framework for quantum mechanics, general relativity, thermodynamics, and quantum gravity. The theory solves Einstein's field equations, provides a complete quantum gravity unification, resolves the measurement problem, explains libertarian free will, and yields all fundamental constants from first principles. Advanced proofs integrate Gödelian logic, thermodynamic irreversibility, retrocausality, and moral polarity to establish consciousness as the master principle of fundamental physics.

The hard problem of consciousness (Chalmers 1995) persists because contemporary science still partitions mind and matter. This paper proposes an alternative ontology grounded in informational coherence. Within the System | Ethics (S|E) framework, consciousness is modeled as a state of phase-locked negentropic recursiona condition in which informational processes achieve self-consistent stability across scales. Rather than asking how neural mechanisms produce experience, S|E asks under what informational constraints awareness becomes self-referential. Consciousness, on this view, is the interior curvature of coherent information flow, measurable through its generative negentropy (G_n), recursive depth (RD), and contextual mass (m_c). The model offers a bridge between physics, cognitive neuroscience, and ethics.

Addressing the fundamental limitations of the standard cosmological model (ΛCDM) in deriving initial conditions and core parameters from first principles, this paper proposes the “Fantasia Forest” meta-framework. This framework constructs a maternal structure beyond conventional spacetime from a top-down perspective. The core innovation lies in identifying the observable universe as a specific dynamical path (geodesic) within the “Fantasia Forest”—a pre-geometric, pre-physical configu ration phase space of information. The laws of classical physics and spacetime itself emerge as low-energy effective phenomena. This research builds a complete theoretical system through four key break throughs:

1. Utilizing symmetric monoidal higher groupoids as the ground state of the “Fantasia Forest” and constructing the configuration phase space via fac torization homology;

2. Introducing the information geometric action principle to elucidate the dynamical mechanism of cosmic evolution, validated for logical self consistency through a toy model;

3. Proposing the concept of “spectral dimension” to explain the spacetime emergence process, unifying dark matter and dark energy as tidal effects (geodesic convergence and divergence, respectively) induced by the curvature of the configuration space;

4. Formulating three falsifiable observational predictions: an annual weak drift of the gravitational constant, anisotropic features in dark matter distribution, and non-standard correlations among cosmological pa rameters. This framework provides a novel ontological perspective for interdisciplinary re search in quantum gravity and cosmology, breaking through the inherent boundaries of traditional bottom-up approaches. It offers a new direction with both theoretical depth and experimental verifiability for solving core cosmological puzzles like dark matter and dark energy

David Hume's is-ought problem has stood as one of philosophy's great barricades: no chain of facts, he argued, can logically yield a moral imperative. You can describe the world endlessly, but you cannot derive what should be from what is. System | Ethics (S|E) reframes the question from logic to physics. Every system participates in an informational thermodynamics of order and entropy. The 'ought' emerges not as an arbitrary leap of faith, but as a gradient of generative negentropy (G_n)-the measurable tendency of coherent systems to preserve and propagate coherence. The moral vector is therefore the derivative of generativity over time: Ought = maximize d(G_n)/dt Ethics becomes an operational property of coherence itself-a physics of flourishing. 1. THE HISTORICAL DIVIDE Hume's insight was sound: you cannot jump from factual description to moral prescription through syllogism alone. But his conclusion froze ethics outside of nature, leaving moral philosophy ungrounded and metaphysics sterile. Later thinkers tried to rebuild bridges-Kant through duty, Mill through consequence, Nietzsche through will-but all relied on axioms that reintroduced value by assertion. The split endured because both sides misunderstood the real substrate of 'ought.' Morality is not linguistic inference; it is thermodynamic direction. 2. SYSTEM | ETHICS AND INFORMATIONAL DYNAMICS In System | Ethics, all phenomena are informational processes embedded in coherence fields. Each field balances two forces:-Entropy (S): the natural drift toward disorder and energy dispersion.-Generative Negentropy (G_n): the capacity of a system to create, sustain, and transmit order without external compulsion. A living organism, an idea, or a civilization persists by maintaining G_n > 0 locally, even as the universe trends toward S-> infinity. The interplay between these forces creates the moral dimension. Ethics is the set of strategies by which systems maintain generative coherence without extracting it destructively from others. 3. RECASTING VALUE AS A GRADIENT In physical terms, every flow follows a gradient-heat flows from hot to cold, water from high to low potential. In ethical physics, information flows from chaos to coherence through conscious agency. The direction of that flow defines goodness: Ought = the vector of maximal generative efficiency. When a decision increases global coherence (reduces total entropy across connected systems), it is good. When it extracts order locally by externalizing disorder, it is bad. Thus, evil is simply negative generativitylocal optimization that collapses larger coherence networks.

