diff --git a/jobsource/careers/cascade.py b/jobsource/careers/cascade.py
index 8b2bad9..c9e0601 100644
--- a/jobsource/careers/cascade.py
+++ b/jobsource/careers/cascade.py
@@ -1,12 +1,13 @@
 """find_careers_page(): orchestrate the Stage 2 tier cascade.
 
 Cascade order (return early on first success):
-  1. ATS detection → ats.detect_and_fetch()       confidence 0.95
-  2. URL patterns  → heuristics.probe_url_patterns()  0.80
-  3. Homepage scan → heuristics.scan_homepage_links()  0.60
-  4. Sitemap       → heuristics.parse_sitemap()        0.50
-  5. Cheap-LLM     → classify_llm (stub, not implemented in this phase)
-  6. Browser agent → agent_fallback (stub, not implemented in this phase)
+  1.  ATS detection  → ats.detect_and_fetch()              confidence 0.95
+  1b. ATS slug-guess → ats.recover_via_slug_guess()        confidence 0.90
+  2.  URL patterns   → heuristics.probe_url_patterns()     confidence 0.80
+  3.  Homepage scan  → heuristics.scan_homepage_links()    confidence 0.60
+  4.  Sitemap        → heuristics.parse_sitemap()          confidence 0.50
+  5.  Cheap-LLM      → classify_llm.classify_careers_link()  confidence 0.55
+  6.  Browser agent  → agent_fallback (not implemented in this phase)
 
 Returns a CareersResult with the URL, confidence, method string, and — when
 the ATS tier resolves — the first open-position URL for free (Stage-3 shortcut).
@@ -24,6 +25,7 @@ from pydantic import BaseModel
 
 from ..http import build_client, request_with_retries
 from . import ats as _ats
+from . import classify_llm as _classify_llm
 from . import heuristics as _heuristics
 
 logger = logging.getLogger(__name__)
@@ -39,7 +41,7 @@ class CareersResult(BaseModel):
 
     careers_url: str | None = None
     confidence: float = 0.0
-    # method values: "ats:{name}" | "url_pattern" | "homepage_scan" | "sitemap" | "none"
+    # method values: "ats:{name}" | "url_pattern" | "homepage_scan" | "sitemap" | "llm_classify" | "none"
     method: str = "none"
     ats_name: str | None = None
     # Free Stage-3 shortcut: populated when ATS tier resolves (first open job URL).
@@ -145,8 +147,23 @@ def find_careers_page(
         except Exception as exc:
             logger.warning("cascade(%s): sitemap tier error: %s", website, exc)
 
-        # All deterministic tiers missed.
-        logger.info("cascade(%s): all deterministic tiers missed", website)
+        # ------------------------------------------------------------------
+        # Tier 5 — Cheap-LLM careers-link classification
+        # ------------------------------------------------------------------
+        try:
+            if homepage_html:
+                anchors = _classify_llm.extract_anchors(homepage_html, website)
+                res = _classify_llm.classify_careers_link(anchors)
+                if res:
+                    logger.info(
+                        "cascade(%s): resolved via llm_classify careers_url=%s confidence=%.2f",
+                        website, res.careers_url, res.confidence,
+                    )
+                    return _finalize(res.careers_url, "llm_classify", 0.55, website, client)
+        except Exception as exc:
+            logger.warning("cascade(%s): llm_classify tier error: %s", website, exc)
+
+        logger.info("cascade(%s): all tiers missed", website)
         return CareersResult()
 
     finally:
diff --git a/jobsource/careers/classify_llm.py b/jobsource/careers/classify_llm.py
index e3a1b63..db78c75 100644
--- a/jobsource/careers/classify_llm.py
+++ b/jobsource/careers/classify_llm.py
@@ -1,13 +1,235 @@
 """Cheap-LLM link classification for careers page and job links (Stage 2, tier 5 / Stage 3, tier 4).
 
-Scaffold stub -- not implemented yet.
+Two typed classification functions backed by Pydantic AI:
+  1. classify_careers_link(anchors) -> CareerLinkResult | None
+     Given a list of (url, text) pairs from a page, pick the single careers/jobs page URL.
+  2. classify_job_link(anchors) -> JobLinkResult | None
+     Given a list of (url, text) pairs from a careers page, pick one specific open-position URL.
+
+Both return None and the cascade falls through gracefully when:
+  - classifier_model or llm_api_key is a placeholder (LLM not configured),
+  - the anchor list is empty,
+  - the LLM call fails for any reason,
+  - the model abstains (index -1) or returns an out-of-range index.
+
+pydantic_ai is imported lazily inside _build_link_agent so a missing package or
+unconfigured provider never breaks module import (graceful-degradation rule #8).
+
+extract_anchors() is also exported here so cascade.py and extract.py can share
+the same anchor-parsing logic without a separate utility module.
 """
-# TODO (Stage 2 tier 5 / Stage 3 tier 4): implement per CLAUDE.md "Cheap-LLM classification".
-# Uses Pydantic AI (model-agnostic) with the `classifier_model` from config.
-# Two typed tasks:
-#   1. classify_careers_link(anchors: list[Anchor]) -> CareerLinkResult
-#      Given extracted <a> tags from a page, pick the careers/jobs page URL.
-#   2. classify_job_link(anchors: list[Anchor]) -> JobLinkResult
-#      Given extracted <a> tags from a careers page, pick one open-position URL.
-# Both return a typed Pydantic result including the chosen URL and confidence.
-# Graceful degradation: if llm_api_key is placeholder or call fails, return None.
+from __future__ import annotations
+
+import logging
+from urllib.parse import urljoin
+
+from bs4 import BeautifulSoup
+from pydantic import BaseModel, Field
+
+from ..config import get_settings
+
+logger = logging.getLogger(__name__)
+
+# Maximum number of anchors forwarded to the LLM (token-budget guard).
+_MAX_ANCHORS = 60
+# Maximum anchor text length, in characters, before truncation.
+_MAX_ANCHOR_TEXT = 80
+
+
+# ---------------------------------------------------------------------------
+# Data models
+# ---------------------------------------------------------------------------
+
+
+class Anchor(BaseModel):
+    """One hyperlink extracted from a page — the LLM's input row."""
+
+    url: str
+    text: str = ""
+
+
+class _LinkChoice(BaseModel):
+    """LLM structured output: 0-based index into the candidate list + confidence."""
+
+    index: int = Field(
+        description=(
+            "0-based index of the best link in the candidate list. "
+            "Use -1 if no link qualifies."
+        )
+    )
+    confidence: float = Field(default=0.0, ge=0.0, le=1.0)
+
+
+class CareerLinkResult(BaseModel):
+    """Public result of classify_careers_link()."""
+
+    careers_url: str
+    confidence: float = 0.0
+
+
+class JobLinkResult(BaseModel):
+    """Public result of classify_job_link()."""
+
+    job_url: str
+    confidence: float = 0.0
+
+
+# ---------------------------------------------------------------------------
+# System-level prompt instructions for each classification task
+# ---------------------------------------------------------------------------
+
+_CAREERS_INSTRUCTIONS = (
+    "You are a link classifier for a job-sourcing pipeline. "
+    "You receive a numbered list of hyperlinks extracted from a company website. "
+    "Identify the single link that leads to the company's main careers or jobs page "
+    "(the page that lists open positions). "
+    "Respond with the 0-based index of the best match and your confidence (0.0–1.0). "
+    "If none of the links leads to a careers or jobs page, respond with index -1."
