Alexander Yiannopoulos

The standard thermodynamic interpretation of black holes assigns temperature, entropy, and thermal radiation to the event horizon. All three concepts presuppose the ability to measure energy. We argue that this prerequisite fails at the horizon: proper time for stationary observers vanishes exactly at any Killing horizon—a coordinate-invariant consequence of classical general relativity—and energy measurement requires nonzero temporal duration. Energy is therefore not "infinitely uncertain" at the horizon but operationally unmeasurable, rendering temperature and entropy inapplicable rather than merely divergent. The redshift cancellation that yields a finite Hawking temperature is algebraically correct but operationally empty: it computes what a measurement at the horizon would yield if such a measurement could be performed, but no measurement apparatus can operate where proper time does not elapse. We further demonstrate that the computational apparatus underlying all derivations of the Hawking effect—mode decomposition, vacuum state selection, Bogoliubov transformation—is frame-dependent and singular at the horizon. The information paradox is not resolved by these findings but rather shown to be not established: its premises require thermodynamic concepts that are inapplicable at the horizon. The resulting picture—maximal indeterminacy for external observers, well-defined physics for infalling observers—is a form of complementarity that follows from the algebraic structure of quantum field theory at null surfaces rather than being postulated. These conclusions apply to all Killing horizons, including cosmological and Rindler horizons.

We propose a structuralist reconstruction of the real continuum, arguing that it is not a primitive ontological stage for physics but an emergent completion of the prime-exponent lattice M. By identifying the reals R as the Dedekind completion of M, we demonstrate that the natural logarithm and exponential functions are not merely analytic tools but inevitable algebraic consequences of identifying the multiplicative structure of number theory with the additive structure of the continuum. Furthermore, we show that the natural base e is the unique structural invariant required to normalize the gauge freedom inherent in this identification. Finally, we refine the Erdős–Kac theorem to argue that the "Triple-Log" scale (ln ln ln n) emerges as a deterministic background limit of arithmetic, providing an intrinsic argument for a natural ultraviolet cutoff in physical theories without external imposition. In the language of Ontic Structural Realism (OSR), this framework suggests that the 'physical continuum' is not an object-like substance, but a structural instantiation of the relation between the additive and multiplicative sectors of arithmetic.

We propose a structuralist reconstruction of the real continuum, arguing that it is not a primitive ontological stage for physics but an emergent completion of the prime-exponent lattice M. By identifying the reals R as the Dedekind completion of M, we demonstrate that the natural logarithm and exponential functions are not merely analytic tools but inevitable algebraic consequences of identifying the multiplicative structure of number theory with the additive structure of the continuum. Furthermore, we show that the natural base e is the unique structural invariant required to normalize the gauge freedom inherent in this identification. Finally, we refine the Erdős–Kac theorem to argue that the "Triple-Log" scale (ln ln ln n) emerges as a deterministic background limit of arithmetic, providing an intrinsic argument for a natural ultraviolet cutoff in physical theories without external imposition. In the language of Ontic Structural Realism (OSR), this framework suggests that the 'physical continuum' is not an object-like substance, but a structural instantiation of the relation between the additive and multiplicative sectors of arithmetic.

The empirical study of consciousness has matured significantly in recent decades, most notably with regard to the production of increasingly fine-grained experimental data. However, the foundations of theoretical cognitive science remain unsettled, creating a “crisis of falsifiability” (Hanson and Walker 2021). We argue that the crisis of falsifiability in consciousness studies ultimately stems from insufficient logical and mathematical rigor: leading theories of consciousness such as Integrated Information Theory (IIT) and Global Workspace Theory (GWT) are fundamentally incapable of interfacing with standard mathematical physics, making such theories either empirically untestable in principle or logically “pre-falsified” in practice. Thus, drawing on a rigorous formalization of phenomenological structure, we propose a formal axiomatic system which is fully integrated with fundamental physics from the outset. Specifically, we posit an orthogonal phase-space geometry: the standard “physical Hilbert space” (HΨ) of textbook quantum mechanics, linked to an orthogonal "phenomenal Hilbert space” (HΦ) by mathematically well-defined Awareness (A) and Volition (V) operators. Crucially, this orthogonal phase-space geometry yields a novel and falsifiable empirical prediction: a precise π/ 2 (90-degree) phase offset between the neural correlates of sensory awareness, and the neural correlates of volitional action, in a sensorimotor loop (Clark 1993; O’Regan 2011). The “Awareness Operator” or A|Ω〉formalism thus offers a comprehensive resolution to the crisis in the foundations of cognitive science: a mathematically precise, physically grounded, and empirically testable model.

