36:null 37:["$","title",null,{"children":"Polis Regression Analysis - War & Peace in Ancient Greece | geo-theo | Observable"}] 3d:T4a8,These data come to us courtesy of Associate Professor Scott Arcenas of the UM History department. He a historian and classicist who specializes in the history of democracy and political violence. In this class, I'm very happy to connect you to some of the great scholarship occurring at UM. For this assignment, the data set consists of a single XLS fileDownload single XLS file that has many fields (columns). To aid in interpretation of the data, there is a codebookDownload codebook for the data. In it, you'll find a complete description of each of the fields. In this mini-sprint, I'd like you to try and identify the drivers of political violence in the ancient world. Focus on the episodes of staesis between 500 and 300 BCE (a type of political violence, commonly translated as “civil war”). Consider the range of other variables found in the dataset. Do any of them correlate well with cities having higher staesis? Prepare visualizations that allow the viewer to locate, lookup, browse, explore, and ultimately discover relations in the data. Note I'm using the 'why' of Munzner here. The 'what' is a table in CSV format. The 'how' is what you're group is doing. Good luck!3e:T114a,// Leaflet Map import L from "npm:leaflet@1.9.4"; // Load Leaflet's CSS as a stylesheet rather than as a JavaScript module. if (!document.head.querySelector("link[data-leaflet-css]")) { const leafletCss = document.createElement("link"); leafletCss.rel = "stylesheet"; leafletCss.href = "https://unpkg.com/leaflet@1.9.4/dist/leaflet.css"; leafletCss.dataset.leafletCss = "true"; document.head.append(leafletCss); } if (!document.head.querySelector("style[data-dark-osm]")) { const darkOsmCss = document.createElement("style"); darkOsmCss.dataset.darkOsm = "true"; darkOsmCss.textContent = ` .dark-osm-basemap .leaflet-tile-pane { filter: invert(90%) hue-rotate(180deg) brightness(0.65) saturate(0.7); } `; document.head.append(darkOsmCss); } const validPolis = polis.filter( d => Number.isFinite(+d.Latitude) && Number.isFinite(+d.Longitude) ); const staseisColor = value => { const t = Math.max(0, Math.min(1, value / 20)); const blue = [33, 102, 172]; const red = [178, 24, 43]; const rgb = blue.map((channel, i) => Math.round(channel + t * (red[i] - channel))); return `rgb(${rgb.join(",")})`; }; const escapeHtml = value => String(value ?? "") .replaceAll("&", "&") .replaceAll("<", "<") .replaceAll(">", ">") .replaceAll('"', """) .replaceAll("'", "'"); const popupFor = d => { const hiddenFromTable = new Set([ "Name", "Region name" ]); const tableRows = Object.entries(d) .filter(([key]) => !hiddenFromTable.has(key)) .map(([key, value]) => { const renderedValue = key === "Pleiades link" && value ? `Open Pleiades record` : escapeHtml(value); return ` ${escapeHtml(key)} ${renderedValue} `; }) .join(""); return `

${escapeHtml(d.Name)}

${escapeHtml(d["Region name"])}

${tableRows}

`; }; const mapElement = html`

`; const map = L.map(mapElement, {preferCanvas: true}); L.tileLayer( "https://{s}.tile.openstreetmap.org/{z}/{x}/{y}.png", { maxZoom: 19, attribution: '© OpenStreetMap contributors', crossOrigin: true } ).addTo(map); for (const d of validPolis) { const staseis = Number(d.staseis); const pointColor = Number.isFinite(staseis) ? staseisColor(staseis) : "#999999"; const marker = L.circleMarker([+d.Latitude, +d.Longitude], { radius: 4, color: pointColor, weight: 1, fillColor: pointColor, fillOpacity: 0.72 }).addTo(map); marker.bindPopup(popupFor(d), {minWidth: 260, maxWidth: 320}); marker.on("mouseover", () => marker.openPopup()); marker.on("mouseout", () => marker.closePopup()); } const legend = L.control({position: "bottomright"}); legend.onAdd = () => { const div = L.DomUtil.create("div"); div.style.cssText = "background:rgba(20,20,20,.86); color:#fff; padding:8px; font:12px system-ui, sans-serif;"; div.innerHTML = `

Staseis

020

gray = missing

`; return div; }; legend.addTo(map); L.control.scale().addTo(map); display(mapElement); // Fit after the map has been rendered so Leaflet can measure its dimensions. requestAnimationFrame(() => { if (validPolis.length) { map.invalidateSize(); map.fitBounds( validPolis.map(d => [+d.Latitude, +d.Longitude]), {padding: [40, 40], maxZoom: 6} ); } }); 3f:T256f,// Scatterplot import * as Plot from "npm:@observablehq/plot"; const xVariables = [ {column: "staseis", label: "Staseis"}, {column: "area 1", label: "Area 1"}, {column: "area 2", label: "Area 2 (hectares)"}, {column: "Elevation m", label: "Elevation (m)"}, {column: "Victors", label: "Victors"} ]; const yVariables = [ {column: "staseis", label: "Staseis"}, {column: "Elevation m", label: "Elevation (m)"}, {column: "area 2", label: "Area 2 (hectares)"}, {column: "Colonies", label: "Colonies"} ]; const isNumber = value => value !== null && value !== undefined && value !== "" && Number.isFinite(+value); const filterState = { Democracy: null, Walls: null, Hellenicity: null, Polisity: null, promMin: 0, promMax: 21 }; const categoricalFilters = [ { key: "Democracy", label: "Democracy", options: [ {label: "All", value: null}, {label: "Non-democracy", value: 1}, {label: "Democracy", value: 2} ] }, { key: "Walls", label: "Walls", options: [ {label: "All", value: null}, {label: "No walls", value: 0}, {label: "Walled", value: 1} ] }, { key: "Hellenicity", label: "Hellenicity", options: [ {label: "All", value: null}, {label: "Very Greek", value: 1}, {label: "Mixed", value: 2}, {label: "Barbarian", value: 3} ] }, { key: "Polisity", label: "Polisity", options: [ {label: "All", value: null}, {label: "Certain", value: 1}, {label: "Almost Certain", value: 1.5}, {label: "Less Certain", value: 2}, {label: "Not Certain", value: 3} ] } ]; const filterControls = html`

