docs: clarify appendix-a Element/TreeType discriminant columns

CodeRabbit flagged the TreeType column for ProvableSumTree as "should be
17" — the technical claim was wrong (11 is the correct TreeType
discriminant per `merk/src/tree_type/mod.rs:77`), but the confusion was
fair: the column header "TreeType" was ambiguous and the table had
several pre-existing inaccuracies in adjacent rows. This commit fixes
the ambiguity AND the bugs.

Changes:
- Rename column header from "TreeType" to "TreeType disc" and add an
  intro paragraph explaining that "Element disc" and "TreeType disc"
  are discriminants of two SEPARATE enums.
- Add the TreeType-variant label to every tree row for consistency
  (some had it, most didn't). The new format is `N (VariantName)` —
  e.g. `5 (ProvableCountTree)` — which CodeRabbit-style auto-review
  can't misread.
- Fix three pre-existing wrong TreeType disc values:
    `BigSumTree`:        4 -> 2
    `CountTree`:         2 -> 3
    `CountSumTree`:      3 -> 4
  (These were drift from the actual `TreeType::discriminant()`
  implementation; the file had `4 (BigSumTree)` etc. but those labels
  were wrong.)
- Swap the row order at Element discriminants 8 and 9 to match the
  actual `Element` enum order:
    8 = `ProvableCountTree`  (was incorrectly listed as `ItemWithSumItem`)
    9 = `ItemWithSumItem`    (was incorrectly listed as `ProvableCountTree`)
- Tighten the `ProvableCountSumTree` Purpose blurb to note "only count
  in hash" since the sum is tracked metadata, not bound — this is the
  half-step variant a future `ProvableCountAndSumTree` would replace.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

Author: QuantumExplorer

docs/book/src/appendix-a.md

@@ -1,25 +1,33 @@
 # Appendix A: Complete Element Type Reference
 
-| Discriminant | Variant | TreeType | Fields | Cost Size | Purpose |
+> **Reading the table.** "Element disc" is the bincode discriminant of
+> the `Element` enum (one byte; persisted at the start of every
+> serialized element). "TreeType disc" is the discriminant of the
+> *separate* `TreeType` enum in `merk/src/tree_type/mod.rs` — it is NOT
+> the same numbering. Most rows list both the TreeType disc and its
+> variant name (e.g. `0 (NormalTree)`) to keep the distinction obvious;
+> `N/A` means the Element variant is not a tree.
+
+| Element disc | Variant | TreeType disc | Fields | Cost Size | Purpose |
 |---|---|---|---|---|---|
 | 0 | `Item` | N/A | `(value, flags)` | varies | Basic key-value storage |
 | 1 | `Reference` | N/A | `(path, max_hop, flags)` | varies | Link between elements |
 | 2 | `Tree` | 0 (NormalTree) | `(root_key, flags)` | TREE_COST_SIZE | Container for subtrees |
 | 3 | `SumItem` | N/A | `(value, flags)` | varies | Contributes to parent sum |
 | 4 | `SumTree` | 1 (SumTree) | `(root_key, sum, flags)` | SUM_TREE_COST_SIZE | Maintains sum of descendants |
-| 5 | `BigSumTree` | 4 (BigSumTree) | `(root_key, sum128, flags)` | BIG_SUM_TREE_COST_SIZE | 128-bit sum tree |
-| 6 | `CountTree` | 2 (CountTree) | `(root_key, count, flags)` | COUNT_TREE_COST_SIZE | Element counting tree |
-| 7 | `CountSumTree` | 3 (CountSumTree) | `(root_key, count, sum, flags)` | COUNT_SUM_TREE_COST_SIZE | Combined count + sum |
-| 8 | `ItemWithSumItem` | N/A | `(value, sum, flags)` | varies | Item with sum contribution |
-| 9 | `ProvableCountTree` | 5 | `(root_key, count, flags)` | COUNT_TREE_COST_SIZE | Provable count tree |
-| 10 | `ProvableCountSumTree` | 6 | `(root_key, count, sum, flags)` | COUNT_SUM_TREE_COST_SIZE | Provable count + sum |
-| 11 | `CommitmentTree` | 7 | `(total_count: u64, chunk_power: u8, flags)` | 12 | ZK-friendly Sinsemilla + BulkAppendTree |
-| 12 | `MmrTree` | 8 | `(mmr_size: u64, flags)` | 11 | Append-only MMR log |
-| 13 | `BulkAppendTree` | 9 | `(total_count: u64, chunk_power: u8, flags)` | 12 | High-throughput append-only log |
-| 14 | `DenseAppendOnlyFixedSizeTree` | 10 | `(count: u16, height: u8, flags)` | 6 | Dense fixed-capacity Merkle storage |
+| 5 | `BigSumTree` | 2 (BigSumTree) | `(root_key, sum128, flags)` | BIG_SUM_TREE_COST_SIZE | 128-bit sum tree |
+| 6 | `CountTree` | 3 (CountTree) | `(root_key, count, flags)` | COUNT_TREE_COST_SIZE | Element counting tree |
+| 7 | `CountSumTree` | 4 (CountSumTree) | `(root_key, count, sum, flags)` | COUNT_SUM_TREE_COST_SIZE | Combined count + sum |
+| 8 | `ProvableCountTree` | 5 (ProvableCountTree) | `(root_key, count, flags)` | COUNT_TREE_COST_SIZE | Provable count tree |
+| 9 | `ItemWithSumItem` | N/A | `(value, sum, flags)` | varies | Item with sum contribution |
+| 10 | `ProvableCountSumTree` | 6 (ProvableCountSumTree) | `(root_key, count, sum, flags)` | COUNT_SUM_TREE_COST_SIZE | Provable count + sum (only count in hash) |
+| 11 | `CommitmentTree` | 7 (CommitmentTree) | `(total_count: u64, chunk_power: u8, flags)` | 12 | ZK-friendly Sinsemilla + BulkAppendTree |
+| 12 | `MmrTree` | 8 (MmrTree) | `(mmr_size: u64, flags)` | 11 | Append-only MMR log |
+| 13 | `BulkAppendTree` | 9 (BulkAppendTree) | `(total_count: u64, chunk_power: u8, flags)` | 12 | High-throughput append-only log |
+| 14 | `DenseAppendOnlyFixedSizeTree` | 10 (DenseAppendOnlyFixedSizeTree) | `(count: u16, height: u8, flags)` | 6 | Dense fixed-capacity Merkle storage |
 | 15 | `NonCounted` | wrapper | `Box<Element>` | inner + 1 byte | Opts inner out of parent count aggregation |
 | 16 | `NotSummed` | wrapper | `Box<Element>` | inner + 1 byte | Opts inner out of parent sum aggregation |
-| 17 | `ProvableSumTree` | 11 | `(root_key, sum: i64, flags)` | SUM_TREE_COST_SIZE | Sum baked into hash (see [Aggregate Sum on Range Queries](aggregate-sum-on-range-queries.md)) |
+| 17 | `ProvableSumTree` | 11 (ProvableSumTree) | `(root_key, sum: i64, flags)` | SUM_TREE_COST_SIZE | Sum baked into hash (see [Aggregate Sum on Range Queries](aggregate-sum-on-range-queries.md)) |
 
 **Notes:**
 - Discriminants 11–14 are **non-Merk trees**: data lives outside a child Merk subtree