+)
+
+_JOB_INSTRUCTIONS = (
+    "You are a link classifier for a job-sourcing pipeline. "
+    "You receive a numbered list of hyperlinks extracted from a careers/jobs page. "
+    "Identify the single link that leads directly to one specific open job-posting detail page "
+    "(a page for exactly one position — not a category page, a filter, or a job listing index). "
+    "Respond with the 0-based index of the best match and your confidence (0.0–1.0). "
+    "If none of the links qualifies as a single-job detail page, respond with index -1."
+)
+
+
+# ---------------------------------------------------------------------------
+# Shared anchor extractor (used by cascade.py Tier 5 and extract.py Tiers 3-4)
+# ---------------------------------------------------------------------------
+
+
+def extract_anchors(html: str, base_url: str) -> list[Anchor]:
+    """Extract deduplicated absolute hyperlinks from HTML.
+
+    Skips mailto:, tel:, # (fragment-only), and javascript: hrefs.
+    Converts relative hrefs to absolute using base_url.
+    Returns only http(s) links in first-seen order, URL-deduplicated.
+    Truncates anchor text to _MAX_ANCHOR_TEXT characters.
+    """
+    if not html:
+        return []
+    soup = BeautifulSoup(html, "lxml")
+    seen_urls: set[str] = set()
+    result: list[Anchor] = []
+    for tag in soup.find_all("a", href=True):
+        href: str = tag["href"].strip()
+        if not href or href.startswith(("mailto:", "tel:", "#", "javascript:")):
+            continue
+        full_url = urljoin(base_url, href)
+        if not full_url.startswith(("http://", "https://")):
+            continue
+        if full_url in seen_urls:
+            continue
+        seen_urls.add(full_url)
+        text = tag.get_text(separator=" ", strip=True)[:_MAX_ANCHOR_TEXT]
+        result.append(Anchor(url=full_url, text=text))
+    return result
+
+
+# ---------------------------------------------------------------------------
+# LLM availability gate
+# ---------------------------------------------------------------------------
+
+
+def _llm_unavailable() -> bool:
+    """Return True when the LLM is not configured (placeholder values in settings)."""
+    s = get_settings()
+    return (
+        s.classifier_model.startswith("PLACEHOLDER")
+        or s.llm_api_key.startswith("PLACEHOLDER")
+    )
+
+
+# ---------------------------------------------------------------------------
+# Agent builder — extracted as a named function to serve as the test seam.
+# Monkeypatch this function in tests to avoid real LLM calls.
+# ---------------------------------------------------------------------------
+
+
+def _build_link_agent(instructions: str):  # type: ignore[return]
+    """Construct a Pydantic AI Agent for link classification.
+
+    pydantic_ai is imported lazily here so a missing package never crashes
+    module import. This function is the primary test seam — monkeypatch it
+    to inject a FakeAgent without touching the real Pydantic AI machinery.
+    """
+    from pydantic_ai import Agent  # lazy import
+
+    return Agent(
+        get_settings().classifier_model,
+        output_type=_LinkChoice,
+        instructions=instructions,
+    )
+
+
+# ---------------------------------------------------------------------------
+# Core shared classifier
+# ---------------------------------------------------------------------------
+
+
+def _render_candidates(anchors: list[Anchor]) -> str:
+    """Format anchors as a numbered list for the LLM prompt."""
+    lines = [f"[{i}] {a.url}  |  {a.text}" for i, a in enumerate(anchors)]
+    return "\n".join(lines)
+
+
+def _choose_link(
+    anchors: list[Anchor],
+    *,
+    instructions: str,
+    label: str,
+) -> "_LinkChoice | None":
+    """Run the LLM classifier on anchors; return a _LinkChoice or None.
+
+    Returns None when the LLM is unconfigured, the list is empty, the model
+    abstains (index -1), the index is out of range, or any exception occurs.
+    """
+    if not anchors or _llm_unavailable():
+        return None
+
+    candidates = anchors[:_MAX_ANCHORS]
+    try:
+        agent = _build_link_agent(instructions)
+        prompt = _render_candidates(candidates)
+        out = agent.run_sync(prompt).output
+        if isinstance(out, _LinkChoice) and 0 <= out.index < len(candidates):
+            return out
+        return None  # abstain (index -1) or out-of-range
+    except Exception as exc:
+        logger.warning("classify_llm(%s): tier error: %s", label, exc)
+        return None
+
+
+# ---------------------------------------------------------------------------
+# Public API
+# ---------------------------------------------------------------------------
+
+
+def classify_careers_link(anchors: list[Anchor]) -> CareerLinkResult | None:
+    """Pick the careers/jobs page URL from a list of extracted anchors (Stage 2, tier 5).
+
+    Returns a CareerLinkResult on success, or None on any no-op / failure.
+    Never raises.
+    """
+    c = _choose_link(anchors, instructions=_CAREERS_INSTRUCTIONS, label="careers")
+    if c is None:
+        return None
+    candidates = anchors[:_MAX_ANCHORS]
+    return CareerLinkResult(careers_url=candidates[c.index].url, confidence=c.confidence)
+
+
+def classify_job_link(anchors: list[Anchor]) -> JobLinkResult | None:
+    """Pick one specific open-position URL from a careers-page anchor list (Stage 3, tier 4).
+
+    Returns a JobLinkResult on success, or None on any no-op / failure.
+    Never raises.
+    """
+    c = _choose_link(anchors, instructions=_JOB_INSTRUCTIONS, label="job")
+    if c is None:
+        return None
+    candidates = anchors[:_MAX_ANCHORS]
+    return JobLinkResult(job_url=candidates[c.index].url, confidence=c.confidence)
diff --git a/jobsource/extract.py b/jobsource/extract.py
index f55f360..a6f7c84 100644
--- a/jobsource/extract.py
+++ b/jobsource/extract.py
@@ -1,12 +1,214 @@
 """Extract one open position URL from a careers page (Stage 3).
 
-Scaffold stub -- not implemented yet.
+Cascade order (return early on first hit):
+  1.  ATS JSON (URL)  — detect ATS board coordinates in the careers URL itself;
+                        call the board's public JSON API for the first posting URL.
+  1b. ATS JSON (HTML) — fetch the careers page; detect ATS board in its HTML;
+                        call the board API. Handles inline JS embeds.
+  2.  JSON-LD         — scan <script type="application/ld+json"> for a
+                        JobPosting node with a `url` field.
+  3.  Job-like anchors — first <a> whose href matches /job|/position|/opening|/vacanc.
+  4.  Cheap-LLM        — classify_job_link() from classify_llm; no-ops gracefully
+                        when the LLM is not configured.
+  5.  Miss            — return (None, "none").
+
+Returns (url: str | None, method: str). Never raises — any tier failure logs
+and falls through. method is one of:
+  "ats:{name}" | "json_ld" | "anchor" | "llm_classify" | "none"
 """
-# TODO (Stage 3): implement per CLAUDE.md "Stage 3 — Extract one open position (return on first hit)".
-# Cascade order (return early on first hit):
-#   1. ATS JSON — if ATS is already known from Stage 2, return first posting URL directly.
-#   2. JobPosting JSON-LD — parse application/ld+json for a `url` field.
-#   3. Job-like anchors — first <a> matching /job, /position, /opening, /vacancy in href.
-#   4. Cheap-LLM classification — Pydantic AI typed output (classifier_model).
-#   5. Browser-agent fallback — handled inside the fused Stage-2 agent call in agent_fallback.py.
