=== def _bbox_center_x ===
def _bbox_center_x(bbox: list[int]) -> float:
    return (int(bbox[0]) + int(bbox[2])) / 2



=== def _bbox_center_y ===
def _bbox_center_y(bbox: list[int]) -> float:
    return (int(bbox[1]) + int(bbox[3])) / 2



=== def _bbox_height ===
def _bbox_height(bbox: list[int]) -> int:
    return max(0, int(bbox[3]) - int(bbox[1]))



=== def _bbox_horizontal_overlap ===
def _bbox_horizontal_overlap(a: list[int], b: list[int]) -> int:
    return max(0, min(int(a[2]), int(b[2])) - max(int(a[0]), int(b[0])))



=== def _bbox_horizontal_overlap_ratio ===
def _bbox_horizontal_overlap_ratio(a: list[int], b: list[int]) -> float:
    width = min(_bbox_width(a), _bbox_width(b))
    if width <= 0:
        return 0.0
    return _bbox_horizontal_overlap(a, b) / width



=== def _bbox_vertical_overlap ===
def _bbox_vertical_overlap(a: list[int], b: list[int]) -> int:
    return max(0, min(int(a[3]), int(b[3])) - max(int(a[1]), int(b[1])))



=== def _bbox_width ===
def _bbox_width(bbox: list[int]) -> int:
    return max(0, int(bbox[2]) - int(bbox[0]))



=== def _cluster_bbox ===
def _cluster_bbox(cluster: list[dict]) -> list[int]:
    return [
        min(int(item["block_bbox"][0]) for item in cluster),
        min(int(item["block_bbox"][1]) for item in cluster),
        max(int(item["block_bbox"][2]) for item in cluster),
        max(int(item["block_bbox"][3]) for item in cluster),
    ]



=== def _figure_caption_blocks ===
def _figure_caption_blocks(blocks: list[dict]) -> list[dict]:
    captions = []
    for block in blocks:
        if block.get("block_label") not in {"figure_title", "paragraph_title", "text"}:
            continue
        text = clean_block_text(block.get("block_content", ""))
        if is_formal_figure_legend(text):
            captions.append(block)
    return captions



=== def _precaption_media_region ===
def _precaption_media_region(
    caption_bbox: list[int],
    cluster_bboxes: list[list[int]],
    blocks: list[dict] | None = None,
    body_column_width: int = 0,

=== def _union_bboxes ===
def _union_bboxes(bbox_list: list[list[int]]) -> list[int]:
    return [
        min(int(bbox[0]) for bbox in bbox_list),
        min(int(bbox[1]) for bbox in bbox_list),
        max(int(bbox[2]) for bbox in bbox_list),
        max(int(bbox[3]) for bbox in bbox_list),
    ]



=== def clean_block_text ===
def clean_block_text(text: str) -> str:
    text = html.unescape(normalize_obsidian_markdown(text)).strip()
    return text



