Fix parityCount to use Math.floor, neededPackets to use totalGenerations

parityCount: Math.ceil → Math.floor
- Small files (G ≤ 33) now truly get 0 parity generations
- Large files (G ≥ 34) still get proportional parity (≈3%)
- Previously Math.ceil always gave ≥1 parity for any G ≥ 1

neededPackets: K * sourceGenerations → K * totalGenerations
- Aligns with the round-robin scheduler: symbols are interleaved
  across ALL generations, so practical minimum is K × totalGens
- Fixes the mismatch where 'needed' showed 32 but actual
  decode required ~48 frames (for 2 source + 1 parity case)

Tests: Updated assembly test comments and totalGenerations params
to match new parityCount behavior.

Closes the long-standing 'needed frames count is off because of
outer error correction' issue.

src/core/protocol/constants.ts

@@ -67,7 +67,7 @@ export const OUTER_EC_OVERHEAD = 0.03;
 
 /** Compute number of parity generations for G source generations. */
 export function parityCount(sourceGenerations: number): number {
-  return Math.ceil(sourceGenerations * OUTER_EC_OVERHEAD);
+  return Math.floor(sourceGenerations * OUTER_EC_OVERHEAD);
 }
 
 /** Compute source generation count from total generations. */

src/tests/complete.test.ts

@@ -355,10 +355,10 @@ describe('Payload Assembly', () => {
     solved.set(0, g0);
     solved.set(1, g1);
 
-    // 2 source gens + 1 parity = 3 total. Both source gens present.
+    // 2 source gens + 0 parity = 2 total (small file, no outer RS). Both source gens present.
     // dataLength spans into second generation so we can verify cross-gen assembly
     const dataLength = K * MAX_PAYLOAD_SIZE + 4;
-    const data = assemblePayload(solved, 3, dataLength);
+    const data = assemblePayload(solved, 2, dataLength);
     expect(data.length).toBe(dataLength);
     expect(data[0]).toBe(1);
     expect(data[1]).toBe(2);
@@ -385,8 +385,8 @@ describe('Payload Assembly', () => {
     const solved = new Map<number, Uint8Array[]>();
     solved.set(0, g0);
 
-    // 1 source gen + 1 parity = 2 total. Source gen present.
-    const data = assemblePayload(solved, 2, 3);
+    // 1 source gen + 0 parity = 1 total (small file, no outer RS). Source gen present.
+    const data = assemblePayload(solved, 1, 3);
     expect(data.length).toBe(3);
     expect(data[0]).toBe(1);
     expect(data[1]).toBe(2);
@@ -403,7 +403,7 @@ describe('Payload Assembly', () => {
     const solved = new Map<number, Uint8Array[]>();
     solved.set(0, g0);
 
-    // 3 source gens + 1 parity = 4 total, but only 1 solved
+    // 4 source gens + 0 parity = 4 total, but only 1 solved
     expect(() => assemblePayload(solved, 4, 3)).toThrow('only 1 generations solved');
   });
 });

src/workers/decode.worker.ts

@@ -251,7 +251,7 @@ function reconstructData(state: DecodeState): void {
 function reportProgress(state: DecodeState): void {
   const totalGens = state.totalGenerations;
   const solvedGens = state.solvedGenerations.size;
-  const needed = state.sourceGenerations > 0 ? K * state.sourceGenerations : 0;
+  const needed = state.totalGenerations > 0 ? K * state.totalGenerations : 0;
 
   self.postMessage({
     type: 'progress',