Postgresql – Is this supposed to be the expected behavior in context of orderability?

In regards to orderability between different agtypes: –
https://age.apache.org/age-manual/master/intro/comparability.html

I was testing the orderability between path and an edge, and I found this odd behavior: –

Comparing a path with an edge with p > e inequality: –

test=# SELECT *
FROM cypher('test', $$
        WITH [{id: 0, label: "label_name_1", properties: {i: 0}}::vertex,
            {id: 2, start_id: 0, end_id: 1, label: "edge_label", properties: {i: 0}}::edge,
           {id: 1, label: "label_name_2", properties: {}}::vertex
           ]::path as p
MATCH (n)-[e]-(m) RETURN p>e
$$) AS (e agtype);
  e   
------
 true
 true
 true
 true
(4 rows)

Fair enough, same result holds when we compare it with p < e inequality

test=# SELECT *
FROM cypher('test', $$
        WITH [{id: 0, label: "label_name_1", properties: {i: 0}}::vertex,
            {id: 2, start_id: 0, end_id: 1, label: "edge_label", properties: {i: 0}}::edge,
           {id: 1, label: "label_name_2", properties: {}}::vertex
           ]::path as p
MATCH (n)-[e]-(m) RETURN p<e
$$) AS (e agtype);
   e   
-------
 false
 false
 false
 false
(4 rows)

But look, when we change the inequality to e > p

test=# SELECT *
FROM cypher('test', $$
        WITH [{id: 0, label: "label_name_1", properties: {i: 0}}::vertex,
            {id: 2, start_id: 0, end_id: 1, label: "edge_label", properties: {i: 0}}::edge,
           {id: 1, label: "label_name_2", properties: {}}::vertex
           ]::path as p
MATCH (n)-[e]-(m) RETURN e>p
$$) AS (e agtype);
  e   
------
 true
 true
 true
 true
(4 rows)

We get true again, which is in direct contradiction to p > e inequality

And when we check for e < p, we get false again

test=# SELECT *
FROM cypher('test', $$
        WITH [{id: 0, label: "label_name_1", properties: {i: 0}}::vertex,
            {id: 2, start_id: 0, end_id: 1, label: "edge_label", properties: {i: 0}}::edge,
           {id: 1, label: "label_name_2", properties: {}}::vertex
           ]::path as p
MATCH (n)-[e]-(m) RETURN e<p
$$) AS (e agtype);
   e   
-------
 false
 false
 false
 false
(4 rows)

Again, in direct contradiction to the first 2 results.

It seems that in the case of edge and path, irrespective of which is which ‘>’ inequality yields true, while ‘<‘ inequality yields false.

Is this the intended behavior or a bug?
And if this is the intended behavior then why?