docs(fast-inbox): correct the is_first_block and sole-block-variant rationale (A-1387)

Author: spalladino

noir-projects/noir-protocol-circuits/crates/rollup-lib/src/abis/block_rollup_public_inputs.nr

@@ -40,11 +40,13 @@ pub struct BlockRollupPublicInputs {
     // stored in the checkpoint header, enabling validation of the blocks included in a checkpoint given their headers.
     pub block_headers_hash: Field,
 
-    // Whether this block range starts at the first block of its checkpoint. Only the first block root sets this true;
-    // merges propagate it from the left rollup and `validate_consecutive_block_rollups` asserts the right rollup's is
-    // false, so it can only reach the checkpoint root through the leftmost leaf. It replaces `in_hash`'s former
-    // structural role: the checkpoint root asserts the merged value is true, and it drives the block-end blob-absorb
-    // flag (the l1-to-l2 tree root is absorbed only for the first block).
+    // Whether this block range starts at the first block of its checkpoint. Only the first block root variants set it
+    // true; merges propagate it from the left rollup (`merge_block_rollups`), and
+    // `validate_consecutive_block_rollups` asserts the right rollup of every merge is not a first block. The flag is
+    // therefore a proof that the range's leftmost leaf is a first-variant block root, which is what lets the
+    // checkpoint root assert its leftmost block is one (`checkpoint_root_inputs_validator`) even though it cannot see
+    // the leaf VK indices. Since only first variants may be fully empty (no txs and no messages), that also confines
+    // a fully-empty filler block to the first position of a checkpoint.
     pub is_first_block: bool,
 
     // Poseidon2 message-bundle sponge threaded across the blocks of the checkpoint. The leftmost block starts from the

noir-projects/noir-protocol-circuits/crates/rollup-lib/src/checkpoint_root/checkpoint_root_single_block_rollup.nr

@@ -21,8 +21,10 @@ use types::{
 //
 // That `is_first_block` assertion is the only thing keeping a message-only block from standing as a checkpoint's sole
 // block. If it is ever relaxed (e.g. replaced by a "leftmost block's start_msg_sponge is empty" check), this entry
-// must be dropped in the same change, or a transaction-less single-block checkpoint — one whose blob omits the
-// first-block l1-to-l2 root — would silently become provable.
+// must be dropped in the same change, because barring the message-only variant from standing alone is what keeps
+// each checkpoint shape to a single valid encoding: a sole transaction-less block carrying a message bundle is
+// already provable as an empty-tx-first block, which accepts a non-empty bundle. It is also what keeps the rule
+// confining fully-empty blocks to the first position enforceable.
 global ALLOWED_PREVIOUS_VK_INDICES: [u32; 4] = [
     BLOCK_ROOT_FIRST_ROLLUP_VK_INDEX,
     BLOCK_ROOT_SINGLE_TX_FIRST_ROLLUP_VK_INDEX,