quack: diff count and plateau as one ternlog fold over two resident planes (Round 5)

.claude/board/entries/2026-10-06-diff-plateau-as-expression-round5.md

@@ -0,0 +1,49 @@
+# 2026-10-06 — Difference and plateau as an expression (Round 5)
+
+## MEASURED
+
+`crates/lance-graph-quack/tests/diff_plateau.rs`, 3 tests, 5 disable runs
+red.
+
+Two resident planes `a`, `b` over one row space. The diff is `a XOR b`,
+its size is `POPCOUNT`, and the plateau is `NOT ANY`. Four paths, each
+checked against a bit-at-a-time row oracle on eleven cases:
+
+- empty diff (1 row and ragged)
+- one bit at row 0, at the last row of word 0 and the first of word 1
+- one bit at the last row of tile 0 and the first of tile 1 (16384 rows)
+- one bit at the last row of a ragged `3 × 16384 + 77`
+- sparse scattered (every 997th row)
+- dense
+
+| path | ops | lowering | scratch slots | slot words written | heap | population bytes |
+|---|---|---|---|---|---|---|
+| A materialized `Vec<u64>` diff | — | — | — | — | — | 6160 (770 words) |
+| B mask-risc `Xor` → Count / Any | 1 | `Ternlog` imm `0x3C` | 0 | 0 | 0 | 0 |
+| C quack `lower`, `(a∧¬b)∨(¬a∧b)` | 5 | `Ternlog` imm `0x3C` | 0 | 0 | 0 | 0 |
+| D quack `lower_fused`, same filter | 1 | `Ternlog` imm `0x3C` | 0 | 0 | 0 | 0 |
+
+The can-fire twin is the same count with a `Range` pred stacked on the
+`Xor` slot. It runs `Tiled` with 2 slots and 512 words written, and still
+matches the oracle, so the zeros above are measurements.
+
+Disable runs, each red: `Xor` replaced by `And`; plateau read as `ANY`;
+quack diff spelled with `AND` instead of `OR`; reference path ANDing words;
+oracle limited to the first word.
+
+## FINDING
+
+- **Diff count and plateau are each one ternlog fold over the two resident
+  planes.** No diff population is written, no scratch slot is provisioned,
+  and execution allocates nothing.
+- **Quack's AND/OR/NOT spelling reaches the same single table** as a direct
+  `Xor`, under plain `lower` too. The program collapse sees through it.
+
+## OPEN
+
+- Two planes over one row space only. A diff between two Lance versions,
+  or between a horizon and `delta.resulting`, would first need both states
+  readable as resident planes over the same rows.
+- A diff over a third plane (diff restricted to a gate) would still fold
+  (≤ 3 planes). A diff that needs a `Pred` (a range, a lane compare) runs
+  `Tiled` and writes slot words, per the twin.

.claude/board/entries/README.md

@@ -25,13 +25,14 @@ index row, (3) no duplicate entry id. Checks 1 and 2 are deliberately
 opposite directions; the stranding this convention prevents shows up in
 exactly one of them, never both.
 
-224 entries, 2026-08-06 .. 2026-10-06.
+225 entries, 2026-08-06 .. 2026-10-06.
 
 | date | entry id | finding | file |
 |---|---|---|---|
 | 2026-10-06 | `v3-v4-dual-reading-round3` |  | [2026-10-06-v3-v4-dual-reading-round3.md](2026-10-06-v3-v4-dual-reading-round3.md) |
 | 2026-10-06 | `quack-r2il-one-evaluator-round4` |  | [2026-10-06-quack-r2il-one-evaluator-round4.md](2026-10-06-quack-r2il-one-evaluator-round4.md) |
 | 2026-10-06 | `D-MORTON-0` |  | [2026-10-06-morton8x8-checked-address.md](2026-10-06-morton8x8-checked-address.md) |
+| 2026-10-06 | `diff-plateau-as-expression-round5` |  | [2026-10-06-diff-plateau-as-expression-round5.md](2026-10-06-diff-plateau-as-expression-round5.md) |
 | 2026-10-06 | `dav-resident-reading-round2` |  | [2026-10-06-dav-resident-reading-round2.md](2026-10-06-dav-resident-reading-round2.md) |
 | 2026-10-06 | `dav-carrier-invariance-quack` |  | [2026-10-06-dav-carrier-invariance-quack.md](2026-10-06-dav-carrier-invariance-quack.md) |
 | 2026-10-05 | `text-to-numeric-boundary-inventory` |  | [2026-10-05-text-to-numeric-boundary-inventory.md](2026-10-05-text-to-numeric-boundary-inventory.md) |