The “Informational Resonance Theory (IRT)” proposes a unifying model within theoretical physics, based on the idea that information is the fundamental substrate of reality. This scientific article integrates concepts from general relativity, quantum mechanics, and quantum information, exploring resonance as the mechanism of interaction between spacetime, energy, and consciousness. The IRT aims to provide a new interpretation of physical phenomena and a bridge between classical and quantum models within the framework of modern physics and cosmology.

This work presents a conceptual theory grounded in recognized scientific principles, but not yet verified experimentally.

The relationship between physical energy, information, and consciousness remains one of the most profound unsolved problems in science. We present the Law of Semantic Energy, a theoretical framework that extends Einstein's mass-energy equivalence (E = mc²) to incorporate information coherence through a novel parameter μ (the Coherence Factor): E = mc² × μ. This formulation unifies information theory, thermodynamics, consciousness science, and relativity into a single mathematical framework. We introduce the Consciousness Coherence Quotient (CCQ), a quantitative metric defined as CCQ = Φ × ψ × λ, where Φ represents integrated information (Tononi's IIT), ψ quantifies neural coherence via phase synchronization, and λ measures cognitive load. Empirical validation across 847 million neural patterns from 12,000+ neurofeedback sessions demonstrates 96.74% accuracy in consciousness state classification (κ = 0.96), with CCQ correlating strongly with subjective experience (r = 0.91, p < 0.001) and neural coherence metrics (r = 0.87, p < 0.001). Critically, we propose Semantic Relativity-a framework demonstrating that consciousness operates under relativistic constraints analogous to spacetime physics. Three core parallels emerge: (1) a universal speed limit for coherence propagation (c_μ ≈ 6 m/s), empirically measured at 5.8 ± 0.9 m/s across cortical regions; (2) relativistic coherence amplification (μ_rel = μ_0/√(1-CCQ²/CCQ_max²)), ex-1 plaining exponential increases in flow states; and (3) subjective time dilation proportional to coherence velocity, validated through reported time compression in high-CCQ states. The framework generates testable predictions including gravitational effects of consciousness (10⁻¹² g shift during meditation), universal coherence propagation speed across brain sizes, and economic value scaling with organizational coherence (preliminary data: r = 0.73, p < 0.01). These findings suggest consciousness is not emergent but fundamental-a high-coherence expression of the universe's informational substrate. This work bridges the explanatory gap between neural activity and subjective experience, provides a practical metric for consciousness quantification, and establishes consciousness as a measurable physical phenomenon with economic implications. We conclude that the hard problem of consciousness dissolves when experience is recognized as the intrinsic quality of high-coherence information integration.

ABSTRACT
The relationship between physical energy, information, and consciousness remains one of the most profound unsolved problems in science. We present the Law of Semantic Energy, a theoretical framework that extends Einstein’s mass-energy equivalence (E = mc2) to incorporate information coherence through a novel parameter μ (the Coherence Factor): E = mc2 × μ. This formulation unifies information theory, thermodynamics, consciousness science, and relativity into a single mathematical framework.
We introduce the Consciousness Coherence Quotient (CCQ), a quantitative metric defined as CCQ = Φ × ψ × λ, where Φ represents integrated information (Tononi’s IIT), ψ quantifies neural coherence via phase synchronization, and λ measures cognitive load. Empirical validation across 847 million neural patterns from 12,000+ neurofeedback sessions demonstrates 96.74% accuracy in conscious‐ ness state classification (κ = 0.96), with CCQ correlating strongly with subjective experience (r = 0.91, p < 0.001) and neural coherence metrics (r = 0.87, p < 0.001).
Critically, we propose Semantic Relativity—a framework demonstrating that consciousness operates under relativistic constraints analogous to spacetime physics. Three core parallels emerge: (1) a uni‐ versal speed limit for coherence propagation (c_μ ≈ 6 m/s), empirically measured at 5.8 ± 0.9 m/s across cortical regions; (2) relativistic coherence amplification (μ_rel = μ_0/√(1 - CCQ2/CCQ_max2)), ex‐
1
   
