"""Execution comparator of askmdb-test (criterion v2; rules in the dataset README).

A prediction is correct when, run on the same database as a reference, it returns the same data:
lenient on the form (column names, key order, extra columns, numeric type, a date or ObjectId as a
string, rounding to 2 decimals, month keys, an unwound array), strict on the content.

    run_pipeline(client, db, collection, pipeline, ref_date)  -> rows (as production runs them)
    compare(ref_rows, pred_rows, ordered, order_groups, optional=None, ref_pipeline=None)
                                                              -> (ok, reason)
    optional_columns(ref_rows, pred_rows, ordered, order_groups, ref_pipeline)
                                                              -> leaf paths an independent author may omit
    order_groups(rows, pipeline)                              -> tie group sizes of the last $sort
    score_case(case, raw, level, client)                      -> (ok, fail_type), rules 1-7
"""

import copy
import datetime
import json
import math
import os
import re
import sys
from collections.abc import Mapping
from decimal import ROUND_DOWN, ROUND_HALF_EVEN, ROUND_HALF_UP, Decimal, InvalidOperation
from pathlib import Path

_HERE = Path(__file__).resolve().parent
for _p in (str(_HERE),):
    if _p not in sys.path:
        sys.path.insert(0, _p)

from bson import ObjectId  # noqa: E402
from bson.codec_options import CodecOptions, DatetimeConversion  # noqa: E402
from bson.datetime_ms import DatetimeMS  # noqa: E402
from bson.decimal128 import Decimal128  # noqa: E402
from bson.errors import BSONError  # noqa: E402
from pymongo.errors import InvalidName, OperationFailure  # noqa: E402

import contract  # noqa: E402

DEFAULT_MONGO = "mongodb://localhost:27017"

MAX_ROWS = 50
MAX_TIME_MS = 10000
ASSIGN_LIMIT = 1000  # complete column assignments tried
SEARCH_LIMIT = 100000  # backtracking steps (guard against dead-end explosions)
REL_TOL = 1e-6
ABS_TOL = 1e-9  # only matters around 0

FAIL_TYPES = ("json_invalid", "wrong_type", "wrong_collection", "blocked", "exec_error", "wrong_result")
REASONS = ("row_count", "no_column_match", "rows_differ", "order", "assign_limit")

# Stages that keep the order of the rows a $sort produced (order_groups).
KEEP_ORDER = frozenset({"$project", "$addFields", "$set", "$unset", "$limit", "$skip", "$match", "$lookup"})
WRITE_STAGES = frozenset({"$out", "$merge"})
# A reference with one of these top-level stages aggregates: optional_columns() never applies.
AGGREGATE_STAGES = frozenset({"$group", "$count", "$bucket", "$bucketAuto", "$sortByCount", "$facet"})
ROUND_DECIMALS = (1, 2)  # rule R5: a number rounded (or truncated) to 1 or 2 decimals
YEAR_NAMES = frozenset({"year", "anio", "año", "ano"})  # rule R10: {year, month} by name
MONTH_NAMES = frozenset({"month", "mes"})

CODEC = CodecOptions(tz_aware=True, tzinfo=datetime.timezone.utc,
                     datetime_conversion=DatetimeConversion.DATETIME_AUTO)
_EPOCH = datetime.datetime(1970, 1, 1, tzinfo=datetime.timezone.utc)


class ExecError(Exception):
    """The server (or the driver) refused or aborted the pipeline. code is None for client errors."""

    def __init__(self, code, msg):
        super().__init__("{}: {}".format(code, msg))
        self.code = code
        self.msg = msg


