search-with-proof: readiness from the budget with a probe, 4096-token tool turns, 40-step tasks

HTTP start waits up to 90 s (CLI 30 s) with TCP then HTTP probing; app stdout
and stderr tails are recorded; tool-call turns get 4096 output tokens with one
retry on truncation; tasks get 40 steps with reminders.

Co-Authored-By: Claude Fable 5.1 <[email protected]>

src/openultrasast/search/budget.py

@@ -9,7 +9,11 @@ class SearchBudget:
     # Recalibrated 2026-10-05 on the first three measured searches: settled cost was ~$0.003 per model call,
     # but worst-case reservations (~$0.027 per call) exhausted the old $0.05 task allowance after 2-4 calls.
     spend_usd: float = 2.00
+    # Both ceilings bound each task: $0.40 and 40 model steps.
     max_call_usd: float = 0.40
+    max_steps: int = 40
+    http_start_seconds: int = 90
+    cli_start_seconds: int = 30
     reason_rounds: int = 4
     intents_per_round: int = 3
     demonstrations: int = 3
@@ -28,6 +32,9 @@ class SearchBudget:
             if value < 0 or (value == 0 and name not in ("retries", "spend_usd")):
                 raise ValueError(f"invalid {name}")
             if name in (
+                "max_steps",
+                "http_start_seconds",
+                "cli_start_seconds",
                 "reason_rounds",
                 "intents_per_round",
                 "demonstrations",
@@ -37,3 +44,17 @@ class SearchBudget:
                 "disk_bytes",
             ) and not isinstance(value, int):
                 raise ValueError(f"{name} must be an integer")
+
+
+def verification_timeout(schema: dict, limits: dict | None = None) -> int:
+    """Resolve the mode's start/command allowance from the search task budget."""
+    key = "http_start_seconds" if schema["start"]["mode"] == "http" else "cli_start_seconds"
+    value = (limits or {}).get(key, getattr(SearchBudget(), key))
+    if type(value) is not int or not 1 <= value <= 300:
+        raise ValueError("invalid verification timeout")
+    return value
+
+
+def verification_run_seconds(schema: dict, timeout: int) -> int:
+    # One readiness operation, all declared steps, and driver shutdown/handshake.
+    return timeout * (1 + len(schema["steps"])) + 5