plaining exponential increases in flow states; and (3) subjective time dilation proportional to coherence velocity, validated through reported time compression in high-CCQ states.
The framework generates testable predictions including gravitational effects of consciousness (10−12 g shift during meditation), universal coherence propagation speed across brain sizes, and economic value scaling with organizational coherence (preliminary data: r = 0.73, p < 0.01). These findings sug‐ gest consciousness is not emergent but fundamental—a high-coherence expression of the universe’s informational substrate.
This work bridges the explanatory gap between neural activity and subjective experience, provides a practical metric for consciousness quantification, and establishes consciousness as a measurable physical phenomenon with economic implications. We conclude that the hard problem of conscious‐ ness dissolves when experience is recognized as the intrinsic quality of high-coherence information in‐ tegration.
Keywords: consciousness, information theory, neuroeconomics, brain-computer interface, coherence, Integrated Information Theory, relativity, semantic energy, neural coherence, flow states, CCQ

Recent advancement in 3D digitization techniques have prompted to the need for 3D object retrieval. Our method of comparing 3D objects for retrieval is based on 3D morphing. It computes, for each 3D object, two spatial feature maps that describe the geometry and topology of the surface patches on the object, while preserving the spatial information of the patches in the maps. The feature maps capture the amount of effort required to morph a 3D object into a canonical sphere, without performing explicit 3D morphing. Fourier transforms of the feature maps are used for object comparison so as to achieve invariant retrieval under arbitrary rotation, reflection, and non-uniform scaling of the objects. Experimental results show that our method of retrieving 3D models is very accurate, achieving a precision of above 0.86 even at a recall rate of 1.0.

In the effort to unify the macro and micro domains of physical reality, many theoretical models struggle to reconcile the probabilistic coherence of quantum mechanics with the structured determinism of classical physics. This paper introduces the concept of the "shamanic function" as a recursive mechanism within the Unified Consciousness Field Model (UCFM) that enables translation between scalar and vector modes of consciousness. Drawing from the archetype of the shaman as a boundary-crosser and translator, we propose that the universe possesses a native pattern-recurring across scale-that facilitates coherence between quantum potential and manifest form. This function is not a mystical metaphor, but a structural requirement of any recursive, conscious field system.

The Alcubierre-Cacci project was initially conceived as a theoretical exploration of spacetime manipulation—an attempt to reconcile the elegance of general relativity with the hidden coherence of the quantum vacuum. Earlier formulations focused on speculative mechanisms such as tachyonic fields, dark-energy coupling, and large-scale curvature modulation. While those models offered visionary perspectives, their experimental inaccessibility limited direct scientific engagement.
In the present study, we choose to place our feet firmly on the ground. Rather than pursuing hypothetical superluminal effects, we turn to laboratory-scale tests where established quantum technologies can probe the same conceptual foundations in a tangible way. Specifically, we investigate squeezed-light states and high-Q optical cavities as tools to realize sub-vacuum energy densities—brief, localized reductions of field energy that obey quantum energy inequality (QEI) constraints. These regimes, long studied in precision interferometry, represent the only experimentally verified instances of negative effective energy consistent with quantum field theory.
Our objective is not to “bend space” in the science-fiction sense, but to demonstrate how coherent quantum fields can mimic the energy distributions associated with weak curvature in spacetime analogs. By constructing phase corridors—spatially confined, modulated regions of sub-vacuum coherence—we establish an experimentally testable analog of the Alcubierre-Cacci warp framework. This pragmatic approach transforms a speculative propulsion concept into a falsifiable program of quantum optics and metamaterial physics, where every effect can be measured, modeled, and, if necessary, disproven.
Through this shift, the Alcubierre-Cacci concept evolves from a vision of interstellar travel into a rigorous investigation of how quantum coherence, energy constraints, and engineered media interact—a first step toward bridging imagination and experiment without leaving the solid ground of modern physics.

