lab(mpf): D-MPF-1 — the Stage 1 math polyfill already exists; one expression, oracle, refusals, cost split

.claude/board/INTEGRATION_PLANS.md

@@ -1,3 +1,6 @@
+## 2026-10-23 — d-mpf-math-polyfill-v1 — the mathematical polyfill API, Stage 1 → `.claude/plans/d-mpf-math-polyfill-v1.md`
+
+**Status:** D-MPF-1 MEASURED, lab only; D-MPF-2.. PROPOSED. The Stage 1 polyfill API is the shipped R2IL procedure layer plus checked scalar arithmetic over mask-risc, with relalg as the rewriting frontend; no new primitive. One expression matches an independent row loop; at 64 K rows it costs under 1 ns/row, at one word ~600 ns per call. Gaps by counterexample: element-wise arithmetic, unsigned compare, floats, one-word fixed cost. Independent of ONNX and of the S0 drafts. Entry `2026-10-23-d-mpf-1-polyfill-probe.md`.
 ## 2026-10-23 — d-onnx-relalg-cap-capstone-1750-v1 — ONNX intake onto existing lance-graph surfaces (capstone S0, #1750) → `.claude/plans/d-onnx-relalg-cap-capstone-1750-v1.md`
 
 **Status:** PROPOSAL, S0 docs only; nothing implemented. The pipeline "ONNX graph → RelAlg polyfill → Cartesian projection → native execution" is false as stated: relalg is a single-table integer selection with Count/Sum/Min/Max/Keep, so it receives only the integer selection/aggregate island; numeric ops route to existing ndarray kernels; Gather/Scatter, control flow and `ai.onnx.ml` are typed refusals. The ONNX `ModelProto` stays the only graph (D-RA-2 = A; no new AST, primitive or executor). The original DR64³ master plan was not found on `main` or 833 branches and is recorded as an OPEN documentation dependency. S1 is blocked on the operator naming one target model and the protobuf fork coordinates. Entry `2026-10-23-d-onnx-relalg-cap-s0-capstone-1750.md`. #1744's S0 (below) kept the base path; the native-first correction (#1753) governs where they differ.

.claude/board/STATUS_BOARD.md

@@ -1,3 +1,15 @@
+## D-MPF — mathematical polyfill API, Stage 1 (2026-10-23)
+
+Lab only (`crates/math-polyfill-probe`). Plan `.claude/plans/d-mpf-math-polyfill-v1.md`; entry `entries/2026-10-23-d-mpf-1-polyfill-probe.md`.
+
+| D-id | scope | status | gate / falsifier |
+|---|---|---|---|
+| **D-MPF-1** | one expression (SUM − k·COUNT, NULL plane) through the existing r2il procedures; oracle; typed refusals; cost split | MEASURED (this branch) | equal to an `i128` row loop at 64..65 537 rows; D1–D3 red; 0.86–0.91 ns/row at 64 K, ~600 ns per call at 64 rows |
+| **D-MPF-2** | attribute the one-word fixed cost (~120 ns mask-risc + ~150 ns dialect) | Measured (#1752) | gate not met, reason recorded: floor alone 39 ns at one word; per-row bottleneck is `masked_sum_i32`'s bit walk (plan §7) |
+| **D-MPF-3** | element-wise integer arithmetic (G1) | Blocked (owner decision) | `lane_plus_lane_is_refused` turns into an admitted, oracle-checked op |
+| **D-MPF-2b** | dense/sparse hybrid masked sum (per-word density threshold) and one mask reused across count/sum/min/max | Measured (#1752) | hybrid th=16 is 2–3.7× (uniform) and 4–5× (clustered) faster than the walk, and never slower; reuse ~2× when sparse; a fused scalar pass is 6× faster at 50 % (plan §9) |
+| **D-MPF-4** | R2IL as a router: attribution of the five things named R2IL, a routing table (DIRECT / COMPOSE / LOWER / REFUSE), and a ClassId → LazyLock → prebound-callable probe against direct ndarray | Measured (#1752) | prebound route == direct ndarray at 64..65 536 rows; one resolution per ClassId, 0 route evaluations and 0 allocations in steady state; frame/focus/scope guard 27–28 ns (4 atomic RMWs); three disable runs red (plan §10) |
+
 ## D-ONNX-CAP — ONNX intake onto existing lance-graph surfaces (2026-10-23)
 
 PROPOSAL, docs only. Plan `.claude/plans/d-onnx-relalg-cap-capstone-1750-v1.md`; entry `entries/2026-10-23-d-onnx-relalg-cap-s0-capstone-1750.md` (#1750; #1744's S0 below kept the base path). ONNX `ModelProto` stays the only graph; relalg receives only the integer selection/aggregate island; no new primitive, AST or executor.