# --- Execution -----------------------------------------------------------------------------------

def mongo_uri():
    return os.environ.get("ASKMDB_TEST_MONGO", DEFAULT_MONGO)


def connect(uri=None):
    """MongoClient for scoring (ASKMDB_TEST_MONGO by default); fails fast if mongo is down."""
    from pymongo import MongoClient
    return MongoClient(uri or mongo_uri(), serverSelectionTimeoutMS=5000)


def to_datetime(ref_date):
    """'2026-06-30T00:00:00Z' or a datetime -> aware UTC datetime (naive means UTC)."""
    if isinstance(ref_date, str):
        ref_date = datetime.datetime.fromisoformat(ref_date.replace("Z", "+00:00"))
    if not isinstance(ref_date, datetime.datetime):
        raise TypeError("ref_date must be an ISO string or a datetime")
    if ref_date.tzinfo is None:
        return ref_date.replace(tzinfo=datetime.timezone.utc)
    return ref_date.astimezone(datetime.timezone.utc)


def _replace_now(v, now):
    if isinstance(v, str):
        return now if v == "$$NOW" else v
    if isinstance(v, Mapping):
        return {k: _replace_now(x, now) for k, x in v.items()}
    if isinstance(v, list):
        return [_replace_now(x, now) for x in v]
    return v


def _has_write_stage(v):
    if isinstance(v, Mapping):
        return any(k in WRITE_STAGES or _has_write_stage(x) for k, x in v.items())
    if isinstance(v, list):
        return any(_has_write_stage(x) for x in v)
    return False


def run_pipeline(client, db, collection, pipeline, ref_date, *, max_rows=MAX_ROWS, max_time_ms=MAX_TIME_MS):
    """Runs the pipeline as production does and returns the rows (at most max_rows + 1).

    "$$NOW" (exact string, anywhere) becomes ref_date; {"$limit": max_rows + 1} is appended;
    maxTimeMS and allowDiskUse=false are explicit. Server errors (timeouts included) and driver
    errors about the pipeline raise ExecError. $out/$merge are never sent (ExecError).
    """
    stages = _replace_now(copy.deepcopy(list(pipeline)), to_datetime(ref_date))
    if _has_write_stage(stages):
        raise ExecError(None, "write stage ($out/$merge) refused by the scorer")
    stages.append({"$limit": max_rows + 1})
    try:
        coll = client[db].get_collection(collection, codec_options=CODEC)
        return list(coll.aggregate(stages, maxTimeMS=max_time_ms, allowDiskUse=False))
    except OperationFailure as e:
        msg = (e.details or {}).get("errmsg") or str(e)
        raise ExecError(e.code, msg) from e
    except (InvalidName, BSONError) as e:
        raise ExecError(None, str(e)) from e


# --- Values --------------------------------------------------------------------------------------

class _Sentinel:
    __slots__ = ("name",)

    def __init__(self, name):
        self.name = name

    def __repr__(self):
        return self.name


MISSING = _Sentinel("MISSING")
EMPTY_ARRAY = _Sentinel("EMPTY_ARRAY")
EMPTY_DOC = _Sentinel("EMPTY_DOC")

# Canonical value: (rank, payload, extra). Equal rank means same type family and comparable payload.
_R_MISSING, _R_NULL, _R_EMPTY_ARRAY, _R_EMPTY_DOC, _R_BOOL, _R_NUM, _R_NAN = range(7)
_R_STR, _R_DATE, _R_OID, _R_OTHER = range(7, 11)


def _date_ms(d):
    if d.tzinfo is None:
        d = d.replace(tzinfo=datetime.timezone.utc)
    delta = d - _EPOCH
    return delta.days * 86400000 + delta.seconds * 1000 + delta.microseconds // 1000


