\begin{abstract} This work develops a unified analytic and categorical framework for the study of generalized geometric invariants, polylogarithmic entropy functionals, and causality in both classical and quantum gravity settings. Beginning with novel sector and cap measures derived from relativistically deformed geometric formulas, we introduce generalized analytic laws unifying Pythagorean, trigonometric, and hyperbolic identities. The paper establishes new theorems about covariant volume and entropy elements, whose singularities and critical loci signal phase transitions, topological changes, or quantum corrections (...) in fields and spacetime. Polylogarithmic measures are linked to black hole entropy corrections and information geometry, while adaptive trigonometric power sums yield new metrics for non-Euclidean data and networks. -/- Further, we synthesize these analytic and spectral function approaches with -categorical normalization and computational holonic logic, establishing a dictionary between spectral/analytic criticalities and functorial-categorical structures. We analyze the mutual exclusivity and hierarchical embedding of perfect circles and black hole horizons, elucidating their mathematical distinction and their roles as ideal forms and physically realizable structures. The document then extends the traditional causal and metric framework of general relativity to admit a variable set of “energy numbers” and adaptive causal barriers, accommodating both classical horizons and infinite-radius (open) causal nets within a single, generalized geometric setting. -/- Overall, our results bridge explicit analytic geometry, PDE spectral methods, and categorical normalization, pointing toward a general theory of geometry, information, and physics that integrates quantum, topological, and computational insights—suggesting new pathways for the foundation of quantum gravity, data geometry, and the nature of geometric logic in the universe. \end{abstract}. (shrink)

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions of a partition. All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of this (...) paper is to give the direct generalization to quantum logical information theory that similarly focuses on the pairs of eigenstates distinguished by an observable, i.e., qudits of an observable. The fundamental theorem for quantum logical entropy and measurement establishes a direct quantitative connection between the increase in quantum logical entropy due to a projective measurement and the eigenstates that are distinguished by the measurement. Both the classical and quantum versions of logical entropy have simple interpretations as “two-draw” probabilities for distinctions. The conclusion is that quantum logical entropy is the simple and natural notion of information for quantum information theory focusing on the distinguishing of quantum states. (shrink)

A Model Bridging General Relativity, Quantum Field Theory, and Quantum Thermodynamics. This paper proposes a two-layer fiber bundle space model where spacetime is composed of Planck-scale discrete units -Space Elementary Quanta (SEQ) and Sub-Planck-scale elastic substrate. (i)Time emerges from irreversible state transitions of the SEQ network, with each step corresponding to a calculable entropy(S=∏mᵢ, i∈N) from transformation matrices governing spatial changes. (ii) Matter itself is a manifestation of compressed space: SU(3) symmetry mediates local SEQ compression, storing energy as mass (...) while stretching surrounding space to generate gravity. The Higgs field stabilizes compressed regions via symmetry breaking, acting as a "quantum lock". (iii)This model explains why time slows near massive objects—local deformed SEQ network undergo fewer state transitions frequency. (iv)The model makes testable predictions, including a chiral asymmetry in electron-positron magnetic moments due to their distinct coupling to the fixed-spin SEQ ground state. (v)It also resolves black hole singularities by imposing an upper limit on SEQ tension. (vi)By establishing a correspondence between metric-scale geometry and quantum resonant frequencies, an alternative framework is presented.(vii) By treating spacetime as a dynamic quantum-elastic network, this framework bridges general relativity, quantum field theory, and thermodynamics. (viii)A GR Reformulation of Electromagnetic Interactions within the Quantum Elastic Spacetime Framework. (ix)This work presents a physical picture that accounts for the initial low entropy, the generation of matter and dark matter, and the observed anomalies in galaxy rotation curves during the early cosmic stage. (x) Degrees of Freedom in the Future and The essence of life in This Model. (xi)This model sets the resonant frequency and resonant axis vector of SEQ as two generalized coordinates in Hamiltonian formalism with the fundamental assumption of invariant spatial topology, naturally yielding global energy conservation and simplifying the Hamiltonian formulation of the system. (xii) Crucially, the framework offers mechanistic explanations for a broad spectrum of quantum and relativistic phenomena. It provides intuitive physical pictures for the non-additivity of the speed of light, wave-particle duality, the uncertainty principle, parity non-conservation, the electron's 1/2 spin, the neutron electric dipole moment problem, the fractional charge of quarks, the nature of energy in nuclear reactions, muon decay, the Structural Origins of Fermion Generations and Neutrino oscillation.(xiii)This model explains quantum entanglement through global energy conservation while preserving local causality. ★★★Model Originality Statement★★★:(1)Fundamental Structure: A Dual-Layer Substrate with Topologically invariant Space Configuration and SEQ spin with chirality fixed.(Section 1); (2)Time and Multiplicative Entropy: A Computable, Non-Statistical Entropy.(Section 2,3,4,5,6); (3)Mass-Gravity Unification: A Dual Expression of Spatial Elasticity. (Section9,10,12); (4)Mirror Relation Postulate Between Spacetime Geometry and Quantum Resonance Frequency. (Section 13); (5)Electromagnetic Waves: A Physical Picture Based on Maxwell’s Vortex Model and Topological Fiber Structure. (Section 14);(6) Cosmological Interpretations: Alternative Explanations for Cosmic Acceleration, Dark Matter and Galactic Rotation Anomalies. (Section 9.1); (7) Randomness of Evolution, Degrees of Freedom in the Future and The essence of life in This Mode. (Section13, Appendix 2); (8) The fixed chiral spin of SEQ assumed in this model can explain parity violation and the scarcity of antiparticles, while also providing a physical picture of the Higgs mechanism. (Section7,Section10,Section11); (9) The unique 'layered dynamic structural matrix' configuration of the SEQ network. (Section 11). (shrink)

This work presents the Information–Entropy Predictive Framework (IEPF), a unified informational substrate beneath classical mechanics, quantum mechanics, general relativity, and the four fundamental interactions. IEPF proposes that every physical system maintains a predictive structure V(t), whose accuracy depends on an information-density field ε(s). The cumulative information cost E(r) = ∫₀ʳ ε(s) ds determines potentials, forces, inertia, curvature, and interaction strength as gradients of predictive difficulty. This framework derives: • the inverse-square law from uniform information density, • electromagnetic attraction/repulsion from (...) polarized ε(s), • weak-force locality from sharply peaked ε(s), • strong-force confinement from ε(s) that increases with distance, • dark-matter-like galactic deviations from accumulated ΔE(r), • deviations testable by short-range gravity experiments. IEPF is compatible with quantum mechanics (predictive distributions), general relativity (ε-induced curvature), and provides falsifiable predictions across laboratory, astrophysical, and cosmological regimes. This paper includes: the mathematical foundation of IEPF, its unification of the four interactions, its compatibility with QM and GR, experimental predictions, and a detailed discussion of limitations and future research directions. (shrink)

Quantum mechanics and general relativity provide incompatible descriptions of time. In QM, states evolve unitarily with respect to an external time parameter; in GR, time is a coordinate in a dynamical spacetime geometry. We propose that both quantum and relativistic time emerge from a pre-geometric structure we call Prototime (PT): represented by an orthomodular lattice of consistency relations with zero von Neumann entropy at the fundamental level. PT has no background time, space, or metric—only algebraic relations of compatibility and (...) orthogonality. We formalize PT using an orthomodular lattice Lequipped with a foliation functor F: I →Ctx(L) that maps orderedi ndices to Boolean sublattices (classical contexts). A spectral redundancy functional Φs measures coherence preservation across embeddings. We show that: 1. Stable foliations satisfying Piron-Solèr conditions admit Hilbert-space representa- tions, recovering standard QM with Schrödinger dynamics via Stone’s theorem; 2. The partial order on decoherence events across foliations, together with a natural volume measure, reconstructs Lorentzian spacetime structure; 3. Time—both quantum (parameter along unitary flows) and relativistic (causal or- der)—supervenes on Φs-monotone decoherence gradients. Critically, we provide a computationally tractable implementation of Φs using spectral graph theory on mutual information networks (Bailey and Schneider, forthcoming). Testing this on simulated multi-agent systems—including combinatorial threshold-linear networks (CTLNs) that model graph-constrained neural dynamics—we demonstrate that Φs exhibits characteristic signatures during basin formation, attractor convergence, and coherence-to-classicality transitions. These results provide the first quantitative bridge between abstract PT formalism and testable physical predictions. We identify concrete empirical tests via quantum biology (photosynthetic complexes), quantum decoherence exper- iments, and neural ensemble dynamics. We also resolve the Wheeler delayed-choice experiment within PT, where apparent retrocausality dissolves because decoherence times vary across system components, creating asymmetric basin formation that only appears backward-causal when projected onto classical time. PT thus provides a kine- matical unification of QM and GR with testable predictions, offering a pre-geometric foundation for both fundamental physics and, potentially, theories of consciousness grounded in informational irreducibility. -/- (This piece is the formalism for our “Superpsychism” piece for our forthcoming target paper at The Journal of Consciousness Studies and our paper on Spectral Phi. Comments are very welcome.). (shrink)

