## Iteration 35 — Phase 8 (close): MPEG-2 investigation — libva CORRECT, HW IDCT precision intrinsic

Closes 2026-05-14, sixth campaign-day milestone after iter34 (kernel 7.0-14 clean ship). User asked "mpeg2 next" after 5/5 PASS; this iteration verifies libva MPEG-2 is genuinely correct (not a coincidence) and documents why the HW != SW gap is unfixable from libva.

### Goal

After iter33 closed MPEG-2 at "libva==kdirect bit-exact, libva!=SW by ≤1 LSB/67 px (HW IDCT precision)", verify:
1. The libva==kdirect bit-exact property holds across non-BBB content (rule out fixture coincidence).
2. libva is sending correct v4l2 ctrl structs to the kernel.
3. The HW != SW divergence stays bounded (within IEEE 1180 MPEG-2 IDCT tolerance).

### Verification

**Multi-fixture libva==kdirect:**

| Source | Length | libva sha-16 | kdirect sha-16 | Match |
|---|---|---|---|---|
| BBB 720p mpeg2 (existing fixture) | 10F | 95c5905890c937d4 | 95c5905890c937d4 | ✓ |
| BBB 720p mpeg2 (full) | 240F | a75015b10fe205ea | a75015b10fe205ea | ✓ |
| Synthetic testsrc 720p MPEG-2 (b=4M, B-frames=2, GOP=12) | 48F | 5557dae9fa99d01b | 5557dae9fa99d01b | ✓ |

libva backend produces bit-exact output to kdirect (ffmpeg-v4l2request) across multiple distinct MPEG-2 streams. Not a fixture coincidence.

**v4l2 ctrl struct verification (iter35 DIAG `LIBVA_MPEG2_DUMP_FRAME=1`):**

```
mpeg2: SEQ size=12  00 05 d0 02 00 00 10 00 00 00 01 01      ← 1280x720, vbv=1M, chroma=1, flags=1 (progressive)
mpeg2: PIC size=32 [0..32]=… 82 00 00 00 0f 0f 0f 0f 01 03   ← flags=0x82 (PROGRESSIVE+FRAME_PRED_DCT), I-pic, FRAME
mpeg2: PIC frame2…  82 00 00 00 01 01 0f 0f 02 03 00 00      ← f_code 1/1, P-pic
mpeg2: QUANT size=256 [0..16]=08 10 10 13 10 13 16 16 …       ← MPEG-2 default intra Q in ZIGZAG order
mpeg2: forward_ref_ts: 0, 1000, 2000, 3000, …                ← α-7 counter scheme; CAPTURE-lookup works
```

All fields semantically correct per V4L2 spec (v4l2-controls.h:1990-2090). Intra Q matrix in zigzag-scan order as required.

**HW-vs-SW divergence quantified:**

| Metric | Value |
|---|---|
| Mean byte-diff (sampled, 240F = 331M bytes) | 0.015 |
| Max byte-diff | 3 |
| Fraction of bytes nonzero-diff (sampled) | ~1.5% |
| SSIM_Y | 0.999919 |
| SSIM_U | 0.999922 |
| SSIM_V | 0.999941 |
| SSIM overall | 0.999923 |

≤3 LSB / pixel and SSIM > 0.9999 — well within IEEE 1180 / ISO/IEC 13818-2 Annex A "implementation-defined IDCT precision" tolerance. Visually identical to SW reference.

**ffmpeg's SW IDCT options also disagree with HW:**

Sweep of `-idct auto|int|simple|simplemmx|simplearm|faani|simpleneon`: produces 4 distinct YUV hashes. None match HW. None match each other except aliases. This confirms IDCT precision differences are expected between any two MPEG-2 implementations.

### Conclusion

MPEG-2 through libva is correct:
- Bit-exact with the canonical kdirect HW reference path across 3 distinct fixtures (288 frames total).
- All V4L2 ctrl struct fields semantically valid per spec.
- HW vs SW residual gap is intrinsic to MPEG-2 IDCT precision tolerance; not fixable at the V4L2/libva layer.

**5/5 codecs PASS** for the libva-vs-kdirect correctness contract. MPEG-2 retains its "L==K, L!=SW(IDCT precision)" status from iter33; no further fix possible or warranted.

### Substrate state at iter35 close

- Backend fork tip `48fd028` (α-25 + α-29 + α-30 + iter29/30/33/35 env-gated DIAG probes).
- Kernel `linux-fresnel-fourier 7.0-14` clean.
- iter35 added `LIBVA_MPEG2_DUMP_FRAME=1` env-gated DIAG to mpeg2.c — env-gated, no behavior change without env.

### Memory entry added

`feedback_mpeg2_hw_sw_idct_precision.md` — HW MPEG-2 IDCT differs from libavcodec SW MPEG-2 IDCT by ≤3 LSB. Per MPEG-2 spec IEEE 1180 tolerance. Not a libva-fixable bug.