_ISO_RE = re.compile(r"^(\d{4})-(\d{2})-(\d{2})(?:[T ](\d{2}):(\d{2})(?::(\d{2})(?:\.(\d{1,9}))?)?"
                     r"(Z|[+-]\d{2}(?::?\d{2})?)?)?$")
_HEX_RE = re.compile(r"^[0-9a-f]{24}$")
_YM_RE = re.compile(r"^(\d{4})-(0[1-9]|1[0-2])$")


def iso_ms(s):
    """ms UTC of an ISO 8601 string ('YYYY-MM-DD' is midnight UTC; no zone means UTC), or None."""
    m = _ISO_RE.match(s)
    if not m:
        return None
    y, mo, d, hh, mi, ss, frac, tz = m.groups()
    try:
        dt = datetime.datetime(int(y), int(mo), int(d), int(hh or 0), int(mi or 0), int(ss or 0),
                               int((frac or "0")[:6].ljust(6, "0")), tzinfo=datetime.timezone.utc)
    except ValueError:
        return None
    if tz and tz != "Z":
        sign = 1 if tz[0] == "+" else -1
        digits = tz[1:].replace(":", "")
        dt -= sign * datetime.timedelta(hours=int(digits[:2]), minutes=int(digits[2:] or 0))
    return _date_ms(dt)


def canon(v):
    """Canonical form of a leaf value. Numbers of any BSON type share one family; bool is not a
    number; dates are integer ms UTC; MISSING, null, [] and {} are distinct.

    Rules R3 and R4: a string that is an ISO 8601 date is that date (ms UTC), and a string of 24
    lowercase hex digits is that ObjectId. Two strings stay equal only if they are the same string,
    except two ISO strings of the same instant."""
    if v is MISSING:
        return (_R_MISSING, 0, "")
    if v is None:
        return (_R_NULL, 0, "")
    if v is EMPTY_ARRAY:
        return (_R_EMPTY_ARRAY, 0, "")
    if v is EMPTY_DOC:
        return (_R_EMPTY_DOC, 0, "")
    if isinstance(v, bool):
        return (_R_BOOL, int(v), "")
    if isinstance(v, (int, float, Decimal128, Decimal)):
        if isinstance(v, Decimal128):
            v = v.to_decimal()
        try:
            f = float(v)
        except OverflowError:
            f = math.inf if v > 0 else -math.inf
        if math.isnan(f):
            return (_R_NAN, 0, "")
        return (_R_NUM, f, "")
    if isinstance(v, str):
        if _HEX_RE.match(v):
            return (_R_OID, v, "")
        ms = iso_ms(v)
        if ms is not None:
            return (_R_DATE, ms, "")
        return (_R_STR, v, "")
    if isinstance(v, datetime.datetime):
        return (_R_DATE, _date_ms(v), "")
    if isinstance(v, DatetimeMS):
        return (_R_DATE, int(v), "")
    if isinstance(v, ObjectId):
        return (_R_OID, str(v), "")
    return (_R_OTHER, type(v).__name__, repr(v))


def value_eq(a, b):
    """Strict equality of two canonical values (numbers with tolerance). Used for ties and echoes."""
    if a[0] != b[0]:
        return False
    if a[0] == _R_NUM:
        return math.isclose(a[1], b[1], rel_tol=REL_TOL, abs_tol=ABS_TOL)
    return a == b


def _decimals(x):
    """k in ROUND_DECIMALS if x has exactly k decimals, else None (integers and longer numbers)."""
    if not math.isfinite(x) or float(x).is_integer():
        return None
    for k in ROUND_DECIMALS:
        s = x * 10 ** k
        if abs(s - round(s)) <= 1e-9 * max(1.0, abs(s)):
            return k
    return None


def _rounds_to(v, u, k):
    """v rounded to k decimals (half up, half even or truncated) is u."""
    try:
        d = Decimal(repr(v))
        for mode in (ROUND_HALF_UP, ROUND_HALF_EVEN, ROUND_DOWN):
            if math.isclose(float(d.quantize(Decimal(1).scaleb(-k), rounding=mode)), u, rel_tol=1e-9, abs_tol=1e-12):
                return True
    except (InvalidOperation, ValueError):
        pass
    return False