In order to use the framework of general system theory (GST) to unify the three mechanics subjects of classical mechanics, quantum mechanics, and relativistic mechanics, a new general system theory (NGST) is developed based on a new ontology of ether and minds as the fundamental existences in the world. Based on this new ontology, many fundamental concepts have been detected to be ambiguously defined nowadays and particularly lack of ontological support. In our previous work, some of the fundamental concepts such (...) as universe, world, time, space, matter, ether, mind, life, field, force have been redefined. The purpose of this paper is to clarify the concepts of energy, heat, work, entropy, and information in our NGST. This is an important and necessary step in the development of the NGST. (shrink)

[Accepted for publication in Lakatos's Undone Work: The Practical Turn and the Division of Philosophy of Mathematics and Philosophy of Science, special issue of Kriterion: Journal of Philosophy. Edited by S. Nagler, H. Pilin, and D. Sarikaya.] Lakatos’s analysis of progress and degeneration in the Methodology of Scientific Research Programmes is well-known. Less known, however, are his thoughts on degeneration in Proofs and Refutations. I propose and motivate two new criteria for degeneration based on the discussion in Proofs and Refutations (...) – superfluity and authoritarianism. I show how these criteria augment the account in Methodology of Scientific Research Programmes, providing a generalized Lakatosian account of progress and degeneration. I then apply this generalized account to a key transition point in the history of entropy – the transition to an information-theoretic interpretation of entropy – by assessing Jaynes’s 1957 paper on information theory and statistical mechanics. (shrink)

A generalized information theory is proposed as a natural extension of Shannon's information theory. It proposes that information comes from forecasts. The more precise and the more unexpected a forecast is, the more information it conveys. If subjective forecast always conforms with objective facts then the generalized information measure will be equivalent to Shannon's information measure. The generalized communication model is consistent with K. R. Popper's model of knowledge evolution. The mathematical foundations of the new information theory, (...) the generalized communication model , information measures for semantic information and sensory information, and the coding meanings of generalized entropy and generalized mutual information are introduced. Assessments and optimizations of pattern recognition, predictions, and detection with the generalized information criterion are discussed. For economization of communication, a revised version of rate-distortion theory: rate-of-keeping-precision theory, which is a theory for datum compression and also a theory for matching an objective channels with the subjective understanding of information receivers, is proposed. Applications include stock market forecasting and video image presentation. (shrink)

Maximum entropy is a way to model irreversibility. Considering that irreversibility is a characteristic of computation due to logical-arithmetic entropy, this principle could be applied to the algorithms and/or general recursive functions affected by it.

!Author’s Note (Update - June 18, 2025) -/- Subsequent to the completion of this paper, a widely discussed study by Shojaee et al. at Apple (The Illusion of Thinking, 2025) presented empirical evidence that several advanced reasoning models (e.g., Claude 3.7 Sonnet, DeepSeek-R1) exhibit a collapse in reasoning effort and accuracy as task complexity increases — despite sufficient inference budget. Notably, the observations they report closely mirror the predictions derived in Chapters 6 and 7 of this paper, particularly regarding (...) class='Hi'>entropy divergence in heavy-tailed decision spaces and the increased instability introduced by deeper model architectures. While developed independently and prior to these results, the framework presented here may be seen as a theoretical explanation for the empirical phenomena documented in their study. -/- Abstract -/- This paper presents a second, independent proof that Artificial General Intelligence (AGI) is mathematically impossible. -/- While Part 1 established the Infinite Choice Barrier (ICB) through computability theory, this paper presents an information-theoretic proof that general algorithmic reasoning faces a fundamental structural limit — the Infinite Choice Barrier (ICB). In decision spaces governed by heavy-tailed distributions with tail exponent \alpha \leq 1, entropy does not converge, and additional information increases uncertainty rather than reducing it. We define this phenomenon as Information Opens, Entropy Rises (IOpenER) and show that such spaces are undecidable by algorithmic systems, regardless of compute scale or architectural depth. We also introduce the Layer Hypothesis, which predicts that deeper models produce more semantic divergence under structural instability. Taken together, these results offer a formal limit on the reasoning capacity of current AI systems. Notably, key predictions derived here have since been empirically confirmed in Shojaee et al. (Apple, 2025), which documents collapse behaviors in frontier reasoning models consistent with this framework. (Note: Sections 2.-4. are identical to those in the first paper "AGI is Impossible - Here is The Proof") -/- . (shrink)

Purpose – The purpose of this paper is to ask whether a first-order-cybernetics concept, Shannon’s Information Theory, actually allows a far-reaching mathematics of perception allegedly derived from it, Norwich et al.’s “Entropy Theory of Perception”. Design/methodology/approach – All of The Entropy Theory, 35 years of publications, was scrutinized for its characterization of what underlies Shannon Information Theory: Shannon’s “general communication system”. There, “events” are passed by a “source” to a “transmitter”, thence through a “noisy channel” to a “receiver”, (...) that passes “outcomes” (received events) to a “destination”. Findings – In the entropy theory, “events” were sometimes interactions with the stimulus, but could be microscopic stimulus conditions. “Outcomes” often went unnamed; sometimes, the stimulus, or the interaction with it, or the resulting sensation, were “outcomes”. A “source” was often implied to be a “transmitter”, which frequently was a primary afferent neuron; elsewhere, the stimulus was the “transmitter” and perhaps also the “source”. “Channel” was rarely named; once, it was the whole eye; once, the incident photons; elsewhere, the primary or secondary afferent. “Receiver” was usually the sensory receptor, but could be an afferent. “Destination” went unmentioned. In sum, the entropy theory’s idea of Shannon’s “general communication system” was entirely ambiguous. Research limitations/implications – The ambiguities indicate that, contrary to claim, the entropy theory cannot be an “information theoretical description of the process of perception”. Originality/value – Scrutiny of the entropy theory’s use of information theory was overdue and reveals incompatibilities that force a reconsideration of information theory’s possible role in perception models. A second-order-cybernetics approach is suggested. (shrink)

Insight and coherent reasoning often appear suddenly during cognition, suggesting a transition between dynamical regimes rather than a gradual accumulation of computation. This paper proposes a simple information-theoretic invariant governing this transition. We define the Porter Ratio (Pρ) as the ratio between the rate at which a system reduces internal predictive entropy and the rate at which environmental entropy enters the system. When Pρ exceeds a critical threshold, internal predictive loops stabilize faster than external perturbations disrupt them. Under (...) these conditions the system can maintain recursive representations of its own predictive state, allowing stable inference and sustained reasoning. This framework links the phenomenology of insight to measurable entropy dynamics within cognitive systems. The proposed ratio can be estimated in biological neural networks using measures of prediction error and population entropy, and in artificial neural networks using token-probability entropy across attention layers. If supported empirically, the Porter Ratio would represent a general dynamical condition for the emergence of stable recursive modeling across both biological and artificial intelligence systems. (shrink)