.claude/board/entries/2026-10-23-d-mpf-1-polyfill-probe.md

@@ -0,0 +1,12 @@
+# 2026-10-23 — E-D-MPF-1: the Stage 1 polyfill already exists; per row it is sub-nanosecond, per one-word call it is ~600 ns
+
+**Status:** MEASURED, lab only (`crates/math-polyfill-probe`). Plan `.claude/plans/d-mpf-math-polyfill-v1.md`.
+
+- The mathematical polyfill API is the shipped R2IL procedure layer (`lance-graph-r2il::procs`) plus checked scalar arithmetic in `FoldDialect`, over mask-risc, with relalg as the rewriting frontend. No new primitive, IR or executor.
+- One expression, `SUM(v | sel) − k·COUNT(sel)` with a NULL presence plane, written only with those procedures, equals an independent `i128` row loop at 64 / 1 000 / 4 096 / 65 537 rows. 9 tests; disable runs D1–D3 each turn named tests red.
+- Typed refusals already exist for lane + lane arithmetic, unsigned compare, overflow and division by zero.
+- Cost (ns per call, medians, 3 runs): at 65 536 rows the expression costs 0.86–0.91 ns/row and beats the scalar loop 1.6×; at 64 rows one fold is ~120 ns in mask-risc plus ~150 ns in the dialect, and the scalar loop (~80 ns) beats the whole expression (~600 ns).
+- Gaps by counterexample: G1 element-wise value arithmetic, G2 unsigned compare, G3 floats, G4 the one-word fixed cost.
+- The ONNX fork `AdaWorldAPI/optimum-onnx-rs` is empty; `AdaWorldAPI/onnx` is not accessible.
+
+Next gate: D-MPF-2 (attribute the one-word fixed cost), and the owner decision on G1.

.claude/board/entries/2026-10-23-d-mpf-2-fixed-cost.md

@@ -0,0 +1,11 @@
+# 2026-10-23 — D-MPF-2: where the native fold's cost goes
+
+**Status:** MEASURED, lab only (`crates/math-polyfill-probe`, PR #1752). Nothing changed outside the probe.
+
+- Per call at 64 rows: scalar 12 ns; ndarray floor 39; mask-risc +57; `Program::new` +20 and 1 allocation; dialect +50. Total ~172 ns.
+- Per row at 64 K rows: mask-risc ≈ ndarray floor. The floor's cost is `ndarray::simd::masked_sum_i32`, a scalar set-bit walk (LLVM: `tzcnt`/`blsr`, no vector register) whose time tracks popcount: 1.7 / 25 / 44 µs at 0 / 50 / 100 % selected. The compare is ~0.09 ns/row.
+- Correction to D-MPF-1: "1.6× faster than the scalar loop" compared against the `i128` filter-chain oracle. An equal-work `i64` loop takes ~11 µs at 64 K rows and is ~3× faster than the fold.
+- Proposal, not made: density-chosen `masked_sum_i32` body (branch-free above ~16 set bits per word, walk below). The branch-free form equals the oracle and is flat in selectivity; the walk is 7–10× faster on empty words.
+- OPEN: whether the mask form beats a scalar loop when the mask is reused or combined (not measured here).
+
+Plan: `.claude/plans/d-mpf-math-polyfill-v1.md` §7.

