QUERY INSIGHTS & EXECUTION PLANNER

Morton Code & Z-Curve Plan Decomposition

BlackGrid maps multi-attribute agent queries into 1D space-filling Z-curves, translating 2D GoogleSQL range predicates into minimal, highly-localized Bigtable RowRangeList scans.

Bigtable RowRanges

5(raw: 5)

Contiguous gRPC SSTable scans

Scan Reduction

86%skipped

36 / 256 morton cells read

Target Query Latency

1.79ms8.57ms

4.8x faster than full scan

Locality / Precision

100%(36 true hits)

Zero false-positives at gap=0

2D Morton Z-Order Curve & Subcell Space

16×16 coordinate grid (0..15 × 0..15) interleaved into 8-bit Morton keys (0x00..0xFF)

Show Z-CurveHex Labels

▲ Temporal Epoch (Y) (Y: 0..15)

Semantic Cluster (X) (X: 0..15) ▶

SQL Predicate Hit

Coalesced Gap (False Positive)

Z-Order Curve

Dynamic SQL Query Bounds (`BETWEEN` ranges)

X Min4

X Max9

Y Min4

Y Max9

Golang Coalesce Gap Optimizer:maxGap = 2 cells

Merges contiguous intervals with gap ≤ 2 to avoid gRPC seek overhead

Morton Bit-Interleaving (X & Y → Z Key)

Spread Bits: x | (y << 1)

Hover over any cell in the 16×16 grid above to inspect its binary bit-interleaving and Bigtable rowkey prefix.

Bigtable Storage Plan Insights

Optimized

Target Tableblackgrid.agent_episodic_memory

RowKey Formatbg#agt_7f#mem#z16#<HEX>

Estimated QPS Capability~4,820 qps/node

Avg Tablet CPU Impact14% per 10k ops

Z-Curve Spatial Locality: Cross-quadrant query spanning multiple Z-seams. Gap coalescing reduced 5 raw ranges down to 5 Bigtable RPC ranges.

AST Engine

-- GoogleSQL via BlackGrid Z-Planner (ZetaSQL AST -> Bigtable RowRangeList)
SELECT
  memory_id,
  agent_session_id,
  MORTON_HEX_2D(semantic_cluster, decay_epoch) AS z_row_prefix,
  cosine_salience,
  payload_proto
FROM `blackgrid.agent_episodic_memory`
WHERE tenant_id = 'agt_7f'
  AND semantic_cluster BETWEEN 4 AND 9
  AND decay_epoch BETWEEN 4 AND 9
ORDER BY z_row_prefix ASC
LIMIT 128;

How BlackGrid Bridges GoogleSQL and Bigtable Z-Curves

1. ZetaSQL AST Extraction

BlackGrid parses standard GoogleSQL queries (e.g. episodic memory semantic cluster & temporal decay), identifying multi-dimensional BETWEEN, >=, and <= predicates to establish a hyper-rectangle bounding box.

2. Morton Interleaving & BIGMIN

Coordinates are mapped to 1D Morton space via bit-twiddling magic numbers. BlackGrid’s Golang planner calculates BIGMIN/LITMAX jumps to prune dead space without evaluating every individual point, preserving sub-millisecond planning latencies.

3. Bigtable RowRangeList RPC

The coalesced Z-intervals are converted directly into Cloud Bigtable RowRange objects. SSTable block reads are localized to specific tablet servers, eliminating secondary index lookup roundtrips for agent memory recall.