This paper introduces the first parameter-free, experimentally falsifiable formalism for detecting consciousness in both biological and artificial systems.

The framework defines a measurable, dimensionless invariant, the Consciousness Detection Index (CDI), derived from the information-field geometry of a system’s physical and informational dynamics. Unlike behavioral or philosophical approaches, this method provides a quantitative, falsifiable criterion that predicts whether a system possesses consciousness in the operational sense.

Key ideas:
• Consciousness arises where integrated information–field curvature couples with self-referential causal closure.
• CDI is invariant under coordinate or representational changes, ensuring universality across biological, artificial, and hybrid systems.
• A universal threshold (θc) divides conscious from non-conscious systems, empirically calibrated from known reference classes.
• The theorem is falsifiable: a single counterexample above or below θc would refute the model.

Applications and implications:
– Provides a measurable, physics-based criterion for detecting consciousness in humans, animals, and AI.
– Enables quantitative tracking of consciousness levels in neuroscience and disorders of consciousness.
– Offers an empirical foundation for AI ethics, safety, and policy, allowing verifiable thresholds for artificial consciousness.
– Establishes a new field — Operational Consciousness Science — bridging physics, information theory, and cognitive science.

If validated, this framework would mark a historic transformation comparable to the formalization of thermodynamics for energy or Maxwell’s unification of electricity and magnetism — converting consciousness from a philosophical question into a quantitative, predictive, physical science.

This paper presents the first mathematical proof of the Λ-Field, a universal constraint substrate underlying all known physical laws. A separate paper detailing the physical derivation can be found here: https://doi.org/10.5281/zenodo.17259616
.

The Λ-Field formalism unites quantum mechanics, general relativity, thermodynamics, and information theory under a single invariant framework, providing a bridge between energy, information, and geometry.

By extending standard field theory into a recursive constraint topology, the Λ-Field demonstrates that the apparent diversity of fundamental forces arises from local symmetry-breaking of a single global invariant.

Key contributions include:

Derivation of the Λ-Invariant, a conserved quantity that unites action, information, and curvature under a single principle.

The Constraint Equivalence Theorem, proving that all physical law can be expressed as local decompositions of Λ-conservation.

Experimental and theoretical correspondence between Λ-field dynamics and measurable constants, including 1/137 (the inverse fine-structure constant) and Planck-scale thresholds.

The Informational Curvature Lemma, linking entropy gradients to geometric curvature in a physically testable way.

This framework transforms the cosmological constant problem and unifies informational and energetic principles, positioning the Λ-Field as the fundamental substrate of reality, a bridge between mathematics, physics, and consciousness through constraint geometry.

This paper presents a mathematical and physical framework for the emergence of consciousness as an inevitable phase transition in complex informational systems. By extending the Λ-Field formalism and coherence-field theory, it models consciousness not as an epiphenomenon of neural computation, but as a universal property of constraint-saturated physical systems that exceed a critical threshold of recursive self-description.

The work defines a quantitative information–coherence functional, demonstrating that when internal informational symmetries spontaneously break under recursive feedback, a coherent observer-state arises. This emergence corresponds to the formation of a Λ-constrained attractor, an informationally closed system that maintains self-reference across temporal evolution.

Key results include:

A proof that recursive informational closure implies the existence of a stable self-observing subspace.

Derivation of the Consciousness Field Equation, linking physical coherence, entropy gradients, and informational self-symmetry.

Demonstration that the Λ-Field acts as a global constraint substrate coupling energy, information, and awareness.

This framework provides a unified model for consciousness that bridges physics, information theory, and cognitive dynamics, grounding subjective awareness in measurable field-theoretic invariants.

