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+# Claude Code
+CLAUDE.md
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-# CLAUDE.md
-
-This file provides guidance to Claude Code (claude.ai/code) when working with code in this repository.
-
-## Project Overview
-
-This is a PhD thesis proposal for developing a methodology to build High-Assurance Hybrid Autonomous Control Systems (HAHACS) for critical infrastructure. The proposal is titled "From Cold Start to Critical: Formal Synthesis of Autonomous Hybrid Controllers."
-
-**Intellectual Merit**: The contribution is architectural unification rather than algorithmic novelty. The methodology provides a systematic decomposition mapping verification techniques to control mode types, composing existing formal methods into a complete framework where none existed.
-
-**Key Insight**: The methodology formalizes EXISTING discrete abstractions from operating procedures (especially nuclear) rather than imposing arbitrary ones. Operating procedures already define go/no-go conditions as discrete predicates - this work provides the formalization and verification framework.
-
-## Document Structure
-
-The proposal uses a modular LaTeX structure with numbered section directories:
-- `main.tex` - Root document that inputs all sections
-- `1-goals-and-outcomes/` - Research statement and goals
-- `2-state-of-the-art/` - Literature review
-- `3-research-approach/` - Core methodology (CURRENTLY ACTIVE WORK)
-- `4-metrics-of-success/` - Success criteria
-- `5-risks-and-contingencies/` - Risk analysis
-- `6-broader-impacts/` - Broader impacts
-- `8-schedule/` - Timeline
-
-Each section directory contains:
-- `v1.tex` (or `v2.tex` for actively revised sections) - Main content
-- `outline.md` (optional) - Planning notes and structure
-
-**IMPORTANT**: Section 3 (research-approach) is currently being revised. `main.tex` inputs `v2.tex` for this section, which contains extensive inline comments and questions prefixed with `%` and `% Q:`.
-
-## Building the Document
-
-```bash
-# Full build with bibliography
-pdflatex main.tex
-bibtex main
-pdflatex main.tex
-pdflatex main.tex
-
-# Quick build (no bibliography updates)
-pdflatex main.tex
-
-# Use latexmk for automated builds
-latexmk -pdf main.tex
-
-# Clean auxiliary files
-latexmk -c
-```
-
-The output is `main.pdf`.
-
-## Key Technical Concepts
-
-### Mathematical Notation
-- **Continuous state space**: X ⊆ ℝⁿ
-- **Discrete modes**: Q = {q₁, q₂, ...}
-- **Per-mode continuous regions**: X_entry,i, X_exit,i, X_safe,i
-- **Discrete predicates**: pᵢ: X → {true, false} (Boolean functions over continuous state)
-
-### Three Control Mode Types
-Each mode type has distinct control objectives and verification methods:
-
-1. **Transitory modes**: Transition between discrete states
-   - Objective: reach(X_entry) → reach(X_exit) while maintaining x(t) ∈ X_safe
-   - Verification: Reachability analysis
-   - Formal: Reach(X_entry, f(x,u), T) ⊆ X_exit ∪ X_safe
-
-2. **Stabilizing modes**: Maintain steady state
-   - Objective: remain(X_target) where X_target ⊂ X_safe
-   - Verification: Barrier certificates
-   - Formal: ∇B(x)·f(x,u) ≤ 0 on boundary ∂X_safe
-
-3. **Expulsory modes**: Safe shutdown under failures
-   - Objective: reach(X_current) → reach(X_safe_shutdown) under parametric uncertainty
-   - Verification: Parametric robust reachability
-   - Formal: Reach(X_current, f(x,u,θ), T) ⊆ X_safe_shutdown for all θ ∈ Θ_failure
-
-### Scope Boundaries
-- **Verify** continuous controllers, not **synthesize** them (analogous to model checking)
-- Assume controllers can be designed using standard control theory
-- Contribution is verification that candidate controllers compose correctly with discrete layer
-
-## Active Development Context
-
-### Current Focus (as of 2026-01-26)
-Editing the research approach section (`3-research-approach/v2.tex`) with a Wednesday (2026-01-28) draft deadline.
-
-### Open Technical Questions
-Questions are embedded in `v2.tex` comments. Key unresolved issues:
-
-**Easier to address:**
-- Hysteresis and sensor noise handling (standard control theory)
-- Mealy machine formalization (presentation issue)
-- Failure detection scope boundaries (precision in claims)
-
-**More challenging:**
-- Timing constraint verification (timed automata integration)
-- Parametric uncertainty bounds methodology
-- Numerical precision in discrete abstraction (task 36 in taskwarrior)
-- Controller design gap (scope vulnerability)
-
-### Taskwarrior Integration
-The user tracks tasks in taskwarrior. The Thesis project has ~45 tasks including:
-- 9 writing tasks for research approach sections (due 2026-01-28)
-- Multiple reading tasks on hybrid systems, reachability, formal methods
-- Outstanding question (task 36): "How do we handle numerical barriers when creating discrete automata?"
-
-Use `task list project:Thesis` to see current tasks.
-
-## Bibliography
-
-References are in `references.bib` using IEEE transaction format. The bibliography includes:
-- Hybrid systems theory and verification
-- Formal methods (reactive synthesis, temporal logic)
-- Control theory (reachability, barrier certificates)
-- Nuclear regulatory documents (NUREG, 10 CFR)
-- Industrial control systems
-
-## Custom LaTeX Class
-
-`dane_proposal_format.cls` provides:
-- NSF-compliant formatting (Times New Roman, 1" margins)
-- Custom `\task{title}{description}` command for numbered tasks
-- TikZ libraries for diagrams
-- Table and figure formatting
-- Default metadata (title, author, advisor)
-
-## Writing Style Notes
-
-- Inline comments in `.tex` files starting with `%` are working notes
-- Comments with `% Q:` indicate open questions requiring research/decisions
-- Sections marked with `\iffalse ... \fi` are draft text, not compiled
-- Text after `\iffalse` blocks are outlines/notes for future writing