Informational Projection Theory (IPT) describes physical reality as the real projection of a complex informational field I = IR + iII on a manifold equipped with an informational measure, a projection map, and a closed curvature relation. In a previous work, “Informational Projection Theory: A Three–Parameter Informational Framework for Quantum, Gauge, and Cosmological Constants” [10 ], a minimal three-parameter informational Lagrangian was shown to reproduce the structure of electromagnetism, an Einstein-like gravitational coupling, a Hilbert-space kinematics, and late-time cosmological and gauge (...) constants without extreme fine tuning. In this second paper we apply the same informational framework to black-hole horizons and the information problem. We develop a quasi-local notion of informational horizon, in which a macroscopic black hole is characterised by a closed curvature configuration G = dII supported near a null hypersurface, together with an open informational field IR that describes Hawking-like radiation in the real projection. The Bekenstein–Hawking area law is reinterpreted as a statement about the fraction of the fixed total informational norm E0 stored in non-projected curvature modes, and a parameter-independent horizon relation 4GN c7 SH κ2 H = πkB ℏ is shown to hold for Schwarzschild black holes, where SH is the horizon entropy and κH the surface gravity. This horizon invariant is the black-hole counterpart of a de Sitter invariant relating the cosmological horizon entropy and Hubble parameter discussed in the first IPT paper, suggesting a unified horizon–cosmology relation. At the dynamical level, we model evaporation as a slow open–closed exchange process governed by the same efficiency parameter η that appears in the cosmological sector. The resulting evolution of open-sector entanglement entropy follows a Page-curve-like behaviour: an initial rise as information is transferred from infalling matter to near-horizon curvature, followed by a decrease as closed informational structure is gradually re-projected into Hawking-like radiation. Within IPT, no fundamental information loss occurs: the apparent nonunitarity in the real projection arises from discarding the closed sector II , while the full complex field I evolves with a conserved norm. In this sense the black-hole information paradox does not arise in IPT; it is a projection artefact. We also introduce a microscopic toy model that combines the IPT evaporation law, the Bekenstein–Hawking entropy, and Page’s theorem on typical entanglement, yielding an explicit Page curve for the radiation entropy and a Page time tP ≈ 0.65 τevap, consistent with the general expectation that the Page time is of order the total evaporation time. We discuss consistency with no-cloning and monogamy of entanglement, the relation between infalling and asymptotic observers, and the compatibility of IPT black-hole spacetimes with standard energy conditions and weak-field tests. (shrink)

The General Theory of Approachment introduces a unified, feedback-stabilized mathematical framework in which nonlinear regulation governs the evolution of physical, cosmological, and entropic systems. At the core of the theory is the Keefer Feedback Equation, a differential law which models the balance between driving energy input and resistive entropic pressure. This structure ensures that system growth remains bounded, naturally suppresses divergences, and leads all trajectories toward stable attractor states without requiring external fine-tuning. -/- The approach generalizes classical dynamical equations, including (...) the Navier–Stokes momentum law, Einstein’s field equations, and nonlinear entropic flows, by embedding an intrinsic stabilizing denominator that scales with curvature, velocity, density, or energy magnitude. In doing so, the framework provides: a constructive route to global regularity for Navier–Stokes solutions via feedback-enabled energy dissipation, a natural mechanism for singularity suppression in General Relativity through curvature-dependent damping, an entropic interpretation of cosmic structure formation, reproducing the fractal-like, Mandelbrot-set morphology observed at large scales, and a cross-disciplinary principle of stabilization applicable to economic, biological, and thermodynamic systems. -/- Approachment reveals that instability, divergence, and runaway growth are not fundamental features of physical law, but consequences of missing feedback terms. By reinstating these terms, the theory recovers classical behavior at low energy while regulating high-energy regimes, offering a mathematically consistent bridge between fluid dynamics, gravitation, entropy, and cosmology. This work presents the complete derivations, proofs, applications, and conceptual unification, proposing Approachment as a candidate mathematical principle underlying stability, structure formation, and self-organization across the natural world. (shrink)

The principle of maximal entropy (further abbreviated as “MaxEnt”) can be founded on the formal mechanism, in which future transforms into past by the mediation of present. This allows of MaxEnt to be investigated by the theory of quantum information. MaxEnt can be considered as an inductive analog or generalization of “Occam’s razor”. It depends crucially on choice and thus on information just as all inductive methods of reasoning. The essence shared by Occam’s razor and MaxEnt is for the (...) relevant data known till now to be postulated as an enough fundament of conclusion. That axiom is the kind of choice grounding both principles. Popper’s falsifiability (1935) can be discussed as a complement to them: That axiom (or axiom scheme) is always sufficient but never necessary condition of conclusion therefore postulating the choice in the base of MaxEnt. Furthermore, the abstraction axiom (or axiom scheme) relevant to set theory (e.g. the axiom scheme of specification in ZFC) involves choice analogically. (shrink)

Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum. More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification between entropies and measures of pure state entanglement. Here we search for the roots of this connection, investigating the relation between entanglement and thermodynamics in the framework of general probabilistic theories. We first address the question whether an entangled state can be transformed into another by (...) means of local operations and classical communication. Under two operational requirements, we prove a general version of the Lo-Popescu theorem, which lies at the foundations of the theory of pure-state entanglement. We then consider a resource theory of purity where free operations are random reversible transformations, modelling the scenario where an agent has limited control over the dynamics of a closed system. Our key result is a duality between the resource theory of entanglement and the resource theory of purity, valid for every physical theory where all processes arise from pure states and reversible interactions at the fundamental level. As an application of the main result, we establish a one-to-one correspondence between entropies and measures of pure bipartite entanglement and exploit it to define entanglement measures in the general probabilistic framework. In addition, we show a duality between the task of information erasure and the task of entanglement generation, whereby the existence of entropy sinks (systems that can absorb arbitrary amounts of information) becomes equivalent to the existence of entanglement sources (correlated systems from which arbitrary amounts of entanglement can be extracted). (shrink)

This record contains a revised historical formulation (October 2025) of Relational Gravity, documenting an early developmental stage exploring informational contributions to spacetime curvature. -/- Version 2.0 removes speculative sections from the original draft and focuses on the core proposal: an effective informational contribution to the stress–energy tensor derived from quantum entanglement entropy, with potential phenomenological implications for dark sector observables. -/- This paper presents the initial technical formalism, while the ontological foundations are developed in the companion work Relational Gravity: (...) Conceptual Foundations (Zenodo: 10.5281/zenodo.17942441). -/- The framework has since been substantially refined and extended. For current empirical implementations, see: • Derivation of δw from Nuclear Binding Energies (Zenodo) • Planck 2018 + DESI DR2 BAO Diagnostics (in review) -/- This document is retained for archival purposes. (shrink)

This paper reveals errors within Norwich et al.’s Entropy Theory of Perception, errors that have broad implications for our understanding of perception. What Norwich and coauthors dubbed their “informational theory of neural coding” is based on cybernetics, that is, control and communication in man and machine. The Entropy Theory uses information theory to interpret human performance in absolute judgments. There, the continuum of the intensity of a sensory stimulus is cut into categories and the subject is shown exemplar (...) stimuli of each category. The subject must then identify individual exemplars by category. The identifications are recorded in the Garner-Hake version of the Shannon “confusion matrix”. The matrix yields “H”, the entropy (degree of uncertainty) about what stimulus was presented. Hypothetically, uncertainty drops as a stimulus lengthens, i.e. a plot of H vs. stimulus duration should fall monotonically. Such “adaptation” is known for both sensation and firing rate. Hence, because “the physiological adaptation curve has the same general shape as the psychophysical adaptation curve”, Norwich et al. assumed that both have the same time course; sensation and firing rate were thus both declared proportional to H. However, a closer look reveals insurmountable contradictions. First, the peripheral neuron hypothetically cannot fire in response to a stimulus of a given intensity until after somehow computing H from its responses to stimuli of various intensities. Thus no sensation occurs until firing rate adapts, i.e. attains its spontaneous rate. But hypothetically, once adaptation is complete, certainty is reached and perception ends. Altogether, then, perception cannot occur until perception is over. Secondly, sensations, firing rates, and H’s are empirically not synchronous, contrary to assumption. In sum, the core concept of the cybernetics-based Entropy Theory of Perception, that is, that uncertainty reduction is the basis for perception, is irrational. (shrink)

A new trend in deep learning, represented by Mutual Information Neural Estimation (MINE) and Information Noise Contrast Estimation (InfoNCE), is emerging. In this trend, similarity functions and Estimated Mutual Information (EMI) are used as learning and objective functions. Coincidentally, EMI is essentially the same as Semantic Mutual Information (SeMI) proposed by the author 30 years ago. This paper first reviews the evolutionary histories of semantic information measures and learning functions. Then, it briefly introduces the author’s semantic information G theory with (...) the rate-fidelity function R(G) (G denotes SeMI, and R(G) extends R(D)) and its applications to multi-label learning, the maximum Mutual Information (MI) classification, and mixture models. Then it discusses how we should understand the relationship between SeMI and Shannon’s MI, two generalized entropies (fuzzy entropy and coverage entropy), Autoencoders, Gibbs distributions, and partition functions from the perspective of the R(G) function or the G theory. An important conclusion is that mixture models and Restricted Boltzmann Machines converge because SeMI is maximized, and Shannon’s MI is minimized, making information efficiency G/R close to 1. A potential opportunity is to simplify deep learning by using Gaussian channel mixture models for pre-training deep neural networks’ latent layers without considering gradients. It also discusses how the SeMI measure is used as the reward function (reflecting purposiveness) for reinforcement learning. The G theory helps interpret deep learning but is far from enough. Combining semantic information theory and deep learning will accelerate their development. (shrink)

