FA-70511 / GIS polygon topology / Open access

Rook and queen polygon adjacency: degenerate edge filter · case 01

Polygons with a repeated corner vertex become rook neighbours of anything sharing that corner.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Zero-length edges from repeated vertices are kept, and two such point-edges at a shared corner match.

VERIFIED REPAIR

At the degenerate edge filter step restore `for a, b in zip(r, r[1:]) if a != b}`, leaving the rest of the model unchanged.

Unsuccessful approach: Filtering on differing x coordinates also discards every vertical edge.

Case contract

Input [polygons, mode] where each polygon is a closed ring of integer vertices on a noded coverage (shared borders use identical vertices). Rook neighbours share at least one non-degenerate edge irrespective of direction; queen neighbours share at least one vertex. Return, for each polygon index, the ascending list of neighbour indexes (never itself).

Why this case matters

Spatial weights for regional statistics, district contiguity checks and map colouring all start from adjacency.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    polys, mode = x
    def edges(r):
        return {tuple(sorted([tuple(a), tuple(b)])) for a, b in zip(r, r[1:])}
    def verts(r):
        return {tuple(p) for p in r}
    E = [edges(p) for p in polys]
    V = [verts(p) for p in polys]
    out = []
    for i in range(len(polys)):
        nb = []
        for j in range(len(polys)):
            if i == j:
                continue
            if mode == 'rook':
                ok = bool(E[i] & E[j])
            else:
                ok = bool(V[i] & V[j])
            if ok:
                nb.append(j)
        out.append(nb)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]]], 'rook'], [[1, 3], [0], [], [0]]), ('control #1', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]]], 'queen'], [[1, 3], [0, 2, 3], [1], [0, 1]]), ('control #2', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[1, 2], [0, 3], [0, 3], [1, 2]]), ('control #3', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'queen'], [[1, 2, 3], [0, 2, 3], [0, 1, 3], [0, 1, 2]]), ('control #4', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[1, 3], [0, 4], [4], [0, 4], [1, 2, 3]]), ('control #5', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'queen'], [[1, 3, 4], [0, 2, 3, 4], [1, 4], [0, 1, 4], [0, 1, 2, 3]]), ('control #6', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[10, 10], [12, 10], [11, 12], [10, 10]]], 'rook'], [[], []]), ('control #16', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[1], [0], []])], [('control #2', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[1, 2], [0, 3], [0, 3], [1, 2]]), ('control #4', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[1, 3], [0, 4], [4], [0, 4], [1, 2, 3]]), ('control #5', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'queen'], [[1, 3, 4], [0, 2, 3, 4], [1, 4], [0, 1, 4], [0, 1, 2, 3]]), ('control #6', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[10, 10], [12, 10], [11, 12], [10, 10]]], 'rook'], [[], []]), ('control #7', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[10, 10], [12, 10], [11, 12], [10, 10]]], 'queen'], [[], []]), ('control #8', [[[[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[], []]), ('control #9', [[[[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0]]), ('control #18', [[[[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[], []])], [('control #4', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[1, 3], [0, 4], [4], [0, 4], [1, 2, 3]]), ('control #7', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[10, 10], [12, 10], [11, 12], [10, 10]]], 'queen'], [[], []]), ('control #8', [[[[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[], []]), ('control #9', [[[[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0]]), ('control #10', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[], []]), ('control #11', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'queen'], [[1], [0]]), ('control #12', [[[[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[1], [0, 2], [1]]), ('control #16', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[1], [0], []])], [('control #9', [[[[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0]]), ('control #10', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[], []]), ('control #11', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'queen'], [[1], [0]]), ('control #12', [[[[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[1], [0, 2], [1]]), ('control #13', [[[[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0, 2], [1]]), ('control #14', [[[[0, 0], [0, 2], [2, 2], [2, 0], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]]], 'rook'], [[1], [0]]), ('control #15', [[[[0, 0], [0, 2], [2, 2], [2, 0], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]]], 'queen'], [[1], [0]]), ('control #18', [[[[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[], []])], [('control #12', [[[[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[1], [0, 2], [1]]), ('control #13', [[[[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0, 2], [1]]), ('control #14', [[[[0, 0], [0, 2], [2, 2], [2, 0], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]]], 'rook'], [[1], [0]]), ('control #15', [[[[0, 0], [0, 2], [2, 2], [2, 0], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]]], 'queen'], [[1], [0]]), ('control #16', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[1], [0], []]), ('control #17', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0, 2], [1]]), ('control #18', [[[[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[], []]), ('control #19', [[[[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0]])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
control #0	`[[1, 3], [0], [], [0]]`	`[[1, 3], [0], [], [0]]`	Passed
control #1	`[[1, 3], [0, 2, 3], [1], [0, 1]]`	`[[1, 3], [0, 2, 3], [1], [0, 1]]`	Passed
control #2	`[[1, 2], [0, 3], [0, 3], [1, 2]]`	`[[1, 2], [0, 3], [0, 3], [1, 2]]`	Passed
control #3	`[[1, 2, 3], [0, 2, 3], [0, 1, 3], [0, 1, 2]]`	`[[1, 2, 3], [0, 2, 3], [0, 1, 3], [0, 1, 2]]`	Passed
control #4	`[[1, 3], [0, 4], [4], [0, 4], [1, 2, 3]]`	`[[1, 3], [0, 4], [4], [0, 4], [1, 2, 3]]`	Passed
control #5	`[[1, 3, 4], [0, 2, 3, 4], [1, 4], [0, 1, 4], [0, 1, 2, 3]]`	`[[1, 3, 4], [0, 2, 3, 4], [1, 4], [0, 1, 4], [0, 1, 2, 3]]`	Passed
control #6	`[[], []]`	`[[], []]`	Passed
control #16	`[[1], [0, 2], [1]]`	`[[1], [0], []]`	Failed