=== def compute_precaption_composite_regions ===
def compute_precaption_composite_regions(blocks: list[dict], page_width: int = 0, page_height: int = 0) -> list[dict]:
    caption_blocks = _figure_caption_blocks(blocks)
    _, clusters = media_clusters(blocks)
    cluster_bboxes = [_cluster_bbox(cluster) for cluster in clusters]
    body_column_width = estimate_body_column_width(blocks, page_width=page_width)
    regions: list[dict] = []
    for caption in caption_blocks:
        caption_bbox = [int(value) for value in caption.get("block_bbox", [0, 0, 0, 0])]
        precaption_region = _precaption_media_region(
            caption_bbox, cluster_bboxes, blocks=blocks, body_column_width=body_column_width
        )
        if not precaption_region:
            continue
        region_blocks = []
        for block in blocks:
            label = block.get("block_label", "")
            bbox = [int(value) for value in block.get("block_bbox", [0, 0, 0, 0])]
            if bbox[3] > caption_bbox[1] + 24:
                continue
            if bbox[3] < precaption_region[1] - 240:
                continue
            vertical_overlap_with_region = _bbox_vertical_overlap(bbox, precaption_region)
            near_region_side = vertical_overlap_with_region > 0 and (
                0 <= precaption_region[0] - bbox[2] <= 80 or 0 <= bbox[0] - precaption_region[2] <= 80
            )
            intersects_region = (
                _bbox_horizontal_overlap(bbox, precaption_region) > 0
                or precaption_region[0] - 24 <= _bbox_center_x(bbox) <= precaption_region[2] + 24
                or near_region_side
            )
            if not intersects_region:
                continue
            if label in {"image", "chart"}:
                if _bbox_vertical_overlap(bbox, precaption_region) <= 0 and bbox[3] < precaption_region[1] - 80:
                    continue
                region_blocks.append(block)
                continue
            if label in {"text", "paragraph_title"}:
                if bbox[3] < precaption_region[1] - 80:
                    continue
                width = _bbox_width(bbox)
                text = clean_block_text(block.get("block_content", ""))
                if is_body_paragraph_like_text_block(
                    block,
                    body_column_width=body_column_width,
                    cluster_bboxes=cluster_bboxes,
                    caption_bbox=caption_bbox,
                ):
                    continue
                if (
                    text
                    and (
                        not re.match(
                            "^(?:Extended\\s+Data\\s+Fig\\.?|Extended\\s+Data\\s+Figure|Figure|Fig\\.?|Table)\\s+\\w+",
                            text,
                            flags=re.IGNORECASE,
                        )
                    )
                    and (
                        width <= int(max(body_column_width, 1) * 0.78)
                        or is_embedded_figure_text_block(block, blocks, page_width=page_width, page_height=page_height)
                    )
                ):
                    region_blocks.append(block)
        media_ids = {block.get("block_id") for block in region_blocks if block.get("block_label") in {"image", "chart"}}
        text_ids = {
            block.get("block_id") for block in region_blocks if block.get("block_label") in {"text", "paragraph_title"}
        }
        if len(media_ids) < 1 or not text_ids or len(region_blocks) < 3:
            continue
        region_bbox = [
            min(int(block["block_bbox"][0]) for block in region_blocks),
            min(int(block["block_bbox"][1]) for block in region_blocks),
            max(int(block["block_bbox"][2]) for block in region_blocks),
            max(int(block["block_bbox"][3]) for block in region_blocks),
        ]
        regions.append(
            {
                "bbox": region_bbox,
                "block_ids": {block.get("block_id") for block in region_blocks},
                "caption_block_id": caption.get("block_id"),
            }
        )
    return regions



=== def estimate_body_column_width ===
def estimate_body_column_width(blocks: list[dict], page_width: int = 0) -> int:
    widths: list[int] = []
    for block in blocks:
        if block.get("block_label") not in {"text", "paragraph_title", "abstract"}:
            continue
        text = clean_block_text(block.get("block_content", ""))
        if (
            not text
            or is_subfigure_label(text)
            or re.match("^(?:Figure|Fig\\.?|Table)\\s+\\w+", text, flags=re.IGNORECASE)
        ):
            continue
        bbox = [int(value) for value in block.get("block_bbox", [0, 0, 0, 0])]
        width = _bbox_width(bbox)
        height = _bbox_height(bbox)
        if width <= 0 or height <= 0:
            continue
        if page_width and width >= int(page_width * 0.82):
            widths.append(width)
            continue
        if width >= 430:
            widths.append(width)
    if not widths:
        return int(page_width * 0.45) if page_width else 520
    widths.sort()
    return widths[len(widths) // 2]



=== def is_body_paragraph_like_text_block ===
def is_body_paragraph_like_text_block(
    block: dict,
    body_column_width: int = 0,
    cluster_bboxes: list[list[int]] | None = None,
    caption_bbox: list[int] | None = None,

