diff --git a/src/utils.ts b/src/utils.ts
index f5f9fe8..0779b25 100644
--- a/src/utils.ts
+++ b/src/utils.ts
@@ -9,9 +9,20 @@ import { StellarSplitError } from "./errors.js";
 const STROOPS_PER_UNIT = 10_000_000n;
 
 /**
- * Format a stroop amount as a human-readable USDC string.
+ * Format a stroop amount as a fixed 7-decimal string.
  *
- * @example formatAmount(10_000_000n) // "1.0000000"
+ * The integer part is `stroops / 10_000_000` and the fractional part is the
+ * remainder, left-padded to 7 digits. No thousands separators or currency
+ * symbol are added; the value is intended for display next to an asset code
+ * such as "USDC". Designed for non-negative amounts.
+ *
+ * @param stroops - Raw on-chain amount in stroops (1 unit = 10,000,000 stroops).
+ * @returns The amount as a `"<whole>.<7-digit fraction>"` string.
+ *
+ * @example
+ * formatAmount(10_000_000n); // "1.0000000"
+ * formatAmount(15_500_000n); // "1.5500000"
+ * formatAmount(7n);          // "0.0000007"
  */
 export function formatAmount(stroops: bigint): string {
   const whole = stroops / STROOPS_PER_UNIT;
@@ -20,9 +31,21 @@ export function formatAmount(stroops: bigint): string {
 }
 
 /**
- * Parse a human-readable USDC string into stroops.
+ * Parse a human-readable decimal amount into stroops.
+ *
+ * Splits `value` on the first `.`; a missing whole part defaults to `"0"` and a
+ * missing fractional part to `""`. The fractional part is right-padded with
+ * zeros and truncated to 7 digits (extra precision is dropped, not rounded).
  *
- * @example parseAmount("1.5") // 15_000_000n
+ * @param value - Decimal string such as `"1.5"`, `"0.25"`, or `"10"`.
+ * @returns The equivalent amount in stroops.
+ * @throws {SyntaxError} If the whole or fractional part is not a valid integer
+ *   (for example `parseAmount("abc")` or `parseAmount("1.2x")`).
+ *
+ * @example
+ * parseAmount("1.5");       // 15_000_000n
+ * parseAmount("2");         // 20_000_000n
+ * parseAmount("0.00000015"); // 1n  (8th decimal is truncated)
  */
 export function parseAmount(value: string): bigint {
   const [whole = "0", frac = ""] = value.split(".");
@@ -31,23 +54,59 @@ export function parseAmount(value: string): bigint {
 }
 
 /**
- * Validate a Stellar public key (G... address).
+ * Report whether `address` is a valid Stellar ed25519 public key (`G...`).
+ *
+ * Delegates to stellar-sdk `StrKey.isValidEd25519PublicKey`, which checks the
+ * version byte, length, and CRC16 checksum. Muxed (`M...`) and secret (`S...`)
+ * keys return `false`.
  *
- * Uses stellar-sdk StrKey.
+ * @param address - Candidate address string.
+ * @returns `true` if `address` is a well-formed `G...` public key.
+ *
+ * @example
+ * isValidStellarAddress("GA7QYNF7SOWQ3GLR2BGMZEHXAVIRZA4KVWLTJJFC7MGXUA74P7UJVSGZ"); // true
+ * isValidStellarAddress("GABC"); // false
+ * isValidStellarAddress("");     // false
  */
 export function isValidStellarAddress(address: string): boolean {
   return StrKey.isValidEd25519PublicKey(address);
 }
 
 /**
- * Case-insensitive comparison of two addresses.
+ * Compare two address strings for equality, ignoring case.
+ *
+ * This is a plain string comparison after lower-casing both operands; it does
+ * not decode or validate either address and does not treat a muxed address as
+ * equal to its underlying `G...` account.
+ *
+ * @param a - First address.
+ * @param b - Second address.
+ * @returns `true` if the two strings are equal when lower-cased.
+ *
+ * @example
+ * addressesEqual("GABC", "gabc"); // true
+ * addressesEqual("GABC", "GXYZ"); // false
  */
 export function addressesEqual(a: string, b: string): boolean {
   return a.toLowerCase() === b.toLowerCase();
 }
 
 /**
- * Convert a base G address and an ID into a muxed M address.
+ * Build a muxed (`M...`) address from a base account and a subaccount id.
+ *
+ * @param address - Base Stellar public key (`G...`).
+ * @param id - Muxed subaccount id (0 to 2^64 - 1).
+ * @returns The muxed account id string (`M...`).
+ * @throws {Error} If `address` is not a valid `G...` public key or `id` is out
+ *   of the unsigned 64-bit range (thrown by the stellar-sdk `Account` /
+ *   `MuxedAccount` constructors).
+ *
+ * @example
+ * const m = toMuxedAddress(
+ *   "GA7QYNF7SOWQ3GLR2BGMZEHXAVIRZA4KVWLTJJFC7MGXUA74P7UJVSGZ",
+ *   42n,
+ * );
+ * // m is the corresponding muxed id, e.g. "MA7QYNF7SOWQ3GLR2BGM...UAAAAAAAAAAAAF6VW"
  */
 export function toMuxedAddress(address: string, id: bigint): string {
   const account = new Account(address, "0");
@@ -56,7 +115,21 @@ export function toMuxedAddress(address: string, id: bigint): string {
 }
 
