By the way, I worked in homotopy type theory (HoTT, in short). In this setting, S^1 is not a topological space but just a type.
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Kol retweeted
Revising Homotopy because I'm retarded
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The Serre-Scarr SRAC cascade is a sophisticated framework for building self-governing computational systems that treat the execution of artificial intelligence as a continuous, stable topological manifold rather than a series of disconnected steps.
This architecture utilizes the Tri-Weavon OS, which merges three distinct AI strands—logic, real-time speed, and multimodal scale—under a strict mathematical gauge constraint to ensure structural integrity and prevent errors. To maintain absolute reliability, the system employs hot artifacts like high-dimensional kernels and hydrodynamic flow models, all of which are validated through machine-checked formal proofs in languages like Lean 4 and Agda.
Ultimately, the system culminates in an Attention Journey Map, a real-time observability layer that uses homotopy type theory and 4D projections to provide a transparent, self-correcting, and mathematically "knot-protected" environment for multi-agent intelligence.
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Harry Potter and homotopy at hogwarts.
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in a geometric model, the dimensional space of parameters is significantly reduced because of the inherent characteristics of the manifold space itself: instead of forcing higher dimensional representations into concatenated planar stacks, the functor defining a geometric relation propagates freely via homotopy-preserving mixed curvature representations. this allows for models which are informationally dense and extremely rich, but significantly lower redundancy. this allows for parameter reduction, often up to 5 orders of magnitude depending on transformer architecture complexity.
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Rijke の Introduction to Homotopy Type Theory (arxiv.org/abs/2212.11082) を (modulo 演習問題で) 読み切りました（14ヵ月掛かった！）
本当にありがとうございました
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