diff --git a/src/lib/schema/fileOps.ts b/src/lib/schema/fileOps.ts
index 969e7e82..26e14c9c 100644
--- a/src/lib/schema/fileOps.ts
+++ b/src/lib/schema/fileOps.ts
@@ -13,6 +13,7 @@ import type { ComponentFile, ComponentType, BlockContent, SubsystemContent } fro
 import type { Position } from '$lib/types';
 import { ALL_COMPONENT_EXTENSIONS, COMPONENT_VERSION } from '$lib/types/component';
 import { cleanNodeForExport } from './cleanParams';
+import { migrateGraphFile } from './migrate';
 import { graphStore, cloneNodeForPaste } from '$lib/stores/graph';
 import { eventStore } from '$lib/stores/events';
 import { settingsStore } from '$lib/stores/settings';
@@ -165,48 +166,6 @@ export function createGraphFile(name?: string): GraphFile {
 	};
 }
 
-/**
- * Migrate old node type format to new format
- * Old: 'pathsim.sources.StepSource' -> New: 'StepSource'
- */
-function migrateNodeType(type: string): string {
-	if (type.startsWith('pathsim.')) {
-		// Extract the last part after the final dot
-		const parts = type.split('.');
-		return parts[parts.length - 1];
-	}
-	return type;
-}
-
-/**
- * Migrate a GraphFile from old format to new format
- */
-function migrateGraphFile(file: GraphFile): GraphFile {
-	const migrateNodes = (nodes: NodeInstance[]): NodeInstance[] => {
-		return nodes.map(node => {
-			const migratedNode = { ...node, type: migrateNodeType(node.type) };
-			// Recursively migrate subsystem graphs (preserving connections, annotations, and events)
-			if (migratedNode.graph) {
-				migratedNode.graph = {
-					nodes: migrateNodes(migratedNode.graph.nodes || []),
-					connections: migratedNode.graph.connections || [],
-					annotations: migratedNode.graph.annotations,
-					events: migratedNode.graph.events
-				};
-			}
-			return migratedNode;
-		});
-	};
-
-	return {
-		...file,
-		graph: file.graph ? {
-			...file.graph,
-			nodes: migrateNodes(file.graph.nodes || [])
-		} : file.graph
-	};
-}
-
 /**
  * Install missing runtime toolboxes referenced by a file's
  * `requiredToolboxes`. Asks the user once, then installs in order.
diff --git a/src/lib/schema/migrate.test.ts b/src/lib/schema/migrate.test.ts
new file mode 100644
index 00000000..15a026b0
--- /dev/null
+++ b/src/lib/schema/migrate.test.ts
@@ -0,0 +1,43 @@
+import { describe, it, expect } from 'vitest';
+import { migrateGraphFile } from './migrate';
+import type { GraphFile, NodeInstance } from '$lib/nodes/types';
+import type { ToolboxRequirement } from '$lib/types/schema';
+
+const chem = (installedVersion: string | null): ToolboxRequirement => ({
+	id: 'pathsim-chem',
+	displayName: 'pathsim-chem',
+	source: { type: 'pypi', pkg: 'pathsim-chem' },
+	importPath: 'pathsim_chem',
+	installedVersion
+});
+
+const polynomial = (coeffs: string): NodeInstance =>
+	({ id: 'p', type: 'Polynomial', name: 'Polynomial', params: { coeffs } }) as unknown as NodeInstance;
+
+const file = (nodes: NodeInstance[], requiredToolboxes?: ToolboxRequirement[]): GraphFile =>
+	({ version: '1.0.0', graph: { nodes, connections: [] }, requiredToolboxes }) as unknown as GraphFile;
+
+const coeffsOf = (f: GraphFile) => f.graph.nodes[0].params?.coeffs;
+
+describe('migrateGraphFile', () => {
+	it('drops the old pathsim module prefix of node types', () => {
+		const node = { ...polynomial('[1]'), type: 'pathsim.sources.StepSource' };
+		expect(migrateGraphFile(file([node])).graph.nodes[0].type).toBe('StepSource');
+	});
+
+	it('reverses the coefficients of the Polynomial of pathsim-chem before 0.4', () => {
+		expect(coeffsOf(migrateGraphFile(file([polynomial('[1, 2, 3]')], [chem('0.3.0')])))).toBe('([1, 2, 3])[::-1]');
+		expect(coeffsOf(migrateGraphFile(file([polynomial('c')], [chem(null)])))).toBe('(c)[::-1]');
+	});
+
+	it('reverses the coefficients inside subsystems', () => {
