hydra: interleaved merge split; merge exactness and bound tests

[zzylol]

What changed

• approxbench --merge-split contiguous|interleaved (default contiguous, today's behavior for every row). Interleaved deals the stream round-robin by record, so each shard is a sample of the whole stream; shard sizes equal the contiguous split's (record j goes to the next shard with room).
• Records carry merge_split next to merge_shards (BenchSection, MergeMetrics, merged_record.schema.json regenerated). Absent on older records = contiguous, so existing results parse; --flat refuses two different splits in one row, as it does two shard counts. MergeSplit lives in aqpbm-core and clap parses it directly.
• The interleaved copy is built only when a merge is requested.
• Plumbing: Requirement.merge_split → scored_row, which hands every merge body (merge, merge-step, merge-accuracy) the stream reordered by wrappers::interleave, so the existing contiguous partition cut yields the round-robin shards. No wrapper signature changes; every row with a merge gets it.
• Documented in README (flag list next to the Hydra merge example; states the round-robin exactly: it runs over the contiguous shard sizes, so with a short last shard shard 0 is not exactly 0, k, 2k, ...) and docs/saturation_study.md.

Why

Spec PR 4 for the Hydra §6.3 study (hydra doc #193 §2.2–2.3): merges across ingest workers split by record, not by time range.

Tests (wrappers::tests, wrappers::hydra_shared::tests, 3.7 s debug)

• interleave_deals_round_robin_at_the_contiguous_sizes.
• merge_split_on_two_squares_must_agree (flatten: absent = contiguous; interleaved + absent is refused).
• hydra-cms / hydra-cs / hydra-hll: a 3×16 grid folded from 4 and 7 shards, under both splits, answers every probed subpopulation (each first label and each pair; every occurring (group, value) for CMS/CS) exactly as the single-stream grid.
• §2.2 bounds on a fixed 20k-record, 2-label stream, W=16 (so groups collide), cells 3×512, β=8: every scored group's error is inside its bound. CMS: f ≤ f̂ ≤ f + ε_c·N_q + β(F_v + ε_c·M)/W, ε_c = e/512. CS: [f − ε_s(L2_q + L2_C), f + ε_s·L2_q + βF_v/W + ε_s·L2_C], ε_s = 1/√512, L2_C = √(β·F2/W) with F2 = Σ_v F_v². HLL: [(1−ε_h)D_q, (1+ε_h)(D_q + β·ΣD/W)], ε_h = 3·1.04/√2^14.

Mutation checks (each fails the named test): interleave returning the stream unchanged; each hydra merge skipping a shard; β = 0 (all three bound tests); inner ε = 0 (CMS, CS); CMS answer 1 under (never-under assert). Inner ε_h = 0 does not fail HLL: at these distinct counts HLL is near-exact. CS margin: passes from β ≈ 4.8 (fails at 4.7), so β = 8 leaves under 2x; cell_cols 1024 would need β ≈ 14 (ε shrinks, the colliders' error does not), so cells stay 3×512. Removing the absent→contiguous default fails the flatten test.

Evidence

cargo fmt --check, cargo clippy --workspace --all-targets -D warnings, cargo test --workspace clean. Release CLI, --merge-shards 8 --metrics accuracy: hydra-cms (hydra_columns.yaml, 3×128, 3×512) and hydra-hll merge_accuracy equal query_accuracy under both splits (are_all 2.5929 / 1.3396); kll-percall --library oxide (deterministic; repeated runs identical) --config k=50 --dataset zipf --size 100000 --zipf-s 1.1 --cardinality 100000 --merge-shards 8 --operations merge --metrics accuracy: merge mean_rank_err 0.012426 contiguous vs 0.012599 interleaved, so the split reaches lossy merges too. Same contiguous command on 653d6a8 vs this head: the record is identical except the new "merge_split": "contiguous" (timings excluded).

🤖 Generated with Claude Code

https://claude.ai/code/session_01FhcWJExZcmVqS6r6rEtjis