refactor: rename register symbol ω → φ

apps/web/e2e/integration-smoke.spec.ts

@@ -190,7 +190,7 @@ test.describe("Sprint 36 — Integration Smoke Test", () => {
       timeout: 5000,
     });
 
-    // r9 should be 102 (0x66) — proving editing ω7 changed the downstream result
+    // r9 should be 102 (0x66) — proving editing φ7 changed the downstream result
     const regHex9 = page.getByTestId("register-hex-9");
     await expect(regHex9).toHaveText(/0x0{14}66/i, { timeout: 5000 });
   });

apps/web/e2e/sprint-03-instructions.spec.ts

@@ -49,7 +49,7 @@ test.describe("Sprint 03 — Flat Instruction List", () => {
     await expect(mnemonicElement).toHaveText(/.+/);
   });
 
-  test("register arguments use omega notation (ω)", async ({ page }) => {
+  test("register arguments use phi notation (φ)", async ({ page }) => {
     // Load the add-jam example (SPI, in wat category — collapsed by default)
     await page.goto("/#/load");
     await page.getByTestId("category-toggle-wat").click();
@@ -69,21 +69,21 @@ test.describe("Sprint 03 — Flat Instruction List", () => {
     const panel = page.getByTestId("instructions-panel");
     await expect(panel).toBeVisible();
 
-    // At least one instruction should contain omega notation
+    // At least one instruction should contain phi notation
     const argsElements = panel.getByTestId("instruction-args");
     const count = await argsElements.count();
     expect(count).toBeGreaterThan(0);
 
-    // Find at least one args element with omega notation
-    let foundOmega = false;
+    // Find at least one args element with phi notation
+    let foundPhi = false;
     for (let i = 0; i < count; i++) {
       const text = await argsElements.nth(i).textContent();
-      if (text?.includes("ω")) {
-        foundOmega = true;
+      if (text?.includes("φ")) {
+        foundPhi = true;
         break;
       }
     }
-    expect(foundOmega).toBe(true);
+    expect(foundPhi).toBe(true);
   });
 
   test("current PC row is visually highlighted", async ({ page }) => {

apps/web/e2e/sprint-04-registers.spec.ts

@@ -41,7 +41,7 @@ test.describe("Sprint 04 — Registers + Status Display", () => {
     await expect(gasValue).toHaveText(/^[\d,]+$/);
   });
 
-  test("all 13 register rows render with omega labels", async ({ page }) => {
+  test("all 13 register rows render with phi labels", async ({ page }) => {
     await loadProgram(page);
 
     const panel = page.getByTestId("registers-panel");
@@ -52,7 +52,7 @@ test.describe("Sprint 04 — Registers + Status Display", () => {
       await expect(row).toBeVisible();
 
       const label = page.getByTestId(`register-label-${i}`);
-      await expect(label).toHaveText(`ω${i}:`);
+      await expect(label).toHaveText(`φ${i}:`);
     }
   });
 

apps/web/e2e/sprint-28-asm-raw-popover.spec.ts

@@ -30,7 +30,7 @@ async function loadProgram(
 }
 
 test.describe("Sprint 28 — ASM/Raw Toggle + Binary Popover", () => {
-  test("ASM mode shows omega notation", async ({ page }) => {
+  test("ASM mode shows phi notation", async ({ page }) => {
     await loadProgram(page, "add-jam");
 
     const panel = page.getByTestId("instructions-panel");
@@ -40,21 +40,21 @@ test.describe("Sprint 28 — ASM/Raw Toggle + Binary Popover", () => {
     const asmBtn = page.getByTestId("display-mode-asm");
     await expect(asmBtn).toBeVisible();
 
-    // Instruction args should contain omega notation
+    // Instruction args should contain phi notation
     const argsElements = panel.locator("[data-testid='instruction-args']");
     const count = await argsElements.count();
     expect(count).toBeGreaterThan(0);
 
-    // At least one arg should contain omega (ω) character
-    let hasOmega = false;
+    // At least one arg should contain phi (φ) character
+    let hasPhi = false;
     for (let i = 0; i < count; i++) {
       const text = await argsElements.nth(i).textContent();
-      if (text?.includes("ω")) {
-        hasOmega = true;
+      if (text?.includes("φ")) {
+        hasPhi = true;
         break;
       }
     }
-    expect(hasOmega).toBe(true);
+    expect(hasPhi).toBe(true);
   });
 
   test("toggling to Raw mode changes displayed text", async ({ page }) => {
@@ -87,7 +87,7 @@ test.describe("Sprint 28 — ASM/Raw Toggle + Binary Popover", () => {
     expect(firstRaw).toMatch(/^[0-9A-F]{2}( [0-9A-F]{2})*$/);
   });
 
