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BIP142 when encoding a segwit P2WPKH address is using a base58 address format (address p2xtZoXeX5X8BP8JfFhQK2nD3emtjch7UeFm in the example).

I understand that BIP142 predates BIP173 but are P2WPKH and Bech32 synonyms now? Is there such a thing as Base58 P2WPKH address?

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are P2WPKH and Bech32 synonyms now?

No. Bech32 is also used for P2WSH addresses. Native segwit and Bech32 are synonyms.

Is there such a thing as Base58 P2WPKH address?

No.

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    Not quite; Bech32 is just the encoding scheme, which is more general than Bitcoin's use of it for P2WSH/P2WPKH addresses. Jul 20 at 19:56
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P2WPKH and bech32 are not quite synonymous.

Native segwit describes a type of output schema in which the scriptPubKey (the "locking script") is composed of a witness version and a witness program. P2WPKH is a native segwit v0 output type.

Bech32 refers to an encoding scheme and an address format to represent a recipient's scriptPubKey in out-of-band communication.

We use "bech32 addresses" to instruct spenders to create "P2WPKH outputs":

  • Pay to Witness Public Key Hash (P2WPKH) and Pay to Witness Script Hash (P2WSH) are native segwit v0 outputs that get represented using bech32 addresses.
  • Pay to Public Key Hash (P2PKH) and Pay to Script Hash (P2SH) use base58 addresses.
  • Pay to Taproot (P2TR) and future native segwit output types will use bech32m addresses.

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