interpolated_state_timeline producing incorrect results

[KamalAman]

Relevant system information:

• OS: OSX
• PostgreSQL version (output of SELECT version();): 15.4-ts2.12.0
• TimescaleDB Toolkit version (output of \dx timescaledb_toolkit in psql): 1.17
• Installation method: docker

Describe the bug
Events are getting doubled up and not merging together properly when they span buckets, this is a similar query as what is documented here, just with a 60 minute window. The second OK record here passes the 3rd, creating extra records with invalid timeframes

To Reproduce

SET TIME ZONE 'UTC';
drop table states_test_k;
CREATE TABLE states_test_k(ts TIMESTAMPTZ, state TEXT);
INSERT INTO states_test_k VALUES
    ('2020-01-01 01:00:00+00', 'OK'),
    ('2020-01-01 01:00:01+00', 'START'),
    ('2020-01-01 01:00:03+00', 'OK'),
    ('2020-01-01 01:00:30+00', 'START'),
    ('2020-01-01 01:00:59+00', 'OK'),
    ('2020-01-01 01:01:30+00', 'START'),
    ('2020-01-01 01:01:59+00', 'OK'),
    ('2020-01-01 01:02:59+00', 'START'),
    ('2020-01-01 01:03:59+00', 'OK'),
    ('2020-01-01 02:01:59+00', 'START');

SELECT
    bucket,
    (interpolated_state_timeline(
        summary,
        bucket,
        '60 min',
        LAG(summary) OVER (ORDER by bucket)
    )).*
FROM (
    SELECT
        time_bucket('1 min'::interval, ts) AS bucket,
        state_agg(ts, state) AS summary
    FROM states_test_k
    GROUP BY time_bucket('1 min'::interval, ts)
) t
order by bucket;

Expected behavior
The results should be

OK	2020-01-01 01:00:00+00	2020-01-01 01:00:01+00
START	2020-01-01 01:00:01+00	2020-01-01 01:00:03+00
OK	2020-01-01 01:00:03+00	2020-01-01 01:00:30+00
START	2020-01-01 01:00:30+00	2020-01-01 01:00:59+00
OK	2020-01-01 01:00:59+00	2020-01-01 01:01:30+00
START	2020-01-01 01:01:30+00	2020-01-01 01:01:59+00
OK	2020-01-01 01:01:59+00	2020-01-01 01:02:59+00
START	2020-01-01 01:02:59+00	2020-01-01 01:03:59+00
OK	2020-01-01 01:03:59+00	2020-01-01 02:01:59+00
START	2020-01-01 02:01:59+00	2020-01-01 02:01:59+00

Actual behavior
The results are incorrect creating invalid time ranges that pass "overlapping" time ranges. All of the double-up are correct OK-OK and START-START

2020-01-01 01:00:00+00	OK	2020-01-01 01:00:00+00	2020-01-01 01:00:01+00
2020-01-01 01:00:00+00	START	2020-01-01 01:00:01+00	2020-01-01 01:00:03+00
2020-01-01 01:00:00+00	OK	2020-01-01 01:00:03+00	2020-01-01 01:00:30+00
2020-01-01 01:00:00+00	START	2020-01-01 01:00:30+00	2020-01-01 01:00:59+00
2020-01-01 01:00:00+00	OK	2020-01-01 01:00:59+00	2020-01-01 02:00:00+00
2020-01-01 01:01:00+00	OK	2020-01-01 01:01:00+00	2020-01-01 01:01:30+00
2020-01-01 01:01:00+00	START	2020-01-01 01:01:30+00	2020-01-01 01:01:59+00
2020-01-01 01:01:00+00	OK	2020-01-01 01:01:59+00	2020-01-01 02:01:00+00
2020-01-01 01:02:00+00	OK	2020-01-01 01:02:00+00	2020-01-01 01:02:59+00
2020-01-01 01:02:00+00	START	2020-01-01 01:02:59+00	2020-01-01 02:02:00+00
2020-01-01 01:03:00+00	START	2020-01-01 01:03:00+00	2020-01-01 01:03:59+00
2020-01-01 01:03:00+00	OK	2020-01-01 01:03:59+00	2020-01-01 02:03:00+00
2020-01-01 02:01:00+00	OK	2020-01-01 02:01:00+00	2020-01-01 02:01:59+00
2020-01-01 02:01:00+00	START	2020-01-01 02:01:59+00	2020-01-01 03:01:00+00

Screenshots

Additional context
interpolated_state_timeline has the potential to be a very powerful feature. However it is producing unexpected results and I am wary of its actual performance on large datasets even if was functioning as expected.

[jamessewell]

Just adding a live link https://dbfiddle.uk/L4WfMlIK