-# Returns (url: str | None, method: str) so callers know which tier resolved it.
+from __future__ import annotations
+
+import json
+import logging
+import re
+from urllib.parse import urlsplit
+
+import httpx
+from bs4 import BeautifulSoup
+
+from .careers import ats as _ats
+from .careers.classify_llm import classify_job_link, extract_anchors
+from .http import build_client, request_with_retries
+
+logger = logging.getLogger(__name__)
+
+# Matches href paths that indicate a single-job detail page.
+_JOB_HREF_RE = re.compile(r"/(job|position|opening|vacanc)", re.IGNORECASE)
+
+
+# ---------------------------------------------------------------------------
+# Internal helpers
+# ---------------------------------------------------------------------------
+
+
+def _get_html(url: str, client: httpx.Client) -> str | None:
+    """Fetch page HTML; return text on success or None on any error/non-2xx."""
+    try:
+        resp = request_with_retries(client, "GET", url, max_retries=1)
+        if resp.status_code < 400:
+            return resp.text
+        logger.info("extract._get_html(%s): HTTP %s", url, resp.status_code)
+        return None
+    except Exception as exc:
+        logger.info("extract._get_html(%s): fetch error: %s", url, exc)
+        return None
+
+
+def _jsonld_job_url(html: str) -> str | None:
+    """Scan every <script type="application/ld+json"> block for a JobPosting url."""
+    soup = BeautifulSoup(html, "lxml")
+    for script in soup.find_all("script", type="application/ld+json"):
+        try:
+            data = json.loads(script.get_text(strip=True))
+        except (json.JSONDecodeError, ValueError):
+            continue
+        url = _find_job_posting_url(data)
+        if url:
+            return url
+    return None
+
+
+def _find_job_posting_url(data: object) -> str | None:
+    """Walk a JSON-LD structure (dict, list, @graph) for a JobPosting url field."""
+    if isinstance(data, list):
+        for item in data:
+            result = _find_job_posting_url(item)
+            if result:
+                return result
+        return None
+    if not isinstance(data, dict):
+        return None
+    # Expand @graph (JSON-LD named graph — a list of typed nodes)
+    graph = data.get("@graph")
+    if graph:
+        result = _find_job_posting_url(graph)
+        if result:
+            return result
+    # Check this node's @type
+    type_val = data.get("@type", "")
+    if isinstance(type_val, list):
+        is_job = "JobPosting" in type_val
+    else:
+        is_job = type_val == "JobPosting"
+    if is_job:
+        url = data.get("url")
+        if url and isinstance(url, str):
+            return url
+    return None
+
+
+def _fetch_ats_position(board: "_ats.ATSBoard", client: httpx.Client) -> str | None:
+    """Call the ATS public JSON API for *board* and return the first job URL or None."""
+    fetch_fn = _ats._FETCH_DISPATCH.get(board.ats_name)
+    if fetch_fn is None:
+        return None
+    fetch = fetch_fn(board, client)  # type: ignore[operator]
+    return fetch.first_url
+
+
+# ---------------------------------------------------------------------------
+# Public entry point
+# ---------------------------------------------------------------------------
+
+
+def extract_open_position(
+    careers_url: str,
+    *,
+    client: httpx.Client | None = None,
+) -> tuple[str | None, str]:
+    """Return (open_position_url, method) for a careers page. Never raises.
+
+    Tries ATS JSON → JSON-LD → job-like anchor → LLM classifier in order,
+    returning on the first hit. method names which tier resolved it.
+    """
+    _managed = client is None
+    if _managed:
+        client = build_client()
+
+    try:
+        # ------------------------------------------------------------------
+        # Tier 1 — ATS JSON from the careers URL string (no page fetch needed)
+        # ------------------------------------------------------------------
+        board = _ats.detect_ats_in_url(careers_url)
+        if board is not None:
+            try:
+                pos_url = _fetch_ats_position(board, client)
+                if pos_url:
+                    logger.info(
+                        "extract(%s): ats:%s from_url pos=%s",
+                        careers_url, board.ats_name, pos_url,
+                    )
+                    return pos_url, f"ats:{board.ats_name}"
+            except Exception as exc:
+                logger.warning("extract(%s): ats url-tier error: %s", careers_url, exc)
+
+        # ------------------------------------------------------------------
+        # Fetch page HTML — shared by all remaining tiers
+        # ------------------------------------------------------------------
+        html = _get_html(careers_url, client)
+        if html is None:
+            logger.info("extract(%s): page fetch failed; skipping remaining tiers", careers_url)
+            return None, "none"
+
+        # ------------------------------------------------------------------
+        # Tier 1b — ATS JSON from page HTML (handles JS-embedded board pages)
+        # ------------------------------------------------------------------
+        html_board = _ats.detect_ats_in_html(html)
+        if html_board is not None:
+            try:
+                pos_url2 = _fetch_ats_position(html_board, client)
+                if pos_url2:
+                    logger.info(
+                        "extract(%s): ats:%s from_html pos=%s",
+                        careers_url, html_board.ats_name, pos_url2,
+                    )
+                    return pos_url2, f"ats:{html_board.ats_name}"
+            except Exception as exc:
+                logger.warning("extract(%s): ats html-tier error: %s", careers_url, exc)
+
+        # ------------------------------------------------------------------
+        # Tier 2 — JobPosting JSON-LD
+        # ------------------------------------------------------------------
+        try:
+            jld_url = _jsonld_job_url(html)
+            if jld_url:
+                logger.info("extract(%s): json_ld pos=%s", careers_url, jld_url)
+                return jld_url, "json_ld"
+        except Exception as exc:
+            logger.warning("extract(%s): json_ld tier error: %s", careers_url, exc)
+
+        # ------------------------------------------------------------------
+        # Tier 3 & 4 — Job-like anchors, then LLM (share one extraction pass)
+        # ------------------------------------------------------------------
+        try:
+            anchors = extract_anchors(html, careers_url)
+        except Exception as exc:
+            logger.warning("extract(%s): anchor extraction error: %s", careers_url, exc)
+            anchors = []
+
+        # Tier 3 — first anchor whose URL *path* matches the job-URL pattern.
+        # We search only the path component so hostnames like jobs.lever.co
+        # don't trigger a false match (e.g. `//jobs` contains `/job`).
+        try:
+            for anchor in anchors:
+                if _JOB_HREF_RE.search(urlsplit(anchor.url).path):
+                    logger.info("extract(%s): anchor pos=%s", careers_url, anchor.url)
+                    return anchor.url, "anchor"
+        except Exception as exc:
+            logger.warning("extract(%s): anchor tier error: %s", careers_url, exc)
+
+        # Tier 4 — cheap-LLM job-link classifier (no-ops when LLM unconfigured)
+        try:
+            llm_result = classify_job_link(anchors)
+            if llm_result is not None:
+                logger.info("extract(%s): llm_classify pos=%s", careers_url, llm_result.job_url)
+                return llm_result.job_url, "llm_classify"
+        except Exception as exc:
+            logger.warning("extract(%s): llm_classify tier error: %s", careers_url, exc)
+
+        logger.info("extract(%s): all tiers missed", careers_url)
+        return None, "none"
+
+    finally:
+        if _managed:
+            client.close()
diff --git a/scripts/e2e_smoke.py b/scripts/e2e_smoke.py
new file mode 100644
index 0000000..5e944aa
--- /dev/null
+++ b/scripts/e2e_smoke.py
@@ -0,0 +1,207 @@
+#!/usr/bin/env python
+"""End-to-end smoke test: Stage 1→3 on a 10-job batch.
