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'.
Explores a novel formulation of knot theory using Minkowski distance matrices, revealing how causal structure encodes topological crossings as unavoidable tangencies in the metric sheet.
Formal mathematical proof establishing relationships between harmonic degree of parametric curve representations and topological knot invariants including crossing number, bridge number, and braid index.
A novel computational approach to knot theory using distance matrices and persistent homology for efficient knot classification with 88.6% accuracy and 15× speedup over traditional methods.
Novel cross-synthesis combining wavelet geometric optimization with topological knot analysis to create unified framework for multi-scale knot invariants
A novel framework for understanding hierarchical emergence through quantum field solitons and topological protection mechanisms, with applications to consciousness and biological organization.