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Jonathan Gadea HarderJonathan Gadea Harder
Jonathan Gadea Harder
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Jonathan Gadea Harder
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feat: add leanblueprint setup with GitHub Pages deployment
- Add blueprint/ folder with LaTeX structure for formalization dependency graph - Write comprehensive content.tex with 7 chapters covering all major results - Create GitHub Pages workflow for automatic deployment - Update lake-manifest.json and lean-toolchain The blueprint documents the formalization structure including: - Preliminaries (probability, Hoeffding) - Drift theorems (additive, multiplicative, negative) - Game theory (minimax, witness games, veto) - LBT preconditions (G1, G2, G3) - Coupling arguments - Applications (FIFO traps, epistasis, persistence) - Capstone validation (28 conjuncts)
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‎.github/workflows/blueprint.yml‎

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name: Blueprint to GitHub Pages
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on:
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push:
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branches: [master]
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workflow_dispatch:
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permissions:
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contents: read
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pages: write
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id-token: write
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concurrency:
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group: "pages"
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cancel-in-progress: false
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jobs:
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build:
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runs-on: ubuntu-latest
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steps:
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- name: Checkout
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uses: actions/checkout@v4
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- name: Install Elan
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run: |
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curl -sSfL https://raw.githubusercontent.com/leanprover/elan/master/elan-init.sh | sh -s -- -y --default-toolchain none
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echo "$HOME/.elan/bin" >> $GITHUB_PATH
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- name: Cache Mathlib
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uses: actions/cache@v4
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with:
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path: |
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.lake/packages/mathlib
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.lake/build
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key: lake-${{ runner.os }}-${{ hashFiles('lakefile.lean', 'lake-manifest.json', 'lean-toolchain') }}
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restore-keys: lake-${{ runner.os }}-
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- name: Build project
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run: lake build
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- name: Install Python dependencies
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run: |
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pip install leanblueprint
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- name: Install LaTeX
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run: |
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sudo apt-get update
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sudo apt-get install -y texlive-full
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- name: Build blueprint web
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run: leanblueprint web
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- name: Upload artifact
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uses: actions/upload-pages-artifact@v3
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with:
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path: blueprint/web
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deploy:
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environment:
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name: github-pages
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url: ${{ steps.deployment.outputs.page_url }}
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runs-on: ubuntu-latest
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needs: build
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steps:
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- name: Deploy to GitHub Pages
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id: deployment
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uses: actions/deploy-pages@v4

‎blueprint/src/blueprint.sty‎

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\DeclareOption*{}
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\ProcessOptions
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\newcommand{\graphcolor}[3]{}