 /**
- * Parse an M address back to its base G address and ID.
+ * Split a muxed (`M...`) address back into its base account and subaccount id.
+ *
+ * Inverse of {@link toMuxedAddress}.
+ *
+ * @param muxed - Muxed account id string (`M...`).
+ * @returns An object with the base `G...` `address` and the numeric `id`.
+ * @throws {Error} If `muxed` is not a valid `M...` address (thrown by
+ *   stellar-sdk `MuxedAccount.fromAddress`).
+ *
+ * @example
+ * const { address, id } = fromMuxedAddress(toMuxedAddress(
+ *   "GA7QYNF7SOWQ3GLR2BGMZEHXAVIRZA4KVWLTJJFC7MGXUA74P7UJVSGZ",
+ *   42n,
+ * ));
+ * // address === "GA7QYNF7SOWQ3GLR2BGMZEHXAVIRZA4KVWLTJJFC7MGXUA74P7UJVSGZ", id === 42n
  */
 export function fromMuxedAddress(muxed: string): { address: string; id: bigint } {
   const parsed = MuxedAccount.fromAddress(muxed, "0");
@@ -67,21 +140,52 @@ export function fromMuxedAddress(muxed: string): { address: string; id: bigint }
 }
 
 /**
- * Return a Unix timestamp (seconds) for a date that is `days` from now.
+ * Compute a Unix timestamp (seconds) `days` days from now.
+ *
+ * Uses `Date.now()` at call time. `days` may be fractional or negative; the
+ * result is floored to a whole second.
+ *
+ * @param days - Number of days from now (1 day = 86,400 seconds).
+ * @returns A Unix timestamp in seconds.
+ *
+ * @example
+ * deadlineFromDays(7); // now (in seconds) + 604800
  */
 export function deadlineFromDays(days: number): number {
   return Math.floor(Date.now() / 1000) + days * 86_400;
 }
 
 /**
- * Return true if a Unix timestamp deadline has passed.
+ * Report whether a Unix timestamp deadline lies strictly in the past.
+ *
+ * Compares `deadline` against the current time floored to whole seconds; a
+ * deadline exactly equal to the current second is not yet expired.
+ *
+ * @param deadline - Unix timestamp in seconds.
+ * @returns `true` if the current time is past `deadline`.
+ *
+ * @example
+ * isExpired(Math.floor(Date.now() / 1000) - 60); // true
+ * isExpired(Math.floor(Date.now() / 1000) + 60); // false
  */
 export function isExpired(deadline: number): boolean {
   return Math.floor(Date.now() / 1000) > deadline;
 }
 
 /**
- * Truncate a Stellar address for display: "GABC...XYZ".
+ * Shorten an address for display as `"<head>...<tail>"`.
+ *
+ * Returns `address` unchanged when it is short enough that truncation would not
+ * save space (length at most `chars * 2 + 3`).
+ *
+ * @param address - Address (or any string) to shorten.
+ * @param chars - Number of leading and trailing characters to keep. Defaults to 4.
+ * @returns The truncated string, or the original when it is already short.
+ *
+ * @example
+ * truncateAddress("GA7QYNF7SOWQ3GLR2BGMZEHXAVIRZA4KVWLTJJFC7MGXUA74P7UJVSGZ");    // "GA7Q...VSGZ"
+ * truncateAddress("GA7QYNF7SOWQ3GLR2BGMZEHXAVIRZA4KVWLTJJFC7MGXUA74P7UJVSGZ", 6); // "GA7QYN...UJVSGZ"
+ * truncateAddress("GABCDEF"); // "GABCDEF" (too short to truncate)
  */
 export function truncateAddress(address: string, chars = 4): string {
   if (address.length <= chars * 2 + 3) return address;
@@ -89,10 +193,31 @@ export function truncateAddress(address: string, chars = 4): string {
 }
 