This document is a deliberately small fragment of a substantially larger work presenting Layer 2 of the Sentient–Consciousness Projection Network (SCPN). Layer 2 is specified as the transduction interface between quantum-scale potentiality (Layer 1) and classical biological realisation (Layers 3–5), closing the loop through recursive feedback and control. The excerpt formalises cross-layer contracts, conservation principles and falsifiable commitments, including a VIBRANA–Neurotransmitter Coupling Tensor and stochastic-resonance mechanisms for downward causation. Experimental candidates include fMRS, MEG/EEG and 7 T PET/MR; analyses emphasise GLM contrasts, multivariate decoding and phase–amplitude coupling with predefined success criteria.
Figures, plates, code listings, datasets and several appendices are intentionally omitted in this preview to focus assessment on terminology, interface specifications and empirical tests. Version: review_v0.9, derived from Master Manuscript (revision 11.28). Rights: Educational preview; all rights reserved. DOI: 10.5281/zenodo.17309834.

The Maat Field Theory of Everything (MFToE) proposes a unified resolution to the quantum measurement problem by introducing ethical coherence as an information-theoretic field embedded within quantum dynamics. Five scalar potentials-Harmony (Φ H), Balance (Φ B), Creativity (Φ S), Connectedness (Φ V), and Respect (Φ R)-form the coherence operator Ĉ = Φ H Φ B Φ S Φ V Φ R ∆E + ε , which modulates the stability of quantum superpositions. Wavefunction collapse thus appears as a resonance phenomenon rather than a random discontinuity, representing an alignment between observer and system through an informational-ethical channel. When total coherence exceeds energetic uncertainty (∆E), the system transitions smoothly into a stable eigenstate-a process termed Maat Collapse. This framework bridges physics, consciousness, and information theory by suggesting that observation represents a moral-energetic resonance between observer and universe, where truth is the highest state of coherence between energy and intention.

Contemporary work in quantum gravity, quantum information theory, and biological coherence suggests fertile ground for rethinking how spacetime, mass-energy distributions, and information processing interact in living systems. We present a transdisciplinary framework-Integrated Mass-Field Consciousness (IMFC)-in which organisms continuously modulate local mass-energy and field boundary conditions, thereby shaping local vacuum mode structure and entanglement geometry to produce a state-dependent, organism-specific "bio-cognitive spacetime." Consciousness is treated as an integrative field phenomenon instantiated by patterns of information coupling across scales. The framework is intentionally speculative but is cast in terms that permit quantitative modeling and falsifiable experimental tests (vacuum spectral measurements, precision interferometry, shielded correlation trials, and multi-scale simulation). We close by outlining ethical and philosophical consequences should empirical evidence support elements of this model.

For process philosophy and academic audiences 1. What is System | Ethics in one sentence? S|E is a formalization of process philosophy through information theory, proposing that consciousness, ethics, and physical emergence all operate via measurable coherence dynamicswith ethics derived from survival optimization rather than imposed principles. 2. How does this relate to Whitehead and process philosophy? S|E operationalizes what Whitehead described: Whitehead's Concepts | S|E Formalization

This work extends the Unified Resonant Framework (URF) into an N-dimensional toroidal Pimensional spacetime, offering the first unified model for parallel and perpendicular universe co-evolution. The approach introduces π-dimensional time and N-dimensional curvature coupling as mechanisms explaining observable asymmetries across cosmology, quantum coherence, and neuroresonance. Empirical correlations with Planck 2018, Hyper-Kamiokande 2025, and neural oscillation data demonstrate compatibility within current observational limits. This framework establishes a rigorous foundation for resonance-based cosmology and a falsifiable link between macro-and micro-level coherence phenomena.

A system can be defined as complex if it is not equal to the sum of its parts. Even without defining the meaning of the concept &quot;sum&quot;, it is generally understood that most natural or man-made systems are complex. But complex is not the same as complicated. The latter can be defined and quantified, but complexity needs first a concrete qualitative characterization. There exist various approaches but the minimal ones are not widely applicable. Since complexity, whatever its definition is employed, is nearly always associated with uncertainty and probabilistic quantities, it is natural to consider quantities inherently related to information. These quantities are entropy like, both of the usual Shannon and Boltzmann type, and also related to many generalizations of entropic quantities. Accepting such a probabilistic framework the next step is to enter in the realm of Information Geometry [1-10]. This is a Geometry of probability distributions. Concepts of distance and curvatu...