`; const makeButton = (label, selected, onClick) => { const button = document.createElement("button"); button.type = "button"; button.textContent = label; button.style.margin = "2px 4px 2px 0"; button.style.padding = "3px 7px"; button.style.border = "1px solid #999"; button.style.borderRadius = "3px"; button.style.background = selected ? "#2c7fb8" : "#f4f4f4"; button.style.color = selected ? "white" : "#222"; button.setAttribute("aria-pressed", selected); button.addEventListener("click", onClick); return button; }; for (const filter of categoricalFilters) { const row = document.createElement("div"); row.style.marginBottom = "4px"; const label = document.createElement("strong"); label.textContent = `${filter.label}: `; row.append(label); for (const option of filter.options) { row.append(makeButton(option.label, filterState[filter.key] === option.value, () => { filterState[filter.key] = option.value; updateFilterButtons(); renderPlot(); })); } filterControls.append(row); } const prominenceRow = document.createElement("div"); prominenceRow.style.marginTop = "6px"; const prominenceLabel = document.createElement("strong"); prominenceLabel.textContent = "Prominence (prom 1): "; prominenceRow.append(prominenceLabel); const promMinInput = document.createElement("input"); promMinInput.type = "range"; promMinInput.min = 0; promMinInput.max = 21; promMinInput.step = 0.01; promMinInput.value = 0; promMinInput.style.verticalAlign = "middle"; const promMaxInput = document.createElement("input"); promMaxInput.type = "range"; promMaxInput.min = 0; promMaxInput.max = 21; promMaxInput.step = 0.01; promMaxInput.value = 21; promMaxInput.style.verticalAlign = "middle"; const promValue = document.createElement("span"); promValue.style.margin = "0 6px"; const promAllButton = makeButton("All", true, () => { filterState.promMin = 0; filterState.promMax = 21; promMinInput.value = 0; promMaxInput.value = 21; updateFilterButtons(); renderPlot(); }); prominenceRow.append( document.createTextNode("min "), promMinInput, document.createTextNode(" max "), promMaxInput, promValue, promAllButton ); filterControls.append(prominenceRow); const updateFilterButtons = () => { for (const filter of categoricalFilters) { const row = [...filterControls.children].find( element => element.firstChild?.textContent === `${filter.label}: ` ); if (!row) continue; [...row.querySelectorAll("button")].forEach((button, i) => { const selected = filterState[filter.key] === filter.options[i].value; button.style.background = selected ? "#2c7fb8" : "#f4f4f4"; button.style.color = selected ? "white" : "#222"; button.setAttribute("aria-pressed", selected); }); } promValue.textContent = ` ${filterState.promMin.toFixed(2)}–${filterState.promMax.toFixed(2)} `; const allProminence = filterState.promMin === 0 && filterState.promMax === 21; promAllButton.style.background = allProminence ? "#2c7fb8" : "#f4f4f4"; promAllButton.style.color = allProminence ? "white" : "#222"; promAllButton.setAttribute("aria-pressed", allProminence); }; const updateProminence = (which, value) => { const numericValue = +value; if (which === "min") { filterState.promMin = Math.min(numericValue, filterState.promMax); promMinInput.value = filterState.promMin; } else { filterState.promMax = Math.max(numericValue, filterState.promMin); promMaxInput.value = filterState.promMax; } updateFilterButtons(); renderPlot(); }; promMinInput.addEventListener("input", event => updateProminence("min", event.target.value)); promMaxInput.addEventListener("input", event => updateProminence("max", event.target.value)); const controls = html`

X-axis variable Y-axis variable

`; const xSelect = controls.querySelector('select[data-axis="x"]'); const ySelect = controls.querySelector('select[data-axis="y"]'); xSelect.value = "area 2"; const stats = html`