.claude/board/entries/2026-10-23-d-mpf-4-classid-route.md

@@ -0,0 +1,18 @@
+# 2026-10-23 — D-MPF-4: R2IL routes once per ClassId; the steady-state cost is the guard, not the route
+
+**Status:** MEASURED, lab (`crates/math-polyfill-probe/examples/classid_route.rs`). Plan `.claude/plans/d-mpf-math-polyfill-v1.md` §10. No production crate, ABI or execution contract changed.
+
+- **Attribution:** five different things are called R2IL, and they stay apart:
+  - r2sleigh's `r2il`: IL types, no executor.
+  - the machine reading: `r2conc` / `r2sym`, scalar machine state.
+  - `ogar-r2il`: the opcode table, readings `0xC400` machine / `0xC401` fold.
+  - `lance-graph-r2il::FoldDialect`: the fold reading only.
+  - mask-risc / `ndarray::simd` / `simd_runtime`.
+
+  The 94–99 ns and 171–172 ns of D-MPF-2 are the cost of choosing the mask-risc and FoldDialect paths per call. They are not a cost of R2IL routing.
+- **Recovered 2–5 ns figures:** each is a direct kernel, not an R2IL call. The one cited as a comparison is `ndarray::simd` AND, AND, popcount over 4 words at 2.2–2.8 ns, against 54–70 ns through r2il + mask-risc (`2026-10-21-d-rft-1-cost-breakdown.md`).
+- **Routing table:** every wired fold-reading op has a DIRECT or COMPOSE route onto existing `ndarray::simd` entrypoints, or is refused. Only machine semantics need R2Sleigh: carry/borrow flags, address-space load/store, branches, width-exact integers.
+- **Measured** (64 rows / 65 536 rows): prebound route without guard 36–39 / ≈ direct ndarray. Guard (`FrameStore::check` + focus + scope) 27–28 ns, 0 allocations; objdump shows 2× `lock cmpxchg` + 2× `lock decq` from `Arc::downgrade`. Per-call `LazyLock` + `match` adds 0–1 ns. Prepared R2IL (FoldDialect's `last_program` as a `CompiledProgram`) = prepared mask-risc, 85–94 ns.
+- **Asserted:** one resolution per ClassId; 0 route evaluations in steady state; LOWER/REFUSE refused at bind; focus, scope and source changes refused at run; rebinding does not re-resolve. Three disable runs red.
+- **Proposal (not made, DR lab owner):** compare `Weak::as_ptr` with `Arc::as_ptr` instead of `Weak::ptr_eq(.., &Arc::downgrade(..))`. Same identity semantics, no atomics. Unmeasured.
+- OPEN: the program-only half of mask-risc's per-call `precheck`/`validate`; mask-sharing callables for multi-op bindings; the U64 unsigned-compare refusal (`lt_u64_to_mask` exists).

.claude/board/entries/README.md

@@ -25,7 +25,7 @@ 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.
 
-455 entries, 2026-08-06 .. 2026-10-23.
+458 entries, 2026-08-06 .. 2026-10-23.
 
 | date | entry id | finding | file |
 |---|---|---|---|
@@ -39,6 +39,9 @@ exactly one of them, never both.
 | 2026-10-23 | `D-TGA-5` |  | [2026-10-23-d-tga-5-squash-gate-preregistration.md](2026-10-23-d-tga-5-squash-gate-preregistration.md) |
 | 2026-10-23 | `D-ONNX-RELALG-CAP` | S0 result: ONNX as import membrane, DR64³ plan not found | [2026-10-23-d-onnx-relalg-cap-s0.md](2026-10-23-d-onnx-relalg-cap-s0.md) |
 | 2026-10-23 | `E-D-ONNX-RELALG-CAP-S0-1` |  | [2026-10-23-d-onnx-relalg-cap-s0-capstone-1750.md](2026-10-23-d-onnx-relalg-cap-s0-capstone-1750.md) |
+| 2026-10-23 | `D-MPF-4` |  | [2026-10-23-d-mpf-4-classid-route.md](2026-10-23-d-mpf-4-classid-route.md) |
+| 2026-10-23 | `D-MPF-2` |  | [2026-10-23-d-mpf-2-fixed-cost.md](2026-10-23-d-mpf-2-fixed-cost.md) |
+| 2026-10-23 | `E-D-MPF-1` |  | [2026-10-23-d-mpf-1-polyfill-probe.md](2026-10-23-d-mpf-1-polyfill-probe.md) |
 | 2026-10-23 | `coresearch-thought-git-markov` |  | [2026-10-23-coresearch-thought-git-markov.md](2026-10-23-coresearch-thought-git-markov.md) |
 | 2026-10-23 | `coresearch-thought-git-markov-cc2` |  | [2026-10-23-coresearch-thought-git-markov-cc2.md](2026-10-23-coresearch-thought-git-markov-cc2.md) |
 | 2026-10-23 | `coresearch-julia-egraphs` |  | [2026-10-23-coresearch-julia-egraphs.md](2026-10-23-coresearch-julia-egraphs.md) |