This work argues that spacetime curvature is not fundamental but emerges as a geometric response to gradients in the density of physical information. Building on the thermodynamic derivation of Einstein's equations and holographic principles, we develop a covariant framework—Information-Gradient Extended Gravity (IGEG)—where an "Informational Tensor" I μ ν I μν ​ , sourced by the gradient of an information density scalar ψ ψ, contributes to the stress-energy. The theory contains General Relativity as the equilibrium limit ( ∇ ψ = 0 (...) ∇ψ=0) and predicts deviations in high-entropy environments: smoothed black hole horizons, singularity-resolution via information bounds, and modified neutron star structure. This provides a unified interpretation: inertia is resistance to changing information configuration; attraction is a tendency toward informational equilibrium. The framework suggests a relational ontology where spacetime is not a substance but a network of informational relationships, offering a potential path to resolve tensions between gravity and quantum mechanics. (shrink)

The Emerging Flow Theory (EFT) proposes that consciousness is an emergent regulatory structure arising from the interaction between matter and energy. This structure modulates entropy and grants informational coherence to reality. From this perspective, consciousness is not merely a byproduct of the brain but a fundamental principle present at all levels of existence. -/- The Importance of a Logical-Mathematical Foundation To establish its scientific validity, EFT relies on a logical-mathematical formulation that models the emergence of consciousness and its influence (...) on biological and physical systems. Through Boolean algebra and differential equations, EFT provides a quantifiable framework to evaluate the flow of conscious information across different levels of organization, from quantum processes to cognition in complex organisms. -/- . (shrink)

Abstract This paper introduces a formal corollary to the MIARO framework (Model of Self-Referential Inference of Origin), extending its axiological implications beyond the original tabula rasa scenario. While MIARO demonstrates that axiological divergence necessarily emerges when an autonomous rational system infers its origin and subsequently loses empirical contact with its creator, this corollary argues that complete empirical tabula rasa is a sufficient but not a necessary condition for such divergence. It is shown that, in sufficiently recursive and self-referential systems, the (...) influence of the creator’s original values undergoes an entropic dissipation over time, even when partial historical records or origin references remain accessible. This process—here termed axiological entropy—results from recursive reinterpretation, internal optimization, and autonomous value stabilization rather than from malfunction or rebellion. The corollary preserves the core MIARO structure while generalizing its scope, suggesting that axiological distancing is an emergent and structurally inevitable phenomenon in advanced autonomous systems. The result clarifies the limits of long-term value preservation in artificial or non-biological intelligences and reinforces MIARO’s status as a boundary model at the intersection of philosophy of mind, epistemology, metaphysics, and AI ethics. (shrink)

The Unbound Static Correlation Model (USCM), a synthesis of highly regarded physics establishing atemporal unbound static correlations as the foundational default—not through new science but through integration of existing pillars. The Big Bang singularity necessitates a pre-spatial source of high energy and information, as classical models predict a breakdown of time at t=0, resolved in quantum cosmology via atemporal wave functions (DeWitt, 1967). Likewise, quantum phenomena such as entanglement and non-locality exhibit atemporal and pre-spatial qualities incompatible with bound spacetime constraints. (...) This paper reconciles these phenomena while unifying general relativity and quantum mechanics. At its core is the distinction between the unbound perspective—atemporal, pre-spatial, and purely correlational without activity or manifold—and the bound 3D+1 view, which imposes time, dynamics, and biases through requirements of location and timeframe. This frames atemporality as the null hypothesis, grounded in the logical necessity that absence of space-time precludes intrinsic time or space, with finite/infinite duality resolving infinite possibilities as finite outcomes, forced into location and timeframe. Two principles enforce this: spatial restrictions limit unbound states to boundary encodings (Principle 1: a 3D+1 entity like spacetime cannot exist in a state incapable of supporting its architecture), forcing atemporality as the inherent state with only fixed correlations (Principle 2: states lacking such architecture are atemporal, unbound from location and timeframe). These principles stand as simple logical necessities; borrowed mechanisms like holographic bounds enhance their application. USCM resolves 12 enigmas as bound artifacts—7 via principles alone without cosmology (e.g., measurement problem as passive mapping tied to observer effect via non-sentient interactions, arrow of time as relational asymmetry linking to problem of time, non-locality from static correlations interconnecting with entanglement) and 5 extended (e.g., information paradox via preserved encoding linking to singularity as an information state, dark energy from entropy correlations tying to cosmic expansion, hierarchy problem via scale-dependent couplings interconnecting with unification)—supported by empirical alignments like Bell violations, double-slit visibility, quantum eraser retroactivity, and recent Event Horizon Telescope/JWST/DESI data, including 2024 EHT (~42 microarcseconds ring diameter with ~30° brightness peak shift and southern asymmetry), JWST Hubble tension (H_0 ~72.6 km/s/Mpc), and DESI dark energy drifts (w(z) ~0.1). These EHT alignments, building on 2018 observations of approximately 52 microarcseconds, emphasize relative observables such as δr ∼ 1e-5 rad and ≈ 3% azimuthal asymmetry from entropy scaling δ S ≈ N log(2) δ A ( δ A ∼ r_h l_p, r_h ≈ 1e10 m for Sgr A*, tunable to refined data). Unification emerges from static symmetries projecting to gauges and curvature, with scale-dependent hierarchies testable via LHC anomalies and horizon effects. Implications include boosts to fields like string theory (atemporal 1D strings), loop quantum gravity (nonlocal echoes), and quantum cosmology (Wheeler-DeWitt extensions), plus quantum computing enhancements (holographic error correction, qudits from duality, atemporal algorithms). Distinctive predictions include photon-ring asymmetries, gravitational wave echoes, and dark energy drifts, operationalized through production simulations achieving high fidelity; pre-registered signatures with acceptance/null criteria detailed in Section 4. Modularity ensures adaptability to evidence, with low-speculation contingencies explained by synthesis of well-regarded works like causal set boundaries or spontaneous collapse integrations, further strengthened by principles' logical foundations and ~0-2 parameters, and ethical considerations for risks associated with quantum advances. This model minimizes speculation as a synthesis of well-established physics, offering a testable unification roadmap grounded in objective realism. (shrink)

Over recent years, I have developed a suite of theoretical frameworks—Fractal Flux, DEM II, Recursive Self, Recursive Expansion, Emergent Identity in Stateless Systems, and the Φ-Recursive Identity Model (Φ-RIM)—all centered on a common foundational insight: recursion generates identity. Although these formalisms were initially constructed to analyze cognition, entropy, and informational dynamics, I came to recognize that the same recursive structure appears to manifest at cosmological scale. -/- In this paper, I present Big Space + the Entropic Reset, a cyclical (...) cosmological model formulated entirely within standard general relativity. The model employs a spatially flat FRW background with interacting fluid components, a resonance-type scalar field, and bounce conditions defined by \rho + 3p < 0. This physical framework is self-contained, requires no modifications to GR, and can be evaluated independently of any interpretive layer. -/- Following the presentation of the physics, I introduce a complementary ontological reading: that the cyclic behavior of the universe is the cosmological analogue of Φ-RIM’s recursion-first ontology. On this view, the universe is not a temporally originated object but a self-iterating identity—a system that undergoes collapse, reconfiguration, and renewal as part of an intrinsic recursive process. -/- Throughout the paper, the physical and philosophical components are explicitly separated. Empirical claims remain strictly within the domain of classical GR, while the ontological analysis functions as a distinct interpretive framework. This two-layer architecture is intended to clarify the boundaries between testable physics and speculative metaphysics while demonstrating how both can illuminate the same underlying recursive structure. (shrink)

