diff --git a/notes_giant_fft.md b/notes_giant_fft.md
index d6494d1..bcd1bdb 100644
--- a/notes_giant_fft.md
+++ b/notes_giant_fft.md
@@ -100,5 +100,18 @@ Full bit-exact FFT = plan generator (0x2f980 split-radix index algebra) + runtim
 (3-level tables) + 6 final kernels (each 0x800-0x1200 bytes of vectorized split-radix butterfly)
 + twiddle. This is the P3 2-4 week body. Architecture fully mapped; transcription not yet done.
 
+### Final kernel 0x1802a24c0 — own vectorized sin/cos, NOT twiddle table
+The big-N kernels compute trig ON THE FLY via an AVX polynomial (vfmadd231ps/213ps chain) with
+range reduction done by float-bit tricks (vpaddd/vpsubd/vpsrad $0x17 = 23-bit shift = exponent
+extract, vpcmpgtd, vblendvps). Polynomial constants (rodata, float, broadcast x8):
+  0x181f81fa0 = 0.333366   0x181f81fc0 = -0.250047  0x181f81fe0 = 0.198225
+  0x181f82000 = -0.164625  0x181f82020 = 0.169649   0x181f82040 = -0.151772
+  0x181f82100 = 0.666667   0x181f821c0 = 0.693147 (= ln 2)  0x181f822c0 = 0.75
+  (0.693147 = ln 2 ⇒ exp-based sin/cos, SVML-like vector math library.)
+=> Small-N path uses the twiddle sin-table (0x39b00); big-N path uses this own polynomial.
+Transcribing this bit-exactly = reimplementing a vector math sin/cos (Cody-Waite + poly + exp),
+plus the split-radix butterfly + integer reorder — the multi-week P3 body.
+
+