‎blueprint/src/content.tex‎

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% Blueprint for Level-Based Theorem Formalization
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% This file contains the dependency graph and proof structure
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% for the formal verification of runtime analysis results.
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\chapter{Preliminaries}
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\section{Probability foundations}
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\begin{definition}[Probability space]
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\label{def:prob_space}
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A probability space $(\Omega, \mathcal{F}, P)$ with sample space, $\sigma$-algebra, and measure.
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\lean{MeasureTheory.ProbabilityMeasure}
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\mathlibok
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\end{definition}
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\begin{definition}[Expected value]
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\label{def:expected_value}
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For random variable $X$ on probability space, $\mathbb{E}[X] = \int X \, dP$.
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\lean{MeasureTheory.integral}
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\mathlibok
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\end{definition}
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\begin{definition}[Conditional expectation]
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\label{def:conditional_expectation}
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$\mathbb{E}[X \mid \mathcal{G}]$ for sub-$\sigma$-algebra $\mathcal{G}$.
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\lean{MeasureTheory.condExp}
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\mathlibok
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\end{definition}
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\begin{lemma}[Hoeffding's inequality]
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\label{lem:hoeffding}
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For independent bounded random variables $X_1, \ldots, X_n$ with $a_i \leq X_i \leq b_i$:
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\[ P\left(\sum_{i=1}^n (X_i - \mathbb{E}[X_i]) \geq t\right) \leq \exp\left(-\frac{2t^2}{\sum_{i=1}^n (b_i - a_i)^2}\right) \]
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\lean{Hoeffding.hoeffding_ineq}
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\uses{def:expected_value}
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\leanok
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\end{lemma}
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\section{Ranking and selection}
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\begin{definition}[Ranking function]
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\label{def:ranking}
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A ranking function $\text{rank}: S \to \mathbb{R}$ that assigns fitness values to solutions.
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\lean{CRNRanking.Ranking}
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\end{definition}
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\begin{definition}[Ranking gap]
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\label{def:ranking_gap}
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For target set $T$, the gap $\Delta = \min_{x \notin T} (\text{rank}(x^*) - \text{rank}(x))$.
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\lean{CRNRanking.Gap}
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\uses{def:ranking}
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\end{definition}
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\chapter{Drift Theorems}
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\section{Additive drift}
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\begin{theorem}[Additive drift theorem]
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\label{thm:additive_drift}
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If $\mathbb{E}[X_{t+1} - X_t \mid X_t] \geq \delta > 0$ for $X_t \notin T$, then $\mathbb{E}[\tau] \leq X_0 / \delta$.
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\lean{DriftTheorems.AdditiveDrift.additive_drift_theorem}
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\uses{def:expected_value}
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\leanok
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\end{theorem}
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\section{Multiplicative drift}
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\begin{theorem}[Multiplicative drift theorem]
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\label{thm:multiplicative_drift}
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If $\mathbb{E}[X_{t+1} \mid X_t] \leq (1 - \delta) X_t$ for $X_t \notin T$, then $\mathbb{E}[\tau] \leq \frac{\ln(X_0)}{\delta}$.
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\lean{DriftTheorems.MultiplicativeDrift.multiplicative_drift_theorem}
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\uses{def:expected_value}
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\leanok
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\end{theorem}
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\section{Negative drift}
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\begin{theorem}[Negative drift theorem]
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\label{thm:negative_drift}
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If $\mathbb{E}[X_{t+1} - X_t \mid X_t] \leq -\delta < 0$ and bounded variance, then $\tau$ is exponentially large.
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\lean{DriftTheorems.NegativeDrift.negative_drift_theorem}
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\uses{def:expected_value, lem:hoeffding}
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\leanok
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\end{theorem}
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\chapter{Game Theory}
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\section{Minimax theorem}
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\begin{theorem}[Minimax theorem]
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\label{thm:minimax}
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For zero-sum game with payoff matrix $A$:
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\[ \max_x \min_y x^T A y = \min_y \max_x x^T A y \]
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\lean{GameTheoryMinimax.minimax_theorem}
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\leanok
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\end{theorem}
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\section{Witness games}
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\begin{definition}[Witness game]
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\label{def:witness_game}
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A game structure for analyzing coevolutionary dynamics.
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\lean{WitnessGameDrift.WitnessGame}
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\end{definition}
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\begin{lemma}[Witness game drift]
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\label{lem:witness_drift}
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The witness game exhibits positive drift toward target solutions.
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\lean{WitnessGameDrift.witness_game_drift}
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\uses{def:witness_game, thm:additive_drift}
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\leanok
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\end{lemma}
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\section{Veto mechanism}
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\begin{definition}[Veto player]
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\label{def:veto_player}
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A player that can reject candidate solutions.
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\lean{WitnessVeto.VetoPlayer}
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\end{definition}
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\begin{lemma}[Veto bounds]
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\label{lem:veto_bounds}
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The veto mechanism provides runtime bounds for escaping local optima.
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\lean{WitnessVeto.veto_runtime_bound}
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\uses{def:veto_player, thm:multiplicative_drift}
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\leanok
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\end{lemma}
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\chapter{Linear Ranking and LBT Preconditions}
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\section{Linear ranking theorem}
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\begin{definition}[LBT precondition G1]
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\label{def:precond_G1}
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Condition for selection to amplify target solutions.
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\lean{LBTPreconditions.precond_G1}
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\uses{def:ranking}
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\end{definition}
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\begin{definition}[LBT precondition G2]
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\label{def:precond_G2}
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Condition for variation to maintain diversity.
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\lean{LBTPreconditions.precond_G2}
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\end{definition}
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\begin{definition}[LBT precondition G3]
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\label{def:precond_G3}
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Condition for population size sufficiency.
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\lean{LBTPreconditions.precond_G3}
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\end{definition}
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\begin{theorem}[Linear ranking theorem]
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\label{thm:linear_ranking}
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Under preconditions G1, G2, G3, the level-based theorem provides runtime bounds.
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\lean{CoEALevelBased.level_based_theorem}
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\uses{def:precond_G1, def:precond_G2, def:precond_G3, thm:additive_drift}
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\leanok
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\end{theorem}
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\section{Selection amplification}
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\begin{lemma}[Selection amplification bound]
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\label{lem:sel_amplification}
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Selection increases the proportion of target solutions by factor $(1 + \delta)$.
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\lean{LBTCoupling.sel_amplification_bound}
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\uses{def:precond_G1, def:ranking_gap}
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\notready
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\end{lemma}
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\chapter{Coupling Arguments}
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\section{LBT Coupling}
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\begin{definition}[Coupling]
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\label{def:coupling}
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A coupling between the idealized and actual process distributions.
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\lean{LBTCoupling.Coupling}
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\end{definition}
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\begin{theorem}[LBT coupling theorem]
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\label{thm:lbt_coupling}
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The coupled process tracks the idealized LBT process with bounded error.
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\lean{LBTCoupling.lbt_coupling_theorem}
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\uses{def:coupling, thm:linear_ranking}
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\notready
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\end{theorem}
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\begin{lemma}[G2 monotonicity]
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\label{lem:g2_monotonicity}
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The G2 condition is preserved under the coupling.
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\lean{LBTCoupling.r_local_G2}
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\uses{def:precond_G2, def:coupling}
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\notready
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\end{lemma}
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\section{Runtime bounds}
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\begin{theorem}[Runtime bound]
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\label{thm:runtime_bound}
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The expected runtime is $O(n \log n)$ for the level-based algorithm.
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\lean{CoEALevelBased.runtime_bound}
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\uses{thm:lbt_coupling, thm:additive_drift}
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\leanok
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\end{theorem}
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\chapter{Applications}
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\section{FIFO trap obstruction}
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\begin{definition}[FIFO trap]
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\label{def:fifo_trap}
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A trap configuration that blocks progress in FIFO-based algorithms.
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\lean{FifoTrapObstruction.FIFOTrap}
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\end{definition}
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\begin{theorem}[FIFO trap runtime]
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\label{thm:fifo_trap_runtime}
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FIFO traps cause exponential runtime for certain problem instances.
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\lean{FifoTrapObstruction.fifo_trap_exponential}
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\uses{def:fifo_trap, thm:negative_drift}
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\leanok
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\end{theorem}
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\section{Signed epistasis}
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\begin{definition}[Signed epistasis skeleton]
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\label{def:epistasis}
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A structure encoding epistatic interactions in fitness landscapes.
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\lean{SignedEpistasisSkeleton.SignedEpistasis}
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\end{definition}
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\begin{lemma}[Epistasis bounds]
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\label{lem:epistasis_bounds}
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Signed epistasis provides bounds on the number of fitness levels.
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\lean{SignedEpistasisSkeleton.epistasis_level_bound}
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\uses{def:epistasis, def:ranking}
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\leanok
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\end{lemma}
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\section{Simultaneous persistence}
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\begin{theorem}[Simultaneous persistence]
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\label{thm:simultaneous_persistence}
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Under coevolutionary dynamics, multiple strategies can persist simultaneously.
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\lean{SimultaneousPersistence.simultaneous_persistence_theorem}
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\uses{thm:minimax, lem:witness_drift}
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\leanok
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\end{theorem}
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\chapter{Capstone Validation}
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\section{Unified paper validation}
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\begin{theorem}[Full paper capstone]
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\label{thm:full_paper_capstone}
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The 28 conjuncts of the paper are formally verified, covering:
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\begin{enumerate}
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\item LBT preconditions (G1, G2, G3)
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\item Linear ranking theorem
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\item Selection amplification
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\item Coupling arguments
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\item Runtime bounds
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\item Applications (FIFO traps, epistasis, persistence)
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\end{enumerate}
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\lean{UnifiedPaperValidation.full_paper_capstone}
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\uses{thm:linear_ranking, thm:runtime_bound, thm:fifo_trap_runtime, lem:epistasis_bounds, thm:simultaneous_persistence}
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\leanok
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\end{theorem}