-  test("toggling back to ASM restores omega notation", async ({ page }) => {
+  test("toggling back to ASM restores phi notation", async ({ page }) => {
     await loadProgram(page, "add-jam");
 
     const panel = page.getByTestId("instructions-panel");
@@ -106,18 +106,18 @@ test.describe("Sprint 28 — ASM/Raw Toggle + Binary Popover", () => {
     const mnemonics = panel.locator("[data-testid='instruction-mnemonic']");
     expect(await mnemonics.count()).toBeGreaterThan(0);
 
-    // Omega notation should be present in args
+    // Phi notation should be present in args
     const argsElements = panel.locator("[data-testid='instruction-args']");
     const count = await argsElements.count();
-    let hasOmega = false;
+    let hasPhi = false;
     for (let i = 0; i < count; i++) {
       const text = await argsElements.nth(i).textContent();
-      if (text?.includes("ω")) {
-        hasOmega = true;
+      if (text?.includes("φ")) {
+        hasPhi = true;
         break;
       }
     }
-    expect(hasOmega).toBe(true);
+    expect(hasPhi).toBe(true);
   });
 
   test("clicking an instruction opens the binary popover", async ({ page }) => {

apps/web/src/components/debugger/RegisterRow.tsx

@@ -111,7 +111,7 @@ export function RegisterRow({
         data-testid={`register-label-${index}`}
         className="text-muted-foreground w-8 shrink-0 select-none"
       >
-        ω{index}:
+        φ{index}:
       </span>
       {editing ? (
         <input

apps/web/src/components/debugger/RegistersPanel.test.tsx

@@ -104,9 +104,9 @@ describe("RegistersPanel — Change Highlighting", () => {
       />,
     );
 
-    // omega3 changed -> should have delta
+    // phi3 changed -> should have delta
     expect(screen.getByTestId("register-delta-3")).toBeDefined();
-    // omega0 did not change -> no delta
+    // phi0 did not change -> no delta
     expect(screen.queryByTestId("register-delta-0")).toBeNull();
     // PC changed -> delta
     expect(screen.getByTestId("pc-delta")).toBeDefined();
@@ -133,7 +133,7 @@ describe("RegistersPanel — Change Highlighting", () => {
       />,
     );
 
-    // Step 1->2: omega5 changes
+    // Step 1->2: phi5 changes
     rerender(
       <RegistersPanel
         snapshot={snap2}
@@ -269,9 +269,9 @@ describe("RegistersPanel — Multi-PVM Divergence", () => {
       />,
     );
 
-    // omega7 differs -> divergence indicator
+    // phi7 differs -> divergence indicator
     expect(screen.getByTestId("register-divergence-7")).toBeDefined();
-    // omega0 matches -> no indicator
+    // phi0 matches -> no indicator
     expect(screen.queryByTestId("register-divergence-0")).toBeNull();
   });
 });

apps/web/src/components/drawer/HostCallTab.tsx

@@ -75,7 +75,7 @@ function Sidebar({
           data-testid="output-preview"
           className="text-xs font-mono border-t border-border pt-1"
         >
-          <span className="text-muted-foreground">ω₇ ← </span>
+          <span className="text-muted-foreground">φ₇ ← </span>
           <span className="text-foreground">
             {outputValue.toString()}
             {outputValue !== NONE && (
@@ -305,7 +305,7 @@ export function HostCallTab({
       setNoneChecked(checked);
       setUserModified(true);
       if (checked) {
-        // NONE: ω₇ = 2^64-1, no memory writes, clean up previously applied mem writes
+        // NONE: φ₇ = 2^64-1, no memory writes, clean up previously applied mem writes
         for (const addr of appliedMemAddrsRef.current) {
           pendingChanges.removeMemoryWrite(addr);
         }
@@ -394,7 +394,7 @@ export function HostCallTab({
           )}
           {noneChecked && (
             <p className="text-xs text-muted-foreground italic">
-              NONE mode: returning ω₇ = 2⁶⁴−1 with no memory writes.
+              NONE mode: returning φ₇ = 2⁶⁴−1 with no memory writes.
             </p>
           )}
           <p

apps/web/src/components/drawer/hostcalls/GasHostCall.tsx

@@ -14,7 +14,7 @@ export function GasHostCall({ info, onEffectsReady }: GasHostCallProps) {
 
   const stableOnEffects = useStableCallback(onEffectsReady);
 