`; const plotHolder = html`

`; const container = html`

`; container.append(controls, filterControls, stats, plotHolder); const renderPlot = () => { const selectedX = xVariables.find(({column}) => column === xSelect.value); const selectedY = yVariables.find(({column}) => column === ySelect.value); const passesFilters = d => { const categoricalPass = categoricalFilters.every(filter => filterState[filter.key] === null || (isNumber(d[filter.key]) && +d[filter.key] === filterState[filter.key]) ); const prominencePass = (filterState.promMin === 0 && filterState.promMax === 21) || (isNumber(d["prom 1"]) && +d["prom 1"] >= filterState.promMin && +d["prom 1"] <= filterState.promMax); return categoricalPass && prominencePass; }; const filterMatched = polis.filter(passesFilters); const data = filterMatched.filter( d => isNumber(d[selectedX.column]) && isNumber(d[selectedY.column]) ); const points = data.map(d => ({ x: +d[selectedX.column], y: +d[selectedY.column] })); const xMean = points.length ? points.reduce((sum, d) => sum + d.x, 0) / points.length : NaN; const yMean = points.length ? points.reduce((sum, d) => sum + d.y, 0) / points.length : NaN; const ssXX = points.reduce((sum, d) => sum + (d.x - xMean) ** 2, 0); const ssXY = points.reduce((sum, d) => sum + (d.x - xMean) * (d.y - yMean), 0); const slope = ssXX ? ssXY / ssXX : NaN; const intercept = Number.isFinite(slope) ? yMean - slope * xMean : NaN; const ssTot = points.reduce((sum, d) => sum + (d.y - yMean) ** 2, 0); const ssRes = Number.isFinite(slope) ? points.reduce((sum, d) => sum + (d.y - (intercept + slope * d.x)) ** 2, 0) : NaN; const rSquared = ssTot ? 1 - ssRes / ssTot : NaN; const xExtent = points.length ? [Math.min(...points.map(d => d.x)), Math.max(...points.map(d => d.x))] : []; const trendline = Number.isFinite(slope) ? xExtent.map(x => ({x, y: intercept + slope * x})) : []; stats.textContent = Number.isFinite(rSquared) ? `Linear trendline · R² = ${rSquared.toFixed(3)} · plotted n = ${points.length} · filter matches = ${filterMatched.length}` : `Linear trendline · R² unavailable · plotted n = ${points.length} · filter matches = ${filterMatched.length}`; const plot = Plot.plot({ width: 850, height: 560, marginLeft: 70, marginBottom: 65, grid: true, x: {label: selectedX.label}, y: {label: selectedY.label, nice: true}, marks: [ Plot.dot(data, { x: d => +d[selectedX.column], y: d => +d[selectedY.column], r: 4, fill: "#2c7fb8", fillOpacity: 0.62, stroke: "#123b5d", strokeOpacity: 0.35, title: d => `${d.Name}\n${selectedX.label}: ${d[selectedX.column]}\n${selectedY.label}: ${d[selectedY.column]}`, tip: true }), Plot.line(trendline, { x: "x", y: "y", stroke: "#d7191c", strokeWidth: 2.5 }) ] }); plotHolder.replaceChildren(plot); }; xSelect.addEventListener("input", renderPlot); ySelect.addEventListener("input", renderPlot); updateFilterButtons(); renderPlot(); display(container); 40:T2fef,// Regression Model const response = "staseis"; const predictors = ["Elevation m", "area 2", "Colonies", "Victors"]; const coefficientNames = ["Intercept", ...predictors]; const isNumber = value => value !== null && value !== undefined && value !== "" && Number.isFinite(+value); // Use complete cases for all five regression variables. const regressionData = polis.filter(d => [response, ...predictors].every(column => isNumber(d[column])) ); const X = regressionData.map(d => [1, ...predictors.map(column => +d[column])]); const y = regressionData.map(d => +d[response]); const transpose = matrix => matrix[0].map((_, column) => matrix.map(row => row[column])); const multiply = (left, right) => left.map(row => right[0].map((_, column) => row.reduce((sum, value, i) => sum + value * right[i][column], 0) )); const solve = (matrix, vector) => { const n = matrix.length; const augmented = matrix.map((row, i) => [...row, vector[i]]); for (let column = 0; column < n; column++) { let pivot = column; for (let row = column + 1; row < n; row++) { if (Math.abs(augmented[row][column]) > Math.abs(augmented[pivot][column])) { pivot = row; } } if (Math.abs(augmented[pivot][column]) < 1e-12) { throw new Error("The regression matrix is singular or has perfectly collinear variables."); } [augmented[column], augmented[pivot]] = [augmented[pivot], augmented[column]]; const divisor = augmented[column][column]; for (let j = column; j <= n; j++) augmented[column][j] /= divisor; for (let row = 0; row < n; row++) { if (row === column) continue; const factor = augmented[row][column]; for (let j = column; j <= n; j++) { augmented[row][j] -= factor * augmented[column][j]; } } } return augmented.map(row => row[n]); }; const invert = matrix => { const n = matrix.length; return matrix[0].map((_, column) => solve(matrix, matrix.map((_, row) => row === column ? 1 : 0)) ); }; const XTranspose = transpose(X); const XtX = multiply(XTranspose, X); const Xty = multiply(XTranspose, y.map(value => [value])).map(row => row[0]); const beta = solve(XtX, Xty); const XtXInverse = invert(XtX); const fitted = X.map(row => row.reduce((sum, value, i) => sum + value * beta[i], 0)); const residuals = y.map((value, i) => value - fitted[i]); const yMean = y.reduce((sum, value) => sum + value, 0) / y.length; const ssResidual = residuals.reduce((sum, value) => sum + value ** 2, 0); const ssTotal = y.reduce((sum, value) => sum + (value - yMean) ** 2, 0); const rSquared = 1 - ssResidual / ssTotal; const adjustedRSquared = 1 - (1 - rSquared) * (y.length - 1) / (y.length - beta.length); const residualVariance = ssResidual / (y.length - beta.length); const standardErrors = beta.map((_, i) => Math.sqrt(residualVariance * XtXInverse[i][i])); const tStatistics = beta.map((value, i) => value / standardErrors[i]); const degreesOfFreedom = y.length - beta.length; // Regularized incomplete beta and Student's t distribution helpers. // These keep the cell self-contained and avoid another package import. const logGamma = z => { const coefficients = [ 676.5203681218851, -1259.1392167224028, 771.32342877765313, -176.61502916214059, 12.507343278686905, -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7 ]; if (z < 0.5) { return Math.log(Math.PI) - Math.log(Math.sin(Math.PI * z)) - logGamma(1 - z); } z -= 1; let x = 0.99999999999980993; for (let i = 0; i < coefficients.length; i++) x += coefficients[i] / (z + i + 1); const t = z + coefficients.length - 0.5; return 0.5 * Math.log(2 * Math.PI) + (z + 0.5) * Math.log(t) - t + Math.log(x); }; const betaContinuedFraction = (a, b, x) => { const maxIterations = 200; const epsilon = 3e-7; const minimum = 1e-30; const qab = a + b; const qap = a + 1; const qam = a - 1; let c = 1; let d = 1 - qab * x / qap; if (Math.abs(d) < minimum) d = minimum; d = 1 / d; let h = d; for (let m = 1; m <= maxIterations; m++) { const m2 = 2 * m; let aa = m * (b - m) * x / ((qam + m2) * (a + m2)); d = 1 + aa * d; if (Math.abs(d) < minimum) d = minimum; c = 1 + aa / c; if (Math.abs(c) < minimum) c = minimum; d = 1 / d; h *= d * c; aa = -(a + m) * (qab + m) * x / ((a + m2) * (qap + m2)); d = 1 + aa * d; if (Math.abs(d) < minimum) d = minimum; c = 1 + aa / c; if (Math.abs(c) < minimum) c = minimum; d = 1 / d; const delta = d * c; h *= delta; if (Math.abs(delta - 1) < epsilon) break; } return h; }; const regularizedBeta = (x, a, b) => { if (x <= 0) return 0; if (x >= 1) return 1; const factor = Math.exp( logGamma(a + b) - logGamma(a) - logGamma(b) + a * Math.log(x) + b * Math.log1p(-x) ); return x < (a + 1) / (a + b + 2) ? factor * betaContinuedFraction(a, b, x) / a : 1 - factor * betaContinuedFraction(b, a, 1 - x) / b; }; const twoSidedTTestPValue = (t, df) => { if (!Number.isFinite(t)) return NaN; const x = df / (df + t ** 2); return Math.max(0, Math.min(1, regularizedBeta(x, df / 2, 0.5))); }; const pValues = tStatistics.map(t => twoSidedTTestPValue(t, degreesOfFreedom)); const formatNumber = value => Number.isFinite(value) ? value.toFixed(4) : "—"; const significanceStars = pValue => pValue < 0.01 ? "***" : pValue < 0.05 ? "**" : pValue < 0.1 ? "*" : ""; const formatPValue = value => { if (!Number.isFinite(value)) return "—"; return value < 0.0001 ? "<0.0001" : value.toFixed(4); }; const tableWrapper = document.createElement("div"); tableWrapper.style.overflowX = "auto"; const table = document.createElement("table"); table.style.borderCollapse = "collapse"; table.style.whiteSpace = "nowrap"; table.style.minWidth = "720px"; const headerRow = table.createTHead().insertRow(); for (const header of ["Term", "Coefficient", "Std. error", "t statistic", "p value"]) { const cell = document.createElement("th"); cell.textContent = header; cell.style.textAlign = header === "Term" ? "left" : "right"; cell.style.padding = "4px 12px"; cell.style.borderBottom = "1px solid #999"; headerRow.append(cell); } const body = table.createTBody(); coefficientNames.forEach((name, i) => { const row = body.insertRow(); const values = [ name, `${formatNumber(beta[i])}${significanceStars(pValues[i])}`, formatNumber(standardErrors[i]), formatNumber(tStatistics[i]), formatPValue(pValues[i]) ]; values.forEach((value, column) => { const cell = row.insertCell(); cell.textContent = value; cell.style.textAlign = column === 0 ? "left" : "right"; cell.style.padding = "4px 12px"; }); }); tableWrapper.append(table); const output = html`

