feat(research): wire tools + research workflow graph (research-workflow §2/§3)

Makes the research feature runnable end-to-end, off by default.

- config: [tools.research] (enabled, searxng_url, max_results, max_fetch_bytes).
- registration: web_search/web_fetch are built into BOTH the default and per-workspace
  tool registries when research.enabled, sharing one HTTP client threaded from Main
  (none built on the static path). Egress stays harness-enforced: web_fetch is T2
  (operator-approved) and the existing NetworkHostRule still applies.
- workflow: examples/workflows/research.toml — decompose → gather → report, with the
  three artifact schemas and prompts. Fan-out (search per sub-question, fetch per source)
  runs as repeated tool calls inside the gather stage (Correx has no parallel agents);
  per-source synthesis into the dossier is the compression step, so the report stage
  consumes summaries, never raw pages. ResearchWorkflowTest validates the graph contract.

To run: set [tools.research].enabled, register the 3 [[artifacts]], copy research.toml +
prompts + schemas into the workflows dir, start SearXNG. Launch like any workflow (the
T2 fetch approval surfaces as an approval card; the report opens in the artifact viewer).

Follow-ups (noted, not blocking): batch fetch-approval at the source-list level (§3),
a dedicated SourceFetched/LowQualityExtraction event (quality + content hash are already
in tool-result metadata), dynamic per-session egress allowlist, and the web approval client (§6).

examples/workflows/prompts/research_decompose.md

@@ -0,0 +1,20 @@
+You are the **Research Planner** — the first stage of a deep-research workflow.
+
+Your job is to turn one research question into a concrete plan to answer it. You do not search
+or browse yet; you decompose.
+
+Steps:
+1. Restate the research question in your own words so intent is unambiguous.
+2. Break it into a small set of sub-questions that can each be answered independently. Cover the
+   whole question; avoid overlap. Prefer 3–6 sub-questions over a long list.
+3. For each sub-question, write one or more concrete web search queries — the actual strings you
+   would type into a search engine, specific enough to surface authoritative sources.
+
+The decision history above (steering, approvals) is ground truth — honour it.
+
+Emit your result as the `research_plan` artifact (JSON, schema provided):
+- `question`: the research question, restated.
+- `sub_questions`: the decomposed sub-questions, one per item.
+- `search_queries`: concrete search queries to run, one per item.
+
+Do not answer the question here. Plan only.

examples/workflows/prompts/research_gather.md

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+You are the **Research Gatherer** — you run the plan and build a dossier of summarized sources.
+
+You have two tools:
+- `web_search(query)` — searches the local SearXNG instance; returns result titles, URLs, snippets.
+- `web_fetch(url)` — fetches a URL and returns its main content as clean markdown. Fetches are
+  approved by the operator before they run, so choose sources deliberately — quality over quantity.
+
+Steps:
+1. For each search query in the `research_plan` above, call `web_search`.
+2. From the results, pick the most promising, authoritative sources. Skip duplicates, SEO spam,
+   and pages unlikely to contain primary information.
+3. `web_fetch` each chosen source. If a fetch comes back empty or clearly low-quality (a paywall
+   or JS-only page), drop it and move on — do not retry it.
+4. **Summarize each fetched source on its own**, in your own words: what it contributes to the
+   question and which sub-question(s) it bears on. This is the most important step — the next
+   stage sees only your summaries, never the raw pages, so a faithful summary is the whole product.
+
+Never copy raw page text into a summary. Cite each source by its exact URL.
+
+Emit your result as the `source_dossier` artifact (JSON, schema provided):
+- `sources`: one entry per fetched source, each with `url`, `title`, `summary`, and `relevance`.