-  // Auto-report ω₇ = currentGas on mount
+  // Auto-report φ₇ = currentGas on mount
   useEffect(() => {
     stableOnEffects({
       registerWrites: new Map([[7, currentGas]]),
@@ -25,7 +25,7 @@ export function GasHostCall({ info, onEffectsReady }: GasHostCallProps) {
   return (
     <div data-testid="gas-host-call" className="flex flex-col gap-2 text-xs">
       <p className="text-muted-foreground">
-        Returns current gas counter in ω₇.
+        Returns current gas counter in φ₇.
       </p>
       <div className="font-mono">
         <span className="text-muted-foreground">Current gas: </span>

apps/web/src/components/drawer/hostcalls/LogHostCall.tsx

@@ -29,7 +29,7 @@ function toHexString(data: Uint8Array): string {
 /**
  * Log host call view (index 100).
  *
- * Log registers: ω7=level, ω8=target_ptr, ω9=target_len, ω10=msg_ptr, ω11=msg_len
+ * Log registers: φ7=level, φ8=target_ptr, φ9=target_len, φ10=msg_ptr, φ11=msg_len
  *
  * Decodes message text from trace memory reads (resumeProposal.memoryWrites)
  * when available, otherwise reads memory from the orchestrator using the

apps/web/src/components/drawer/hostcalls/StorageHostCall.tsx

@@ -244,7 +244,7 @@ export function StorageHostCall({
   const isRead = info.hostCallIndex === 3;
   const regs = info.currentState.registers;
 
-  // For read: ω7=serviceId, ω8=keyPtr, ω9=keyLen, ω10=dest, ω11=offset, ω12=maxLen
+  // For read: φ7=serviceId, φ8=keyPtr, φ9=keyLen, φ10=dest, φ11=offset, φ12=maxLen
   const serviceId = regs[7] ?? 0n;
   const keyPtr = Number(regs[8] ?? 0n);
   const keyLen = Number(regs[9] ?? 0n);
@@ -271,7 +271,7 @@ export function StorageHostCall({
       // Only seed if key doesn't already exist (don't overwrite user edits)
       if (!storageTable.store.get(fullKey)) {
         // The trace's memory write at destAddr is the sliced value; we need to reconstruct the full value.
-        // The ω₇ return value from the proposal is the full value length.
+        // The φ₇ return value from the proposal is the full value length.
         const _fullLen = Number(proposal.registerWrites.get(7) ?? 0n);
         // For simplicity, seed the sliced portion — this is what the trace knows about.
         const mw = proposal.memoryWrites.find((w) => w.address === destAddr);

apps/web/src/components/drawer/hostcalls/host-call-registers.ts

@@ -10,7 +10,7 @@ export interface RegisterMeta {
   format: RegisterFormat;
 }
 
-/** Metadata for the output register (typically ω₇). */
+/** Metadata for the output register (typically φ₇). */
 export interface OutputRegisterMeta {
   index: number;
   label: string;

apps/web/src/components/drawer/trace-display.test.ts

@@ -82,7 +82,7 @@ describe("formatEntryLines", () => {
   it("formats header line with ecalli index and gas", () => {
     const entry = makeEntry({ index: 2, gas: 999n });
     const lines = formatEntryLines(entry);
-    expect(lines[0]).toBe("ecalli 2, ω7 = 999");
+    expect(lines[0]).toBe("ecalli 2, φ7 = 999");
   });
 
   it("formats memory reads", () => {
@@ -106,7 +106,7 @@ describe("formatEntryLines", () => {
       registerWrites: new Map([[7, 42n]]),
     });
     const lines = formatEntryLines(entry);
-    expect(lines).toContainEqual("  ω7 ← 42");
+    expect(lines).toContainEqual("  φ7 ← 42");
   });
 
   it("formats gas update when gasAfter is present", () => {
@@ -134,7 +134,7 @@ describe("formatEntryLines", () => {
     const entry = makeEntry({ index: 0, gas: 100n });
     const lines = formatEntryLines(entry);
     expect(lines).toHaveLength(1);
-    expect(lines[0]).toBe("ecalli 0, ω7 = 100");
+    expect(lines[0]).toBe("ecalli 0, φ7 = 100");
   });
 });
 

apps/web/src/components/drawer/trace-display.ts

@@ -50,7 +50,7 @@ export function formatEntryLines(entry: TraceEntry): string[] {
   const name = getHostCallName(entry.index);
   const lines: string[] = [];
 
-  lines.push(`ecalli ${entry.index}, ω7 = ${entry.gas}`);
+  lines.push(`ecalli ${entry.index}, φ7 = ${entry.gas}`);
 
   // Memory reads
   for (const mr of entry.memoryReads) {
@@ -66,7 +66,7 @@ export function formatEntryLines(entry: TraceEntry): string[] {
 
   // Register writes
   for (const [reg, val] of entry.registerWrites) {
-    lines.push(`  ω${reg} ← ${val}`);
+    lines.push(`  φ${reg} ← ${val}`);
   }
 
   // Gas update

apps/web/src/hooks/useDebuggerActions.ts

@@ -149,7 +149,7 @@ export function persistWriteToStorage(
   const keyHex = deriveKeyHex(hc);
   if (!keyHex) return;
 
