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As of my understanding, stateless NAT is using 1:1 translation, meaning it needs one IPv4 address for one IPv6 address vice versa, thus not preserving IPv4. Since the CLAT is supposed to be router/gateway for the local network, meaning the local side of CLAT is private IPv4 address (RFC1918),but as of my understanding IPv4-embedded IPv6 containing private IPv4 address is supposed to be dropped either by the receiver or the intermediate party (NAT64 translator).

Why does CLAT use Stateless NAT64?

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as of my understanding IPv4-embedded IPv6 containing private IPv4 address is supposed to be dropped either by the receiver or the intermediate party (NAT64 translator)

That is only true of using the well-known prefix (64:ff9b::/96):

3.1. Restrictions on the Use of the Well-Known Prefix

The Well-Known Prefix MUST NOT be used to represent non-global IPv4 addresses, such as those defined in [RFC1918] or listed in Section 3 of [RFC5735]. Address translators MUST NOT translate packets in which an address is composed of the Well-Known Prefix and a non- global IPv4 address; they MUST drop these packets.

The well-known prefix is not the only prefix that can be used (see my highlights in the paragraph below the figure):

2.2. IPv4-Embedded IPv6 Address Format

IPv4-converted IPv6 addresses and IPv4-translatable IPv6 addresses follow the same format, described here as the IPv4-embedded IPv6 address Format. IPv4-embedded IPv6 addresses are composed of a variable-length prefix, the embedded IPv4 address, and a variable- length suffix, as presented in the following diagram, in which PL designates the prefix length:

+--+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
|PL| 0-------------32--40--48--56--64--72--80--88--96--104---------|
+--+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
|32|     prefix    |v4(32)         | u | suffix                    |
+--+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
|40|     prefix        |v4(24)     | u |(8)| suffix                |
+--+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
|48|     prefix            |v4(16) | u | (16)  | suffix            |
+--+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
|56|     prefix                |(8)| u |  v4(24)   | suffix        |
+--+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
|64|     prefix                    | u |   v4(32)      | suffix    |
+--+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
|96|     prefix                                    |    v4(32)     |
+--+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+

                             Figure 1

In these addresses, the prefix shall be either the "Well-Known Prefix" or a "Network-Specific Prefix" unique to the organization deploying the address translators. The prefixes can only have one of the following lengths: 32, 40, 48, 56, 64, or 96. (The Well-Known Prefix is 96 bits long, and can only be used in the last form of the table.)

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