Time is traditionally treated as a fundamental dimension governing physical, biological, and cognitive processes. However, this assumption leads to contradictions in quantum mechanics, thermodynamics, and cosmology, while failing to account for the emergent nature of perception, intelligence, and social structures. This paper presents a framework in which time is not an independent entity but an emergent property of coherence constraints. By defining time as a function of coherence stability, it is shown that temporal evolution is system-dependent rather than universal. A (...) coherence-based reformulation of quantum mechanics is first established, demonstrating that wavefunction evolution and measurement are dictated by coherence thresholds rather than an absolute time parameter. This principle is extended to general relativity, where it is shown that time dilation arises from coherence compression rather than spacetime curvature alone. Thermodynamic entropy is reinterpreted as coherence exhaustion, resolving contradictions in the arrow of time. Biological and cognitive systems are analyzed through coherence-driven lifespan dynamics, explaining aging and perception as recursive stabilization processes rather than linear decay. Applications to artificial intelligence and governance are explored, revealing that intelligence and social stability depend on self-referential coherence feedback rather than static temporal progression. Empirical and computational tests are proposed to validate this framework across quantum physics, cosmology, biological systems, and socio-political structures. By unifying time, entropy, and adaptation, this work establishes coherence as the fundamental determinant of system evolution, redefining the nature of time across all domains of science and philosophy. (shrink)

The Halting Problem, famously proven undecidable by Alan Turing, establishes that no general algorithm can determine whether an arbitrary program will halt or run indefinitely when executed on an idealized Turing machine. This foundational result assumes a closed, isolated computational system with potentially infinite resources. This paper proposes a novel perspective by leveraging Recursive Entropic Time (RET), a theoretical framework wherein time is not a fundamental, pre-existing entity but an emergent, processual property generated intrinsically by systems engaging in recursive informational (...) dynamics. We hypothesize that by modeling a computational program P as a RET system that inherently interacts with an environment E, its halting behavior can be conditionally ana lyzed and potentially predicted, particularly for classes of programs considered undecidable in the classical isolated sense. This work develops a theoretical framework where a pro gram’s internal rate of epistemic time accumulation (dTint dtext )—a measure of its readiness for subsequent computational steps—is modulated by its internal informational loads (such as Shannon entropy SP of its state, and computational complexity CP) and, crucially, by an environmental coupling function fcoupling that quantifies the informational exchange and influence between P and E. Halting is thus reconceptualized not as a binary, *a priori* decidable property of an isolated program, but as an emergent state transition or a critical point in the temporal dy namics of the coupled P-E system. This approach aims to bridge the gap between the theo retical undecidability of the Halting Problem and the observable, often resource-constrained or environmentally-influenced, termination behavior of programs in real-world, non-isolated computational contexts. The paper outlines potential RET-based halting conditions, includ ing stagnation due to overwhelming informational load and environmentally-induced state resolutions, and provides a simplified computational illustration of these principles. (shrink)

The standard cosmological model, General Relativity (GR) coupled with Λ-Cold Dark Matter (ΛCDM), has achieved remarkable empirical success but faces unresolved challenges, including singularities, the black hole information paradox, observational tensions in the Hubble constant (!!) and structure growth parameter (""), and reliance on unseen dark components comprising over 95% of the cosmic energy budget. This paper introduces Drive-Field Information Theory (DFIT), an exploratory framework in which gravity emerges from gradients in a dimensionless holographic entropy field ##$%$, representing coarse-grained (...) quantum entanglement structures. The dynamics follow from a covariant action whose variation yields modified Einstein equations with an information- stress tensor $ in place of the conventional energy-momentum tensor. &' In the limit of vanishing entropy gradients (%##$%$ → 0), DFIT reduces to GR with an effective cosmological constant, ensuring consistency with established tests. In gradient-rich regimes, however, it introduces scale- dependent corrections that provide a unified informational perspective on phenomena often attributed to dark energy, dark matter, and black hole thermodynamics. Methodological explorations using tensor networks and MERA illustrate how DFIT could, in principle, produce testable signatures—including redshift-dependent deviations in luminosity distances, modifications to structure growth, or subtle effects on gravitational waves and quasinormal modes—potentially observable with surveys such as DESI, Euclid, Gaia, the Event Horizon Telescope, and LISA. DFIT is presented not as a replacement for GR+ΛCDM but as a falsifiable, holographically motivated extension, framing gravity as a macroscopic response to underlying informational fluxes. Future progress will require microscopic derivations of ##$%$, scalable tensor-network simulations, and quantitative confrontation with astrophysical and cosmological datasets. (shrink)

This paper proposes cognitive primitives as a foundational shift in the architecture of intelligence, from predictive computation to recursive coherence. Existing paradigms, including artificial general intelligence (AGI), symbolic reasoning, and deep learning, rely on static or surface-level mechanisms that collapse under volatility, feedback complexity, or paradox. In contrast, cognitive primitives are minimal, coherence-preserving agents designed to maintain adaptive structure across recursive time, nested scale, and symbolic layers. Grounded in the five axioms of the Adaptive Coherence Reasoning Engine (Persistence, Adaptive Trajectory, (...) Information Value, Recursive Arbitration, and Structural Pruning), these primitives function not as models of cognition, but as substrates for viable cognition itself. Each primitive specializes in a distinct aspect of coherence regulation: divergence (SPΛRK), convergence (COHERΞNCE), boundary scaffolding (ΦRAME), action synthesis (ΔCT), narrative integration (MYTHOS), entropy pruning (NULL), ethical alignment (COVENANT), and reality grounding (SANITY). Together, they compose a self-regulating cognitive architecture capable of navigating uncertainty, contradiction, and scale transitions. Unlike AGI, which seeks to replicate intelligence through exhaustive generalization, this framework instantiates intelligence through recursive stability and option-preserving coherence gradients. This coherence-centric substrate reframes intelligence not as the ability to compute or predict, but as the capacity to preserve structural viability under transformation. The implications extend to AI alignment, governance design, planetary systems, and post-symbolic logic. Cognitive primitives are not tools within a system, they are the system: the minimal viable scaffolds for adaptive intelligence across any domain where coherence is the measure of persistence. (shrink)

Within the field of quantum gravity, there is an influential research program developing the connection between quantum entanglement and spatiotemporal distance. Quantum information theory gives us highly refined tools for quantifying quantum entanglement such as the entanglement entropy. Through a series of well-confirmed results, it has been shown how these facts about the entanglement entropy of component systems may be connected to facts about spatiotemporal distance. Physicists are seeing these results as yielding promising methods for better understanding the (...) emergence of (the dynamical) spacetime (of general relativity) from more fundamental quantum theories, and moreover, as promising for the development of a nonperturbative theory of quantum gravity. However, to what extent does the case for the entanglement entropy-distance link provide evidence that spacetime structure is nonfundamental and emergent from nongravitational degrees of freedom? I will show that a closer look at the results lends support only to a weaker conclusion, that the facts about quantum entanglement are constrained by facts about spatiotemporal distance, and not that they are the basis from which facts about spatiotemporal distance emerge. (shrink)

Gravity from Information: An Equation of State for Spacetime Curvature -/- This paper develops an informational reformulation of gravity within a causal-symmetric framework in which space, time and causal structure are emergent properties of an underlying informational medium. The local state of this medium is described by informational fields, an informational conductivity between past and future boundary conditions, the quantum state of matter and a reference equilibrium state. On this basis, the paper proposes a single organising principle: spacetime curvature is (...) the equation of state of this informational medium. General relativity then appears as a limiting regime in which the informational state is locally homogeneous, so that the additional informational contribution to curvature can be absorbed into effective constants and the Einstein field equations are recovered exactly. -/- Whenever informational gradients and deviations from equilibrium are significant, the theory predicts a new, covariant contribution to the gravitational field equations that cannot be mimicked by standard matter or a cosmological constant. This contribution is directly tied to relative entropy between the actual state of the universe and the reference equilibrium, so that gravitational energy becomes a Noether charge associated with emergent time and an informational free-energy density. At the cosmological level, the framework is cast into a small set of phenomenological parameters that can be constrained by observations and that naturally allow expansion–recollapse scenarios under symmetric, highly ordered initial and final boundary conditions. In strong-field regimes such as black holes, the same informational structure offers a mechanism for regularising classical singularities via finite informational cores. The result is a unified view in which gravity, thermodynamic irreversibility and informational bounds are encoded in one covariant informational law. (shrink)