+
+Usage:  .venv/bin/python scripts/e2e_smoke.py
+"""
+from __future__ import annotations
+
+import logging
+import sys
+import time
+from dataclasses import dataclass, field
+
+# Make sure we run from the repo root so imports resolve correctly.
+sys.path.insert(0, ".")
+
+logging.basicConfig(
+    level=logging.WARNING,       # keep jobspy/httpx chatter suppressed
+    format="%(name)s: %(message)s",
+)
+# Enable our own modules at INFO so we see cascade method names.
+for _mod in ("jobsource.resolve", "jobsource.careers.cascade",
+             "jobsource.careers.ats", "jobsource.careers.heuristics",
+             "jobsource.careers.classify_llm", "jobsource.extract"):
+    logging.getLogger(_mod).setLevel(logging.INFO)
+
+from jobsource.careers.cascade import find_careers_page
+from jobsource.config import get_settings
+from jobsource.extract import extract_open_position
+from jobsource.http import build_client
+from jobsource.models import RawJob
+from jobsource.resolve import resolve_website
+from jobsource.sources.jobspy_source import JobSpySource
+
+
+# ---------------------------------------------------------------------------
+# Per-record result
+# ---------------------------------------------------------------------------
+
+@dataclass
+class Result:
+    job_id: str
+    company: str
+    website: str | None = None
+    careers_url: str | None = None
+    careers_method: str | None = None
+    position_url: str | None = None
+    position_method: str | None = None
+    error: str | None = None
+
+
+# ---------------------------------------------------------------------------
+# Main runner
+# ---------------------------------------------------------------------------
+
+BATCH_SIZE = 10
+SEARCH_TERM = "software engineer"
+LOCATION = "United States"
+HOURS_OLD = 72
+
+
+def run() -> None:
+    settings = get_settings()
+    print(f"\n{'='*64}")
+    print(f"  E2E smoke  batch={BATCH_SIZE}  search={SEARCH_TERM!r}  hours_old={HOURS_OLD}")
+    print(f"{'='*64}\n")
+
+    # ------------------------------------------------------------------
+    # Stage 1 — Ingest
+    # ------------------------------------------------------------------
+    print("Stage 1: ingesting…")
+    source = JobSpySource()
+    t0 = time.perf_counter()
+    raw_jobs: list[RawJob] = source.fetch_recent_jobs(
+        search_terms=[SEARCH_TERM],
+        location=LOCATION,
+        hours_old=HOURS_OLD,
+        results_wanted=BATCH_SIZE + 10,   # fetch a few extra to cover dupes
+    )
+    elapsed = time.perf_counter() - t0
+    raw_jobs = raw_jobs[:BATCH_SIZE]
+    print(f"  Ingested {len(raw_jobs)} unique jobs in {elapsed:.1f}s\n")
+
+    if not raw_jobs:
+        print("No jobs returned — aborting.")
+        return
+
+    results: list[Result] = []
+
+    with build_client() as client:
+        for raw in raw_jobs:
+            res = Result(job_id=raw.job_id, company=raw.company)
+            print(f"[{raw.job_id}] {raw.company}")
+
+            # -------------------------------------------------------
+            # Stage 1b — Resolve website
+            # -------------------------------------------------------
+            try:
+                res.website = resolve_website(
+                    raw.company, raw.website, client=client
+                )
+            except Exception as exc:
+                res.error = f"resolve: {exc}"
+                print(f"    resolve ERROR: {exc}")
+                results.append(res)
+                continue
+
+            if not res.website:
+                print(f"    website: UNRESOLVED")
+                results.append(res)
+                continue
+            print(f"    website: {res.website}")
+
+            # -------------------------------------------------------
+            # Stage 2 — Find careers page
+            # -------------------------------------------------------
+            try:
+                cr = find_careers_page(
+                    res.website,
+                    company_name=raw.company,
+                    client=client,
+                )
+                res.careers_url = cr.careers_url
+                res.careers_method = cr.method
+            except Exception as exc:
+                res.error = f"cascade: {exc}"
+                print(f"    careers ERROR: {exc}")
+                results.append(res)
+                continue
+
+            if not res.careers_url:
+                print(f"    careers: MISSED  (method={cr.method})")
+                results.append(res)
+                continue
+            print(f"    careers: {res.careers_url}  [{cr.method}  conf={cr.confidence:.2f}]")
+
+            # -------------------------------------------------------
+            # Stage 3 — Extract one open position
+            # -------------------------------------------------------
+            try:
+                pos_url, pos_method = extract_open_position(
+                    res.careers_url, client=client
+                )
+                res.position_url = pos_url
+                res.position_method = pos_method
+            except Exception as exc:
+                res.error = f"extract: {exc}"
+                print(f"    position ERROR: {exc}")
+                results.append(res)
+                continue
+
+            if res.position_url:
+                print(f"    position: {res.position_url}  [{pos_method}]")
+            else:
+                print(f"    position: MISSED  (method={pos_method})")
+
+            results.append(res)
+            print()
+
+    # ------------------------------------------------------------------
+    # Summary
+    # ------------------------------------------------------------------
+    n_total        = len(results)
+    n_website      = sum(1 for r in results if r.website)
+    n_careers      = sum(1 for r in results if r.careers_url)
+    n_position     = sum(1 for r in results if r.position_url)
+    n_errors       = sum(1 for r in results if r.error)
+
+    print(f"\n{'='*64}")
+    print(f"  SUMMARY  ({n_total} jobs processed)")
+    print(f"{'='*64}")
+    print(f"  Stage 1  ingested          {n_total:>3}")
+    print(f"  Stage 1b website resolved  {n_website:>3} / {n_total}  ({n_website/n_total*100:.0f}%)")
+    print(f"  Stage 2  careers found     {n_careers:>3} / {n_website}  ({n_careers/max(n_website,1)*100:.0f}% of resolved)")
+    print(f"  Stage 3  position found    {n_position:>3} / {n_careers}  ({n_position/max(n_careers,1)*100:.0f}% of careers)")
+    print(f"  Errors                     {n_errors:>3}")
+
+    # careers method breakdown
+    if n_careers:
+        method_counts: dict[str, int] = {}
+        for r in results:
+            if r.careers_method and r.careers_url:
+                method_counts[r.careers_method] = method_counts.get(r.careers_method, 0) + 1
+        print(f"\n  Careers method breakdown:")
+        for m, c in sorted(method_counts.items(), key=lambda x: -x[1]):
+            print(f"    {m:<30} {c}")
+
+    # position method breakdown
+    if n_position:
+        pos_method_counts: dict[str, int] = {}
+        for r in results:
+            if r.position_method and r.position_url:
+                pos_method_counts[r.position_method] = pos_method_counts.get(r.position_method, 0) + 1
+        print(f"\n  Position method breakdown:")
+        for m, c in sorted(pos_method_counts.items(), key=lambda x: -x[1]):
+            print(f"    {m:<30} {c}")
+
+    # CSV-ready output
+    print(f"\n{'='*64}")
+    print("  company_name, career_page_url, open_position_url")
+    print(f"{'='*64}")
+    for r in results:
+        print(f"  {r.company!r}, {r.careers_url or ''!r}, {r.position_url or ''!r}")
+    print()
+
+
+if __name__ == "__main__":
+    run()
diff --git a/tests/test_cascade.py b/tests/test_cascade.py
index bc3ef82..7eb6101 100644
--- a/tests/test_cascade.py
+++ b/tests/test_cascade.py
@@ -550,3 +550,112 @@ class TestSlugGuessTier:
         result = find_careers_page("https://www.acme.com", client=FakeClient())
         assert result.method == "url_pattern"
         assert result.careers_url == "https://acme.com/careers"
+
+
+# ---------------------------------------------------------------------------
+# Tier 5 — Cheap-LLM careers-link classification
+# ---------------------------------------------------------------------------
+
+
+class TestLLMClassifyTier:
+    """Tier 5 fires after sitemap, no-ops when LLM returns None, and is skipped on earlier hits."""