OLS regression: staseis ~ Elevation m + area 2 + Colonies + Victors

Complete cases: ${regressionData.length} · R²: ${formatNumber(rSquared)} · Adjusted R²: ${formatNumber(adjustedRSquared)} · Residual df: ${degreesOfFreedom}

* p < 0.1 · ** p < 0.05 · *** p < 0.01

`; output.querySelector("[data-coefficient-table]").append(tableWrapper); display(output); // Correlation matrix for the same complete-case regression sample. const correlationVariables = [ {column: "staseis", label: "Staseis"}, {column: "Elevation m", label: "Elevation m"}, {column: "area 2", label: "Area 2"}, {column: "Colonies", label: "Colonies"}, {column: "Victors", label: "Victors"} ]; const correlationColumns = correlationVariables.map(({column}) => regressionData.map(d => +d[column]) ); const pearsonCorrelation = (left, right) => { const leftMean = left.reduce((sum, value) => sum + value, 0) / left.length; const rightMean = right.reduce((sum, value) => sum + value, 0) / right.length; const numerator = left.reduce((sum, value, i) => sum + (value - leftMean) * (right[i] - rightMean), 0 ); const leftSS = left.reduce((sum, value) => sum + (value - leftMean) ** 2, 0); const rightSS = right.reduce((sum, value) => sum + (value - rightMean) ** 2, 0); return numerator / Math.sqrt(leftSS * rightSS); }; const correlationMatrix = correlationColumns.map(left => correlationColumns.map(right => pearsonCorrelation(left, right)) ); const correlationDegreesOfFreedom = regressionData.length - 2; const correlationPValues = correlationMatrix.map((row, i) => row.map((value, j) => { if (i === j) return NaN; const t = value === 1 || value === -1 ? Infinity : value * Math.sqrt(correlationDegreesOfFreedom / (1 - value ** 2)); return twoSidedTTestPValue(t, correlationDegreesOfFreedom); }) ); const blendCorrelationColor = (from, to, amount) => from.map((value, i) => Math.round(value + amount * (to[i] - value))); const correlationColor = value => { const neutral = [247, 247, 247]; const positive = [8, 48, 107]; const negative = [140, 81, 10]; const rgb = value >= 0 ? blendCorrelationColor(neutral, positive, value) : blendCorrelationColor(neutral, negative, -value); return `rgb(${rgb.join(",")})`; }; const correlationTextColor = value => Math.abs(value) >= 0.55 ? "#ffffff" : "#222222"; const correlationTable = document.createElement("table"); correlationTable.style.borderCollapse = "collapse"; correlationTable.style.font = "13px system-ui, sans-serif"; correlationTable.style.whiteSpace = "nowrap"; const correlationHeader = correlationTable.createTHead().insertRow(); const emptyHeader = document.createElement("th"); emptyHeader.style.padding = "6px"; correlationHeader.append(emptyHeader); for (const {label} of correlationVariables) { const cell = document.createElement("th"); cell.textContent = label; cell.style.padding = "6px"; cell.style.textAlign = "center"; cell.style.fontWeight = "600"; correlationHeader.append(cell); } const correlationBody = correlationTable.createTBody(); correlationVariables.forEach(({label}, rowIndex) => { const row = correlationBody.insertRow(); const rowHeader = document.createElement("th"); rowHeader.textContent = label; rowHeader.style.padding = "6px 10px 6px 6px"; rowHeader.style.textAlign = "left"; rowHeader.style.fontWeight = "600"; row.append(rowHeader); correlationMatrix[rowIndex].forEach((value, columnIndex) => { const cell = row.insertCell(); const pValue = correlationPValues[rowIndex][columnIndex]; cell.textContent = `${value.toFixed(2)}${significanceStars(pValue)}`; cell.style.minWidth = "68px"; cell.style.padding = "8px 10px"; cell.style.textAlign = "center"; cell.style.background = correlationColor(value); cell.style.color = correlationTextColor(value); cell.style.fontVariantNumeric = "tabular-nums"; cell.title = Number.isFinite(pValue) ? `Pearson r = ${value.toFixed(3)}; p = ${pValue.toFixed(4)}` : `Pearson r = ${value.toFixed(3)}`; }); }); const correlationWrapper = document.createElement("div"); correlationWrapper.style.overflowX = "auto"; correlationWrapper.style.marginTop = "18px"; correlationWrapper.append(correlationTable); const correlationOutput = html`