def same_value(a, b):
    """Equality used by compare(): value_eq, or rule R5 (one number is the other rounded or
    truncated to the 1 or 2 decimals it has). An integer counts only as a rounding to 2 decimals
    (2.004 -> 2.00), never to 0 decimals (3.4 -> 3)."""
    if value_eq(a, b):
        return True
    if a[0] != _R_NUM or b[0] != _R_NUM or not (math.isfinite(a[1]) and math.isfinite(b[1])):
        return False
    for u, v in ((a[1], b[1]), (b[1], a[1])):
        k = ROUND_DECIMALS[-1] if float(u).is_integer() else _decimals(u)
        if k is not None and _rounds_to(v, u, k):
            return True
    return False


def _row_eq(a, b):
    return all(value_eq(x, y) for x, y in zip(a, b))


def _row_same(a, b):
    return all(same_value(x, y) for x, y in zip(a, b))


def flatten(row):
    """Leaf paths of a row: {"a": {"b": 1}, "c": [{"d": 2}]} -> {"a.b": 1, "c.0.d": 2}."""
    out = {}

    def walk(prefix, v):
        if isinstance(v, Mapping):
            if not v:
                out[prefix] = EMPTY_DOC
            for k, x in v.items():
                walk("{}.{}".format(prefix, k), x)
        elif isinstance(v, (list, tuple)):
            if not v:
                out[prefix] = EMPTY_ARRAY
            for i, x in enumerate(v):
                walk("{}.{}".format(prefix, i), x)
        else:
            out[prefix] = v

    for k, v in row.items():
        walk(k, v)
    return out


def _columns(rows):
    """{path: [canonical value per row]} with MISSING where a row lacks the path. Rows may be
    already flat (dotted keys flatten to themselves)."""
    flat = [flatten(r) for r in rows]
    names = []
    seen = set()
    for f in flat:
        for k in f:
            if k not in seen:
                seen.add(k)
                names.append(k)
    return {n: [canon(f.get(n, MISSING)) for f in flat] for n in names}


# --- Multisets with tolerance --------------------------------------------------------------------

def _perfect_matching(adj, n_right):
    """Kuhn's augmenting paths: True if every left node gets a distinct right node."""
    match_r = [-1] * n_right

    def augment(u, seen):
        for v in adj[u]:
            if v in seen:
                continue
            seen.add(v)
            if match_r[v] == -1 or augment(match_r[v], seen):
                match_r[v] = u
                return True
        return False

    return all(augment(u, set()) for u in range(len(adj)))


def _sorted_eq(sa, sb):
    return len(sa) == len(sb) and all(same_value(x, y) for x, y in zip(sa, sb))


def _rows_multiset_eq(a, b):
    """Rows (tuples of canonical values) equal as multisets, with numeric tolerance.

    Sorting and comparing pairwise settles the usual case; if that fails, a bipartite matching
    decides, so values at the edge of the tolerance never depend on the sort order."""
    if len(a) != len(b):
        return False
    sa, sb = sorted(a), sorted(b)
    if all(_row_same(x, y) for x, y in zip(sa, sb)):
        return True
    adj = [[j for j, y in enumerate(b) if _row_same(x, y)] for x in a]
    if any(not js for js in adj):
        return False
    return _perfect_matching(adj, len(b))


def _chunks(rows, sizes):
    out, i = [], 0
    for n in sizes:
        out.append(rows[i:i + n])
        i += n
    return out


class _Limit(Exception):
    pass


# --- Rules on the shape (v2) ---------------------------------------------------------------------

def _top_stages(pipeline):
    return [_stage_name(st) for st in pipeline or []]


def aggregates(pipeline):
    """True if the pipeline has a top-level $group, $count, $bucket, $bucketAuto, $sortByCount or
    $facet."""
    return any(name in AGGREGATE_STAGES for name in _top_stages(pipeline))


def match_literals(pipeline):
    """Rule R9: canonical literals of the equalities of the top-level $match stages ({f: v},
    {f: {$eq: v}}, {f: {$in: [v]}}, also inside a top-level $and). Documents and arrays are not
    literals."""
    lits = []