+		const sub = { id: 's', type: 'Subsystem', name: 'S', params: {}, graph: { nodes: [polynomial('[1, 2]')], connections: [] } };
+		const migrated = migrateGraphFile(file([sub as unknown as NodeInstance], [chem('0.2.8')]));
+		expect(migrated.graph.nodes[0].graph?.nodes[0].params?.coeffs).toBe('([1, 2])[::-1]');
+	});
+
+	it('keeps the core Polynomial', () => {
+		expect(coeffsOf(migrateGraphFile(file([polynomial('[1, 2, 3]')])))).toBe('[1, 2, 3]');
+		expect(coeffsOf(migrateGraphFile(file([polynomial('[1, 2, 3]')], [chem('0.4.0')])))).toBe('[1, 2, 3]');
+	});
+});
diff --git a/src/lib/schema/migrate.ts b/src/lib/schema/migrate.ts
new file mode 100644
index 00000000..30f00cd5
--- /dev/null
+++ b/src/lib/schema/migrate.ts
@@ -0,0 +1,82 @@
+/**
+ * Migrations of saved graph files to the current format, applied on load
+ */
+
+import type { NodeInstance, GraphFile } from '$lib/nodes/types';
+import type { ToolboxRequirement } from '$lib/types/schema';
+
+/**
+ * pathsim-chem up to 0.3 had its own `Polynomial` with the coefficients in
+ * ascending order, which replaced the core block of the same name. It was
+ * removed in 0.4, so these nodes now load as `pathsim.blocks.Polynomial`,
+ * which takes the coefficients in descending order (numpy.polyval).
+ */
+const CHEM_POLYNOMIAL_REMOVED = [0, 4];
+
+/**
+ * Migrate old node type format to new format
+ * Old: 'pathsim.sources.StepSource' -> New: 'StepSource'
+ */
+function migrateNodeType(type: string): string {
+	if (type.startsWith('pathsim.')) {
+		// Extract the last part after the final dot
+		const parts = type.split('.');
+		return parts[parts.length - 1];
+	}
+	return type;
+}
+
+/** Whether a version string is older than [major, minor], unknown versions count as older */
+function olderThan(version: string | null | undefined, [major, minor]: number[]): boolean {
+	const match = version?.match(/^(\d+)\.(\d+)/);
+	if (!match) return true;
+	const [maj, min] = [Number(match[1]), Number(match[2])];
+	return maj < major || (maj === major && min < minor);
+}
+
+/** Whether the file was saved with a pathsim-chem that still had its own Polynomial */
+function hasChemPolynomial(requirements: ToolboxRequirement[] | undefined): boolean {
+	const chem = requirements?.find((r) => r.importPath === 'pathsim_chem');
+	return !!chem && olderThan(chem.installedVersion, CHEM_POLYNOMIAL_REMOVED);
+}
+
+/** Reverse the coefficients of a chem Polynomial for the core block */
+function migrateChemPolynomial(node: NodeInstance): NodeInstance {
+	const coeffs = node.params?.coeffs;
+	if (typeof coeffs !== 'string' || !coeffs.trim()) return node;
+	return { ...node, params: { ...node.params, coeffs: `(${coeffs})[::-1]` } };
+}
+
+/**
+ * Migrate a GraphFile from old format to new format
+ */
+export function migrateGraphFile(file: GraphFile): GraphFile {
+	const chemPolynomial = hasChemPolynomial(file.requiredToolboxes);
+
+	const migrateNodes = (nodes: NodeInstance[]): NodeInstance[] => {
+		return nodes.map(node => {
+			let migratedNode = { ...node, type: migrateNodeType(node.type) };
+			if (chemPolynomial && migratedNode.type === 'Polynomial') {
+				migratedNode = migrateChemPolynomial(migratedNode);
+			}
+			// Recursively migrate subsystem graphs (preserving connections, annotations, and events)
+			if (migratedNode.graph) {
+				migratedNode.graph = {
+					nodes: migrateNodes(migratedNode.graph.nodes || []),
+					connections: migratedNode.graph.connections || [],
+					annotations: migratedNode.graph.annotations,
+					events: migratedNode.graph.events
+				};
+			}
+			return migratedNode;
+		});
+	};
+
+	return {
+		...file,
+		graph: file.graph ? {
+			...file.graph,
+			nodes: migrateNodes(file.graph.nodes || [])
+		} : file.graph
+	};
+}