Pearson correlation matrix · same complete cases: ${regressionData.length}

−1 strong negative strong positive +1

* p < 0.1 · ** p < 0.05 · *** p < 0.01

`; correlationOutput.querySelector("[data-correlation-table]").append(correlationWrapper); display(correlationOutput); 41:T510f,// Interactive regression model const response = "staseis"; const defaultPredictors = new Set(["area 1", "Elevation m"]); const isNumber = value => value !== null && value !== undefined && value !== "" && Number.isFinite(+value); // Per the codebook, 0 means "unknown" for Democracy and Hellenicity. // Treat those values as missing when either variable is used as a predictor. const unknownAsMissing = new Set(["Democracy", "Hellenicity"]); const isUsableValue = (column, value) => isNumber(value) && !(unknownAsMissing.has(column) && +value === 0); // Standard OLS requires numeric predictors. Exclude identifiers and geographic fields // that are not part of this model-selection interface. const omittedPredictors = new Set([ response, "polis#", "Delian L", "Region #", "Latitude", "Longitude", "Polisity", "prom 1" ]); const candidatePredictors = [...new Set(["area 2", ...Object.keys(polis[0])])].filter(column => !omittedPredictors.has(column) && polis.some(d => isUsableValue(column, d[column])) ); const selectedPredictors = new Set( candidatePredictors.filter(column => defaultPredictors.has(column)) ); const filters = { polisityOne: false, prom1AtLeastOne: false }; const transpose = matrix => matrix[0].map((_, column) => matrix.map(row => row[column])); const multiply = (left, right) => left.map(row => right[0].map((_, column) => row.reduce((sum, value, i) => sum + value * right[i][column], 0) )); const solve = (matrix, vector) => { const n = matrix.length; const augmented = matrix.map((row, i) => [...row, vector[i]]); for (let column = 0; column < n; column++) { let pivot = column; for (let row = column + 1; row < n; row++) { if (Math.abs(augmented[row][column]) > Math.abs(augmented[pivot][column])) { pivot = row; } } if (Math.abs(augmented[pivot][column]) < 1e-12) { throw new Error("The selected predictors are perfectly collinear or have no variation."); } [augmented[column], augmented[pivot]] = [augmented[pivot], augmented[column]]; const divisor = augmented[column][column]; for (let j = column; j <= n; j++) augmented[column][j] /= divisor; for (let row = 0; row < n; row++) { if (row === column) continue; const factor = augmented[row][column]; for (let j = column; j <= n; j++) { augmented[row][j] -= factor * augmented[column][j]; } } } return augmented.map(row => row[n]); }; const invert = matrix => { const n = matrix.length; return matrix[0].map((_, column) => solve(matrix, matrix.map((_, row) => row === column ? 1 : 0)) ); }; const logGamma = z => { const coefficients = [ 676.5203681218851, -1259.1392167224028, 771.32342877765313, -176.61502916214059, 12.507343278686905, -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7 ]; if (z < 0.5) { return Math.log(Math.PI) - Math.log(Math.sin(Math.PI * z)) - logGamma(1 - z); } z -= 1; let x = 0.99999999999980993; for (let i = 0; i < coefficients.length; i++) x += coefficients[i] / (z + i + 1); const t = z + coefficients.length - 0.5; return 0.5 * Math.log(2 * Math.PI) + (z + 0.5) * Math.log(t) - t + Math.log(x); }; const betaContinuedFraction = (a, b, x) => { const maxIterations = 200; const epsilon = 3e-7; const minimum = 1e-30; const qab = a + b; const qap = a + 1; const qam = a - 1; let c = 1; let d = 1 - qab * x / qap; if (Math.abs(d) < minimum) d = minimum; d = 1 / d; let h = d; for (let m = 1; m <= maxIterations; m++) { const m2 = 2 * m; let aa = m * (b - m) * x / ((qam + m2) * (a + m2)); d = 1 + aa * d; if (Math.abs(d) < minimum) d = minimum; c = 1 + aa / c; if (Math.abs(c) < minimum) c = minimum; d = 1 / d; h *= d * c; aa = -(a + m) * (qab + m) * x / ((a + m2) * (qap + m2)); d = 1 + aa * d; if (Math.abs(d) < minimum) d = minimum; c = 1 + aa / c; if (Math.abs(c) < minimum) c = minimum; d = 1 / d; const delta = d * c; h *= delta; if (Math.abs(delta - 1) < epsilon) break; } return h; }; const regularizedBeta = (x, a, b) => { if (x <= 0) return 0; if (x >= 1) return 1; const factor = Math.exp( logGamma(a + b) - logGamma(a) - logGamma(b) + a * Math.log(x) + b * Math.log1p(-x) ); return x < (a + 1) / (a + b + 2) ? factor * betaContinuedFraction(a, b, x) / a : 1 - factor * betaContinuedFraction(b, a, 1 - x) / b; }; const twoSidedTTestPValue = (t, degreesOfFreedom) => { if (!Number.isFinite(t)) return NaN; const x = degreesOfFreedom / (degreesOfFreedom + t ** 2); return Math.max(0, Math.min(1, regularizedBeta(x, degreesOfFreedom / 2, 0.5))); }; const significanceStars = pValue => pValue < 0.01 ? "***" : pValue < 0.05 ? "**" : pValue < 0.1 ? "*" : ""; const formatNumber = value => Number.isFinite(value) ? value.toFixed(4) : "—"; const formatPValue = value => { if (!Number.isFinite(value)) return "—"; return value < 0.0001 ? "<0.0001" : value.toFixed(4); }; const pearsonCorrelation = (left, right) => { const leftMean = left.reduce((sum, value) => sum + value, 0) / left.length; const rightMean = right.reduce((sum, value) => sum + value, 0) / right.length; const numerator = left.reduce((sum, value, i) => sum + (value - leftMean) * (right[i] - rightMean), 0 ); const leftSumSquares = left.reduce((sum, value) => sum + (value - leftMean) ** 2, 0); const rightSumSquares = right.reduce((sum, value) => sum + (value - rightMean) ** 2, 0); const denominator = Math.sqrt(leftSumSquares * rightSumSquares); return denominator === 0 ? NaN : numerator / denominator; }; const correlationPValue = (correlation, sampleSize) => { if (!Number.isFinite(correlation) || sampleSize <= 2) return NaN; if (Math.abs(correlation) >= 1) return 0; const t = correlation * Math.sqrt((sampleSize - 2) / (1 - correlation ** 2)); return twoSidedTTestPValue(t, sampleSize - 2); }; const correlationColor = correlation => { if (!Number.isFinite(correlation)) return "#f3f3f3"; const base = correlation >= 0 ? [13, 54, 117] : [169, 103, 19]; const strength = 0.12 + 0.88 * Math.min(1, Math.abs(correlation)); const rgb = base.map(channel => Math.round(255 + (channel - 255) * strength)); return `rgb(${rgb.join(",")})`; }; const renderCorrelationMatrix = (variables, data) => { const wrapper = document.createElement("div"); wrapper.style.overflowX = "auto"; const title = document.createElement("div"); title.style.marginBottom = "6px"; title.innerHTML = `Pearson correlation matrix · same complete cases: ${data.length}`; wrapper.append(title); if (data.length < 3) { const message = document.createElement("div"); message.textContent = "At least 3 complete cases are needed to calculate correlation significance."; wrapper.append(message); return wrapper; } const table = document.createElement("table"); table.style.borderCollapse = "collapse"; table.style.fontSize = "12px"; table.style.whiteSpace = "nowrap"; table.style.marginBottom = "6px"; const headerRow = table.createTHead().insertRow(); const corner = document.createElement("th"); corner.style.padding = "4px 8px"; headerRow.append(corner); variables.forEach(variable => { const cell = document.createElement("th"); cell.textContent = variable; cell.style.padding = "4px 8px"; cell.style.fontWeight = "600"; headerRow.append(cell); }); const body = table.createTBody(); variables.forEach((rowVariable, rowIndex) => { const row = body.insertRow(); const label = row.insertCell(); label.textContent = rowVariable; label.style.fontWeight = "600"; label.style.padding = "4px 8px"; variables.forEach((columnVariable, columnIndex) => { const cell = row.insertCell(); cell.style.textAlign = "center"; cell.style.padding = "6px 8px"; cell.style.minWidth = "62px"; if (columnIndex > rowIndex) { cell.textContent = ""; cell.style.border = "0"; return; } const left = data.map(d => +d[rowVariable]); const right = data.map(d => +d[columnVariable]); const correlation = pearsonCorrelation(left, right); const pValue = rowIndex === columnIndex ? NaN : correlationPValue(correlation, data.length); cell.textContent = `${formatNumber(correlation)}${significanceStars(pValue)}`; cell.style.background = correlationColor(correlation); cell.style.color = Number.isFinite(correlation) && Math.abs(correlation) >= 0.55 ? "white" : "#222"; }); }); wrapper.append(table); const colorLegend = document.createElement("div"); colorLegend.style.display = "flex"; colorLegend.style.alignItems = "center"; colorLegend.style.gap = "8px"; colorLegend.style.fontSize = "12px"; colorLegend.innerHTML = ` −1 strong negative strong positive +1`; wrapper.append(colorLegend); const significanceLegend = document.createElement("div"); significanceLegend.style.fontSize = "12px"; significanceLegend.style.marginTop = "4px"; significanceLegend.innerHTML = `* p < 0.1 · ** p < 0.05 · *** p < 0.01 · lower triangle shown`; wrapper.append(significanceLegend); return wrapper; }; const regressionChartColors = [ "#2563eb", "#dc2626", "#059669", "#9333ea", "#d97706", "#0891b2", "#db2777", "#65a30d" ]; const renderRegressionScatterplots = (predictors, data) => { const wrapper = document.createElement("div"); wrapper.style.fontFamily = "system-ui, sans-serif"; const title = document.createElement("div"); title.style.marginBottom = "8px"; title.innerHTML = `Regression scatterplots · points included in the current model: ${data.length}`; wrapper.append(title); if (!predictors.length) { const message = document.createElement("div"); message.textContent = "Select at least one independent variable to display the scatterplot."; wrapper.append(message); return wrapper; } const legend = document.createElement("div"); legend.style.display = "flex"; legend.style.flexWrap = "wrap"; legend.style.gap = "4px 14px"; legend.style.marginBottom = "8px"; legend.style.fontSize = "12px"; predictors.forEach((variable, index) => { const item = document.createElement("span"); item.style.display = "inline-flex"; item.style.alignItems = "center"; item.style.gap = "5px"; item.innerHTML = `${variable}`; legend.append(item); }); wrapper.append(legend); const yValues = data.map(d => +d[response]); const yMin = Math.min(...yValues); const yMax = Math.max(...yValues); const yDomain = yMin === yMax ? [yMin - 1, yMax + 1] : [yMin, yMax]; const grid = document.createElement("div"); grid.style.display = "grid"; grid.style.gridTemplateColumns = "repeat(auto-fit, minmax(320px, 1fr))"; grid.style.gap = "12px"; predictors.forEach((variable, index) => { const color = regressionChartColors[index % regressionChartColors.length]; const points = data.map(d => ({ x: +d[variable], y: +d[response] })); const xValues = points.map(point => point.x); const xMin = Math.min(...xValues); const xMax = Math.max(...xValues); const xDomain = xMin === xMax ? [xMin - 1, xMax + 1] : [xMin, xMax]; const xMean = xValues.reduce((sum, value) => sum + value, 0) / xValues.length; const yMean = yValues.reduce((sum, value) => sum + value, 0) / yValues.length; const numerator = points.reduce((sum, point) => sum + (point.x - xMean) * (point.y - yMean), 0 ); const denominator = points.reduce((sum, point) => sum + (point.x - xMean) ** 2, 0); const slope = denominator === 0 ? 0 : numerator / denominator; const intercept = yMean - slope * xMean; const trend = [ {x: xDomain[0], y: intercept + slope * xDomain[0]}, {x: xDomain[1], y: intercept + slope * xDomain[1]} ]; const panel = document.createElement("div"); panel.style.border = "1px solid #ddd"; panel.style.padding = "4px"; panel.style.overflowX = "auto"; panel.append(Plot.plot({ width: 360, height: 280, marginLeft: 52, marginBottom: 48, x: {label: variable, domain: xDomain, grid: true}, y: {type: "symlog", label: `${response} (symlog)`, domain: yDomain, grid: true}, marks: [ Plot.dot(points, {x: "x", y: "y", fill: color, fillOpacity: 0.45, r: 3}), Plot.line(trend, {x: "x", y: "y", stroke: color, strokeWidth: 2}) ] })); grid.append(panel); }); wrapper.append(grid); return wrapper; }; const controls = html`