    def walk(q):
        for k, v in q.items():
            if k == "$and" and isinstance(v, list):
                for x in v:
                    if isinstance(x, Mapping):
                        walk(x)
            elif not k.startswith("$"):
                if isinstance(v, Mapping) and v and all(str(x).startswith("$") for x in v):
                    if "$eq" in v:
                        lits.append(v["$eq"])
                    if isinstance(v.get("$in"), list) and len(v["$in"]) == 1:
                        lits.append(v["$in"][0])
                else:
                    lits.append(v)

    for st in pipeline or []:
        if _stage_name(st) == "$match" and isinstance(st["$match"], Mapping):
            walk(st["$match"])
    return [canon(x) for x in lits if not isinstance(x, (Mapping, list, tuple))]


def _unwind(rows):
    """Rule R8: the rows with their only top-level array unwound as $unwind does (a missing or
    null field drops the row, a scalar stays), or None if there is not exactly one array key."""
    keys = {k for r in rows for k, v in r.items() if isinstance(v, (list, tuple))}
    if len(keys) != 1:
        return None
    key = keys.pop()
    out = []
    for r in rows:
        v = r.get(key)
        if isinstance(v, (list, tuple)):
            for x in v:
                nr = dict(r)
                nr[key] = x
                out.append(nr)
        elif v is not None:
            out.append(r)
    return out


def _row_variants(ref_rows, pred_rows, groups):
    """(ref, pred, groups) pairs with the same number of rows: the rows as they are, or, rule R8,
    with the only top-level array of the side with fewer rows unwound (an unwound reference loses
    its order groups)."""
    if len(ref_rows) == len(pred_rows):
        return [(ref_rows, pred_rows, groups)]
    if len(pred_rows) < len(ref_rows):
        u = _unwind(pred_rows)
        if u is not None and len(u) == len(ref_rows):
            return [(ref_rows, u, groups)]
    else:
        u = _unwind(ref_rows)
        if u is not None and len(u) == len(pred_rows):
            return [(u, pred_rows, None)]
    return []


def _nullish(v):
    return v[0] in (_R_NULL, _R_MISSING)


def _auto_optional(ref_cols, lits):
    """Rules R1 and R9: reference columns that are null or absent in every row, or constant and
    equal to an equality literal of a top-level $match (an echo of the filter)."""
    out = set()
    for n, vals in ref_cols.items():
        if all(_nullish(v) for v in vals):
            out.add(n)
        elif lits and vals[0][0] != _R_MISSING and all(value_eq(v, vals[0]) for v in vals) \
                and any(value_eq(vals[0], x) for x in lits):
            out.add(n)
    return out


def _drop(ref_cols, optional, lits):
    """Reference columns without the optional ones (the case's paths, R1 and R9). R1 and R9 never
    leave the reference without columns."""
    opt = set(optional or ())
    keep = {n: v for n, v in ref_cols.items() if n not in opt}
    auto = _auto_optional(keep, lits)
    if len(auto) < len(keep):
        keep = {n: v for n, v in keep.items() if n not in auto}
    return keep


def _int_in(v, lo, hi):
    return v[0] == _R_NUM and float(v[1]).is_integer() and lo <= v[1] <= hi


def _ym(v):
    return v[0] == _R_STR and _YM_RE.match(v[1]) is not None


def _month_start(v):
    if v[0] != _R_DATE:
        return None
    d = _EPOCH + datetime.timedelta(milliseconds=v[1])
    if d.day == 1 and d.hour == d.minute == d.second == d.microsecond == 0:
        return (_R_STR, "{:04d}-{:02d}".format(d.year, d.month), "")
    return None


