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+# Integrating bend → ecdsa lumbda search loop
+
+The motivating workload behind `bend` is ecdsafail-challenge candidate
+search: the lumbda search loop (`ecdsa/lumbda/search.lsp` in
+www.foxhop.net) emits circuit variants, scores each, picks the lowest.
+At toy scale it runs in lumbda's own simulator (`sim.lsp`). At
+upstream scale (12.8M ops, 1,355 qubits, 1.3M bits) it needs the CUDA
+prototype (`ecdsa/cuda/demo_upstream`, byte-identical to upstream Rust
+`eval_circuit`).
+
+`bend` is the glue.
+
+## Where things stand
+
+In www.foxhop.net's `ecdsa/cuda/`:
+
+| binary | purpose | upstream byte-parity? |
+|--------|---------|----------------------|
+| `demo` | hand-crafted 21-op circuit, CPU↔GPU smoke | n/a |
+| `demo_ops` | ops.bin loader, LFSR RNG, scoring | gate counts ✓ |
+| `demo_upstream` | SHAKE + secp256k1 register init | full (every digit) |
+| `demo_multi` | multi-candidate batch driver, S-exp portal output | per candidate |
+
+Each writes an S-expression portal lumbda can ingest directly.
+
+## The new GPU op for bend's registry
+
+Add a `cuda-sim-ops-bin` op (analogous to today's `cuda-shake-fanout`):
+
+```scheme
+;; in bend.lsp
+(define (bend-sim-cost args)
+  "(cuda-sim-ops-bin path n-batches) — cost = n-batches × 12.8M ops
+   approx 100 ns/op host."
+  (let ((n-batches (car (cdr args))))
+    (* n-batches 12788119 100)))
+
+(bend-register-op! 'cuda-sim-ops-bin bend-sim-cost)
+```
+
+## Worker handler
+
+```scheme
+;; in gpu-worker.lsp
+(define (handle-cuda-sim-ops-bin args)
+  (let* ((ops-path (car args))
+         (n-batches (car (cdr args)))
+         (portal-out (gensym-path "/tmp/bend-cuda-sim" ".portal"))
+         (cmd (string-append
+               "/home/fox/git/www.foxhop.net/ecdsa/cuda/demo_ops "
+               ops-path
+               " --batches " (number->string n-batches)
+               " --portal " portal-out)))
+    (system cmd)            ; or spawn-process-stdio + wait
+    (let ((result (read-from-string (file->string portal-out))))
+      (delete-file portal-out)
+      (list 'ok result))))
+```
+
+Note: `system` doesn't exist as a lumbda primitive today; either add
+one (~10 LoC per tier) or spawn through `spawn-process-stdio` and
+read stdout to confirm completion before reading the portal.
+
+## Search-loop side
+
+`ecdsa/lumbda/search.lsp` currently does:
+
+```scheme
+(define (eval-variant variant-id cases)
+  (let ((circ (emit-variant variant-id ...)))
+    (simulate circ)        ; in-process lumbda sim.lsp
+    ...))
+```
+
+With bend:
+
+```scheme
+(load "bend.lsp")
+(define (eval-variant-cuda variant-id ops-bin-path)
+  (let* ((result (bend!-call
+                  (list 'cuda-sim-ops-bin ops-bin-path 141))))
+    ;; result shape from demo_ops's portal:
+    ;;   (cuda-multi-result (ops-path …) (status OK)
+    ;;     (totals (clifford N) (toffoli N))
+    ;;     (timing-ms …))
+    (let ((totals (section result 'totals)))
+      (list variant-id
+            (car (cdr (assoc 'toffoli totals)))
+            (car (cdr (assoc 'clifford totals)))))))
+```
+
+Each variant emits its own `ops.bin` (the upstream binary format we
+parse with `ops_loader.c`), the search loop bends it to a GPU worker,
+worker calls `demo_ops`, returns the portal, lumbda picks the
+winner.
+
+## What's missing before this lands
+
+1. `system` or equivalent primitive in lumbda (Python/C/asm) — one of:
+   - synchronous subprocess wait
+   - `spawn-process-stdio` + wait via reading "done" line
+2. Lumbda's emitter side needs to produce upstream-format `ops.bin`
+   files. Toy 4-bit circuits don't need this; real secp256k1 circuits
+   would require Phase B step 7+ (Solinas mod-mul + Bernstein-Yang
+   mod-inv) to close before there are interesting variants to bend.
+3. The search-loop scoring rule needs adaptation: today it scores
+   `avg_toffoli × peak_qubits`; the CUDA portal returns Σ counts over
+   141 batches × 64 shots, so dividing by 9024 gives the
+   per-shot avg upstream uses.
+
+## Why this design
+
+- `bend` already does the routing decision: small toy circuits stay
+  in lumbda's in-process `sim.lsp`; large ones bend to GPU.
+- Wire protocol identical to `cuda-shake-fanout` — no new primitive
+  beyond a Scheme registration entry.
+- `demo_ops --portal` output already matches lumbda's S-expression
+  ingestion contract (see `ecdsa/cuda/main_ops.c` portal writer).
+- Worker pool elasticity: any GPU host can register
+  `cuda-sim-ops-bin` and become eligible to receive candidate
+  evaluations. Coordinator's load-aware dispatch (`DESIGN-go-gpu.md`)
+  handles fan-out across multiple GPU hosts.
+
+This is a half-day's wire-up once Phase B step 7 closes and lumbda
+gains a `system`-equivalent primitive. Until then, the architecture
+is documented; the integration waits.