# Phase 2B Aligned Numerical Prototype

## Decision

VEA-B passes the isolated fixed-shape Phase 2B gate on NVIDIA GB10. The selected
kernel computes `B=1, H=1, Q=128, KV=192, D=128` from prequantized Q/K/V with
three increasing K64 epochs. It is retained as research only. Ragged tails,
preparation, complete H3 shapes, block integration, trajectories, and production
dispatch remain out of scope.

## Exactness

The four-warp checkpoint oracle reproduces the installed public SageAttention
2.2.0 output. The ten-warp VEA-B kernel matches the oracle byte-for-byte for:

- final BF16 output, SHA-256
  `75d4169c9ae0692b24a463a64b538f852acba5a5567404728c8af60c16fb8e1b`;
- INT32-to-FP32 QK scores;
- per-epoch online-softmax `m` and `d`;
- FP8 E4M3 probability words and FP32 rescale values;
- FP16 PV partial words and FP32 `RO` after every epoch;
- final reciprocal values.

The selected source also completes 1,000 consecutive fast launches with the
same output hash and no deadlock.

## Selected Kernel

- 320 threads: two K/V producer warps, four QK/softmax owners, and four
  PV/output owners.
- Two ready, two free, and two K-ready CUDA block-scope mbarriers.
- Two K/V and probability slots with strict epoch reuse.
- Final reciprocal publication is folded into the final score-ready handoff.
- Probability and V fragments are processed as ordered 8-column MMA pairs.
- A per-lane volatile shared retirement slot aliases scale metadata only after a
  warp phase boundary. It constrains ptxas scheduling without changing
  arithmetic or allocating additional shared memory.

Ptxas and runtime attributes report 168 registers/thread, zero stack frame,
zero spill stores/loads, zero local bytes/thread, 51.2 KiB dynamic shared
memory, and one resident CTA/SM. NCU independently reports zero local-memory
spilling requests, 168 registers/thread, one register/shared-memory-limited
block per SM, and ten theoretical active warps (`20.83%`).

## Synchronization And Safety

- Compute Sanitizer memcheck: `0 errors`.
- Compute Sanitizer racecheck: `0 hazards`, `0 errors`, `0 warnings`.
- QK epoch 1 overlaps PV epoch 0 by 49,317 clocks.
- QK epoch 2 overlaps PV epoch 1 by 46,408 clocks.

The retirement alias initially produced racecheck WAR warnings because lanes
could overwrite scale metadata before sibling lanes completed their reads. The
selected variant adds an explicit warp phase boundary before the first write.

## Timing

The final 2,000-sample single-launch run measures VEA-B p50 `0.016288 ms` and
public Sage2 p50 `0.019840 ms`, a prototype-only `1.218x` ratio. Single-launch
CV is `5.95%`, reflecting a bimodal microsecond-scale distribution.

The authoritative stability run uses 500 event samples with 20 identical
launches per sample and reports per-launch values. VEA-B p50 is `0.014426 ms`,
CV `0.87%`; public Sage2 p50 is `0.014871 ms`, CV `1.23%`; the ratio is `1.031x`.
This is fixed-shape screening evidence, not a complete-attention speedup claim.

## Rejected Variants

| Variant | Result |
| --- | --- |
| Initial combined ownership | Exact, 352 local bytes/thread |
| Sequential PV fragments | Exact, material spills remained |
| Union role state | Exact, 208 local bytes/thread |
| Role-separated epoch loops | Exact, 40 local bytes/thread |
| `setmaxnreg` redistribution | Compiled at 200 registers, rejected at launch for excessive resources |
| Shared persistent `RO` fragment | Final BF16 exact, FP32 `RO` diverged at epoch 1 and stack usage increased |
| Inner-pair warp fence | Exact, but increased the fast stack frame |
| Selected shared retirement alias | Exact, zero local memory; race-clean after warp phase boundary |

## Evidence

- `/home/daniel/StoryStudioAssets/H3-output/h3-blackwell-runtime/research/vortex_exact_attention/phase2b/probes/authoritative-batched-final.json`
- `/home/daniel/StoryStudioAssets/H3-output/h3-blackwell-runtime/research/vortex_exact_attention/phase2b/probes/authoritative-final.json`
- `/home/daniel/StoryStudioAssets/H3-output/h3-blackwell-runtime/research/vortex_exact_attention/phase2b/probes/memcheck-final.log`
- `/home/daniel/StoryStudioAssets/H3-output/h3-blackwell-runtime/research/vortex_exact_attention/phase2b/probes/racecheck-final.log`
- `/home/daniel/StoryStudioAssets/H3-output/h3-blackwell-runtime/research/vortex_exact_attention/phase2b/vea-b-final.ncu-rep`
- `/home/daniel/StoryStudioAssets/H3-output/h3-blackwell-runtime/research/vortex_exact_attention/phase2b/fixtures/aligned-q128-kv192-seed73021/manifest.json`

## Advancement Limit

Phase 2B authorizes no production integration. The next phase must add ragged
tails and complete-shape work distribution, then pass canonical attention,
blocks 0/24/49, trajectory, resident-service, sanitizer, and complete-block
performance gates before any dispatch proposal.