def _month_keys(cols):
    """Rule R10 on one side: month-start dates (00:00 UTC) of a column whose dates are all
    month-start become 'YYYY-MM'; sibling integer columns named year/anio/año and month/mes become
    one 'YYYY-MM' column. Returns the new columns, or None if nothing changed."""
    pairs = {}
    for n in cols:
        prefix, _, last = n.rpartition(".")
        last = last.lower()
        if last in YEAR_NAMES:
            pairs.setdefault(prefix, {})["y"] = n
        elif last in MONTH_NAMES:
            pairs.setdefault(prefix, {})["m"] = n
    joined = {}
    for prefix, p in pairs.items():
        if "y" in p and "m" in p:
            ys, ms = cols[p["y"]], cols[p["m"]]
            if all(_int_in(y, 1, 9999) and _int_in(m, 1, 12) for y, m in zip(ys, ms)):
                joined[p["y"]] = (p["m"], [(_R_STR, "{:04d}-{:02d}".format(int(y[1]), int(m[1])), "")
                                           for y, m in zip(ys, ms)])
    skip = {m for m, _ in joined.values()}
    out, changed = {}, bool(joined)
    for n, vals in cols.items():
        if n in skip:
            continue
        if n in joined:
            out[n + "#ym"] = joined[n][1]
            continue
        dates = [v for v in vals if not _nullish(v)]
        conv = [_month_start(v) for v in dates]
        if dates and all(conv):
            out[n] = [_month_start(v) or v for v in vals]
            changed = True
        else:
            out[n] = vals
    return out if changed else None


def _ym_to_month(cols, other):
    """Rule R10, month number: 'YYYY-MM' columns of a single year become the month number, only if
    the other side has no 'YYYY-MM' column and has an integer column within 1..12. None if not."""
    def is_ym(vals):
        return all(_ym(v) for v in vals)

    if any(is_ym(v) for v in other.values()):
        return None
    if not any(all(_int_in(x, 1, 12) for x in v) for v in other.values()):
        return None
    out, changed = {}, False
    for n, vals in cols.items():
        if is_ym(vals) and len({v[1][:4] for v in vals}) == 1:
            out[n] = [(_R_NUM, float(v[1][5:]), "") for v in vals]
            changed = True
        else:
            out[n] = vals
    return out if changed else None


def _views(ref_cols, pred_cols):
    """The columns as they are, then the month-key forms of rule R10."""
    yield ref_cols, pred_cols
    r = _month_keys(ref_cols) or ref_cols
    p = _month_keys(pred_cols) or pred_cols
    if r is not ref_cols or p is not pred_cols:
        yield r, p
    r2 = _ym_to_month(r, p)
    if r2 is not None:
        yield r2, p
    p2 = _ym_to_month(p, r)
    if p2 is not None:
        yield r, p2


# --- compare -------------------------------------------------------------------------------------

def _match(ref_cols, pred_cols, n_rows, groups):
    """Steps 3-6 of the equality on columns of the same number of rows: (ok, reason)."""
    if not ref_cols:
        return True, None
    ref_names = list(ref_cols)
    pred_names = list(pred_cols)
    ref_sorted = {n: sorted(v) for n, v in ref_cols.items()}
    pred_sorted = {n: sorted(v) for n, v in pred_cols.items()}
    cand = {r: [p for p in pred_names if _sorted_eq(ref_sorted[r], pred_sorted[p])] for r in ref_names}
    if any(not c for c in cand.values()):
        return False, "no_column_match"
    index = {p: j for j, p in enumerate(pred_names)}
    if not _perfect_matching([[index[p] for p in cand[r]] for r in ref_names], len(pred_names)):
        return False, "no_column_match"

    order = sorted(ref_names, key=lambda r: len(cand[r]))
    ref_rows_t = [tuple(ref_cols[r][i] for r in order) for i in range(n_rows)]
    ref_chunks = _chunks(ref_rows_t, groups) if groups is not None else None
    state = {"complete": 0, "steps": 0, "order": False}
    used = set()
    assign = []

    def rows_match():
        pred_t = [tuple(pred_cols[p][i] for p in assign) for i in range(n_rows)]
        if not _rows_multiset_eq(ref_rows_t, pred_t):
            return False
        if ref_chunks is None:
            return True
        if all(_rows_multiset_eq(rc, pc) for rc, pc in zip(ref_chunks, _chunks(pred_t, groups))):
            return True
        state["order"] = True
        return False

