Lineage traversal

Use the standard SQL WITH RECURSIVE form against the lineage table:

WITH RECURSIVE chain(did, parent, depth) AS (
  SELECT did, parent, 0
  FROM lineage
  WHERE did = 'did:oas:l1fe:agent:web-research@3.4.0'
  UNION ALL
  SELECT l.did, l.parent, chain.depth + 1
  FROM lineage l, chain
  WHERE l.did = chain.parent AND chain.depth < 16
)
SELECT * FROM chain ORDER BY depth;

Or use the LINEAGE() function

SELECT *
FROM LINEAGE('did:oas:l1fe:agent:web-research@3.4.0', 16);

The function returns (did, parent, depth, signed_at) rows ordered by ascending depth. Equivalent to the CTE above, but shorter.

Bound the depth

Always bound recursion. depth < 16 is a reasonable default; chains deeper than ~10 are extremely rare in practice.