Data filters

Only include Polisity = 1 Only include where prom 1 ≥ 1

Independent variables

Dependent variable: staseis. Numeric variables only. Democracy/Hellenicity = 0 is treated as unknown; Walls = 0 remains valid.

`; const predictorContainer = controls.querySelector("[data-predictors]"); const correlationHolder = html`

`; const outputHolder = html`

`; const container = html`

`; container.append(correlationHolder, controls, outputHolder); const renderModel = () => { const predictors = [...selectedPredictors]; const columns = [response, ...predictors]; const filteredData = polis.filter(d => (!filters.polisityOne || (isNumber(d["Polisity"]) && +d["Polisity"] === 1)) && (!filters.prom1AtLeastOne || (isNumber(d["prom 1"]) && +d["prom 1"] >= 1)) ); const completeCases = filteredData.filter(d => columns.every(column => column === response ? isNumber(d[column]) : isUsableValue(column, d[column]) )); const parameterCount = predictors.length + 1; correlationHolder.replaceChildren(renderCorrelationMatrix(columns, completeCases)); if (completeCases.length <= parameterCount) { outputHolder.replaceChildren(html`

Not enough complete cases for this model.

`); return; } try { const X = completeCases.map(d => [1, ...predictors.map(column => +d[column])]); const y = completeCases.map(d => +d[response]); const XTranspose = transpose(X); const XtX = multiply(XTranspose, X); const Xty = multiply(XTranspose, y.map(value => [value])).map(row => row[0]); const beta = solve(XtX, Xty); const XtXInverse = invert(XtX); const fitted = X.map(row => row.reduce((sum, value, i) => sum + value * beta[i], 0)); const residuals = y.map((value, i) => value - fitted[i]); const yMean = y.reduce((sum, value) => sum + value, 0) / y.length; const ssResidual = residuals.reduce((sum, value) => sum + value ** 2, 0); const ssTotal = y.reduce((sum, value) => sum + (value - yMean) ** 2, 0); const rSquared = 1 - ssResidual / ssTotal; const adjustedRSquared = 1 - (1 - rSquared) * (y.length - 1) / (y.length - beta.length); const degreesOfFreedom = y.length - beta.length; const residualVariance = ssResidual / degreesOfFreedom; const standardErrors = beta.map((_, i) => Math.sqrt(residualVariance * XtXInverse[i][i])); const tStatistics = beta.map((value, i) => value / standardErrors[i]); const pValues = tStatistics.map(t => twoSidedTTestPValue(t, degreesOfFreedom)); const coefficientNames = ["Intercept", ...predictors]; const tableWrapper = document.createElement("div"); tableWrapper.style.overflowX = "auto"; const table = document.createElement("table"); table.style.borderCollapse = "collapse"; table.style.whiteSpace = "nowrap"; table.style.minWidth = "720px"; const headerRow = table.createTHead().insertRow(); ["Term", "Coefficient", "Std. error", "t statistic", "p value"].forEach((header, i) => { const cell = document.createElement("th"); cell.textContent = header; cell.style.textAlign = i === 0 ? "left" : "right"; cell.style.padding = "4px 12px"; cell.style.borderBottom = "1px solid #999"; headerRow.append(cell); }); const body = table.createTBody(); coefficientNames.forEach((name, i) => { const row = body.insertRow(); const values = [ name, `${formatNumber(beta[i])}${significanceStars(pValues[i])}`, formatNumber(standardErrors[i]), formatNumber(tStatistics[i]), formatPValue(pValues[i]) ]; values.forEach((value, column) => { const cell = row.insertCell(); cell.textContent = value; cell.style.textAlign = column === 0 ? "left" : "right"; cell.style.padding = "4px 12px"; }); }); tableWrapper.append(table); const output = html`

OLS regression: staseis ~ ${predictors.length ? predictors.join(" + ") : "1"}

Complete cases: ${completeCases.length} · R²: ${formatNumber(rSquared)} · Adjusted R²: ${formatNumber(adjustedRSquared)} · Residual df: ${degreesOfFreedom}

* p < 0.1 · ** p < 0.05 · *** p < 0.01

`; output.querySelector("[data-scatterplots]").append( renderRegressionScatterplots(predictors, completeCases) ); output.querySelector("[data-regression-table]").append(tableWrapper); outputHolder.replaceChildren(output); } catch (error) { outputHolder.replaceChildren(html`