SHA-256 / 249159aedf51bdb04f345fee9cb9e75d921384d093120a51b2f5e8844201592c

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    polys, mode = x
    def edges(r):
        return {tuple(sorted([tuple(a), tuple(b)])) for a, b in zip(r, r[1:]) if a[0] != b[0]}
    def verts(r):
        return {tuple(p) for p in r}
    E = [edges(p) for p in polys]
    V = [verts(p) for p in polys]
    out = []
    for i in range(len(polys)):
        nb = []
        for j in range(len(polys)):
            if i == j:
                continue
            if mode == 'rook':
                ok = bool(E[i] & E[j])
            else:
                ok = bool(V[i] & V[j])
            if ok:
                nb.append(j)
        out.append(nb)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]]], 'rook'], [[1, 3], [0], [], [0]]), ('control #1', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]]], 'queen'], [[1, 3], [0, 2, 3], [1], [0, 1]]), ('control #2', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[1, 2], [0, 3], [0, 3], [1, 2]]), ('control #3', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'queen'], [[1, 2, 3], [0, 2, 3], [0, 1, 3], [0, 1, 2]]), ('control #4', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[1, 3], [0, 4], [4], [0, 4], [1, 2, 3]]), ('control #5', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'queen'], [[1, 3, 4], [0, 2, 3, 4], [1, 4], [0, 1, 4], [0, 1, 2, 3]]), ('control #6', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[10, 10], [12, 10], [11, 12], [10, 10]]], 'rook'], [[], []]), ('control #16', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[1], [0], []])], [('control #2', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[1, 2], [0, 3], [0, 3], [1, 2]]), ('control #4', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[1, 3], [0, 4], [4], [0, 4], [1, 2, 3]]), ('control #5', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'queen'], [[1, 3, 4], [0, 2, 3, 4], [1, 4], [0, 1, 4], [0, 1, 2, 3]]), ('control #6', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[10, 10], [12, 10], [11, 12], [10, 10]]], 'rook'], [[], []]), ('control #7', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[10, 10], [12, 10], [11, 12], [10, 10]]], 'queen'], [[], []]), ('control #8', [[[[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[], []]), ('control #9', [[[[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0]]), ('control #18', [[[[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[], []])], [('control #4', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[1, 3], [0, 4], [4], [0, 4], [1, 2, 3]]), ('control #7', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[10, 10], [12, 10], [11, 12], [10, 10]]], 'queen'], [[], []]), ('control #8', [[[[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[], []]), ('control #9', [[[[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0]]), ('control #10', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[], []]), ('control #11', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'queen'], [[1], [0]]), ('control #12', [[[[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[1], [0, 2], [1]]), ('control #16', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[1], [0], []])], [('control #9', [[[[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0]]), ('control #10', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[], []]), ('control #11', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'queen'], [[1], [0]]), ('control #12', [[[[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[1], [0, 2], [1]]), ('control #13', [[[[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0, 2], [1]]), ('control #14', [[[[0, 0], [0, 2], [2, 2], [2, 0], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]]], 'rook'], [[1], [0]]), ('control #15', [[[[0, 0], [0, 2], [2, 2], [2, 0], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]]], 'queen'], [[1], [0]]), ('control #18', [[[[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[], []])], [('control #12', [[[[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[1], [0, 2], [1]]), ('control #13', [[[[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0, 2], [1]]), ('control #14', [[[[0, 0], [0, 2], [2, 2], [2, 0], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]]], 'rook'], [[1], [0]]), ('control #15', [[[[0, 0], [0, 2], [2, 2], [2, 0], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]]], 'queen'], [[1], [0]]), ('control #16', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[1], [0], []]), ('control #17', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0, 2], [1]]), ('control #18', [[[[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[], []]), ('control #19', [[[[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0]])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
control #0	`[[3], [], [], [0]]`	`[[1, 3], [0], [], [0]]`	Failed
control #1	`[[1, 3], [0, 2, 3], [1], [0, 1]]`	`[[1, 3], [0, 2, 3], [1], [0, 1]]`	Passed
control #2	`[[2], [3], [0], [1]]`	`[[1, 2], [0, 3], [0, 3], [1, 2]]`	Failed
control #3	`[[1, 2, 3], [0, 2, 3], [0, 1, 3], [0, 1, 2]]`	`[[1, 2, 3], [0, 2, 3], [0, 1, 3], [0, 1, 2]]`	Passed
control #4	`[[3], [4], [], [0], [1]]`	`[[1, 3], [0, 4], [4], [0, 4], [1, 2, 3]]`	Failed
control #5	`[[1, 3, 4], [0, 2, 3, 4], [1, 4], [0, 1, 4], [0, 1, 2, 3]]`	`[[1, 3, 4], [0, 2, 3, 4], [1, 4], [0, 1, 4], [0, 1, 2, 3]]`	Passed
control #6	`[[], []]`	`[[], []]`	Passed
control #16	`[[], [], []]`	`[[1], [0], []]`	Failed