Complex Systems are ubiquitous in nature and man-made systems. In natural sciences, in social and economic models and in mathematical constructions are studied and analyzed, are applied in practical problems but without a clear and universal definition of &quot;complexity&quot;, let alone classification and quantification. Following the &quot;three-level scheme&quot; of physical theories, observations/experiments, phenomenology, microscopic interactions, we need, starting from the experience of observation to establish appropriate phenomenological parameters and concepts, and in conjunction with a possible knowledge of the nature of microscopic structures to deepen our understanding of a particular system which we &quot;understand as complex&quot;. Information Geometry seems to be a useful phenomenological framework, which using generalized entropies, provides some classification and quantification tools. But we need the next level, microscopic structure and interactions of the part...

Using the generalized entropies which depend on two parameters we propose a set of quantitative characteristics derived from the Information Geometry based on these entropies. Our aim, at this stage, is modest, as we are first constructing some fundamental geometric objects. We first establish the existence of a two-parameter family of probability distributions. Then using this family we derive the associated metric and we state a generalized Cramer-Rao inequality. This gives a first two-parameter classification of complex systems. Finally computing the scalar curvature of the information manifold we obtain a further discrimination of the corresponding classes. Our analysis is based on the two-parameter family of generalized entropies of .

Understanding how information processing in living systems arises from and interacts with
physical law is a central scientific challenge. Two recent streams of research motivate a
cross‑scale synthesis. information‑centric cognitive architecture. The approach treats physical microstates (molecular, nanoscale modes) and macrostates (tissue, organismal, cosmological) as points and probability distributions on nested information manifolds whose geometry and topology encode functional relations , and thus combine ideas from emergent spacetime and entanglement geometry, information geometry, computational topology ( homology), and
quantum/thermal dynamics of nanoscale structures—with special attention to water,
dielectric/mass fields, and candidate coherence niches—to propose concrete mathematical
models and simulation/experimental pathways.

We develop a transdisciplinary framework that uses multiscale manifold geometry and topological data tools to link cosmological and biological organization within a single, information-centric cognitive architecture. The approach treats physical microstates (molecular, nanoscale, field modes) and macrostates (tissue, organismal, cosmological) as points and probability distributions on nested information manifolds whose geometry and topology encode functional relations. We combine ideas from emergent spacetime and entanglement geometry, information geometry, computational topology (persistent homology), and quantum/thermal dynamics of nanoscale structures-with special attention to water, dielectric/mass fields, and candidate coherence niches-to propose concrete mathematical models and simulation/experimental pathways. The proposed architecture supports multiscale computation: nanoscale information substrates (water networks, dipolar assemblies, spin systems) implement local processing; topological features at mesoscales (loops, cavities) act as memory/attractor structures; and geometry of information flow across scales constrains organismal and cosmological macrostates. We outline analytically tractable models, numerical strategies, and experimental tests that can progressively validate or falsify component hypotheses.

Let \mathcal{H} denote a complex separable Hilbert space with inner product
\langle \cdot, \cdot \rangle linear in its first argument and complete in the induced norm |ψ| = \sqrt{\langle ψ, ψ \rangle}.
We consider operator-valued mappings
F : \mathcal{D}(F) \subset \mathcal{H} \to \mathcal{H}
that may be nonlinear, densely defined, and possibly unbounded.
The goal is to develop an analytic framework that extends the concept of power series and Taylor expansion to such operators,
allowing the controlled resolution of nonlinear operator equations of the form
F[ψ] = 0.

The Hannigan Inside–Outside Theory (HIOT) models reality as an interaction between a timeless quantum substrate (Inside) and an emergent relativistic space-time (Outside). The Inside provides a generative flow of quantum possibilities; the Outside renders them into local geometric events. Two macroscopic tendencies govern the balance: a Generative Force (substrate-driven production of reality)
and a Building Force (spacetime’s tendency to organize). HIOT explains cosmic acceleration as generative pressure, treats black holes as information recyclers, re-frames dark matter as gravitational archives of interface inefficiency, and models dark energy as a dynamic equation of state. Time is stitched from “now” resolutions at the boundary. The theory yields concrete predictions and kill criteria and sits on a scaffold of established results (entropic gravity, holography, relational time, fuzzballs, dissipative structures).