+
+    def _patch_all_deterministic_miss(self, monkeypatch, *, homepage_html: str = "<html/>") -> None:
+        """Patch tiers 1–4 to all miss; leaves Tier 5 for the caller to control."""
+        monkeypatch.setattr(
+            "jobsource.careers.cascade._safe_get_html",
+            lambda website, client: homepage_html,
+        )
+        monkeypatch.setattr("jobsource.careers.cascade._ats.detect_and_fetch", lambda *a, **kw: None)
+        monkeypatch.setattr("jobsource.careers.cascade._ats.recover_via_slug_guess", lambda *a, **kw: None)
+        monkeypatch.setattr("jobsource.careers.cascade._heuristics.probe_url_patterns", lambda *a, **kw: None)
+        monkeypatch.setattr("jobsource.careers.cascade._heuristics.scan_homepage_links", lambda *a, **kw: None)
+        monkeypatch.setattr("jobsource.careers.cascade._heuristics.parse_sitemap", lambda *a, **kw: None)
+        # Prevent _finalize from making network calls
+        monkeypatch.setattr("jobsource.careers.cascade._ats.detect_ats_in_url", lambda url: None)
+
+    def test_llm_classify_hit_returns_055_confidence(self, monkeypatch):
+        from jobsource.careers.classify_llm import Anchor, CareerLinkResult
+
+        self._patch_all_deterministic_miss(
+            monkeypatch,
+            homepage_html='<html><body><a href="/careers">Careers</a></body></html>',
+        )
+        monkeypatch.setattr(
+            "jobsource.careers.cascade._classify_llm.extract_anchors",
+            lambda html, base_url: [Anchor(url="https://acme.com/careers", text="Careers")],
+        )
+        monkeypatch.setattr(
+            "jobsource.careers.cascade._classify_llm.classify_careers_link",
+            lambda anchors: CareerLinkResult(careers_url="https://acme.com/careers", confidence=0.85),
+        )
+        result = find_careers_page("https://www.acme.com", client=FakeClient())
+        assert result.method == "llm_classify"
+        assert result.confidence == 0.55  # fixed tier-level confidence from cascade
+        assert result.careers_url == "https://acme.com/careers"
+
+    def test_llm_classify_none_falls_through_to_method_none(self, monkeypatch):
+        from jobsource.careers.classify_llm import Anchor
+
+        self._patch_all_deterministic_miss(monkeypatch)
+        monkeypatch.setattr(
+            "jobsource.careers.cascade._classify_llm.extract_anchors",
+            lambda html, base_url: [Anchor(url="https://acme.com/about", text="About")],
+        )
+        monkeypatch.setattr(
+            "jobsource.careers.cascade._classify_llm.classify_careers_link",
+            lambda anchors: None,
+        )
+        result = find_careers_page("https://www.acme.com", client=FakeClient())
+        assert result.method == "none"
+        assert result.careers_url is None
+
+    def test_tier5_skipped_when_homepage_html_is_none(self, monkeypatch):
+        """When the homepage fetch returns None, Tier 5 is silently bypassed."""
+        llm_called: list[bool] = []
+        self._patch_all_deterministic_miss(monkeypatch)
+        monkeypatch.setattr(
+            "jobsource.careers.cascade._safe_get_html",
+            lambda website, client: None,
+        )
+        monkeypatch.setattr(
+            "jobsource.careers.cascade._classify_llm.classify_careers_link",
+            lambda anchors: llm_called.append(True) or None,
+        )
+        find_careers_page("https://www.acme.com", client=FakeClient())
+        assert llm_called == []
+
+    def test_tier5_not_called_when_sitemap_hits(self, monkeypatch):
+        """When sitemap resolves, the cascade returns before reaching Tier 5."""
+        llm_called: list[bool] = []
+        monkeypatch.setattr(
+            "jobsource.careers.cascade._safe_get_html",
+            lambda website, client: "<html/>",
+        )
+        monkeypatch.setattr("jobsource.careers.cascade._ats.detect_and_fetch", lambda *a, **kw: None)
+        monkeypatch.setattr("jobsource.careers.cascade._ats.recover_via_slug_guess", lambda *a, **kw: None)
+        monkeypatch.setattr("jobsource.careers.cascade._heuristics.probe_url_patterns", lambda *a, **kw: None)
+        monkeypatch.setattr("jobsource.careers.cascade._heuristics.scan_homepage_links", lambda *a, **kw: None)
+        monkeypatch.setattr(
+            "jobsource.careers.cascade._heuristics.parse_sitemap",
+            lambda *a, **kw: "https://acme.com/careers",
+        )
+        monkeypatch.setattr("jobsource.careers.cascade._ats.detect_ats_in_url", lambda url: None)
+        monkeypatch.setattr(
+            "jobsource.careers.cascade._classify_llm.classify_careers_link",
+            lambda anchors: llm_called.append(True) or None,
+        )
+        result = find_careers_page("https://www.acme.com", client=FakeClient())
+        assert result.method == "sitemap"
+        assert llm_called == []
+
+    def test_tier5_error_falls_through_gracefully(self, monkeypatch):
+        """A Tier 5 exception should not abort the cascade."""
+        self._patch_all_deterministic_miss(monkeypatch)
+        monkeypatch.setattr(
+            "jobsource.careers.cascade._classify_llm.extract_anchors",
+            lambda html, base_url: (_ for _ in ()).throw(RuntimeError("classify boom")),
+        )
+        result = find_careers_page("https://www.acme.com", client=FakeClient())
+        assert result.method == "none"
+        assert result.careers_url is None
diff --git a/tests/test_classify_llm.py b/tests/test_classify_llm.py
new file mode 100644
index 0000000..15a3016
--- /dev/null
+++ b/tests/test_classify_llm.py
@@ -0,0 +1,256 @@
+"""Tests for careers/classify_llm.py — all network-free via monkeypatching."""
+from __future__ import annotations
+
+import pytest
+
+from jobsource.careers.classify_llm import (
+    Anchor,
+    CareerLinkResult,
+    JobLinkResult,
+    _LinkChoice,
+    classify_careers_link,
+    classify_job_link,
+    extract_anchors,
+)
+
+
+# ---------------------------------------------------------------------------
+# Fake helpers
+# ---------------------------------------------------------------------------
+
+
+class _FakeResult:
+    """Minimal stand-in for a Pydantic AI run result."""
+
+    def __init__(self, output: _LinkChoice) -> None:
+        self.output = output
+
+
+class _FakeAgent:
+    """Stand-in for a Pydantic AI Agent; returns a fixed _LinkChoice."""
+
+    def __init__(self, choice: _LinkChoice) -> None:
+        self._choice = choice
+
+    def run_sync(self, prompt: str) -> _FakeResult:
+        return _FakeResult(self._choice)
+
+
+class _RaisingAgent:
+    """Stand-in that raises on run_sync, simulating an LLM failure."""