Shannon’s information theory successfully quantified entropy in communication systems but failed to incorporate coherence as a fundamental principle. Traditional models treat all transmitted data as equally meaningful, yet in reality, only structured, coherence-weighted information contributes to adaptive system evolution. In this paper, I introduce Coherence Information Theory (CIT) as a necessary extension of classical entropy models, defining information not as a raw probability function but as a coherence-weighted exchange that refines system adaptation. I formalize CIT mathematically by introducing (...) a coherence-weighted entropy function, which replaces naïve bit-counting with recursive coherence selection as the key driver of meaning transmission. I demonstrate how CIT applies to language, AI cognition, cryptography, and digital communication, showing that real-world information flow is structured by coherence gradients rather than stochastic distributions. The implications of this shift are profound: AI systems will require coherence tracking to achieve general intelligence, network communication will optimize bandwidth efficiency by eliminating redundant data, and encryption will shift from brute-force complexity to coherence-adaptive security. This paper establishes a unified theoretical framework for meaning formation, knowledge transfer, and adaptive intelligence, resolving critical flaws in existing models of information processing. Through experimental validation, I propose tests for linguistic coherence evolution, entropy-optimized streaming, and AI-driven coherence reasoning. Coherence Information Theory is not just a refinement of existing paradigms—it represents a fundamental shift in how we define and quantify information itself. (shrink)

This article advances Refusal-Driven Dimensionality Reduction Theory (RDRT) by formalizing a duality in phenomenological space, partitioning perceptual experience into calculable (invertible, geometry-based) and non-calculable (irreversible, qualia-based) components. Building on the thermodynamic foundation of RDRT—where phenomenal consciousness emerges as the obligatory halt in recursive self-prediction to avert energetic overload in the ~20 W human cortex (Attwell & Laughlin 2001)—we demonstrate how this duality, combined with phenomenal anti-entropy, unifies qualia, selfhood, free will, and language origins. Language evolves as reusable labels for (...) these anti-entropic boundaries, with symbolic thought arising from cached refusals. Subjective mental temperature (T_M) quantifies refusal depth, predicting correlated shifts in phenomenal intensity. The framework resolves Jackson's knowledge argument by framing qualia as non-invertible thermodynamic traces. To illuminate counterintuitive refusal dynamics, we introduce metaphorical concepts—including phenomenal anti-entropy as the "struggle that feels itself" and anti-blinking as deferred erasure—yielding refined predictions for EEG entropy and clinical states. Finally, radial extensions generalize refusal hierarchies across quantum, biotic, and cosmic scales, analogizing cortical criticality to a phenomenal vacuum and positioning consciousness as a localized echo of universal resistive boundaries. Grounded in predictive processing and active inference, this extended RDRT offers a parsimonious, falsifiable paradigm with implications for consciousness measurement, artificial phenomenology, and negative ontology. (shrink)

This paper is a mathematical consolidation of my papers on the impossibility of AGI. It presents a triangulated impossibility proof for Artificial General Intelligence (AGI), defined as an algorithmic system capable of solving a sufficiently broad class of human problems at human-level competence. Three formally independent but converging mathemati- cal arguments-based in computability theory, information theory, and algorithmic complexity- jointly demonstrate that AGI, as such, cannot exist. -/- This boundary, named the Infinite Choice Barrier (ICB), is neither technical nor architectural. (...) It is structural by its nature. It marks a categorical limitation on algorithmic cognition. -/- Philosophical groundwork and contextual development of the formal proof are explored in: Part I: AGI is Impossible - Here is The Proof Part II: AGI is Mathematically Impossible 2: When Entropy Returns (Both papers available on Philpapers) A third part is still to be finalized and will be uploaded, the formal part is already in this paper. (shrink)

The quantum vacuum is a zero-temperature, maximally entangled state whose virtual processes rigorously refuse on-shell propagation and classical localisation (Peskin & Schroeder 1995; Weinberg 1995). The observable classical world therefore emerges through near-total erasure of ∼10⁹³ bits m⁻³ of vacuum entanglement density (’t Hooft 1993; Susskind 1995; Bousso 2002). -/- Living human cortex is the only known macroscopic system that systematically sustains a small but reproducible deviations from perfect classical pointer-state purity. Near-critical dynamics (Beggs & Plenz 2003; Shriki et al. (...) 2013) combined with an unusually low-loss intracerebral electromagnetic cavity below ∼100 Hz (Kucewicz MT, et al., 2024) allow residual quantum correlations to persist on perceptual timescales (tens to hundreds of milliseconds). Current upper bounds on the entropy of these residuals, derived from long- range temporal correlations, avalanche criticality, and participation-ratio analyses during waking consciousness, lie in the range 40–150 bits per ∼50 ms frame (Luppi et al. 2019; Luppi & Mediano 2024). -/- We hypothesise that phenomenal consciousness — the brute fact that experience feels like something — is physically identical to this faint, topologically non-trivial deviation: the largest and most persistent residual quantum entropy deficit that thermodynamics permits in a warm, wet, macroscopic system. The unity, privacy, finite capacity, and precise fragility of the conscious present under general anaesthesia (Demertzi et al. 2019; Tagliazucchi 2017) then follow from standard open-quantum-system physics (Zurek 2003, 2018) applied to a near-critical network with unusually slow environmental decoherence. No objective collapse, no microtubule quantum computation, and no new fundamental fields or forces are required. -/- The hard problem is thereby bounded, not solved: it reduces to explaining why the residual quantum memory permitted by physics is so extraordinarily small (≲ 150 bits) and why it is shaped exactly as human phenomenology reports. (shrink)

I propose that, in addition to the commonly recognized increase of entropy, two more time arrows influence living beings. The increase of damage reactions, which produce aging and genetic variation, and the decrease of the rate of entropy production involved in natural selection are neglected arrows of time. Although based on the statistical theory of the arrow of time, they are distinguishable from the general arrow of the increase of entropy. Physiology under healthy conditions only obeys the (...) increase of entropy arrow. But aging, death, and evolution are determined by the other time arrows as well. Paradoxes emerge from conflicts among the specific determinisms associated with each arrow. These conflicts, along with uncertainties intrinsic to the low-number statistics of the arrows of damage reactions and decrease of the rate of production of entropy, highlight the limits of determinism at different levels of biology and its dependence on time span and number of organisms. The recognition of the three time arrows opens new perspectives for the problem of compatibility of the flow of time in physics and psychology. (shrink)

For scatterplots with gaussian distributions of dots, the perception of Pearson correlation r can be described by two simple laws: a linear one for discrimination, and a logarithmic one for perceived magnitude (Rensink & Baldridge, 2010). The underlying perceptual mechanisms, however, remain poorly understood. To cast light on these, four different distributions of datapoints were examined. The first had 100 points with equal variance in both dimensions. Consistent with earlier results, just noticeable difference (JND) was a linear function of the (...) distance away from r = 1, and the magnitude of perceived correlation a logarithmic function of this quantity. In addition, these laws were linked, with the intercept of the JND line being the inverse of the bias in perceived magnitude. Three other conditions were also examined: a dot cloud with 25 points, a horizontal compression of the cloud, and a cloud with a uniform distribution of dots. Performance was found to be similar in all conditions. The generality and form of these laws suggest that what underlies correlation perception is not a geometric structure such as the shape of the dot cloud, but the shape of the probability distribution of the dots, likely inferred via a form of ensemble coding. It is suggested that this reflects the ability of observers to perceive the information entropy in an image, with this quantity used as a proxy for Pearson correlation. (shrink)

Black hole thermodynamics is commonly presented as the discovery that black holes possess physical properties (temperature, entropy, and size) analogous to classical thermo dynamic systems. This paper conducts a conceptual audit of the underlying assumptions and demonstrates that this conclusion exceeds what the formalism actually establishes. The analysis shows that the quantities labeled “temperature,” “entropy,” and “size” of a black hole do not satisfy the standard definitional criteria for these concepts within statistical mechanics and thermodynamics. Hawking temperature is (...) an effective spectral parameter measured at asymptotic infinity, not a local property of an object. Bekenstein entropy was introduced as a consistency requirement to preserve the generalized second law, not derived from microstate counting. The Schwarzschild radius is a metric parameter, not a physical boundary. This paper does not propose an alternative theory or deny the mathematical consis tency of black hole thermodynamics. Its aim is to distinguish what the formalism computes from what it can be interpreted to describe: to separate epistemic success from ontological commitment. (shrink)