‎blueprint/src/extra_styles.css‎

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/* This file contains CSS tweaks for this blueprint.
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* As an example, we included CSS rules that put
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* a vertical line on the left of theorem statements
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* and proofs.
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* */
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div.theorem_thmcontent {
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border-left: .15rem solid black;
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}
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div.proposition_thmcontent {
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border-left: .15rem solid black;
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}
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div.lemma_thmcontent {
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border-left: .1rem solid black;
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}
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div.corollary_thmcontent {
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border-left: .1rem solid black;
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}
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div.proof_content {
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border-left: .08rem solid grey;
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}

‎blueprint/src/latexmkrc‎

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# This file configures the latexmk command you can use to compile
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# the pdf version of the blueprint
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$pdf_mode = 1;
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$pdflatex = 'xelatex -synctex=1';
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@default_files = ('print.tex');

‎blueprint/src/macros/common.tex‎

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% In this file you should put all LaTeX macros and settings to be used both by
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% the pdf version and the web version.
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% This should be most of your macros.
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% The theorem-like environments defined below are those that appear by default
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% in the dependency graph. See the README of leanblueprint if you need help to
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% customize this.
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% The configuration below use the theorem counter for all those environments
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% (this is what the [theorem] arguments mean) and never resets it.
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% If you want for instance to number them within chapters then you can add
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% [chapter] at the end of the next line.
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\newtheorem{theorem}{Theorem}
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\newtheorem{proposition}[theorem]{Proposition}
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\newtheorem{lemma}[theorem]{Lemma}
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\newtheorem{corollary}[theorem]{Corollary}
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\theoremstyle{definition}
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\newtheorem{definition}[theorem]{Definition}

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