build: align proven lib path to zig-out/ in zig-api and lol-gateway build.zig

zig-api/ffi/zig/build.zig: change DEFAULT_PROVEN_LIB_PATH from
zig-out-standalone/lib to zig-out/lib, matching proven's standard
zig build output path. The zig-out-standalone → zig-out symlink
was a workaround created 2026-04-17 and is now removed from
verification-ecosystem/proven/ffi/zig/; consumers must point
directly to zig-out/lib.

standards/lol/api/zig-gateway/build.zig: same path fix for the
lol-gateway consumer.

emergency-button and emergency-room build.zig files updated in the
ambientops repo (separate commit).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

Author: hyperpolymath

zig-api/ffi/zig/build.zig

@@ -15,16 +15,18 @@
 //                     process.zig uses as a second gate in safePathDefault.
 //                     Build with:
 //                       cd verification-ecosystem/proven/ffi/zig
-//                       zig build --build-file build_standalone.zig \
-//                           --prefix zig-out-standalone
-//                     The default proven_lib_path below points to that output.
+//                       zig build
+//                     Output lands in zig-out/lib/libproven_ffi.a (standard zig build output).
+//                     The default proven_lib_path below points to that location.
 
 const std = @import("std");
 
 /// Path to the directory containing libproven_ffi.a.
 /// Override with -Dproven-lib-path=/absolute/path.
+/// Points to proven's standard zig-out/lib output (not zig-out-standalone —
+/// that symlink was removed 2026-04-17; zig build now outputs to zig-out/ directly).
 const DEFAULT_PROVEN_LIB_PATH =
-    "/var/mnt/eclipse/repos/verification-ecosystem/proven/ffi/zig/zig-out-standalone/lib";
+    "/var/mnt/eclipse/repos/verification-ecosystem/proven/ffi/zig/zig-out/lib";
 
 /// Path to the directory containing proven.h (the C ABI header).
 const DEFAULT_PROVEN_INCLUDE_PATH =