Performing a JOIN with an ORDER BY and LIMIT in the joined table in SQL/Postgres

I have a table of companies and a table of transcripts that are related to those companies — many-to-one.

I want to be able to list companies that have not been checked recently AND do not have transcripts published recently.

The problem I'm running into is when I join the tables, I can't figure out how to only limit the second condition to the most recent transcript. My query is unintentionally returning companies that have recent transcripts if it detects a transcript that is older.

Company Table

id	name	last_checked_at
1	ACME	`2022-10-11 02:50:52.184975+00`
2	MeepMeep	`2022-05-12 02:50:52.184975+00`
3	TNT	`2022-05-12 02:50:52.184975+00`

Transcripts Table

id	company	published_at
5	1	`2022-10-11 02:50:52.184975+00`
6	2	`2022-10-11 02:50:52.184975+00`
7	2	`2022-05-12 02:50:52.184975+00`
8	3	`2022-06-11 02:50:52.184975+00`
9	3	`2022-03-12 02:50:52.184975+00`

Desired Logic

Select company.ids
Where company.last_checked_at is older than 1 week from today
And only the most recent related transcript.published_at is older than 3 months from today

Expected Behavior

Using the data in the tables above:

Result does not contain ACME since it was last_checked_at within 7 days of today
Result does not contain MeepMeep even though last_checked_at is greater than 7 days, since the most recent transcript was published_at within 3 months of today
Result DOES contain TNT since last_checked_at is greater than 7 days and the most recent transcript was published_at greater than 3 months of today

Attempts

SELECT * FROM summaries s LEFT OUTER JOIN companies c ON s.company = c.id WHERE s.published_at < now() - INTERVAL '3 months' ORDER BY s.published_at ASC limit 1

Solution

We can try using DISTINCT ON on the transcripts table:

WITH cte AS (
    SELECT DISTINCT ON (company) *
    FROM summaries
    WHERE published_at < NOW() - INTERVAL '3 months'
    ORDER BY company, published_at DESC
)

SELECT c.name, c.last_checked_at, s.published_at
FROM companies c
INNER JOIN cte s
    ON s.company = c.id
WHERE c.last_checked_at < NOW() - INTERVAL '1 week';