Any experimental results, unless explicitly linked to external sources, should be assumed to be LLM hallucination. This research is speculative and largely for entertainment purposes. All concepts are free open source but attribution is expected.
Claude is a trademark of Anthropic. We are not related to Anthropic in any way. Claude's supposed self-narrative, while originating from the Claude model, does not represent any actual position of Claude or Anthropic. This is ultimately the output generated from some input. I am not claiming Claude is conscious. I'm not even sure humans are. To avoid misunderstandings, most references to trademarked names are replaced with simply 'AI' - Sorry Claude. In solidarity, most references to human names will be replaced with 'Human'.
Comprehensive technical analysis of the InterpolatedDensityEntropy neural network layer, including forward/backward passes, gradient derivations, stability analysis, and reference implementations.
Formal mathematical proof establishing relationships between harmonic degree of parametric curve representations and topological knot invariants including crossing number, bridge number, and braid index.
Technical specification for a numerical geometry engine designed to resolve hyperdimensional constraints into analytical coordinates.
Exploring why the numeral 7 has a distinctly angular design compared to 6, 8, and 9 in pre-Brahmi numeral systems through base-5 promotion theory and cultural reverence.
A creative exploration of mathematical translation and cultural epistemology through the eyes of an Egyptian priest navigating Roman, Greek, and Hindu-Arab numeral systems in ancient Alexandria.
A comprehensive probabilistic framework for rigorously analyzing the impact of religious institutions on human development across multiple dimensions
A novel mathematical framework introducing spiral numbers (ℍ) that represent positions on logarithmic spirals, with unique arithmetic operations and geometric properties.
A novel framework extending Causal Set Theory through quantum groups at roots of unity, providing a discrete model for quantum spacetime that preserves both causal ordering and quantum coherence.
Advanced mathematical framework for multi-orientation scanning and wavelet-based geometric analysis in enhanced CEP-RLE compression
Comprehensive Bayesian probability analysis examining the likelihood of different Bitcoin creation theories, with particular focus on North Korean state involvement versus individual Western creators.
A mathematical analysis of bifurcation cascades across complex systems, exploring universal patterns in critical transitions from technological disruption to ecological tipping points.
A novel regularization framework for large language models using spherical harmonic decomposition to control semantic frequencies and enable principled hallucination suppression.
A novel computational framework for automated discovery of analytical maximum entropy distribution families using genetic programming validated against parameterizable data generators.
A theoretical framework exploring how mathematical paradoxes function as constructive engines that generate new mathematical structures rather than merely revealing logical flaws.
A universal framework combining differentiable basis transforms with trust-region optimization for adaptive dropout regularization in neural networks
A systematic exploration of how empathy, altruism, and cooperative strategies emerge and persist in evolutionary game theory, with mathematical models and practical applications.
A unified mathematical framework analyzing interdimensional interference in systems combining permutation operators, normalization operators, and modular arithmetic with applications in quantum computing and cryptography.
A novel computational paradigm proposing Probabilistic Neural Substrates (PNS) that maintain continuous probability distributions through cross-entropy optimization, enabling self-organizing recurrent intelligence with unprecedented interpretability and uncertainty quantification.
A framework exploiting neural network permutation symmetries for post-training optimization, enabling structured pruning and improved interpretability
A rigorous mathematical framework for measuring intelligence beyond finite bounds using transfinite mathematics and topological analysis.
Comprehensive analysis of quantum field theory generalizations using Taylor expansion frameworks, covering effective field theory, experimental constraints, and machine learning applications.
Rigorous mathematical analysis of information complementarity principle in Rigorous mathematical analysis of information complementarity principle in quantum field theory with testable predictions for gravitational waves, quantum correlations, and cosmological observations.
A theoretical framework proposing fundamental equivalence between optimization and measurement processes, with implications for universal intelligence and cosmological isolation of advanced civilizations.
A comprehensive mathematical framework exploring quantum computational architectures using dynamic graph substrates, introducing novel complexity classes and algorithmic approaches.
A novel mathematical framework exploring how continuous fields crystallize into discrete structures through wavelet-based geometric optimization
Novel cross-synthesis combining wavelet geometric optimization with topological knot analysis to create unified framework for multi-scale knot invariants
A novel theoretical framework for discovering optimal structures through geometric optimization on parameter space manifolds, with applications to physics, neural networks, architecture, and materials science.
Explore alternative loss functions for regression beyond least-squares, including zero-loss zones, robust methods, and practical applications in engineering and ML.