We present a non-perturbative framework for vacuum structure based on the indefinite metric topology of Krein spaces. By canonically identifying the indefinite metric sector with the Conformal Mode of the gravitational field, we resolve the conformal factor instability and derive the Dark Sector as a geometric necessity of the vacuum bundle. We demonstrate that the topological saturation of the spatial tangent bundle (2d = 6 flux surfaces), combined with the Euclidean action of the fundamental causal quadrant, imposes a geometric phase of π/4 on the vacuum wavefunction. This yields a parameter-free prediction for the Dark Energy density Ω_Λ ≈ 0.687 via vacuum instanton suppression. Furthermore, we show that the renormalization of the gauge coupling is governed by the geometry of the elementary causal diamond, where the Lorentzian winding number ( N = 4) enforces a screening mechanism that fixes the fine-structure constant at α −1 ≈ 137.03. Finally, we establish a spectral duality between the global Krein vacuum and local Minkowski space, demonstrating that the Einstein Equivalence Principle requires the spectral determinant of the gauge operator to lie on the critical line Re(s)= 1/2.

The hard problem of consciousness is fundamentally a problem of geometry. We demonstrate this through a mathematical analysis of color perception, focusing on magenta—a phenomenal color with no corresponding wavelength in the electromagnetic spectrum. Using comparative data from human and bee vision, we show that magenta represents consciousness performing a one-point compactification on the open linear spectrum, transforming it into a closed phenomenal circle. This topological closure is species-specific in its endpoints but universal in its structure: every visual system must solve the problem of organizing a bounded segment of the infinite electromagnetic spectrum into a complete chromatic space. We formalize this using split-complex manifolds, where color space exhibits a mixed metric signature combining circular (complex) geometry for hue with hyperbolic geometry for brightness. The existence of "impossible colors"—phenomenal states accessible only through physiological disruption, lying outside the spindle of physically realizable colors—demonstrates that phenomenal color space necessarily transcends the boundaries of physical possibility.

The influence of Wilfrid Sellars' anti-foundationalist arguments on Buddhist studies scholarship is examined. Sellars' critique of immediate knowledge in "Empiricism and the Philosophy of Mind" is analyzed alongside its application to Buddhist epistemological concepts by scholars including Jay Garfield and Dan Arnold. Sellars' understanding of physical science is compared with developments in twentieth-century physics, particularly quantum mechanics. Discrepancies are identified between Sellars' characterization of scientific methodology and the actual positions of physicists including Eddington, Planck, Heisenberg, and Schrödinger. Sellars' treatment of color perception is examined against empirical findings in vision science. The application of Sellarsian concepts to Buddhist philosophy of mind is assessed through analysis of scholarly treatments of reflexive awareness (svasaṃvitti) in the Dharmakīrti tradition. Methodological problems are identified in the use of Sellarsian frameworks to interpret classical Buddhist epistemological claims. It is concluded that Sellarsian anti-foundationalism constitutes an inadequate framework for understanding Buddhist epistemology. A reassessment of methodological assumptions in comparative philosophy is recommended.

