✔ PASS Graph & Hierarchy task_088_Q88_state_machine_transition_verification Scaled: 1M+ Records Ordered: Yes

Transactional State Machine Transition Sequence Verification

Candidate Latency (1M Rows)

0.66 ms

(1.2x slower than golden)

Golden Latency (1M Rows)

0.55 ms

DuckDB in-memory engine

Underlying Data Volume

5 rows

140 B across 1 table

Evaluated Model

gemini-3.8-flash-low

Gen Latency: 14.5s

✔ Correctness Verified on 1M+ Records

Candidate SQL output matches ground truth golden query across all multiset rows and numeric tolerances (tol=1e-3). Zero data skew or anti-patterns detected on full dataset scale.

1. Analytical Significance & What It Means

Scenario & Frontier Trap

Business Scenario & Problem

Financial compliance requires payment transactions to strictly follow the state sequence: INITIATED -> AUTHORIZED -> CAPTURED -> SETTLED. Any transaction skipping steps is flagged as fraudulent.

⚡ The Frontier Trap (Why LLMs Fail)

Verifying status counts without checking transition sequence allows out-of-order state transitions.

Prompt / User Request Given to Model

Financial compliance requires payment transactions to strictly follow the state sequence: INITIATED -> AUTHORIZED -> CAPTURED -> SETTLED. Any transaction skipping steps is flagged as fraudulent.

Execute the required analytical SQL calculation in DuckDB.
Expected output columns: tx_id, current_state, next_state, audit_validation_result.
Results should be ordered as specified.

2. Underlying Tables, Row Counts & Data Volume

1 Tables (5 rows • 140 B)

Production-scale fixtures loaded into the isolated DuckDB sandbox with at least 1,000,000 records per table:

📊 payment_status_audit 5 rows 140 B Data Volume

tx_id (INTEGER) step_order (INTEGER) status (VARCHAR)

Data Preview (showing sample rows from 5 total rows):

#	tx_id	step_order	status
1	1	1	INITIATED
2	1	2	AUTHORIZED
3	1	3	CAPTURED
4	2	1	INITIATED
5	2	2	CAPTURED

3. Graphical Query Execution Plan & Cost Bottlenecks

Physical Operator Tree (DuckDB 2.0 Profiler)

Visual flowchart of the physical execution pipeline. Operators with high relative costs (≥ 20% of query runtime or heavy latency) are visually highlighted:

Pipeline Latency Distribution (Total Plan Time: 0.66 ms) Nodes consuming ≥ 20% of query runtime are highlighted with glowing borders

📐 PROJECTION 0.3%

Latency: 0.00 ms

Rows In/Out: 5

Data Vol: 516 B

📁 Projections: ['CAST(#0 AS INTEGE...

⏳ ORDER_BY 19.5%

Latency: 0.13 ms

Rows In/Out: 5

Data Vol: 501 B

📐 PROJECTION 1.6%

Latency: 0.01 ms

Rows In/Out: 5

Data Vol: 757 B

📁 Projections: ['CAST(#0 AS TINYIN...

📐 PROJECTION 5.2%

Latency: 0.03 ms

Rows In/Out: 5

Data Vol: 772 B

📁 Projections: ['tx_id', 'current_...

📐 PROJECTION 0.1%

Latency: 0.00 ms

Rows In/Out: 5

Data Vol: 692 B

📁 Projections: ['tx_id', 'current_...

📐 PROJECTION 0.1%

Latency: 0.00 ms

Rows In/Out: 5

Data Vol: 712 B

📁 Projections: ['#0', '#1', '#2', ...

🪟 WINDOW 69.2%

Latency: 0.46 ms

Rows In/Out: 5

Data Vol: 712 B

📁 Projections: lead(status, 1, NUL...