+
+    def run_sync(self, prompt: str) -> _FakeResult:
+        raise RuntimeError("LLM unavailable")
+
+
+def _real_settings():
+    """Fake settings object with non-placeholder values."""
+    return type("S", (), {
+        "classifier_model": "openai:gpt-4o-mini",
+        "llm_api_key": "sk-real-key",
+    })()
+
+
+# ---------------------------------------------------------------------------
+# extract_anchors
+# ---------------------------------------------------------------------------
+
+_SAMPLE_HTML = """
+<html><body>
+  <a href="/about">About Us</a>
+  <a href="/careers">Careers</a>
+  <a href="https://external.com/jobs">External Jobs</a>
+  <a href="mailto:info@acme.com">Email</a>
+  <a href="#section">Anchor</a>
+  <a href="javascript:void(0)">JS link</a>
+  <a href="/careers">Duplicate careers link</a>
+</body></html>
+"""
+
+
+class TestExtractAnchors:
+    def test_resolves_relative_to_absolute(self):
+        anchors = extract_anchors(_SAMPLE_HTML, "https://acme.com")
+        urls = [a.url for a in anchors]
+        assert "https://acme.com/about" in urls
+        assert "https://acme.com/careers" in urls
+
+    def test_preserves_already_absolute_urls(self):
+        anchors = extract_anchors(_SAMPLE_HTML, "https://acme.com")
+        urls = [a.url for a in anchors]
+        assert "https://external.com/jobs" in urls
+
+    def test_skips_mailto(self):
+        anchors = extract_anchors(_SAMPLE_HTML, "https://acme.com")
+        assert all("mailto:" not in a.url for a in anchors)
+
+    def test_skips_hash_fragments(self):
+        anchors = extract_anchors(_SAMPLE_HTML, "https://acme.com")
+        # A pure # anchor resolves to base_url itself (https://acme.com) —
+        # it starts with http so it passes the scheme check but we skip hrefs
+        # that start with "#". Verify the JavaScript link is also gone.
+        assert all("javascript:" not in a.url for a in anchors)
+
+    def test_deduplicates_by_url(self):
+        anchors = extract_anchors(_SAMPLE_HTML, "https://acme.com")
+        urls = [a.url for a in anchors]
+        assert urls.count("https://acme.com/careers") == 1
+
+    def test_captures_anchor_text(self):
+        anchors = extract_anchors(_SAMPLE_HTML, "https://acme.com")
+        career_anchor = next(a for a in anchors if a.url == "https://acme.com/careers")
+        assert career_anchor.text == "Careers"
+
+    def test_empty_html_returns_empty_list(self):
+        assert extract_anchors("", "https://acme.com") == []
+
+    def test_html_with_no_links_returns_empty_list(self):
+        assert extract_anchors("<html><body><p>No links here.</p></body></html>", "https://acme.com") == []
+
+    def test_text_truncated_at_max_length(self):
+        long_text = "x" * 200
+        html = f'<html><body><a href="/careers">{long_text}</a></body></html>'
+        anchors = extract_anchors(html, "https://acme.com")
+        assert len(anchors) == 1
+        assert len(anchors[0].text) <= 80
+
+
+# ---------------------------------------------------------------------------
+# Graceful degradation: placeholder settings → always None
+# ---------------------------------------------------------------------------
+
+
+class TestPlaceholderGate:
+    """When classifier_model or llm_api_key is a placeholder, classifiers no-op."""
+
+    def test_classify_careers_link_returns_none_with_placeholder(self):
+        anchors = [Anchor(url="https://acme.com/careers", text="Careers")]
+        assert classify_careers_link(anchors) is None
+
+    def test_classify_job_link_returns_none_with_placeholder(self):
+        anchors = [Anchor(url="https://acme.com/jobs/123", text="Engineer")]
+        assert classify_job_link(anchors) is None
+
+    def test_classify_careers_link_returns_none_on_empty_list(self, monkeypatch):
+        monkeypatch.setattr(
+            "jobsource.careers.classify_llm.get_settings",
+            _real_settings,
+        )
+        assert classify_careers_link([]) is None
+
+    def test_classify_job_link_returns_none_on_empty_list(self, monkeypatch):
+        monkeypatch.setattr(
+            "jobsource.careers.classify_llm.get_settings",
+            _real_settings,
+        )
+        assert classify_job_link([]) is None
+
+
+# ---------------------------------------------------------------------------
+# Success paths via _build_link_agent monkeypatch
+# ---------------------------------------------------------------------------
+
+
+class TestClassifySuccess:
+    def _patch_agent(self, monkeypatch, choice: _LinkChoice) -> None:
+        monkeypatch.setattr(
+            "jobsource.careers.classify_llm.get_settings",
+            _real_settings,
+        )
+        monkeypatch.setattr(
+            "jobsource.careers.classify_llm._build_link_agent",
+            lambda instructions: _FakeAgent(choice),
+        )
+
+    def test_careers_pick_returns_mapped_url(self, monkeypatch):
+        anchors = [
+            Anchor(url="https://acme.com/about", text="About"),
+            Anchor(url="https://acme.com/careers", text="Careers"),
+        ]
+        self._patch_agent(monkeypatch, _LinkChoice(index=1, confidence=0.95))
+        result = classify_careers_link(anchors)
+        assert result is not None
+        assert isinstance(result, CareerLinkResult)
+        assert result.careers_url == "https://acme.com/careers"
+        assert result.confidence == 0.95
+
+    def test_job_pick_returns_mapped_url(self, monkeypatch):
+        anchors = [
+            Anchor(url="https://acme.com/jobs/", text="All Jobs"),
+            Anchor(url="https://acme.com/jobs/123", text="Software Engineer"),
+        ]
+        self._patch_agent(monkeypatch, _LinkChoice(index=1, confidence=0.85))
+        result = classify_job_link(anchors)
+        assert result is not None
+        assert isinstance(result, JobLinkResult)
+        assert result.job_url == "https://acme.com/jobs/123"
+        assert result.confidence == 0.85
+
+    def test_careers_first_index_zero(self, monkeypatch):
+        anchors = [Anchor(url="https://acme.com/jobs", text="Jobs")]
+        self._patch_agent(monkeypatch, _LinkChoice(index=0, confidence=0.70))
+        result = classify_careers_link(anchors)
+        assert result is not None
+        assert result.careers_url == "https://acme.com/jobs"
+
+
+# ---------------------------------------------------------------------------
+# Abstain and failure paths
+# ---------------------------------------------------------------------------
+
+
+class TestClassifyFailurePaths:
+    def _patch_real_settings(self, monkeypatch) -> None:
+        monkeypatch.setattr(
+            "jobsource.careers.classify_llm.get_settings",
+            _real_settings,
+        )
+
+    def test_abstain_index_minus_one_returns_none(self, monkeypatch):
+        self._patch_real_settings(monkeypatch)
+        monkeypatch.setattr(
+            "jobsource.careers.classify_llm._build_link_agent",
+            lambda instructions: _FakeAgent(_LinkChoice(index=-1, confidence=0.0)),
+        )
+        anchors = [Anchor(url="https://acme.com/about", text="About")]
+        assert classify_careers_link(anchors) is None
+
+    def test_out_of_range_index_returns_none(self, monkeypatch):
+        self._patch_real_settings(monkeypatch)
+        monkeypatch.setattr(
+            "jobsource.careers.classify_llm._build_link_agent",
+            lambda instructions: _FakeAgent(_LinkChoice(index=99, confidence=0.9)),
+        )
+        anchors = [Anchor(url="https://acme.com/careers", text="Careers")]
+        assert classify_careers_link(anchors) is None
+
+    def test_run_sync_exception_returns_none(self, monkeypatch):
+        self._patch_real_settings(monkeypatch)
+        monkeypatch.setattr(
+            "jobsource.careers.classify_llm._build_link_agent",
+            lambda instructions: _RaisingAgent(),
+        )
+        anchors = [Anchor(url="https://acme.com/careers", text="Careers")]
+        assert classify_careers_link(anchors) is None
+
+    def test_build_agent_exception_returns_none(self, monkeypatch):
+        self._patch_real_settings(monkeypatch)
+
+        def boom(instructions: str):
+            raise RuntimeError("import error")
+
+        monkeypatch.setattr(
+            "jobsource.careers.classify_llm._build_link_agent",
+            boom,
+        )
+        anchors = [Anchor(url="https://acme.com/careers", text="Careers")]
+        assert classify_careers_link(anchors) is None
+
+    def test_job_classify_run_sync_exception_returns_none(self, monkeypatch):
+        self._patch_real_settings(monkeypatch)
+        monkeypatch.setattr(
+            "jobsource.careers.classify_llm._build_link_agent",
+            lambda instructions: _RaisingAgent(),
+        )
+        anchors = [Anchor(url="https://acme.com/jobs/123", text="Engineer")]
+        assert classify_job_link(anchors) is None
diff --git a/tests/test_extract.py b/tests/test_extract.py
new file mode 100644
index 0000000..df79dc4
--- /dev/null
+++ b/tests/test_extract.py
@@ -0,0 +1,309 @@
+"""Tests for extract.py (Stage 3) — all network-free via monkeypatching."""