=== def is_embedded_figure_text_block ===
def is_embedded_figure_text_block(block: dict, blocks: list[dict], page_width: int = 0, page_height: int = 0) -> bool:
    label = block.get("block_label", "")
    if label not in {"text", "paragraph_title"}:
        return False
    if label == "paragraph_title":
        return False
    text = clean_block_text(block.get("block_content", ""))
    if not text:
        return False
    if is_formal_figure_legend(text):
        return False
    bbox = [int(value) for value in block.get("block_bbox", [0, 0, 0, 0])]
    width = _bbox_width(bbox)
    height = _bbox_height(bbox)
    if width <= 0 or height <= 0:
        return False
    if label == "paragraph_title" and is_subfigure_label(text):
        return True
    caption_blocks = _figure_caption_blocks(blocks)
    cluster_index, clusters = media_clusters(blocks)
    cluster_bboxes = [_cluster_bbox(cluster) for cluster in clusters]
    body_column_width = estimate_body_column_width(blocks, page_width=page_width)
    del cluster_index
    nearest_media = None
    nearest_media_distance = None
    close_media_count = 0
    stacked_media_above = False
    stacked_media_below = False
    side_media = False
    for cluster_bbox in cluster_bboxes:
        horizontal_ratio = _bbox_horizontal_overlap_ratio(bbox, cluster_bbox)
        vertical_overlap = _bbox_vertical_overlap(bbox, cluster_bbox)
        top_gap = int(bbox[1]) - int(cluster_bbox[3])
        bottom_gap = int(cluster_bbox[1]) - int(bbox[3])
        center_inside_x = int(cluster_bbox[0]) <= _bbox_center_x(bbox) <= int(cluster_bbox[2])
        center_inside_y = int(cluster_bbox[1]) <= _bbox_center_y(bbox) <= int(cluster_bbox[3])
        if (
            horizontal_ratio >= 0.45
            and (0 <= top_gap <= 48 or 0 <= bottom_gap <= 48 or vertical_overlap > 0)
            or (center_inside_x and abs(_bbox_center_y(bbox) - _bbox_center_y(cluster_bbox)) <= max(80, height * 4))
        ):
            close_media_count += 1
        if horizontal_ratio >= 0.5 and 0 <= top_gap <= 90:
            stacked_media_above = True
        if horizontal_ratio >= 0.5 and 0 <= bottom_gap <= 90:
            stacked_media_below = True
        if vertical_overlap > 0 and (
            0 <= int(bbox[0]) - int(cluster_bbox[2]) <= 60 or 0 <= int(cluster_bbox[0]) - int(bbox[2]) <= 60
        ):
            side_media = True
        dx = 0
        if int(bbox[2]) < int(cluster_bbox[0]):
            dx = int(cluster_bbox[0]) - int(bbox[2])
        elif int(cluster_bbox[2]) < int(bbox[0]):
            dx = int(bbox[0]) - int(cluster_bbox[2])
        dy = 0
        if int(bbox[3]) < int(cluster_bbox[1]):
            dy = int(cluster_bbox[1]) - int(bbox[3])
        elif int(cluster_bbox[3]) < int(bbox[1]):
            dy = int(bbox[1]) - int(cluster_bbox[3])
        distance = dx + dy
        if nearest_media_distance is None or distance < nearest_media_distance:
            nearest_media_distance = distance
            nearest_media = cluster_bbox
            del center_inside_y
    nearest_caption_above = None
    nearest_caption_below = None
    for caption in caption_blocks:
        cb = [int(value) for value in caption.get("block_bbox", [0, 0, 0, 0])]
        if cb[3] <= bbox[1] and (nearest_caption_above is None or cb[3] > nearest_caption_above[3]):
            nearest_caption_above = cb
        if cb[1] >= bbox[3] and (nearest_caption_below is None or cb[1] < nearest_caption_below[1]):
            nearest_caption_below = cb
    media_between_block_and_caption = 0
    media_x_covering_block = 0
    precaption_region = None
    if nearest_caption_below:
        precaption_region = _precaption_media_region(nearest_caption_below, cluster_bboxes)
        for cluster_bbox in cluster_bboxes:
            if cluster_bbox[1] >= nearest_caption_below[1] + 24:
                continue
            if cluster_bbox[3] <= bbox[1] - 24:
                continue
            media_between_block_and_caption += 1
            if (
                cluster_bbox[0] - 24 <= _bbox_center_x(bbox) <= cluster_bbox[2] + 24
                or _bbox_horizontal_overlap_ratio(bbox, cluster_bbox) >= 0.35
            ):
                media_x_covering_block += 1
    if nearest_caption_above:
        caption_gap = bbox[1] - nearest_caption_above[3]
        left_align_gap = abs(bbox[0] - nearest_caption_above[0])
        effective_page_width = max(page_width, width)
        if (
            0 <= caption_gap <= 72
            and left_align_gap <= 80
            and (width >= int(effective_page_width * 0.45))
            and (not stacked_media_above)
        ):
            return False
    if is_body_paragraph_like_text_block(
        block,
        body_column_width=body_column_width,
        cluster_bboxes=cluster_bboxes,
        caption_bbox=nearest_caption_below,
    ):
        return False
    score = 0.0
    if is_subfigure_label(text):
        score += 4.0
    if width <= int(max(body_column_width, 1) * 0.78):
        score += 1.4
    elif width <= int(max(body_column_width, 1) * 0.9):
        score += 0.5
    if label == "paragraph_title" and len(text) <= 24:
        score += 0.8
    if height <= 26:
        score += 0.8
    elif height <= 34:
        score += 0.4
    if page_width and width <= int(page_width * 0.22):
        score += 0.5
    if close_media_count >= 2:
        score += 2.0
    elif close_media_count == 1:
        score += 1.1
    if stacked_media_above and stacked_media_below:
        score += 2.2
    elif stacked_media_above or stacked_media_below:
        score += 0.9
    if side_media:
        score += 1.0
    if nearest_caption_below and nearest_media:
        caption_gap = nearest_caption_below[1] - bbox[3]
        media_gap = min(
            abs(bbox[1] - nearest_media[3]),
            abs(nearest_media[1] - bbox[3]),
            abs(_bbox_center_y(bbox) - _bbox_center_y(nearest_media)),
        )
        if 0 <= caption_gap <= 120 and media_gap <= 80:
            score += 0.8
    if nearest_caption_below:
        caption_gap = nearest_caption_below[1] - bbox[3]
        if 0 <= caption_gap <= 520 and media_between_block_and_caption >= 3:
            score += 0.9
        if 0 <= caption_gap <= 520 and media_x_covering_block >= 2:
            score += 1.3
        if (
            0 <= caption_gap <= 520
            and media_x_covering_block >= 1
            and (width <= int(max(page_width, width) * 0.82))
            and (height <= 96)
        ):
            score += 0.8
        if precaption_region:
            region_overlap = _bbox_horizontal_overlap_ratio(bbox, precaption_region)
            within_region_y = (
                int(precaption_region[1]) - 24 <= int(bbox[1]) <= int(precaption_region[3]) + 24
                and int(bbox[3]) <= int(nearest_caption_below[1]) + 24
            )
            if region_overlap >= 0.55 and within_region_y:
                score += 1.5
            if (
                int(precaption_region[0]) - 24 <= _bbox_center_x(bbox) <= int(precaption_region[2]) + 24
                and within_region_y
                and (media_between_block_and_caption >= 2)
            ):
                score += 1.1
    if len(text) <= 22:
        score += 0.15
    return score >= 2.6



