DAL

    const kp = all.get(pk);    if (!kp) throw new Error(`Missing signer ${pk}`);    return sign(message, kp.seed);  });  return { wire: concat(shortvec(sigs.length), ...sigs, message), signature: b58encode(sigs[0]), message };} /** A transaction where some signatures are left empty (to be added by a wallet such as Phantom). */export function buildPartiallySignedTx(feePayer: Keypair, instructions: Instruction[], recentBlockhash: string, others: Keypair[] = []) {  const { message, signers } = compileMessage(feePayer.publicKey, instructions, recentBlockhash);  const all = new Map([feePayer, ...others].map(k => [k.publicKey, k]));  const sigs = signers.map(pk => { const kp = all.get(pk); return kp ? sign(message, kp.seed) : new Uint8Array(64); });  return { wire: concat(shortvec(sigs.length), ...sigs, message), message, signers };} /** Program-derived address (same algorithm as PublicKey.findProgramAddressSync). */export function findProgramAddress(seeds: Uint8Array[], programId: string): string {  for (let bump = 255; bump >= 0; bump--) {    const h = createHash('sha256');    for (const s of seeds) h.update(s);    h.update(Uint8Array.of(bump)); h.update(b58decode(programId)); h.update(utf8('ProgramDerivedAddress'));    const out = new Uint8Array(h.digest());    if (!isOnCurve(out)) return b58encode(out);  }

1. Line 52 /** Program-derived address (same algorithm as PublicKey.findProgramAddressSync). */: Derives a PDA from seeds and the program ID and returns the address with its canonical bump.
2. Line 54 for (let bump = 255; bump >= 0; bump--) {: Uses the bump seed, the extra byte that pushes the derived address off the ed25519 curve.

 export const associatedTokenAddress = (owner: string, mint: string) =>  findProgramAddress([b58decode(owner), b58decode(PROGRAMS.token), b58decode(mint)], PROGRAMS.ata); /** Creates the owner's token account for the mint if it does not exist yet (payer covers the deposit). */export function createAtaIdempotentIx(payer: string, owner: string, mint: string): Instruction {  return {    programId: PROGRAMS.ata,    keys: [      { pubkey: payer, isSigner: true, isWritable: true },      { pubkey: associatedTokenAddress(owner, mint), isSigner: false, isWritable: true },      { pubkey: owner, isSigner: false, isWritable: false },      { pubkey: mint, isSigner: false, isWritable: false },      { pubkey: PROGRAMS.system, isSigner: false, isWritable: false },      { pubkey: PROGRAMS.token, isSigner: false, isWritable: false }    ],    data: u8(1)  };} /** SPL Token TransferChecked between the owners' associated token accounts. */export function transferCheckedIx(owner: string, toOwner: string, mint: string, amount: bigint | number, decimals: number): Instruction {  return {    programId: PROGRAMS.token,

1. Line 27 findProgramAddress([b58decode(owner), b58decode(PROGRAMS.token), b58decode(mint)], PROGRAM: Derives a PDA from seeds and the program ID and returns the address with its canonical bump.
2. Line 45 /** SPL Token TransferChecked between the owners' associated token accounts. */: A checked token transfer, which also verifies the mint and decimals.