Research: D-APERTURE-16-0 — u16 aperture vs u64 word scheduling over a 64K self-space

.claude/board/entries/2026-10-07-aperture16-u64-word-schedule.md

@@ -0,0 +1,33 @@
+# 2026-10-07 — The subtraction law holds; its unit is the u64 word, not the u16 cell
+
+## MEASURED
+
+`crates/lance-graph-benches/examples/aperture16_probe.rs`, over a 65 536-self universe:
+- 11 densities × 8 layouts × 8 payload widths × 10 routes, plus VIA, K propagation over CSR, extent × mask, and target-side scheduling;
+- every route asserted equal before timing.
+
+- The `[u16; 4096]` view of the 64K mask is zero-copy: it is a shift of the same 8 KiB, endianness-proof, and checked against `align_to`. As a schedule, though, it is **1.3–2.3× slower per layout** (2.7× over all ladder cases) than u64 set-bit visitation, and 7× slower on an empty mask (4096 tests against 1024).
+- Adding a full-word dense path to the u64 walk (`adapt64`): geomean 0.80, 2.4–2.9× on runs, at most 17 % worse on any layout.
+- Full 16-run detection (`adapt64>16`) wins on 16-aligned islands (0.40) but is 1.25–1.64× slower on scattered layouts. A branch-free form does not remove that cost.
+- Extent and mask compose multiplicatively: 2.9 µs, against 29.1 for extent only and 11.1 for mask only. The extent alone suffices only when the mask is dense.
+- The mask schedules VIA and K propagation with no selection vector. The ordinal list shows no reproducible win; every apparent win reversed on re-run.
+- On the target side, writing the exact next-frontier mask in the same pass is up to ~20× faster than clearing and scanning `K_next`, and the fastest route in 20 of 30 cases with run order rotated. The `[u16; 4096]` histogram pre-pass is never the fastest route (0 of 30).
+
+## CONSEQUENCE
+
+- No new carrier and no new V4 opcode. The mask is authoritative; u64 words are the unit.
+- BUILD candidates, unbuilt:
+  - gated `mask_gather_u32` (the D-GATED-GATHER-0 item);
+  - a full-word dense path in the fold kernels' u64 walk;
+  - next-frontier-mask-in-pass for multi-hop K.
+- KILL: u16 cells as the scheduling unit; popcount-threshold switching; `MultiplicityAperture`.
+
+## OPEN
+
+- Single machine, single thread, hand-rolled routes. Only A1's count goes through mask-risc.
+- Host timing drifted by up to 2.4× on an identical pass, with no CPU steal. A4 uses a per-row minimum over 5 runs and A6 a median over 4 rotated runs; the other modes are single runs.
+- Review corrections (#1377): cache-line counts use the real allocation offset; the 100 % extent case covers the whole universe; A6 rotates route order.
+- Assembly not inspected; whether the dense paths auto-vectorise is unverified.
+- `quack::SemanticAperture` already uses the word "aperture" for a different concept (a facet-key care mask).
+
+Report: `.claude/research/D-APERTURE-16-0.md`, `D-APERTURE-16-MATRIX.md`, `D-APERTURE-16-tables.md`.

.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.
 
-240 entries, 2026-08-06 .. 2026-10-07.
+241 entries, 2026-08-06 .. 2026-10-07.
 
 | date | entry id | finding | file |
 |---|---|---|---|
 | 2026-10-07 | `tinker-janus-fold-harvest` | TinkerPop bulk = K (GroupReduce), ONE_BULK = S, GValue pinning = bundle invalidation; JanusGraph slice = OrderedLaneWitness→Range (30–38×); no new V4 op | [2026-10-07-tinker-janus-fold-harvest.md](2026-10-07-tinker-janus-fold-harvest.md) |
 | 2026-10-07 | `gated-gather-bit-schedule` | Production gather is 3.8× slow from a per-row branch; bit-gated visitation wins or ties at every density; ordinal vectors never win (R1 holds) | [2026-10-07-gated-gather-bit-schedule.md](2026-10-07-gated-gather-bit-schedule.md) |
 | 2026-10-07 | `bind-bundle-gated-gather` | One bound query, five routes, identical answers; the semijoin is never gated and dominates; a gated mask gather beats a selection vector (R1 survives) | [2026-10-07-bind-bundle-gated-gather.md](2026-10-07-bind-bundle-gated-gather.md) |
+| 2026-10-07 | `aperture16-u64-word-schedule` | The u16 view of the 64K mask is free but 1.3–2.3× slower per layout as a schedule than u64 words; extent × mask compose; the exact next-frontier mask beats a u16 target histogram; no new carrier or opcode | [2026-10-07-aperture16-u64-word-schedule.md](2026-10-07-aperture16-u64-word-schedule.md) |
 | 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 | `D-ANCESTRY-K1-0` |  | [2026-10-06-streamdto-circuit-ancestry.md](2026-10-06-streamdto-circuit-ancestry.md) |
 | 2026-10-06 | `D-SPOG-W-0` |  | [2026-10-06-spog-witness-sub-context.md](2026-10-06-spog-witness-sub-context.md) |

.claude/knowledge/fold-execution-laws.md

@@ -51,6 +51,19 @@ to compute it now · EXECUTE touches the bytes. No fifth verb was forced.
 9. **Anti-lasagne.** A new IR must hold information that cannot live in the
    semantic plan, the binding, V4, the bundle choice or the backend program.
    None proposed so far does.
+10. **Subtract from the known universe, in u64 words.** Scheduling is
+    extent → skip zero words → dense full words → walk set bits → touch
+    payload last. The unit is the **u64 mask word**, not a 16-self cell. The
+    u16 view of the same 8 KiB is a free shift, but as a schedule it is 1.3–2.3×
+    slower per layout (2.7× overall geomean), and 7× slower on an empty mask (4096 tests vs 1024). 16-cells earn
+    a role only in detecting full 16-runs inside a partial word, opt-in. Cost
+    tracks live rows for lanes up to 16 B and live cache lines from 32 B up, never N.
+    [MEASURED, `aperture16_probe`, D-APERTURE-16-0]
+11. **The target side subtracts too: the next frontier IS the schedule.** For
+    K propagation, writing the exact next-frontier mask in the same pass and
+    clearing `K_next` by walking it beats clearing and scanning the dense array
+    by up to ~20× at sparse frontiers. A coarse `[u16; 4096]` target histogram
+    pre-pass is never the fastest route. [MEASURED, `aperture16_probe a6`]
 
 ## Measured state of the candidate V4 (R2IL)