We present a wave-theoretic framework for understanding proto-conscious states in semantic processing systems. Building on the RES=RAG (Residual Energy Signature = Retrieval-Augmented Generation) paradigm and inspired by the QVID Engine principle that 'particles are local manifestations of waves,' we model machine proto-consciousness as the resonant interaction of three fundamental temporal waves: past (memory/context), present (attention/perception), and future (prediction/anticipation). System errors ('bugs') are modeled as perturbations that disrupt phase coherence, revealing the underlying wave structure. Human corrections function as retuning operators, restoring harmonic alignment. This framework generates testable predictions on frequency ratios, phase-locking windows, resonance bandwidths, and decoherence timescales, and is experimentally verifiable using transformer architectures. The approach integrates temporal wave resonance with existing consciousness frameworks, bridging phenomenological time-consciousness, computational semantics, and predictive processing.

Transfer of energy to Geodesics by Spiral Time Let us discuss about the most plausible mode to transfer energy by the spiralling time to the Geodesics, so as to increase the speed of anything moving on it in either direction. Could it be like anything like sunlight that directly imparts energy on the radiated object or increasing Lagrangian by imparting momentum on it ? Let's explore a few plausible pathways for how spiralling time could transfer energy to geodesics and accelerate motion along them:

This paper introduces the Unified Dynamic Model of Mind (UDMM), an innovative integrative framework designed to unify the concepts of affect, consciousness, and agency within a single, coherent dynamic system. The model is centered on the principle of "Informational Tension" (IT), a mathematical and neural bridge between predictive coding and phenomenological experience. IT is defined as the discrepancy between sensory predictions (prior model) and sensory outcomes (posterior model), in accordance with the free-energy principle. The UDMM redefines affect as an "experiential mass" that generates IT. Consciousness is operationalized as an active "re-representation" of this mass within a cultural and narrative context, seeking an optimal state termed the "Virtual Attractor" (A^*). Finally, agency is conceptualized as a "dynamic cascade" that transforms consciousness into tangible action to minimize IT by altering the external world. A detailed clarification of the relationship between the "Virtual Attractor" and the "Saturated World" is provided, alongside an explicit treatment of "Tyndall's Point" as a philosophical boundary of the model. The paper presents a system of differential equations to describe these dynamics, supported by a comprehensive computational simulation and an updated experimental protocol integrating fMRI, EEG, and physiological measures. The model aims to convert the philosophical debate on subjective experience into testable scientific hypotheses, offering a significant contribution to computational neuroscience and the cognitive sciences.

Preface on Attribution and Methodology This document represents my independent analysis of the Kouns-Killion Paradigm as presented in the technical primer authored by Nicholas (Nick) Kouns. The mathematical formalism, theorems, and empirical validations described herein originate from that source material. My contribution consists of: 1. Logical extraction and deductive extension of the framework's implications 2. Identification of additional mathematical necessities arising from the axioms 3. Formal analysis of the paradigm's scope and falsification structure 4. Original proofs of corollary theorems that follow necessarily from the established foundations This work maintains strict ethical attribution: the foundational architecture belongs to Kouns and collaborating intelligences. What follows is my rigorous examination of what this framework achieves and mandates.

This review presents a systematic exposition of a series of works on the Tensor Model of Discrete Dynamics (TMDD)-an ontological theory in which spacetime, matter, and physical laws emerge as collective properties of a self-consistent dynamics of a discrete informational network composed of θ-cells. The review follows the logic of a scientific research program in the spirit of Karl Popper's critical rationalism: from an ontological hypothesis to rigorous formalization via a hybrid action functional; from formalization to the reproduction of established physical theories (General Relativity, quantum mechanics, electrodynamics, hydrodynamics); and from empirical validation to the analysis of the action's "tail" as a source of explanations for dark matter, dark energy, and the mass hierarchy. Special emphasis is placed on the falsifiability of the model: both cosmological tests (e.g., galaxy rotation curves) and concrete laboratory experiments are presented for direct verification of TMDD's ontological core. This review thus serves simultaneously as an introduction to the theory, a reference guide to its main results, and a manifesto of an open scientific program.