SHA-256 / 19906d55a1c6ee46fc19dc7f4d74e943a56e4106e959780706a55b1822faef99

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    polys, mode = x
    def edges(r):
        return {tuple(sorted([tuple(a), tuple(b)])) for a, b in zip(r, r[1:]) if a != b}
    def verts(r):
        return {tuple(p) for p in r}
    E = [edges(p) for p in polys]
    V = [verts(p) for p in polys]
    out = []
    for i in range(len(polys)):
        nb = []
        for j in range(len(polys)):
            if i == j:
                continue
            if mode == 'rook':
                ok = bool(E[i] & E[j])
            else:
                ok = bool(V[i] & V[j])
            if ok:
                nb.append(j)
        out.append(nb)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]]], 'rook'], [[1, 3], [0], [], [0]]), ('control #1', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]]], 'queen'], [[1, 3], [0, 2, 3], [1], [0, 1]]), ('control #2', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[1, 2], [0, 3], [0, 3], [1, 2]]), ('control #3', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'queen'], [[1, 2, 3], [0, 2, 3], [0, 1, 3], [0, 1, 2]]), ('control #4', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[1, 3], [0, 4], [4], [0, 4], [1, 2, 3]]), ('control #5', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'queen'], [[1, 3, 4], [0, 2, 3, 4], [1, 4], [0, 1, 4], [0, 1, 2, 3]]), ('control #6', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[10, 10], [12, 10], [11, 12], [10, 10]]], 'rook'], [[], []]), ('control #16', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[1], [0], []])], [('control #2', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[1, 2], [0, 3], [0, 3], [1, 2]]), ('control #4', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[1, 3], [0, 4], [4], [0, 4], [1, 2, 3]]), ('control #5', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'queen'], [[1, 3, 4], [0, 2, 3, 4], [1, 4], [0, 1, 4], [0, 1, 2, 3]]), ('control #6', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[10, 10], [12, 10], [11, 12], [10, 10]]], 'rook'], [[], []]), ('control #7', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[10, 10], [12, 10], [11, 12], [10, 10]]], 'queen'], [[], []]), ('control #8', [[[[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[], []]), ('control #9', [[[[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0]]), ('control #18', [[[[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[], []])], [('control #4', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]], [[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[1, 3], [0, 4], [4], [0, 4], [1, 2, 3]]), ('control #7', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[10, 10], [12, 10], [11, 12], [10, 10]]], 'queen'], [[], []]), ('control #8', [[[[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[], []]), ('control #9', [[[[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0]]), ('control #10', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[], []]), ('control #11', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'queen'], [[1], [0]]), ('control #12', [[[[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[1], [0, 2], [1]]), ('control #16', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[1], [0], []])], [('control #9', [[[[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0]]), ('control #10', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'rook'], [[], []]), ('control #11', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]]], 'queen'], [[1], [0]]), ('control #12', [[[[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[1], [0, 2], [1]]), ('control #13', [[[[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0, 2], [1]]), ('control #14', [[[[0, 0], [0, 2], [2, 2], [2, 0], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]]], 'rook'], [[1], [0]]), ('control #15', [[[[0, 0], [0, 2], [2, 2], [2, 0], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]]], 'queen'], [[1], [0]]), ('control #18', [[[[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[], []])], [('control #12', [[[[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[1], [0, 2], [1]]), ('control #13', [[[[0, 2], [2, 2], [2, 4], [0, 4], [0, 2]], [[2, 2], [4, 2], [4, 4], [2, 4], [2, 2]], [[4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0, 2], [1]]), ('control #14', [[[[0, 0], [0, 2], [2, 2], [2, 0], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]]], 'rook'], [[1], [0]]), ('control #15', [[[[0, 0], [0, 2], [2, 2], [2, 0], [0, 0]], [[2, 0], [4, 0], [4, 2], [2, 2], [2, 0]]], 'queen'], [[1], [0]]), ('control #16', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[1], [0], []]), ('control #17', [[[[0, 0], [2, 0], [2, 2], [0, 2], [0, 0]], [[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0, 2], [1]]), ('control #18', [[[[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'rook'], [[], []]), ('control #19', [[[[2, 0], [4, 0], [4, 2], [4, 2], [2, 2], [2, 0]], [[4, 2], [4, 2], [6, 2], [6, 4], [4, 4], [4, 2]]], 'queen'], [[1], [0]])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
control #0	`[[1, 3], [0], [], [0]]`	`[[1, 3], [0], [], [0]]`	Passed
control #1	`[[1, 3], [0, 2, 3], [1], [0, 1]]`	`[[1, 3], [0, 2, 3], [1], [0, 1]]`	Passed
control #2	`[[1, 2], [0, 3], [0, 3], [1, 2]]`	`[[1, 2], [0, 3], [0, 3], [1, 2]]`	Passed
control #3	`[[1, 2, 3], [0, 2, 3], [0, 1, 3], [0, 1, 2]]`	`[[1, 2, 3], [0, 2, 3], [0, 1, 3], [0, 1, 2]]`	Passed
control #4	`[[1, 3], [0, 4], [4], [0, 4], [1, 2, 3]]`	`[[1, 3], [0, 4], [4], [0, 4], [1, 2, 3]]`	Passed
control #5	`[[1, 3, 4], [0, 2, 3, 4], [1, 4], [0, 1, 4], [0, 1, 2, 3]]`	`[[1, 3, 4], [0, 2, 3, 4], [1, 4], [0, 1, 4], [0, 1, 2, 3]]`	Passed
control #6	`[[], []]`	`[[], []]`	Passed
control #16	`[[1], [0], []]`	`[[1], [0], []]`	Passed

SHA-256 / 39114ce31479e65c2200f57ef392cca0e8276c818e1cec3417b345b1f1583a48

Verification & scope

Stipulated deterministic toy contract on a bounded input domain; results are rounded as stated and no conformance with any published standard or library is claimed. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:48:21.327527+00:00.

Case digest / 879e7053a66b01007d0b1e59f9181f74a3b48a1e0f46acc65053fe153fb6c70d