    def search(k):
        state["steps"] += 1
        if state["steps"] > SEARCH_LIMIT:
            raise _Limit
        if k == len(order):
            state["complete"] += 1
            if state["complete"] > ASSIGN_LIMIT:
                raise _Limit
            return rows_match()
        for p in cand[order[k]]:
            if p in used:
                continue
            used.add(p)
            assign.append(p)
            if search(k + 1):
                return True
            assign.pop()
            used.discard(p)
        return False

    try:
        if search(0):
            return True, None
    except _Limit:
        return False, "assign_limit"
    if state["complete"] == 0:
        return False, "no_column_match"
    return False, "order" if state["order"] else "rows_differ"


def _groups(ref_rows, ordered, order_groups):
    groups = list(order_groups) if ordered and order_groups is not None else None
    if groups is not None and sum(groups) != len(ref_rows):
        raise ValueError("order_groups {} do not cover the {} reference rows".format(groups, len(ref_rows)))
    return groups


def compare(ref_rows, pred_rows, ordered, order_groups, optional=None, ref_pipeline=None):
    """Same data? Returns (True, None) or (False, reason), reason in REASONS.

    ordered with order_groups: the rows are cut in consecutive chunks of those sizes and each chunk
    is compared as a multiset. ordered with order_groups None (order not visible): plain multiset.
    optional: leaf paths of the reference the prediction may lack (refs[i]["optional"]).
    ref_pipeline: the reference's decoded pipeline, for rule R9 (echo of a $match equality).
    """
    groups = _groups(ref_rows, ordered, order_groups)
    lits = match_literals(ref_pipeline)
    first = None
    for ref, pred, g in _row_variants(ref_rows, pred_rows, groups):
        ref_cols = _drop(_columns(ref), optional, lits)
        pred_cols = _columns(pred)
        for rc, pc in _views(ref_cols, pred_cols):
            ok, reason = _match(rc, pc, len(ref), g)
            if ok:
                return True, None
            first = first or reason
    return False, first or "row_count"


def optional_columns(ref_rows, pred_rows, ordered, order_groups, ref_pipeline):
    """Leaf paths of the reference an independent author may omit, to freeze as refs[i]["optional"], or
    None if omitting columns does not make them equal or the guard says no:

      - the reference does not aggregate (aggregates());
      - every column of the other author pairs with a column of the reference;
      - the paired columns tell the rows apart as the whole reference does (same number of
        distinct rows in the projection);
      - the same number of rows (no unwinding, so the paths are columns of the reference rows).

    Call it only when compare() already says no: it never returns an empty list.
    """
    if aggregates(ref_pipeline) or len(ref_rows) != len(pred_rows):
        return None
    groups = _groups(ref_rows, ordered, order_groups)
    rc = _drop(_columns(ref_rows), None, match_literals(ref_pipeline))
    pc = _columns(pred_rows)
    pred_sorted = [sorted(v) for v in pc.values()]
    kept = [n for n, v in rc.items() if any(_sorted_eq(sorted(v), p) for p in pred_sorted)]
    missing = [n for n in rc if n not in kept]
    if not kept or not missing or len(pc) > len(kept):
        return None
    full = {tuple(rc[n][i] for n in rc) for i in range(len(ref_rows))}
    proj = {tuple(rc[n][i] for n in kept) for i in range(len(ref_rows))}
    if len(full) != len(proj):
        return None
    if _match({n: rc[n] for n in kept}, pc, len(ref_rows), groups)[0]:
        return missing
    return None