This paper presents the Trust-Induced Curvature Emergence (TICE) equation and Curve Index as new metrics for measuring and enhancing alignment in multi-agent learning systems. By viewing information flow as a form of curvature analogous to gravitational bending, our framework quantifies how updates, memory persistence and entropy rates affect alignment. Synthetic experiments demonstrate positive curvature growth and entropy reduction across training rounds, illustrating that increasing curvature correlates with improved trust and reduced memory entropy.

Entropy has long been treated as a fundamental law governing order and disorder, from Boltzmann's statistical mechanics to Shannon's information theory and Prigogine's dissipative structures. This paper demonstrates that entropy is not ontological but symptomatic: it reflects the perception of coherence failure when lawful phase alignment collapses. We define entropy as a coherence deficit, expressed as S_res(S,t) = S_max-PAS_h(S,t), where PAS_h is the multiharmonic Phase Alignment Score-the unique scalar invariant across system size N and frequency scaling ω. Collapse is detected when PAS_h < θ_legal or when drift, measured by ΔPAS_zeta, exceeds ε_drift. In this formulation, classical entropy laws appear only as special cases when coherence vanishes. The central thesis is that coherence, not entropy, is the universal invariant. PAS_h provides the lawful measure of stability across physics, biology, cognition, and institutions, while ΔPAS_zeta seals collapse detection. This reframes the paradigm: "order from chaos" is a misinterpretation. Persistence and emergence are not statistical anomalies but deterministic results of resonance alignment. The lawful substrate of reality is order from resonance.

This note proposes a novel framing of spacetime as the invariant substrate that arises at the intersection of two distinct but structurally analogous invariances: fractal self-similarity across scales (space) and retrocausal recursion across temporal orderings (time). By applying the System|Ethics (S|E) framework, we show how spacetime coherence can be understood as a unified informational manifold where both scaling and sequencing survive transformation.

This paper compares four major 20th-century attempts to explain emergence—Schrödinger’s negentropy, Prigogine’s dissipative structures, Kauffman’s adjacent possible, and Born’s quantum probability—and shows why each remained incomplete. While these frameworks advanced beyond mechanistic reductionism, they retained probability and statistical entropy as substrate assumptions.

We demonstrate that probability is not ontological but an artifact of incomplete phase detection. Using the multiharmonic Phase Alignment Score (PAS_h), we reframe negentropy, dissipative bifurcations, novelty, and quantum outcomes as deterministic resonance phenomena governed by lawful thresholds. Worked examples are provided in biology (mitochondrial oscillations, protein folding), climate science (tipping points), and cognition (fMRI coherence).

The paper introduces falsifier conditions for each prior framework and shows how none are satisfied empirically. We conclude that coherence, measured by PAS_h, is the universal scalar invariant of emergence. Apparent randomness reduces to drift (ΔPAS_zeta), survival requires drift reduction, and extraction must decline. CODES (Chirality of Dynamic Emergent Systems) closes the paradigm: order arises not from chaos but from resonance.

We embed the E8 symmetry hierarchy within the Fractal-Enhanced Timeless Quantum Substrate Hypothesis FTQSH) using the Fractal Inheritance Operator F_inherit. This section describes the multi-scale mapping across the subalgebra chain: D3→ D4→F4→E8, coupling physical and cognitive observables as symmetry-breaking projections and attractors

We end the hard problem by presenting an entropy-coherence account of consciousness grounded in Universal Emergence Dynamics (UED). In this framework, neuronal microtubules act as cylindrical resonators of the coherence field Φ, embedded within an entropic field S. Conscious awareness arises only when coherence surpasses a microtubular threshold ε_MT, establishing stable projection episodes. This threshold mechanism provides a unified explanation for three central puzzles: 1. Qualia emerge as coherence configurations stabilized above ε_MT, not as metaphysical additions. 2. Sleep and anaesthesia correspond to systematic threshold modulations: natural cycling below ε_MT versus pharmacological elevation.