Seralize incorrectly duplicates element in case of circular reference in array

Description

The following code:

<?php

$a = ['id'=>1,'parent'=>null,'child'=>null];
$b = ['id'=>2,'parent'=>null,'child'=>null];
$a['child'] =&$b;
$b['parent'] = &$a;
echo serialize($a);

Resulted in this output:

a:3:{s:2:"id";i:1;s:6:"parent";N;s:5:"child";a:3:{s:2:"id";i:2;s:6:"parent";a:3:{s:2:"id";i:1;s:6:"parent";N;s:5:"child";R:4;}s:5:"child";N;}}

The problem is that in the 'child' array with id 2, 'parent' duplicates the root array with id 1 instead of directly referencing it, something along the lines of :

a:3:{s:2:"id";i:1;s:6:"parent";N;s:5:"child";a:3:{s:2:"id";i:2;s:6:"parent";R:1;s:5:"child";N;}}

In any case, the parent array shouldn't be duplicated, as this can cause traversal issues or modifications that won't properly propagate if code tries to modify the de-serialized array (for instance modifying element 2's parent will not propagate to the root as it should), for instance :

If I modify the original array :

$a['id'] = 3;
echo($a['id'].','.$a['child']['parent']['id']);

echoes (properly) :

3,3

However, if I unserialize the aformentioned string, and apply the same operation, it echoes :

3,1

The reference is lost, as is apparent from the serialized form.

(Of course this is a trivial example but corresponds to something I've encountered working with graph-type arrays)

PHP Version

PHP 8.1.21 (FPM,CLI)

Operating System

Debian 10 x64 (on WSL2 on Windows 10 x64) ; Debian 11 x64 (native)

Start by running the provided PHP reproducer and comparing the serialized output with the expected circular-reference form. Trace PHP's array serialization and unserialization behavior for circular references; the issue is done when the parent array is preserved by reference and modifying it after unserialization propagates to the root.