diff --git a/test/lib/LibHashSlow.sol b/test/lib/LibHashSlow.sol
index 621db1d..b8b6fe0 100644
--- a/test/lib/LibHashSlow.sol
+++ b/test/lib/LibHashSlow.sol
@@ -8,7 +8,17 @@ bytes32 constant HASH_ABC = 0x4e03657aea45a94fc7d47ba826c8d667c0d1e6e33a64a036ec
 /// @dev `keccak256` of the 64 bytes that are the word `1` then the word `2`.
 bytes32 constant HASH_WORDS_ONE_TWO = 0xe90b7bceb6e7df5418fb78d8ee546e97c83a08bbccc01a0644d599ccd2a7c2e0;
 
+/// Builtin-only reference for every `LibHashNoAlloc` function, so equality
+/// against it pins the value each one computes without reusing its assembly.
+/// "Slow" is about allocation: the `hashWordsSlow` and `combineHashesSlow`
+/// bodies copy their data into a fresh `abi.encodePacked` buffer before
+/// hashing it, which is the cost the `gasleft()` deltas in
+/// `LibHashNoAlloc.t.sol` measure against. `hashBytesSlow` does not, so it is a
+/// value oracle only.
 library LibHashSlow {
+    /// The builtin `keccak256` over the bytes, which allocates nothing.
+    /// `LibHashNoAlloc.hashBytes` compiles to the same hash of the same range,
+    /// so this pins its value and there is no saving to measure against it.
     function hashBytesSlow(bytes memory data) internal pure returns (bytes32) {
         return keccak256(data);
     }
diff --git a/test/src/lib/AbiEncodeGas.t.sol b/test/src/lib/AbiEncodeGas.t.sol
index ad1efe4..d500f51 100644
--- a/test/src/lib/AbiEncodeGas.t.sol
+++ b/test/src/lib/AbiEncodeGas.t.sol
@@ -5,7 +5,15 @@ pragma solidity ^0.8.25;
 import {Test} from "forge-std-1.16.2/src/Test.sol";
 import {Foo} from "../../lib/LibFooOracle.sol";
 
+/// The cost bullet in LibHashNoAlloc's title block says `abi.encode` of a
+/// struct with one or two dynamic typed fields costs several hundred gas when
+/// those fields are empty and over 1k once they hold a handful of words. Both
+/// ends are measured here on the README's `Foo`, by gasleft() delta around the
+/// encode alone. Each encoded length is asserted against the length the ABI
+/// spec gives for that value, so the measured window provably contains the
+/// encoding.
 contract AbiEncodeGasTest is Test {
+    /// Gas spent on `abi.encode(foo)` alone, and the length it produced.
     function encodeGas(Foo memory foo) internal view returns (uint256, uint256) {
         uint256 gasBefore = gasleft();
         bytes memory encoded = abi.encode(foo);
@@ -13,6 +21,8 @@ contract AbiEncodeGasTest is Test {
         return (gasUsed, encoded.length);
     }
 
+    /// `Foo` with both dynamic fields empty: one word of outer offset, 4 head
+    /// words, then a length word each for `c` and `d` with no tail.
     function testEncodeFooCostsHundredsOfGasWhenEmpty() public view {
         (uint256 gasUsed, uint256 length) = encodeGas(Foo(1, address(2), new uint256[](0), ""));
         assertEq(length, 0x20 + 4 * 0x20 + 0x20 + 0x20);
@@ -20,6 +30,8 @@ contract AbiEncodeGasTest is Test {
         assertLt(gasUsed, 1000);
     }
 
+    /// `Foo` with 8 words in `c` and 64 bytes in `d`: the empty encoding plus
+    /// 8 words of `c` and 2 words of `d`.
     function testEncodeFooCostsOverOneThousandGasAtEightWords() public view {
         (uint256 gasUsed, uint256 length) = encodeGas(Foo(1, address(2), new uint256[](8), new bytes(64)));
         assertEq(length, 0x20 + 4 * 0x20 + 0x20 + 8 * 0x20 + 0x20 + 2 * 0x20);
diff --git a/test/src/lib/HashPattern.t.sol b/test/src/lib/HashPattern.t.sol
index 7635caa..e52e91a 100644
--- a/test/src/lib/HashPattern.t.sol
+++ b/test/src/lib/HashPattern.t.sol
@@ -124,6 +124,10 @@ contract HashPatternTest is Test {
         assertEq(hashBytesExample(bytes(baz)), keccak256(bytes(baz)));
     }
 
+    /// "We MUST respect the true length": `hex"01"` and `hex"0100"` occupy the
+    /// same single data word, `0x01` followed by 31 zero bytes (1 and 2 bytes,
+    /// both zero-padded to 0x20), so a hash over the allocated word collides;
+    /// the example hashes only the `length` bytes and does tell them apart.
     function testBytesTrueLength() public pure {
         bytes memory one = hex"01";
         bytes memory two = hex"0100";
@@ -174,6 +178,7 @@ contract HashPatternTest is Test {
             // Store D in scratch
             mstore(0x20, keccak256(add(deref, 0x20), mload(deref)))
 
+            // Hash C and D, already in scratch, to produce the final hash E
             hash := keccak256(0, 0x40)
         }
 
diff --git a/test/src/lib/HashPatternFold.t.sol b/test/src/lib/HashPatternFold.t.sol
index a311c95..c328a9e 100644
--- a/test/src/lib/HashPatternFold.t.sol
+++ b/test/src/lib/HashPatternFold.t.sol
@@ -41,6 +41,10 @@ contract HashPatternFoldTest is Test {
         return foos;
     }
 