🔍 TABLE_SCAN 4.0%

Latency: 0.03 ms

Rows In/Out: 5

Data Vol: 120 B

📁 memory.main.payment_status_audit

Operator	Cost %	Latency	Processed Rows	Details / Table	Status
WINDOW	69.2%	0.46 ms	5	Projections: lead(status, 1, NULL::VARCHAR) OVER	Normal
ORDER_BY	19.5%	0.13 ms	5	-	Normal
PROJECTION	5.2%	0.03 ms	5	Projections: ['tx_id', 'current_state', 'next_st	Normal
TABLE_SCAN	4.0%	0.03 ms	5	memory.main.payment_status_audit	Normal
PROJECTION	1.6%	0.01 ms	5	Projections: ['CAST(#0 AS TINYINT)', '__internal	Normal
PROJECTION	0.3%	0.00 ms	5	Projections: ['CAST(#0 AS INTEGER)', '__internal	Normal
PROJECTION	0.1%	0.00 ms	5	Projections: ['#0', '#1', '#2', '#3']	Normal
PROJECTION	0.1%	0.00 ms	5	Projections: ['tx_id', 'current_state', 'next_st	Normal

4. Queries Executed (Candidate vs Golden Ground Truth)

Beautified & Syntax Highlighted

-- Validate that every state transition matches the legal state machine rules
WITH transitions AS
  (SELECT tx_id,
          status AS current_state,
          lead(status) OVER (PARTITION BY tx_id
                             ORDER BY step_order) AS next_state
   FROM payment_status_audit)
SELECT tx_id,
       current_state,
       next_state,
       CASE
           WHEN next_state IS NULL THEN 'TERMINAL_STATE'
           WHEN current_state = 'INITIATED'
                AND next_state = 'AUTHORIZED' THEN 'VALID'
           WHEN current_state = 'AUTHORIZED'
                AND next_state = 'CAPTURED' THEN 'VALID'
           WHEN current_state = 'CAPTURED'
                AND next_state = 'SETTLED' THEN 'VALID'
           ELSE 'INVALID_ILLEGAL_STATE_JUMP'
       END AS audit_validation_result
FROM transitions
ORDER BY tx_id,
         current_state;

-- Validate that every state transition matches the legal state machine rules
 WITH transitions AS
  (SELECT tx_id,
          status AS current_state,
          lead(status) OVER (PARTITION BY tx_id
                             ORDER BY step_order) AS next_state
   FROM payment_status_audit)
SELECT tx_id,
       current_state,
       next_state,
       CASE
           WHEN next_state IS NULL THEN 'TERMINAL_STATE'
           WHEN current_state = 'INITIATED'
                AND next_state = 'AUTHORIZED' THEN 'VALID'
           WHEN current_state = 'AUTHORIZED'
                AND next_state = 'CAPTURED' THEN 'VALID'
           WHEN current_state = 'CAPTURED'
                AND next_state = 'SETTLED' THEN 'VALID'
           ELSE 'INVALID_ILLEGAL_STATE_JUMP'
       END AS audit_validation_result
FROM transitions
ORDER BY tx_id,
         current_state;

CREATE TABLE payment_status_audit (tx_id INT, step_order INT, status VARCHAR);

-- Valid tx 1

INSERT INTO payment_status_audit
VALUES (1, 1, 'INITIATED'),
       (1, 2, 'AUTHORIZED'),
       (1, 3, 'CAPTURED');

-- Invalid tx 2: Jumped directly from INITIATED to CAPTURED!

INSERT INTO payment_status_audit
VALUES (2, 1, 'INITIATED'),
       (2, 2, 'CAPTURED');

5. Query Results & Expected Ground Truth

Tabular Comparison

Actual Candidate Output (5 rows × 4 cols)

#	tx_id	current_state	next_state	audit_validation_result
1	1	AUTHORIZED	CAPTURED	VALID
2	1	CAPTURED	NULL	TERMINAL_STATE
3	1	INITIATED	AUTHORIZED	VALID
4	2	CAPTURED	NULL	TERMINAL_STATE
5	2	INITIATED	CAPTURED	INVALID_ILLEGAL_STATE_JUMP

Expected Golden Output (5 rows × 4 cols)

#	tx_id	current_state	next_state	audit_validation_result
1	1	AUTHORIZED	CAPTURED	VALID
2	1	CAPTURED	NULL	TERMINAL_STATE
3	1	INITIATED	AUTHORIZED	VALID
4	2	CAPTURED	NULL	TERMINAL_STATE
5	2	INITIATED	CAPTURED	INVALID_ILLEGAL_STATE_JUMP

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