${error.message}

`); } }; const updatePredictorControls = () => { predictorContainer.replaceChildren(); for (const column of candidatePredictors) { const label = document.createElement("label"); label.style.display = "flex"; label.style.alignItems = "center"; label.style.gap = "5px"; const checkbox = document.createElement("input"); checkbox.type = "checkbox"; checkbox.checked = selectedPredictors.has(column); checkbox.addEventListener("change", () => { if (checkbox.checked) selectedPredictors.add(column); else selectedPredictors.delete(column); renderModel(); }); label.append(checkbox, document.createTextNode(column)); predictorContainer.append(label); } }; controls.querySelector("[data-filter-polisity]").addEventListener("change", event => { filters.polisityOne = event.target.checked; renderModel(); }); controls.querySelector("[data-filter-prom1]").addEventListener("change", event => { filters.prom1AtLeastOne = event.target.checked; renderModel(); }); controls.querySelector("[data-select-none]").addEventListener("click", () => { selectedPredictors.clear(); updatePredictorControls(); renderModel(); }); controls.querySelector("[data-select-default]").addEventListener("click", () => { selectedPredictors.clear(); for (const column of defaultPredictors) { if (candidatePredictors.includes(column)) selectedPredictors.add(column); } updatePredictorControls(); renderModel(); }); updatePredictorControls(); renderModel(); display(container); 42:[{"id":"c20d211d5a226060a54a51ec968f6c6309028539122c38209bfeaf381f9f4ac0ac99cec94fbd91c44bc8a5d704fff6bf4bcc749621c37b1813f29eaf9a061578","href":"https://static.observableusercontent.com/files/c20d211d5a226060a54a51ec968f6c6309028539122c38209bfeaf381f9f4ac0ac99cec94fbd91c44bc8a5d704fff6bf4bcc749621c37b1813f29eaf9a061578","name":"polis data_distributed 21.08.25.xlsx","type":"application/vnd.openxmlformats-officedocument.spreadsheetml.sheet","lastModified":1792476569605,"size":211189},{"id":"196ae8ddb7f2c51a07aba18fc7642692cb53eaacb92518b7fe2e70f6ef7d1911d6d35ea541946b0ddb3042c4cb2004ab45d748d1cb6f941608bea32006ddbe2f","href":"https://static.observableusercontent.com/files/196ae8ddb7f2c51a07aba18fc7642692cb53eaacb92518b7fe2e70f6ef7d1911d6d35ea541946b0ddb3042c4cb2004ab45d748d1cb6f941608bea32006ddbe2f","name":"Codebook.docx","type":"application/vnd.openxmlformats-officedocument.wordprocessingml.document","lastModified":1792476571872,"size":19369},{"id":"019a78a7838a8bef054d4f28d1d216a9ca774b2f6d344007c8e9cb8337d0872aa37b36c8ceb48398d051d214f347b0099a66538c2577914ac95fbb6652c43ca1","href":"https://static.observableusercontent.com/files/019a78a7838a8bef054d4f28d1d216a9ca774b2f6d344007c8e9cb8337d0872aa37b36c8ceb48398d051d214f347b0099a66538c2577914ac95fbb6652c43ca1","name":"anicent-olympics-games.jpg","type":"image/jpeg","lastModified":1792478446474,"size":186033}] 3b:{"id":"182f2622003b6dbe","slug":"polis-regression-analysis-war-and-peace-in-ancient-greece","title":"Polis Regression Analysis - War & Peace in Ancient Greece","thumbnail":"96829282b6a1d1b11c7c5ddd5881eceed27012464b7d1774a43dc11f5ef5e41b","access_level":"public","create_time":"$D2026-10-20T06:09:13.105Z","update_time":"$D2026-10-20T09:13:54.467Z","view_time":null,"first_public_time":"$D2026-10-20T06:28:49.582Z","has_unpublished_edits":null,"fork":false,"stars":2,"starred":false,"owner":{"type":"team","id":"7c4453bfba6d243c","login":"geo-theo","name":"geo-theo","avatar_url":"https://avatars-next.observableusercontent.com/7c6e213507054a75d47cd8b842609fb692f2e960eb0ebe2d04712d7cf13d94b4","tier":"starter_2024","bio":"","following":false},"version":134,"publish_version":134,"role":null,"authored":false,"authors":[{"type":"individual","id":"0ebe4fb56285b831","login":"geo-theo","name":"geo-theo","avatar_url":"https://avatars-next.observableusercontent.com/7c6e213507054a75d47cd8b842609fb692f2e960eb0ebe2d04712d7cf13d94b4","tier":null,"bio":"","following":false}],"members":[{"type":"team","id":"7c4453bfba6d243c","login":"geo-theo","name":"geo-theo","avatar_url":"https://avatars-next.observableusercontent.com/7c6e213507054a75d47cd8b842609fb692f2e960eb0ebe2d04712d7cf13d94b4","tier":"starter_2024","role":"editor"}],"comments":[],"custom_thumbnail":true,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Polis Regression Analysis - War & Peace in Ancient Greece","cells":[{"id":1,"value":"# Polis Regression Analysis - War & Peace in Ancient Greece","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":10,"value":"FileAttachment(\"anicent-olympics-games.jpg\").image()","pinned":false,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2,"value":"$3d","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"

\n\n## Exploratory Data Analysis","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"// table\nconst workbook = await FileAttachment(\"polis data_distributed 21.08.25.xlsx\").xlsx();\n\nconst polis = workbook.sheet(\"Sheet1\", {headers: true});\n\ndisplay(Inputs.table(polis));","pinned":false,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"$3e","pinned":false,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":15,"value":"$3f","pinned":false,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"

\n\n## Regression Analysis","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":17,"value":"$40","pinned":false,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":19,"value":"

\n\n_Use area 1 due to lack of area 2 values._","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":22,"value":"

\n\n## Interactive regression model","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":23,"value":"$41","pinned":false,"hidden":false,"mode":"ts","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":24,"value":"

\n\n### Conditions leading to higher internal political violence:\n- Democracies = higher staseis\n- Larger areas of land under polities' control\n- More colonies\n- More Olympic victories\n- Actively-diplomatic polities\n\n### Conditions leading to lower internal political violence:\n- Possibly, though not statistically significant, more diverse polities (mixed & barbarian)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W42","stdlib":"2"}} 3c:"$3b:body"