 /**
- * Format a Stellar address for display, e.g. "GABCD...WXYZ".
+ * Shorten an address for display with configurable head and tail lengths.
+ *
+ * Unlike {@link truncateAddress}, this always truncates and throws rather than
+ * returning a short input unchanged.
  *
- * @throws {StellarSplitError} with code `INVALID_RECIPIENT` if `address` is
+ * @param address - Address to format.
+ * @param opts - Optional lengths.
+ * @param opts.leading - Leading characters to keep. Defaults to 5.
+ * @param opts.trailing - Trailing characters to keep. Defaults to 4.
+ * @returns The formatted `"<leading>...<trailing>"` string.
+ * @throws {StellarSplitError} With code `INVALID_RECIPIENT` if `address` is
  *   shorter than `leading + trailing + 3`.
+ *
+ * @example
+ * formatAddress("GA7QYNF7SOWQ3GLR2BGMZEHXAVIRZA4KVWLTJJFC7MGXUA74P7UJVSGZ");
+ * // "GA7QY...VSGZ"
+ * formatAddress("GA7QYNF7SOWQ3GLR2BGMZEHXAVIRZA4KVWLTJJFC7MGXUA74P7UJVSGZ", {
+ *   leading: 8,
+ *   trailing: 6,
+ * });
+ * // "GA7QYNF7...UJVSGZ"
+ *
+ * @example
+ * // Throws StellarSplitError { code: "INVALID_RECIPIENT" }
+ * formatAddress("GABC");
  */
 export function formatAddress(
   address: string,
@@ -111,7 +236,26 @@ export function formatAddress(
 }
 
 /**
- * Validates if a caller is in the invoice's allowed callers list.
+ * Check whether a caller is permitted to act on an invoice.
+ *
+ * When `invoice.allowed_callers` is `undefined` or `null` the invoice is open
+ * and every caller is allowed. Otherwise the caller must appear in the list
+ * (exact, case-sensitive string match).
+ *
+ * @param invoice - Invoice whose `allowed_callers` list is consulted.
+ * @param callerAddress - Address requesting to act on the invoice.
+ * @returns `{ allowed: true }` when permitted, otherwise
+ *   `{ allowed: false, reason: "caller not in allowlist" }`.
+ *
+ * @example
+ * validateCallerAllowlist({ ...invoice, allowed_callers: null }, "GABC");
+ * // { allowed: true }
+ *
+ * validateCallerAllowlist(
+ *   { ...invoice, allowed_callers: ["GXYZ"] },
+ *   "GABC",
+ * );
+ * // { allowed: false, reason: "caller not in allowlist" }
  */
 export function validateCallerAllowlist(
   invoice: Invoice,
@@ -127,7 +271,41 @@ export function validateCallerAllowlist(
 }
 
 /**
- * Computes the penalty amount owed for a late payment.
+ * Compute the late-payment penalty owed for an invoice at a given payment time.
+ *
+ * Returns a zero penalty (`penaltyBps: 0`, `penaltyAmount: 0n`, `tier: null`)
+ * when any of the following hold:
+ * - `invoice.penalty_deadline` is not set, or the payment is on or before it;
+ * - `invoice.penalty_tiers` is missing or empty;
+ * - no configured tier applies to the number of days late.
+ *
+ * Otherwise days late is `ceil((paymentTimestamp - penalty_deadline) / 86400)`,
+ * and the highest tier whose `days_late` threshold is met is selected. The
+ * penalty amount is `sum(recipient.amount) * tier.penalty_bps / 10_000`
+ * (integer bigint division). `tier` is the index of the applied tier within the
+ * original `invoice.penalty_tiers` array.
+ *
+ * @param invoice - Invoice carrying `penalty_deadline`, `penalty_tiers`, and
+ *   `recipients`.
+ * @param paymentTimestamp - Unix timestamp (seconds) the payment is made.
+ * @returns The penalty in basis points, the penalty amount in stroops, and the
+ *   index of the applied tier (or `null` when no penalty applies).
+ *
+ * @example
+ * const invoice = {
+ *   penalty_deadline: 1_000_000,
+ *   penalty_tiers: [
+ *     { days_late: 1, penalty_bps: 100 },
+ *     { days_late: 7, penalty_bps: 500 },
+ *   ],
+ *   recipients: [{ address: "GABC", amount: 100_000_000n }],
+ * } as Invoice;
+ *
+ * calculatePenalty(invoice, 1_000_000 + 3 * 86_400);
+ * // { penaltyBps: 100, penaltyAmount: 1_000_000n, tier: 0 }
+ *
+ * calculatePenalty(invoice, 1_000_000); // on time
+ * // { penaltyBps: 0, penaltyAmount: 0n, tier: null }
  */
 export function calculatePenalty(
   invoice: Invoice,
@@ -136,13 +314,13 @@ export function calculatePenalty(
   if (!invoice.penalty_deadline || paymentTimestamp <= invoice.penalty_deadline) {
     return { penaltyBps: 0, penaltyAmount: 0n, tier: null };
   }
-  
+
   if (!invoice.penalty_tiers || invoice.penalty_tiers.length === 0) {
     return { penaltyBps: 0, penaltyAmount: 0n, tier: null };
   }
 
   const daysLate = Math.ceil((paymentTimestamp - invoice.penalty_deadline) / 86400);
-  
+
   // Sort tiers by days_late descending to find the highest applicable tier
   const sortedTiers = [...invoice.penalty_tiers].sort((a, b) => b.days_late - a.days_late);
   const applicableTier = sortedTiers.find(tier => daysLate >= tier.days_late);