-  // For write, value is at ω9/ω10
+  // For write, value is at φ9/φ10
   const valPtr = Number(hc.currentState.registers[9] ?? 0n);
   const valLen = Number(hc.currentState.registers[10] ?? 0n);
 

apps/web/src/hooks/useDisassembly.test.tsx

@@ -28,7 +28,7 @@ describe("useDisassembly", () => {
     expect(result.current).toEqual([]);
   });
 
-  it("args use omega notation, rawArgs use numeric indices", () => {
+  it("args use phi notation, rawArgs use numeric indices", () => {
     const bytes = new Uint8Array(
       readFileSync(resolve(fixturesDir, "generic/add.pvm")),
     );
@@ -39,14 +39,14 @@ describe("useDisassembly", () => {
     expect(instructions.length).toBeGreaterThan(0);
 
     // Find instructions that have register arguments
-    const withRegArgs = instructions.filter((i) => i.args.includes("ω"));
+    const withRegArgs = instructions.filter((i) => i.args.includes("φ"));
     expect(withRegArgs.length).toBeGreaterThan(0);
 
     for (const instr of withRegArgs) {
-      // ASM args should contain omega
-      expect(instr.args).toMatch(/ω\d+/);
-      // Raw args should NOT contain omega, should contain plain numbers
-      expect(instr.rawArgs).not.toContain("ω");
+      // ASM args should contain phi
+      expect(instr.args).toMatch(/φ\d+/);
+      // Raw args should NOT contain phi, should contain plain numbers
+      expect(instr.rawArgs).not.toContain("φ");
       // Raw args should be non-empty (they have register operands)
       expect(instr.rawArgs.length).toBeGreaterThan(0);
     }

apps/web/src/hooks/useDisassembly.ts

@@ -16,14 +16,14 @@ export interface DecodedInstruction {
   mnemonic: string;
   rawBytes: Uint8Array;
   args: string;
-  /** Numeric-only argument string (register indices as numbers, no omega notation). */
+  /** Numeric-only argument string (register indices as numbers, no phi notation). */
   rawArgs: string;
   /** Index of the basic block this instruction belongs to (0-based). */
   blockIndex: number;
 }
 
 function regName(index: number): string {
-  return `ω${index}`;
+  return `φ${index}`;
 }
 
 function formatImm(decoder: { getI32(): number }): string {

apps/web/src/hooks/useDivergenceCheck.test.tsx

@@ -112,8 +112,8 @@ describe("useDivergenceCheck", () => {
       useDivergenceCheck(snapshots, "typeberry", 0),
     );
     expect(result.current.summary).toBe("2 registers");
-    expect(result.current.details).toContain("ω3:");
-    expect(result.current.details).toContain("ω7:");
+    expect(result.current.details).toContain("φ3:");
+    expect(result.current.details).toContain("φ7:");
   });
 
   it("shows 1 register for single register divergence", () => {
@@ -186,7 +186,7 @@ describe("useDivergenceCheck", () => {
     );
 
     // PC diverges (typeberry vs polkavm), Gas diverges (typeberry vs ananas),
-    // register ω3 diverges (typeberry vs both)
+    // register φ3 diverges (typeberry vs both)
     expect(result.current.summary).toBe("PC, Gas, 1 register");
 
     // Details should have entries for each diverging PVM
@@ -196,9 +196,9 @@ describe("useDivergenceCheck", () => {
     // Gas diverges only with ananas, PC only with polkavm
     expect(details).toContain("Gas:");
     expect(details).toContain("PC:");
-    // ω3 diverges with both
-    const omega3Lines = details.split("\n").filter((l) => l.startsWith("ω3:"));
-    expect(omega3Lines.length).toBe(2);
+    // φ3 diverges with both
+    const phi3Lines = details.split("\n").filter((l) => l.startsWith("φ3:"));
+    expect(phi3Lines.length).toBe(2);
   });
 
   it("reports divergence from perspective of selected PVM", () => {

apps/web/src/hooks/useDivergenceCheck.ts

@@ -81,7 +81,7 @@ export function useDivergenceCheck(
         if (selected.registers[i] !== other.registers[i]) {
           divergentRegIndices.add(i);
           detailLines.push(
-            `\u03C9${i}: ${selectedPvmId}=0x${BigInt.asUintN(64, selected.registers[i]).toString(16)}, ${pvmId}=0x${BigInt.asUintN(64, other.registers[i]).toString(16)}`,
+            `\u03C6${i}: ${selectedPvmId}=0x${BigInt.asUintN(64, selected.registers[i]).toString(16)}, ${pvmId}=0x${BigInt.asUintN(64, other.registers[i]).toString(16)}`,
           );
         }
       }