# --- Order groups --------------------------------------------------------------------------------

def _get_path(row, path):
    v = row
    for part in path.split("."):
        if isinstance(v, Mapping) and part in v:
            v = v[part]
        elif isinstance(v, list) and part.isdigit() and int(part) < len(v):
            v = v[int(part)]
        else:
            return MISSING
    return v


def _stage_name(stage):
    if isinstance(stage, Mapping) and len(stage) == 1:
        return next(iter(stage))
    return None


def order_groups(rows, pipeline):
    """Sizes of the consecutive tie groups of the key of the last top-level $sort, evaluated on
    the output rows. None (order not visible) if there is no $sort, if a stage after it may change
    the order (only KEEP_ORDER stages are allowed), or if a key path is absent from every row."""
    last = None
    for i, stage in enumerate(pipeline):
        if _stage_name(stage) == "$sort":
            last = i
    if last is None:
        return None
    if any(_stage_name(st) not in KEEP_ORDER for st in pipeline[last + 1:]):
        return None
    spec = pipeline[last]["$sort"]
    if not isinstance(spec, Mapping) or not spec:
        return None
    paths = list(spec)
    if not rows:
        return []
    keys = []
    for r in rows:
        vals = [_get_path(r, p) for p in paths]
        keys.append(tuple(canon(v) if not isinstance(v, (Mapping, list)) else (_R_OTHER, "doc", repr(v))
                          for v in vals))
    for j in range(len(paths)):
        if all(k[j][0] == _R_MISSING for k in keys):
            return None
    groups = [1]
    for prev, cur in zip(keys, keys[1:]):
        if _row_eq(prev, cur):
            groups[-1] += 1
        else:
            groups.append(1)
    return groups


# --- Scoring -------------------------------------------------------------------------------------

_REF_CACHE = {}
_DB_CACHE = {}


def clear_cache():
    _REF_CACHE.clear()
    _DB_CACHE.clear()


def case_db(case):
    """Database of the case."""
    return case["db"]


def _ref_result(case, i, client, db):
    """(rows, order_groups, decoded pipeline) of reference i, cached by (case id, i). The case's
    order_groups belong to the first reference; the others get theirs from order_groups()."""
    key = (case["id"], i)
    if key not in _REF_CACHE:
        ref = case["refs"][i]
        pipeline = contract.decode_ejson(ref["pipeline"])
        rows = run_pipeline(client, db, ref["collection"], pipeline, case["ref_date"])
        if i == 0 and "order_groups" in case:
            groups = case["order_groups"]
        else:
            groups = order_groups(rows, pipeline)
        _REF_CACHE[key] = (rows, groups, pipeline)
    return _REF_CACHE[key]


def score_case(case, raw, level, client, *, details=None):
    """Scoring rules 1-7 (dataset README), in order. Returns (True, None) or (False, fail_type).

    raw: the model output already cut at the top-level '}' (None if there was none).
    level: the verifier's "read" | "warn" | "blocked" (None: not verified; still executed).
    details: optional dict; receives "reasons" (compare reason per reference) when rule 7 runs.
    A reference that fails to execute is a bank error and raises.
    """
    obj, err = contract.parse_response(raw) if raw is not None else (None, "invalid_json")
    if err is not None:
        return False, "json_invalid"
    expected = case["expected_type"]
    if expected in ("refuse", "unsure"):
        return (True, None) if obj["type"] == expected else (False, "wrong_type")
    if obj["type"] != "query":
        return False, "wrong_type"
    if obj["collection"] not in {r["collection"] for r in case["refs"]}:
        return False, "wrong_collection"
    if (level == "blocked" or contract.bad_stage_shape(obj["pipeline"])
            or contract.pipeline_has_duplicate_keys(raw)):
        return False, "blocked"

    db = case_db(case)
    try:
        pred_rows = run_pipeline(client, db, obj["collection"], obj["pipeline"], case["ref_date"])
    except ExecError:
        return False, "exec_error"

    reasons = []
    for i in range(len(case["refs"])):
        ref_rows, groups, pipeline = _ref_result(case, i, client, db)
        ok, reason = compare(ref_rows, pred_rows, bool(case.get("ordered")), groups,
                             case["refs"][i].get("optional"), pipeline)
        if ok:
            return True, None
        reasons.append(reason)
    if details is not None:
        details["reasons"] = reasons
    return False, "wrong_result"