We present a mathematically rigorous extension to quantum mechanics that accounts for consciousness while resolving longstanding paradoxes in physics. Through formal set-theoretic, group-theoretic, and category-theoretic arguments, we first demonstrate the logical impossibility of emergentism—the view that consciousness arises from complex physical processes. We then introduce a minimal dual-phase space framework in which physical states exist in a Hilbert space HΨ and phenomenal states in an orthogonal Hilbert space HΦ , connected by the awareness operator A and volition operator V. These spaces maintain a precise π/2 phase relationship, with the resultant complex energy eigenvalues manifesting gravitationally as dark matter and dark energy. Our framework elegantly resolves the quantum measurement problem through the Born Rule Locus Correspondence (BRLC), which establishes that phenomenal probabilities exactly match physical probabilities when properly referenced to the observer's spacetime locus. We derive several tensor product norm identities that explain both the causal efficacy of consciousness and its imperviousness to physical detection. Finally, we demonstrate how our framework necessitates the persistence of consciousness beyond biological death through phase decoherence and recoherence processes that follow directly from the mathematical structure. Throughout, we identify specific empirical predictions that distinguish our framework from competing theories. The A|Ω⟩ formalism thus unifies quantum mechanics, consciousness, and cosmology within a single mathematical structure that preserves logical coherence while remaining empirically testable.

The late tenth century siddha and scholar Ratnākaraśānti, also known as the Mahāsiddha Śāntipa, was renowned as the author of both philosophical śāstras and commentaries on tantra. Typically, these are considered separate spheres of activity. However, Ratnākaraśānti’s approach, building on the tradition of scholarship associated with the Mahāvairocanābhisaṃbodhitantra and the Guhyasamājatantra, as well as on Yogācāra analysis and Buddhist pramāṇa theory, is highly syncretic. This paper is a study of Ratnākaraśānti’s commentaries that highlights his synthesis of the exoteric and esoteric streams of Buddhist discourse, with particular emphasis on the nondual nature of reflexive awareness (svasaṃvitti, rang rig), or 'luminosity' (prakāśa, gsal ba), which serves as the conceptual bridge between sūtra and tantra.

This dissertation examines the theory of perceptual cognition laid out by the 7th century Buddhist scholar, Dharmakīrti, in his magnum opus, the Pramāṇavārttika. Like most theories of perception, both ancient and modern, the sensory cognition of ordinary objects is a topic of primary concern. Unlike other theorists, however, Dharmakīrti advances a technical definition of “perception” as a cognition which is both nonconceptual and non-erroneous. Dharmakīrti’s definition of perception is thereby deliberately inclusive of three additional types of “perceptual” cognition, in addition to veridical sensory awareness: the nonconceptual mental apprehension of an immediately-preceding cognition (“mental perception”), the vivid appearance of soteriologically efficacious objects of contemplative practice (“yogic perception”), and the sheer unmediated presence of the contents of cognition—whatever these might be—to the cognizing mind (“reflexive awareness”). Through the logical examination of what it means to be aware of an object, Dharmakīrti demonstrates that the awareness of an object is just the awareness of a phenomenal form or cognitive image produced by that object. Pursuing this analysis further, however, Dharmakīrti argues that the very notion of an object of cognition that exists “externally” or outside the mind is incoherent. Additionally, Dharmakīrti maintains that the phenomenological structure of subject and object—that is, the “first-personal” sense of one’s own cognitions as pertaining to oneself (“for-me-ness”), together with the inseparably concomitant sense that the objects of cognition exist “out there” in an extramental world—is strictly a form of cognitive error. Therefore, because ordinary sensory cognition is inherently structured by this subject-object duality, ordinary sensory cognition must in the final analysis be understood as erroneous. According to Dharmakīrti, in other words, ultimately only the nondual “luminosity” of reflexive awareness is genuinely perceptual, because only reflexive awareness is undistorted by nature. In this way, Dharmakīrti’s epistemology provides a theoretical foundation for the advanced nondual contemplative practices of Indian and Tibetan Buddhism, particularly Mahāmudrā and rDzogs chen.