+from __future__ import annotations
+
+import pytest
+
+from jobsource.careers.ats import ATSBoard, ATSFetch
+from jobsource.careers.classify_llm import Anchor, JobLinkResult
+from jobsource.extract import _find_job_posting_url, _jsonld_job_url, extract_open_position
+
+
+# ---------------------------------------------------------------------------
+# Fake helpers
+# ---------------------------------------------------------------------------
+
+
+class FakeResponse:
+    def __init__(self, status_code: int, text: str = "", url: str = "https://example.com") -> None:
+        self.status_code = status_code
+        self.text = text
+        self.url = url
+
+
+class FakeClient:
+    pass
+
+
+# ---------------------------------------------------------------------------
+# _find_job_posting_url (pure function)
+# ---------------------------------------------------------------------------
+
+
+class TestFindJobPostingUrl:
+    def test_flat_dict_job_posting(self):
+        data = {"@type": "JobPosting", "url": "https://acme.com/jobs/1"}
+        assert _find_job_posting_url(data) == "https://acme.com/jobs/1"
+
+    def test_list_of_nodes(self):
+        data = [
+            {"@type": "Organization", "name": "Acme"},
+            {"@type": "JobPosting", "url": "https://acme.com/jobs/2"},
+        ]
+        assert _find_job_posting_url(data) == "https://acme.com/jobs/2"
+
+    def test_graph_expansion(self):
+        data = {
+            "@context": "https://schema.org",
+            "@graph": [
+                {"@type": "WebPage"},
+                {"@type": "JobPosting", "url": "https://acme.com/jobs/3"},
+            ],
+        }
+        assert _find_job_posting_url(data) == "https://acme.com/jobs/3"
+
+    def test_type_as_list(self):
+        data = {"@type": ["Thing", "JobPosting"], "url": "https://acme.com/jobs/4"}
+        assert _find_job_posting_url(data) == "https://acme.com/jobs/4"
+
+    def test_no_job_posting_returns_none(self):
+        data = {"@type": "Organization", "name": "Acme"}
+        assert _find_job_posting_url(data) is None
+
+    def test_job_posting_without_url_returns_none(self):
+        data = {"@type": "JobPosting"}
+        assert _find_job_posting_url(data) is None
+
+    def test_scalar_input_returns_none(self):
+        assert _find_job_posting_url("not a dict") is None
+        assert _find_job_posting_url(42) is None
+
+
+# ---------------------------------------------------------------------------
+# _jsonld_job_url (parses HTML)
+# ---------------------------------------------------------------------------
+
+
+class TestJsonldJobUrl:
+    def test_finds_url_in_json_ld_block(self):
+        html = """
+        <html><head>
+          <script type="application/ld+json">
+          {"@type": "JobPosting", "url": "https://acme.com/jobs/99"}
+          </script>
+        </head></html>
+        """
+        assert _jsonld_job_url(html) == "https://acme.com/jobs/99"
+
+    def test_invalid_json_block_skipped(self):
+        html = """
+        <html><head>
+          <script type="application/ld+json">NOT JSON{{</script>
+          <script type="application/ld+json">{"@type": "JobPosting", "url": "https://ok.com/job/1"}</script>
+        </head></html>
+        """
+        assert _jsonld_job_url(html) == "https://ok.com/job/1"
+
+    def test_no_job_posting_returns_none(self):
+        html = """
+        <html><head>
+          <script type="application/ld+json">{"@type": "Organization"}</script>
+        </head></html>
+        """
+        assert _jsonld_job_url(html) is None
+
+    def test_no_script_returns_none(self):
+        assert _jsonld_job_url("<html><body>No scripts</body></html>") is None
+
+
+# ---------------------------------------------------------------------------
+# extract_open_position — tier integration (network-free)
+# ---------------------------------------------------------------------------
+
+
+class TestExtractOpenPositionTiers:
+    def _patch_base(self, monkeypatch, *, html: str | None = None) -> None:
+        """Patch ATS detect functions to miss and HTTP fetch to return html."""
+        monkeypatch.setattr(
+            "jobsource.extract._ats.detect_ats_in_url",
+            lambda url: None,
+        )
+        monkeypatch.setattr(
+            "jobsource.extract._ats.detect_ats_in_html",
+            lambda html: None,
+        )
+        if html is not None:
+            monkeypatch.setattr(
+                "jobsource.extract.request_with_retries",
+                lambda *a, **kw: FakeResponse(200, html),
+            )
+
+    # -- Tier 1: ATS from URL ------------------------------------------------
+
+    def test_ats_from_url_returns_first_job(self, monkeypatch):
+        board = ATSBoard(
+            ats_name="greenhouse",
+            slug="acme",
+            careers_url="https://boards.greenhouse.io/acme",
+        )
+        monkeypatch.setattr(
+            "jobsource.extract._ats.detect_ats_in_url",
+            lambda url: board,
+        )
+        monkeypatch.setattr(
+            "jobsource.extract._ats._FETCH_DISPATCH",
+            {"greenhouse": lambda b, c: ATSFetch(first_url="https://boards.greenhouse.io/acme/jobs/1", job_count=5)},
+        )
+        url, method = extract_open_position(
+            "https://boards.greenhouse.io/acme", client=FakeClient()
+        )
+        assert url == "https://boards.greenhouse.io/acme/jobs/1"
+        assert method == "ats:greenhouse"
+
+    def test_ats_from_url_with_no_jobs_falls_through(self, monkeypatch):
+        board = ATSBoard(
+            ats_name="lever",
+            slug="acme",
+            careers_url="https://jobs.lever.co/acme",
+        )
+        monkeypatch.setattr("jobsource.extract._ats.detect_ats_in_url", lambda url: board)
+        monkeypatch.setattr(
+            "jobsource.extract._ats._FETCH_DISPATCH",
+            {"lever": lambda b, c: ATSFetch(first_url=None, job_count=0)},
+        )
+        monkeypatch.setattr(
+            "jobsource.extract._ats.detect_ats_in_html", lambda html: None
+        )
+        # Page has no JSON-LD, no job-path anchors, LLM returns None.