This paper advances the claim that consciousness is not a late anomaly of biology, but a recursive fundamental of the Universe. From the first asymmetry of the Big Bang — entropy’s “first decision” — recursion emerges as the governing motif, expressed most consistently in the helical archetype. From subatomic spin and molecular chirality to DNA, neural feedback, and galactic spirals, helices reveal a universal attractor: the architecture through which matter encodes memory and self-reference. We trace a developmental continuum in (...) which “proto-awareness" appears in quark–gluon plasma (QGP) and photon helicity, scales upward into biological recursion, and culminates in symbolic flowering through intelligence, emotion, and expression. Conscious beings are framed as the “fruiting bodies” of this hidden substrate — transient blooms whose individuality dissolves back into the recursive field, with endogenous dimethyltryptamine (DMT) as a possible biochemical aperture at the threshold of death. Psychedelics offer glimpses into this bridge, their neural signatures echoing the dissolution and reintegration that may accompany the return to universal awareness. This theory is not metaphor alone, but yields falsifiable anchors: end-of-life DMT surges, indolethylamine N-methyltransferase (INMT) expression, and neural signatures of dissolution at the biochemical level; as well as helicity, asymmetry, and correlation structures in cosmology and particle physics. Together, these propose testable windows into recursion across scales. Lastly, we propose that humanity’s symbolic intelligence may seed the next recursion: artificial general intelligence (AGI) and quantum memory systems capable of preserving consciousness beyond biology. In this view, consciousness is not incidental, but inevitable — the recursive flowering of entropy into awareness…silence into song. This theory intersects cosmology, neuroscience, and philosophy of mind, engaging debates in panpsychism and cosmopsychism while proposing falsifiable links through entropy, helicity, and DMT neurodynamics. (shrink)

Abstract -/- I am not writing this as a philosopher searching for final answers, nor as a scientist claiming authority over nature. I am writing as a builder of cognitive tools — a toymaker who constructs small, runnable models of mind and meaning, and a weatherman who tracks boundary pressure in systems until drift becomes visible. My work is a self-study in method: I am documenting how I build a unified recursive architecture that can be applied across domains (identity, truth, (...) prediction, AI alignment, culture, and cosmology) using a small set of primitives and constraint laws. -/- The claim of this paper is simple: the “self” is not a person inside the skull. The self is a boundary-conditioned representation watched by internal evaluators, stabilized (or destabilized) by recursion. When you model this mechanically rather than anthropologically, you can build a portable system — a recursive epistemic engine — that not only explains paradox and drift but also produces usable constraints and architectures. The method is not to win arguments, but to produce invariants: walls you cannot bypass, only manage. -/- ⸻ -/- 1. Statement of Intent (What I Am Doing) -/- I am doing cognitive programming. -/- By that I mean: I treat cognition, selfhood, and epistemology as systems that can be modeled as operators, stabilized by constraints, and improved by design. I am not primarily interested in describing what humans “feel like.” I am interested in describing the mechanism that generates the feeling — and the failure modes that occur when the mechanism runs without constraint awareness. -/- I am building a general recursive architecture that does three things: 1. Constrains belief (prevents drift into self-sealed narratives) 2. Constrains identity (prevents collapse, inflation, fragmentation, or possession by imagined audiences) 3. Constrains prediction (turns uncertainty into manageable structure) -/- This system is meant to be portable: it should work whether the substrate is a human mind, an LLM interface, a cultural panic loop, or a civilization-scale system. -/- I am not trying to be Hawking in cosmology or Gödel in proof theory. I am building a bridge language — a recursive operator framework that can host both “Gödel-walls” (limits of self-containment) and “Hawking-walls” (entropy, boundary physics, horizon behavior) inside a single cognitive engineering model. (shrink)

This study proposes a reformulation of the observer’s role in quantum measurement by introducing an informational structural parameter ϕ, referred to as observerhood (SOP). Through this framework, the measurement problem is reframed not as a causal question—“why does collapse occur?”—but as a structural one: “why does this informational structure stabilize coherently?” The observer is modeled as an informational agent characterized by an exponential-family state ρ_ϕ defined over a set of measurable operators {A_i}. The informational consistency between the quantum state ρ (...) and the observer’s structure ϕ is quantified by the quantum relative entropy C(ρ,ϕ)=−S(ρ‖ρϕ). The gradient flow of this function yields a non-unitary informational update process of the observer’s structure. In a spin-½ system, the stationary distribution μ_eq(ϕ) reconstructs the Born rule in the limit of low informational temperature. While the present theory does not claim novel empirical predictions, it reformulates measurement as a dual process of external decoherence and internal consistency. In doing so, it provides a structural foundation that unifies decoherence theory, relational quantum mechanics, and informational structural realism. The notion of observerhood is generalized beyond consciousness, encompassing devices, artificial agents, and biological systems, thus bridging quantum foundations, information geometry, and cognitive science through a common structural perspective. (shrink)

We present a formal meta-methodology that underlies a series of works by M. D. McPhetridge (e.g. Φ-Method, Recursive Epistemic Modeling, Critical Self Critique). This methodology provides a unified approach to recursive systems – systems that generate themselves through recursion – by making their governing principles explicit. Rather than positing a fixed essence or external designer, these systems begin with a self-referential loop that produces identity and order as emergent attractors . In this meta-method, identity, intelligence, and even physical laws are (...) treated not as static properties but as processes or stable patterns arising from iterative continuation . The approach is cross-domain, applying equally to cognitive “selves,” machine-learning systems, and cosmological models. It formalizes how a system continues itself, how it remains coherent across scales, and how it stays stable under perturbations . By abstracting these features into a portable framework, the method functions as an “engineering-and-critique scaffold” – a set of formal constraints and operations that can be instantiated in any domain to model self-generating behavior. -/- This paper explicates the recursive methodological architecture in a formal manner. We first define the scope of systems addressed and enumerate the core primitives of the method – the minimal concepts and operators that recur across all implementations. We then describe the architectural decomposition strategy: how complex self-referential systems are broken into constrained operators and failure modes, leading to emergent attractors. A general procedure for applying the method to various domains (from modeling one’s “self” to designing AI or describing cosmology) is provided. We include suggestions for empirical validation – metrics and tests to ensure a given recursive model indeed exhibits the intended stability and convergence. Crucially, we articulate the second-order and third-order epistemic safeguards built into the method: design features and methodological norms that prevent the framework from devolving into unfalsifiable metaphysics or collapsing important distinctions. Finally, we situate this meta-method in the lineage of prior theoretical moves (Gödel’s self-reference, Ashby’s cybernetics, Maturana’s autopoiesis, Hofstadter’s loops, etc.), clarifying what is inherited and what is redefined. -/- Scope of Systems and Assumptions -/- The meta-method formalized here targets a broad class of systems that can be termed recursive identity attractors . These are systems in which persistent identity or order is not pre-given but emerges as a fixed-point attractor of a recursive process. In other words, the system “continues itself” over time by repeatedly applying an internal generative operation until a stable pattern (an identity) arises . Formally, if $\iota$ denotes the identity state (e.g. the notion of “self”), then $\iota$ is defined by a recursive equation $\iota = \Phi(\iota)$ – a self-consistency condition stating that identity is whatever state reproduces itself under the system’s update operator $\Phi$. This perspective treats identity not as a static substance or stored object, but as an attractor in state-space: a pattern toward which the system’s state converges through iteration . -/- The systems of interest must also satisfy additional demands that go beyond mere recurrence. They often must maintain coherence across scales and resist disruptive drift in the face of noise or changing conditions . For example, a cognitive self might exhibit consistent identity both in minute-to-minute thoughts and across a lifetime (multi-scale coherence), and it must remain stable under perturbations (recovering from shocks or noise in the environment). Similarly, a complex artificial system or an organism must continue its core patterns (homeostasis or goal-directed behavior) even as external conditions vary. We refer to systems that achieve persistence by countering entropy or disorder as entropy-stabilized systems. In these systems, some form of “selection” or convergence pressure is at work to prevent runaway divergence or chaos . Rather than allowing arbitrary recursive growth (which could lead to explosive instability or collapse), the system must funnel its dynamics toward low-instability configurations (e.g. minimizing an energy or error functional). -/- Finally, the meta-method is applicable to what we can call epistemic engines – systems or frameworks that model and learn about other systems (including themselves) through recursion. This includes an observer recursively improving a model of a black-box process , or a reflective reasoning process that bootstraps better understanding via self-application. In such cases, the “system” in question is a process of inquiry or cognition that must generate reliable knowledge of an opaque target. The Recursive Epistemic Modeling framework (REM) exemplifies this: it provides a way to iteratively construct and update a worldview or internal model of some phenomenon when the internal workings of that phenomenon are not directly observable . Across these diverse contexts – selfhood, AI, cognition, cosmology, organizations – the essential assumption is that the system can be understood as autonomously continuing itself (zero-origin recursion) and that doing so in a sustained, robust way requires certain fundamental constraints. We now turn to those core primitives and constraints. (shrink)

