[AdaWorldAPI]

What

p(X, Z) :- r(X, Y), s(Y, Z) keeps both ends. Until now it was refused at admission. The lab probe now answers it as an integer matrix product over two DR64² 0/1 tiles. This is the falsifier from plan d-dynbag-holographic-bags-v1.md §7.5, with results in §7.6.

• xlog-relcomp-probe src/ncompose.rs:
  • admit_pair admits XLOG's body in both join orders its optimizer emits. It admits a ChainJoin only when its own relations match its fallback. Bounds are refused, and q(Y) is still never admitted as p(X, Z).
  • pair_counts builds the 0/1 tiles over DR LocalMap axes (base relations are sets) and multiplies them with ndarray::simd::matmul_i8_to_i32.
• Tests: tests/litho.rs part 4.
• Cost probe: examples/ncompose_cost.rs. It reports ns per call against relcomp::compose, and prints which matmul_i8_to_i32 tier ran.

Results

• Equality: ℕ per (x, z) matches both oracles: scalar witness enumeration, and a bag walk of XLOG's own RIR for p. It holds on the fixture and on a 300-case random differential, with ids 0..6 per axis so that ℕ ≠ B in more than 100 cases.

• Projection: count > 0 equals relcomp::compose on the DR64 register in every case.

• Disable runs, both red:

  • Swapping the operands is caught only by the differential; the hand fixture passes.
  • Reading the result as B before counting fails both tests.

• Bug found while testing: XLOG's ChainJoin sometimes puts s first. The first version of admit_pair refused that order; it now admits it, checked against the fallback.

• Cost (MEASURED). The host is an Intel Xeon, model 0x55 (Skylake-SP / Cascade Lake class), 4 vCPU VM, with AVX-512 VNNI and no AMX. The product ran on its AVX-512 VNNI VPDPBUSD tier. Two runs agreed within 1%.

  case	compose (B)	matmul_i8_to_i32 (ℕ, tiles prepared)	pair_counts (ℕ, from tuples)
  sparse, 4 × 4 tuples	55 ns	20,762 ns	21,402 ns
  dense 64 × 64	2,369 ns	20,716 ns	158,756 ns

  Through matmul_i8_to_i32's current signature, a 64² tile costs about 21 µs whatever the density: exact, but 400× slower than B on sparse input and 9× on dense. 64³ multiply-adds is only about 4,096 VPDPBUSD instructions. HYPOTHESIS (not profiled): the time is the per-call pack_contig, u8 shift copy, output Vec, bias pass and copy back (plan §7.4). Two candidates follow, both for ndarray::simd, backend-first:

  • a non-allocating entry point;
  • a bit-packed i1 × i1 → i32 word (popcount of R[x] ∧ Sᵀ[z]), which is D-DYNBAG-3.

• Correction. The first version of this PR said "no VNNI, scalar tier". I had grepped /proc/cpuinfo for avx512vnni, but the kernel spells it avx512_vnni. The numbers did not change on re-run, and the example now prints the tier.

• AMX (ndarray .claude/AMX_GOTCHAS.md):

  • This host has no AMX: model 0x55 is pre-Sapphire Rapids, so amx_available() == false is genuine (Gotcha 4 does not apply).
  • A later AMX measurement must not be certified on a shared VM (Gotcha 14: tile state is silently corrupted under host contention).
  • Its parity tests must also run under deliberate CPU contention, and a skipped tile test is not a pass (Gotcha 9).

Validation

• cargo test --release: every probe suite green (one #[ignore] that was already there).
• cargo clippy --release --all-targets -- -D warnings: clean.

Still open:

• Bounds on X or Z.
• Chains longer than two atoms: counts would exceed i8 after one hop (§7.3).
• Cross-tile compose (MISSING-7).

🤖 Generated with Claude Code

https://claude.ai/code/session_01XAqKMNZqKXSaeb9g2ypywF

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