+        # Use a neutral href that won't trigger the job-path pattern.
+        monkeypatch.setattr(
+            "jobsource.extract.request_with_retries",
+            lambda *a, **kw: FakeResponse(200, "<html><body><a href='/team'>Team</a></body></html>"),
+        )
+        monkeypatch.setattr("jobsource.extract.classify_job_link", lambda anchors: None)
+        url, method = extract_open_position("https://acme.example.com/careers", client=FakeClient())
+        assert url is None
+        assert method == "none"
+
+    # -- Tier 1b: ATS from page HTML ----------------------------------------
+
+    def test_ats_from_html_returns_first_job(self, monkeypatch):
+        gh_board = ATSBoard(
+            ats_name="greenhouse",
+            slug="vercel",
+            careers_url="https://boards.greenhouse.io/vercel",
+        )
+        monkeypatch.setattr("jobsource.extract._ats.detect_ats_in_url", lambda url: None)
+        monkeypatch.setattr("jobsource.extract._ats.detect_ats_in_html", lambda html: gh_board)
+        monkeypatch.setattr(
+            "jobsource.extract._ats._FETCH_DISPATCH",
+            {"greenhouse": lambda b, c: ATSFetch(first_url="https://boards.greenhouse.io/vercel/jobs/42", job_count=73)},
+        )
+        monkeypatch.setattr(
+            "jobsource.extract.request_with_retries",
+            lambda *a, **kw: FakeResponse(200, '<script src="greenhouse"></script>'),
+        )
+        url, method = extract_open_position("https://vercel.com/careers", client=FakeClient())
+        assert url == "https://boards.greenhouse.io/vercel/jobs/42"
+        assert method == "ats:greenhouse"
+
+    # -- Tier 2: JSON-LD ----------------------------------------------------
+
+    def test_jsonld_returns_job_url(self, monkeypatch):
+        html = """
+        <html><head>
+          <script type="application/ld+json">
+          {"@type": "JobPosting", "url": "https://acme.com/jobs/77"}
+          </script>
+        </head><body></body></html>
+        """
+        self._patch_base(monkeypatch, html=html)
+        url, method = extract_open_position("https://acme.com/careers", client=FakeClient())
+        assert url == "https://acme.com/jobs/77"
+        assert method == "json_ld"
+
+    # -- Tier 3: job-like anchor --------------------------------------------
+
+    def test_job_anchor_matched_by_pattern(self, monkeypatch):
+        html = """
+        <html><body>
+          <a href="/about">About</a>
+          <a href="/jobs/software-engineer-123">Software Engineer</a>
+        </body></html>
+        """
+        self._patch_base(monkeypatch, html=html)
+        url, method = extract_open_position("https://acme.com/careers", client=FakeClient())
+        assert url == "https://acme.com/jobs/software-engineer-123"
+        assert method == "anchor"
+
+    def test_opening_anchor_matched(self, monkeypatch):
+        html = '<html><body><a href="/openings/42">Open Role</a></body></html>'
+        self._patch_base(monkeypatch, html=html)
+        url, method = extract_open_position("https://acme.com/careers", client=FakeClient())
+        assert url == "https://acme.com/openings/42"
+        assert method == "anchor"
+
+    # -- Tier 4: LLM --------------------------------------------------------
+
+    def test_llm_classify_fires_when_no_job_anchor(self, monkeypatch):
+        html = '<html><body><a href="/about">About</a><a href="/team">Team</a></body></html>'
+        self._patch_base(monkeypatch, html=html)
+        monkeypatch.setattr(
+            "jobsource.extract.classify_job_link",
+            lambda anchors: JobLinkResult(job_url="https://acme.com/about", confidence=0.60),
+        )
+        url, method = extract_open_position("https://acme.com/careers", client=FakeClient())
+        assert url == "https://acme.com/about"
+        assert method == "llm_classify"
+
+    def test_llm_returns_none_falls_through_to_none(self, monkeypatch):
+        html = '<html><body><a href="/about">About</a></body></html>'
+        self._patch_base(monkeypatch, html=html)
+        monkeypatch.setattr(
+            "jobsource.extract.classify_job_link",
+            lambda anchors: None,
+        )
+        url, method = extract_open_position("https://acme.com/careers", client=FakeClient())
+        assert url is None
+        assert method == "none"
+
+    # -- Page fetch failure -------------------------------------------------
+
+    def test_fetch_failure_returns_none(self, monkeypatch):
+        monkeypatch.setattr("jobsource.extract._ats.detect_ats_in_url", lambda url: None)
+        monkeypatch.setattr(
+            "jobsource.extract.request_with_retries",
+            lambda *a, **kw: (_ for _ in ()).throw(RuntimeError("timeout")),
+        )
+        url, method = extract_open_position("https://acme.com/careers", client=FakeClient())
+        assert url is None
+        assert method == "none"
+
+    def test_non_200_fetch_returns_none(self, monkeypatch):
+        monkeypatch.setattr("jobsource.extract._ats.detect_ats_in_url", lambda url: None)
+        monkeypatch.setattr(
+            "jobsource.extract.request_with_retries",
+            lambda *a, **kw: FakeResponse(404, ""),
+        )
+        url, method = extract_open_position("https://acme.com/careers", client=FakeClient())
+        assert url is None
+        assert method == "none"
+
+    # -- All tiers miss ------------------------------------------------------
+
+    def test_all_miss_returns_none_none(self, monkeypatch):
+        html = '<html><body><a href="/about">About</a></body></html>'
+        self._patch_base(monkeypatch, html=html)
+        monkeypatch.setattr("jobsource.extract.classify_job_link", lambda anchors: None)
+        url, method = extract_open_position("https://acme.com/careers", client=FakeClient())
+        assert url is None
+        assert method == "none"
+
+    # -- ATS tier error falls through ---------------------------------------
+
+    def test_ats_fetch_error_falls_through(self, monkeypatch):
+        board = ATSBoard(ats_name="ashby", slug="acme", careers_url="https://jobs.ashbyhq.com/acme")
+        monkeypatch.setattr("jobsource.extract._ats.detect_ats_in_url", lambda url: board)
+        monkeypatch.setattr(
+            "jobsource.extract._ats._FETCH_DISPATCH",
+            {"ashby": lambda b, c: (_ for _ in ()).throw(RuntimeError("api down"))},
+        )
+        monkeypatch.setattr("jobsource.extract._ats.detect_ats_in_html", lambda html: None)
+        html = '<html><body><a href="/jobs/42">Engineer</a></body></html>'
+        monkeypatch.setattr(
+            "jobsource.extract.request_with_retries",
+            lambda *a, **kw: FakeResponse(200, html),
+        )
+        url, method = extract_open_position("https://jobs.ashbyhq.com/acme", client=FakeClient())
+        # urljoin("https://jobs.ashbyhq.com/acme", "/jobs/42") → root-relative
+        assert url == "https://jobs.ashbyhq.com/jobs/42"
+        assert method == "anchor"