spec(search-with-proof): brief and requirements for review

After reviewing Cairn: detection so far classified excerpts and hit a precision
wall; this adds directed search with an objective goal (a re-verified
demonstration), a fact/intent board, and reason/explore steps as AX Tasks on
kube-ax. Design only learns from Cairn (AGPL); no code copied.

Co-Authored-By: Claude Opus 5.5 <[email protected]>

.kiro/specs/search-with-proof/brief.md

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+# Brief: search with proof
+
+Maintainer, 2026-10-05, after reviewing Cairn (github.com/oritera/Cairn): "we are still not progressing through the
+state space search / not finding what we need and the progress is sort of slow ... i think something is missing."
+And: "I'd move to primarily executing in the cluster."
+
+## What was missing
+
+Every detection step so far classifies: it scores one function excerpt and then tries to make the score precise
+enough to block. Calibration, Wilson bounds, pooled block gates, prompt variants and trained models all hit the same
+wall: ranking is decent (within-pair AUC about 0.76), but precision at the top cannot be proven to 95% on our data.
+
+Cairn treats a security problem as a directed search with an objectively checkable goal. A shared board holds
+confirmed facts, open intents and human hints. A reasoner proposes independent intents; explorers with real tools
+each confirm one fact; the loop ends when the goal is demonstrably met.
+
+Three things follow for OpenUltraSAST:
+
+1. **An objective success condition.** A finding is demonstrated when a test or proof of concept fails on the
+   vulnerable code and passes on the fixed code (or, for a push, fails on head and passes on base where applicable).
+   A demonstrated finding is right by construction; it needs no calibration and no training data, so it generalises
+   to unseen repositories by construction.
+2. **Exploration with tools.** Agents that read other files, follow callers, build and run the code, instead of a
+   single-shot judgement of one excerpt.
+3. **Search state per repository and push.** Facts and intents accumulate on a board instead of every question
+   starting from zero.
+
+## Shape
+
+- The cheap layers (quick rules, engine, classifier) become triage: they rank candidates.
+- Agentic search runs only on the top-ranked candidates of a push, under a per-push budget.
+- BLOCK only on a demonstrated finding. Advisory for plausible, unproven ones. "Could not demonstrate" is recorded as
+  such, never as "not vulnerable".
+- Execution is primarily in the kube-ax cluster: reason and explore steps are AX Tasks; the VM coordinates.
+- Model access: a scoped, budget-limited key in the cluster, managed by the operator.
+
+## Not in scope
+
+Copying Cairn code (AGPL-3.0; this repository is Apache-2.0). Offensive use against systems we do not own: all
+execution is against code under analysis, inside gVisor sandboxes.