=== def is_formal_figure_legend ===
def is_formal_figure_legend(text: str) -> bool:
    cleaned = clean_block_text(text)
    if not cleaned:
        return False
    return bool(
        re.match(
            "^(?:Extended\\s+Data\\s+Fig\\.?\\s+\\w+|Extended\\s+Data\\s+Figure\\s+\\w+|Extended\\s+Data\\s+Table\\s+\\w+|Supplementary\\s+Fig\\.?\\s+\\w+|Supplementary\\s+Figure\\s+\\w+|Supplementary\\s+Table\\s+\\w+|Supplementary\\s+Video\\s+\\w+|Figure\\s+\\d+|Fig\\.?\\s+\\d+|Table\\s+\\d+|Scheme\\s+\\w+|Graphical\\s+Abstract(?:\\s*[:|.\\-].*)?)",
            cleaned,
            flags=re.IGNORECASE,
        )
    )



=== def is_numbered_figure_caption ===
def is_numbered_figure_caption(text: str) -> bool:
    cleaned = clean_block_text(text)
    if not re.match(r"^(?:Figure|Fig\.?)\s+\d+\b", cleaned, flags=re.IGNORECASE):
        return False
    return not re.match(
        r"^(?:Figure|Fig\.?)\s+\d+\s+(?:shows?|illustrates?|depicts?|describes?|summarizes?)\b",
        cleaned,
        flags=re.IGNORECASE,
    )



=== def is_subfigure_label ===
def is_subfigure_label(text: str) -> bool:
    compact = re.sub("\\s+", " ", text.strip().lower())
    return bool(
        re.fullmatch("(?:\\([a-z]\\)\\s*)+", compact)
        or re.fullmatch("[a-z]", compact)
        or re.fullmatch("[a-z]\\)", compact)
    )



=== def media_clusters ===
def media_clusters(blocks: list[dict]) -> tuple[dict[int, int], list[list[dict]]]:
    media = [b for b in blocks if b.get("block_label") in {"image", "chart"}]
    clusters: list[list[dict]] = []
    block_to_cluster: dict[int, int] = {}
    for block in media:
        x1, y1, x2, y2 = block.get("block_bbox", [0, 0, 0, 0])
        assigned = None
        for idx, cluster in enumerate(clusters):
            cx1 = min(item["block_bbox"][0] for item in cluster) - 40
            cy1 = min(item["block_bbox"][1] for item in cluster) - 40
            cx2 = max(item["block_bbox"][2] for item in cluster) + 40
            cy2 = max(item["block_bbox"][3] for item in cluster) + 40
            vertical_overlap = max(0, min(y2, cy2) - max(y1, cy1))
            min_height = max(1, min(y2 - y1, cy2 - cy1))
            if x2 < cx1:
                horizontal_gap = cx1 - x2
            elif x1 > cx2:
                horizontal_gap = x1 - cx2
            else:
                horizontal_gap = 0
            overlaps_cluster = not (x2 < cx1 or x1 > cx2 or y2 < cy1 or y1 > cy2)
            side_by_side_panel = vertical_overlap >= int(min_height * 0.35) and horizontal_gap <= 60
            if overlaps_cluster or side_by_side_panel:
                assigned = idx
                break
        if assigned is None:
            assigned = len(clusters)
            clusters.append([])
        clusters[assigned].append(block)
        block_to_cluster[block.get("block_id", -1)] = assigned
    return (block_to_cluster, clusters)