Chronohaze Notes Feed https://lyuf09.github.io/chronohaze/ Research notes and blog-style updates from Chronohaze, focused on optimization, Isabelle/HOL, and mathematical structure. en Mon, 23 Mar 2026 12:00:00 +0000 Chronohaze static feed builder What I Really Got When a Dual Route Failed https://lyuf09.github.io/chronohaze/post/what-i-really-got-when-a-dual-route-failed.html https://lyuf09.github.io/chronohaze/post/what-i-really-got-when-a-dual-route-failed.html Mon, 23 Mar 2026 12:00:00 +0000 When the most natural Lagrangian dual routes collapse to the trivial 0 bound, what remains is a dual-based structural score tied to Range(B), cycle consistency, and instance difficulty. From One Theorem to a Framework: New Progress on My Isabelle Project in Submodular Optimization https://lyuf09.github.io/chronohaze/post/theorem-to-framework-isabelle-submodular.html https://lyuf09.github.io/chronohaze/post/theorem-to-framework-isabelle-submodular.html Sat, 14 Mar 2026 12:00:00 +0000 From the theorem line for classical greedy to a LazyGreedy extension, a StochasticGreedy skeleton, and an Isabelle/HOL library that can keep growing. Metalcore Piano Lab | From Audio to Chart: A Discretization Experiment (WIP) https://lyuf09.github.io/chronohaze/post/metalcore-piano-lab.html https://lyuf09.github.io/chronohaze/post/metalcore-piano-lab.html Sat, 07 Feb 2026 12:00:00 +0000 From continuous audio to playable charts: onset detection, beat grids, section alignment, and playability constraints. Spring 2026 | A New Research Direction https://lyuf09.github.io/chronohaze/post/spring-2026.html https://lyuf09.github.io/chronohaze/post/spring-2026.html Thu, 29 Jan 2026 12:00:00 +0000 Beginning undergraduate research in Cornell ORIE on first-order methods for constrained and composite optimization. An Ongoing Isabelle Research Project: Formalising Submodular Greedy https://lyuf09.github.io/chronohaze/post/isabelle-submodular-greedy.html https://lyuf09.github.io/chronohaze/post/isabelle-submodular-greedy.html Mon, 29 Dec 2025 12:00:00 +0000 Formalising the greedy (1 − 1/e) guarantee for monotone submodular maximisation under cardinality constraints. My First Isabelle Formalization Project https://lyuf09.github.io/chronohaze/post/first-isabelle-proof.html https://lyuf09.github.io/chronohaze/post/first-isabelle-proof.html Sat, 18 Oct 2025 12:00:00 +0000 Embedding verifiability into proof writing: from motivation to the Nemhauser–Wolsey theorem.