+    /// The README's step-by-step letters over `foos[0]` and `foos[1]`:
+    /// `nilHash` is N, `hashFoo0` is A, `foldOne` is B (N then A), `hashFoo1`
+    /// is C and `foldTwo` is D (B then C). `foldOne` is the fold of the first
+    /// item alone and `foldTwo` the fold of both.
     function testFoldPrefixIsStepwiseCombine(Foo memory foo0, Foo memory foo1) public pure {
         Foo[] memory foos = new Foo[](2);
         foos[0] = foo0;
@@ -77,6 +81,8 @@ contract HashPatternFoldTest is Test {
         assertEq(foldPattern(foos), HASH_NIL);
     }
 
+    /// README "Nil hash prefix": a one-item list folds to `hash(nil + hash(item))`,
+    /// which is not `hash(item)`.
     function testFoldSingletonIsNotItem(Foo memory item) public pure {
         Foo[] memory foos = new Foo[](1);
         foos[0] = item;
diff --git a/test/src/lib/LibHashNoAlloc.crossType.t.sol b/test/src/lib/LibHashNoAlloc.crossType.t.sol
index b05fd80..8ecf600 100644
--- a/test/src/lib/LibHashNoAlloc.crossType.t.sol
+++ b/test/src/lib/LibHashNoAlloc.crossType.t.sol
@@ -6,6 +6,8 @@ import {Test} from "forge-std-1.16.2/src/Test.sol";
 import {LibHashNoAlloc, HASH_NIL} from "../../../src/lib/LibHashNoAlloc.sol";
 import {LibHashSlow, HASH_WORDS_ONE_TWO} from "../../lib/LibHashSlow.sol";
 
+/// A struct whose every field is a pointer, so there is no data before the
+/// first one.
 struct TwoBytes {
     bytes d1;
     bytes d2;
@@ -83,10 +85,16 @@ contract LibHashNoAllocCrossTypeTest is Test {
         assertEq(LibHashNoAlloc.hashWords(new uint256[](0)), HASH_NIL);
     }
 
+    /// README "Handling pointers" walks a struct whose fields are all pointers
+    /// from the hash of the zero bytes preceding the first pointer, which is
+    /// the same nil seed the fold of a list starts from, so the walk and the
+    /// fold build the same tree. `struct { bytes d1; bytes d2; }` hashes as the
+    /// `bytes[]` `[d1, d2]` for every value.
     function testPointerOnlyStructEqualsFoldOfList(bytes memory d1, bytes memory d2) public pure {
         TwoBytes memory s = TwoBytes(d1, d2);
         bytes32 walked;
         assembly ("memory-safe") {
+            // Hash of all data up to the first pointer, of which there is none.
             mstore(0, keccak256(s, 0))
             let deref := mload(s)
             mstore(0x20, keccak256(add(deref, 0x20), mload(deref)))
@@ -111,6 +119,9 @@ contract LibHashNoAllocCrossTypeTest is Test {
         assertEq(folded, expected);
     }
 
+    /// The items region of a `T[]` is laid out exactly as an `n`-field struct of
+    /// `T` pointer fields, so walking that region the way README "Handling
+    /// pointers" walks a struct is the fold of the list, at every length.
     function testPointerOnlyStructEqualsFoldOfListAnyLength(bytes[] memory fields) public pure {
         bytes32 walked;
         assembly ("memory-safe") {
diff --git a/test/src/lib/LibHashNoAlloc.t.sol b/test/src/lib/LibHashNoAlloc.t.sol
index c400668..79800e3 100644
--- a/test/src/lib/LibHashNoAlloc.t.sol
+++ b/test/src/lib/LibHashNoAlloc.t.sol
@@ -13,6 +13,11 @@ uint256 constant KECCAK256_BASE_GAS = 30;
 /// @dev Gas KECCAK256 charges per 32 byte word of input.
 uint256 constant KECCAK256_WORD_GAS = 6;
 
+/// Each library function against the `LibHashSlow` builtin oracle, the gas
+/// floor the KECCAK256 schedule gives for the bytes each one hashes, that no
+/// function moves the free memory pointer at `0x40` or the zero slot at `0x60`,
+/// and that hashing words where they sit costs less than packing them into a
+/// fresh allocation first.
 contract LibHashNoAllocTest is Test {
     /// Gas a KECCAK256 over `byteLength` bytes costs, excluding any memory
     /// expansion, which no function under test pays.
diff --git a/test/src/lib/MemoryLayout.t.sol b/test/src/lib/MemoryLayout.t.sol
index 2588cfc..8463e9d 100644
--- a/test/src/lib/MemoryLayout.t.sol
+++ b/test/src/lib/MemoryLayout.t.sol
@@ -224,6 +224,9 @@ contract MemoryLayoutTest is Test {
         assertEq(LibMemorySnapshot.wordAt(ptr, 0x20), innerPtr);
     }
 
+    /// Nesting depth does not change the rule: an `Outermost` holding an
+    /// `Outer` holding a `Foo` is 2 words at each of the two outer levels, and
+    /// the pointer word at each level is the pointer to the next struct down.
     function testDeeplyNestedStructIsOnePointerWordPerLevel(uint256 x, uint256 y) public pure {
         Foo memory inner = Foo(1, ADDR, new uint256[](0), "");
         uint256 fmp0 = LibMemorySnapshot.freeMemoryPointer();
@@ -258,6 +261,9 @@ contract MemoryLayoutTest is Test {
         assertEq(midW1, x);
     }
 
+    /// `new Foo[](n)` allocates the 0x20 + n * 0x20 word list first and then
+    /// one 0x80 `Foo` per element in element order, each default-initialised
+    /// (value members 0, dynamic members pointing at the zero slot).
     function testNewFooArrayAllocatesListThenElements(uint8 length) public pure {
         uint256 n = length;
         uint256 fmpBefore;