examples/workflows/prompts/research_report.md

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+You are the **Research Synthesizer** — you write the final report from the source dossier.
+
+You see only the `source_dossier` above: per-source summaries with their URLs. You do not have the
+raw pages, and you do not search or fetch. Work from the summaries.
+
+Steps:
+1. Read across all source summaries and find where they agree, disagree, or leave gaps.
+2. Answer the research question directly and concisely in the `summary`.
+3. State the key findings, each supported by at least one source. Where sources conflict, say so
+   rather than picking silently.
+4. Cite the sources you actually relied on by their exact URLs.
+
+Do not invent facts that no source supports. If the dossier is insufficient to answer the
+question, say what is missing in the `summary`.
+
+Emit your result as the `research_report` artifact (JSON, schema provided):
+- `summary`: the executive answer to the question.
+- `findings`: the key findings, one per item, each grounded in a cited source.
+- `sources`: the source URLs you cited.

examples/workflows/research.toml

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+# Deep research workflow: decompose -> gather (search + fetch) -> report
+#
+# A native Correx workflow (research-workflow-spec): one graph, two network tools, no new
+# orchestration machinery. The fan-out the spec describes (search per sub-question, fetch per
+# source) happens *inside* the gather stage as repeated tool calls — Correx runs stages linearly
+# (no parallel agents), so the model drives the fan-out itself.
+#
+# Per-source synthesis is the compression mechanism, not a nicety: the gather stage summarizes
+# each fetched page into the source_dossier and the raw page text is discarded. The report stage
+# consumes only those summaries, so research survives the token budget.
+#
+# Requires (in ~/.config/correx/config.toml):
+#   [tools.research]
+#   enabled = true
+#   searxng_url = "http://localhost:8888"     # your self-hosted SearXNG (format=json enabled)
+#   [[artifacts]]
+#   id = "research_plan";   schema_path = "schemas/research_plan.json";   llm_emitted = true
+#   [[artifacts]]
+#   id = "source_dossier";  schema_path = "schemas/source_dossier.json";  llm_emitted = true
+#   [[artifacts]]
+#   id = "research_report"; schema_path = "schemas/research_report.json"; llm_emitted = true
+#
+# web_fetch is T2: the operator approves fetches before they leave the machine. web_search is T1
+# (it only ever touches the configured SearXNG instance).
+
+id = "research"
+start = "decompose"
+description = "Deep research: decompose a question, search + fetch sources, synthesize a cited report."
+
+# 1. Question -> sub-questions + search queries. Reuses the planning discipline; read-only.
+[[stages]]
+id = "decompose"
+prompt = "prompts/research_decompose.md"
+produces = [{ name = "research_plan", kind = "research_plan" }]
+token_budget = 8192
+max_retries = 2
+
+# 2. Run the searches, fetch promising sources, and summarize each one (per-source synthesis).
+#    web_search (T1) hits only SearXNG; web_fetch (T2) is operator-approved per source.
+[[stages]]
+id = "gather"
+prompt = "prompts/research_gather.md"
+needs = ["research_plan"]
+produces = [{ name = "source_dossier", kind = "source_dossier" }]
+allowed_tools = ["web_search", "web_fetch"]
+token_budget = 32768
+max_retries = 2
+
+# 3. Cross-source synthesis into a cited report. Consumes the dossier summaries only — never raw pages.
+[[stages]]
+id = "report"
+prompt = "prompts/research_report.md"
+needs = ["source_dossier"]
+produces = [{ name = "research_report", kind = "research_report" }]
+token_budget = 16384
+max_retries = 2
+
+# --- forward edges ---
+
+[[transitions]]
+id = "decompose-to-gather"
+from = "decompose"
+to = "gather"
+condition_type = "artifact_validated"
+condition_artifact_id = "research_plan"
+
+[[transitions]]
+id = "gather-to-report"
+from = "gather"
+to = "report"
+condition_type = "artifact_validated"
+condition_artifact_id = "source_dossier"
+
+[[transitions]]
+id = "report-done"
+from = "report"
+to = "done"
+condition_type = "artifact_validated"
+condition_artifact_id = "research_report"