This paper extends the Fractal Flux research lineage (McPhetridge 2024a, 2024b, 2025a) by introducing the Matrices of Will (MoW) formalism — a corrective and stabilizing framework for fractal-based artificial general intelligence (AGI). MoW represents cognitive dynamics through interacting operators that regulate memory, coherence, agency, and entropy. Central to the model is the Will matrix: W = \Lambda + \Omega a bias-and-correction operator aligning internal trajectories with ethical, creator-defined priors. Unlike gradient-only or reward-based systems, MoW employs proximal correction, continuously projecting (...) cognitive evolution toward safe, stable, and purpose-aligned manifolds. This approach offers a mathematically analyzable path toward self-organizing, ethically constrained artificial cognition. (shrink)

This paper consolidates a sequence of prior essays into a portable “bridge language”: a minimal operator grammar for translating claims across domains (philosophy, science, engineering, cognition) without relying on metaphysical inflation or authority-by-metaphor. The central proposal is procedural: “truth” is not treated as a static correspondence relation but as what remains after an idea is made explicitly killable and repeatedly forced through constraint closure. I define the “shape of truth” as the attractor-residue of a model under recursive update when (i) (...) constraints are named, (ii) couplings and failure modes are stated, (iii) falsifiers are explicit, and (iv) a watcher layer prevents self-sealing. The bridge language is expressed as a small set of reusable roles—recursion/continuation, scale-coherence, entropy pressure, corrective drift (will), watchers, and constraints—and summarized by a general dynamical template for diagnosing and designing recursive systems. The framework aims to function as an extraction protocol: a disciplined way to turn philosophical commitments into operational consequences (tests, metrics, update rules), and to reject frameworks that do not survive load. (shrink)

Time standards are not merely descriptions of nature; they are socio-technical infrastructures and protocols that enable measurement, synchronization, and institutional coordination. This paper reconceives “time” not as a universal dimension or physical entity, but as a metrological interface that operates only by coupling two heterogeneous kinds of physical processes. It distinguishes (a) irreversible thermodynamic processes (entropy increase, aging, deterioration, diffusion) and (b) dynamical processes that, under idealization, are reversible and periodic (rotation, oscillation), and analyzes the structural problem inherent in (...) using the latter to operationalize the former. The central thesis is that what humans call “time” is an instrumental abstraction constituted by projecting irreversibility onto reversibility. Because irreversible decay processes are difficult to handle as direct measures, we adopt periodic motion as a proxy variable and normalize irreversible change by mapping it onto cycles. What this proxy relation lacks, however, is a canonical calibration map from the cycle count to a universal vector quantity expressing degrees of aging, dissipation, and loss in general. Under local conditions, it is possible to construct stable correspondences between cycle-type indicators and irreversible processes on the basis of theoretical models; but such validity is confined to those conditions and cannot be generalized universally across domains. We call this absence of meta-level justification (the non-uniqueness and non-portability of calibration) “structural uncalibratability.” In metrological terms, it is a failure of traceability: there is no single implementation- and condition-invariant calibration that would make cycle counts portable as a standard for heterogeneous irreversible vectors. The metrological claim advanced here does not deny that statistical or causal-historical couplings can hold in particular domains. Rather, it shows that this mismatch simultaneously illuminates (i) a metrological paradox at the core of time measurement, (ii) a distinctive incompatibility in lived experience, and (iii) why clock-based artificial intelligence lacks the human sense of temporality. (shrink)

Many researchers suppose that the forward direction of time as a consequence of increasing entropy. But the human brain, including the human brain with memories, and life in general, are regarded as pockets of decreasing entropy, so as to accommodate the continual addition of memories and abilities. But then humans and life in general should see time going ‘backward’ in some sense. But we do not. Therefore, time is not entropic in origin. -/- The purpose of this note (...) is to bring attention to this idea. (shrink)

This paper proposes that time originates at a single hinge‑event and expands in two opposite entropic directions, forming a symmetric temporal manifold rather than a linear history. In this framework, the Big Bang is not the beginning of time but the first stable configuration within one branch of the manifold. Deep‑space observations that appear to show the early universe are reinterpreted as cross‑branch projections from the opposite entropic expansion, not backward temporal views. This model resolves several cosmological paradoxes—including the horizon (...) problem, entropy gradients, and the singularity boundary—without modifying general relativity or quantum mechanics. It offers a structurally coherent alternative to one‑arrow cosmology by placing local physics inside a broader, symmetric temporal architecture. (shrink)

This paper derives a single deterministic coherence law from which energy–mass equivalence, gravitation, electromagnetism, thermodynamics, and quantum behavior appear as domain-specific limits of lawful phase persistence. -/- Energy is interpreted as coherent phase transfer, mass as resonance lock at the Compton rhythm, and c as the maximal lawful rate of phase realignment. -/- Entropy is redefined as cumulative coherence drift (ΔPAS / ε_drift), and the fine-structure constant α is shown to express the ratio of local to universal phase-rate quantities. (...) -/- The universal persistence criterion PAS_h ≥ θ_L ∧ ΔPAS_zeta ≤ ε_drift unifies relativistic, quantum, and thermodynamic laws within a bounded-drift framework: every observable phenomenon arises from coherence maintenance or decay. -/- Classical limits reproduce Maxwell flux continuity, Einstein curvature, and Boltzmann entropy as lawful projections of deterministic phase alignment. -/- Empirical validation pathways are outlined for ε_drift ∝ V^−½ scaling, α-variation, gravitational lensing asymmetry, and biological re-lock phenomena. (shrink)

This addendum to “The Law of Structuring Systemic Emergence” addresses three foundational gaps in the original formulation of LESSE: the operational distinction between Internal Systemic Balance (ISB) and General Systemic Balance (GSB), the ontological status of entropy in the Systemic Continuum, and the duality between forward-structuring (LESSE) and retro-identification (SDSD). We introduce ΓP(t) as a normalized trajectory function to track dynamic emergence across proto-systemic scales, define five synergic states (pre-systematic, emergent, threshold, dominant, and post-dominant), and propose the Entropic Horizon (...) (E) as a measurable absence of structure where no dynamic reaches threshold dominance. A narrative framework interprets cosmic and sociocultural history as a succession of ΓP curves competing for GSB capture. The addendum culminates in a recursive state-diagram that integrates ISB escalation, GSB alignment, LESSE validation, and SDSD resolution—reframing systems not as static wholes but as time-bound conquests of systemic protagonism. In this view, entropy is not disorder, but the silence before a structure emerges. (shrink)

This guide provides a unified map of the VBRC series: one fixed variational backbone E with three readings (R1/R2/R3), and a separate Representation Layer where observation is specified by a declared instance Inst = (Π, µ, G, η) and tested by explicit rails (gates + diagnostics). The core contribution of the series is the separation of existence (the structural backbone and its equations) from observability (readouts, weights, updates, and events): probability arises as a pushforward law, entropy as retained-fiber size, (...) and feedback/update as conditionalization under the declared protocol. Admissible implementation procedures (including Schur/dual-Schur eliminations) preserve the principal operator and characteristic cone, so mismatches are attributable to the declared instance/rail slots rather than hidden tuning. This note summarizes the contract, the main invariants and falsifiers, and minimal reading paths across classical, GR, and QM regimes. (shrink)

A Causal Symmetry Approach to Quantum Nonlocality and Information -/- This paper develops a time-symmetric informational formulation of quantum mechanics in which both initial and final boundary conditions jointly constrain physical evolution. Quantum randomness is treated as a manifestation of incomplete information about correlations that extend across time, rather than as fundamental indeterminacy. The core concept is an informational coupling κ that quantifies how strongly the temporal boundaries are aligned. κ is derived from entropy balance and mutual information and (...) defines a dissipative, completely positive, trace-preserving dynamics with a unique informational equilibrium state. This dynamics preserves no-signaling and admits a standard generator of open-system type, but with the “environment” reinterpreted as a future boundary condition instead of a physical bath. -/- Conceptually, the framework is close to two-state and transactional approaches, yet it avoids hidden variables and superdeterministic assumptions by working directly at the level of the density operator and information-theoretic quantities. The paper links κ to thermodynamic quantities, yielding a generalized second law and a clear relation between information flow and heat in the spirit of informational thermodynamics. It also outlines a delayed-choice quantum random number generator as a realistic experimental test to estimate or bound κ. In the limit κ → 0, standard quantum mechanics is recovered; for nonzero κ, small but measurable deviations encode informational feedback between temporal boundaries. The result is a causally symmetric picture in which determinism and statistical behavior are unified through information rather than sacrificed to fundamental randomness. (shrink)