FA-51641 / Raster clipping / Open access

Sutherland hodgman raster rect: degenerate output · case 01

Clipped polygons that collapse to a point or a segment are emitted as polygons.

Verified by executionVariant 1 · 12 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Clipped polygons that collapse to a point or a segment are emitted as polygons.

THE FAILURE

Clipped polygons that collapse to a point or a segment are emitted as polygons.

Unsuccessful approach: Dropping single points still emits two-vertex slivers.

Case contract

Each command is a polygon vertex list with exact coordinates. It is clipped in continuous raster coordinates against x>=0, x<=size, y>=0 and y<=size in that order with Sutherland-Hodgman: each stage walks edges from the previous vertex to the current vertex, emits the boundary intersection when entering before the inside vertex, emits the intersection when leaving, and chains its output into the next stage. Boundary points are inside. Cyclically repeated consecutive vertices are then removed; fewer than three remaining vertices yields an empty polygon. Vertices are returned as exact rational strings.

Why this case matters

Raster clipping decides which pixels a primitive may touch; a single wrong clip decision writes outside the target or scissor, or silently drops visible coverage.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(commands, size):
    def stage(poly,inside,cross):
        res=[]
        for i in range(len(poly)):
            cur=poly[i]
            prev=poly[i-1]
            if inside(cur):
                if not inside(prev): res.append(cross(prev,cur))
                res.append(cur)
            elif inside(prev):
                res.append(cross(prev,cur))
        return res
    def at_x(k):
        return lambda p,c: (Fraction(k),p[1]+(c[1]-p[1])*(k-p[0])/(c[0]-p[0]))
    def at_y(k):
        return lambda p,c: (p[0]+(c[0]-p[0])*(k-p[1])/(c[1]-p[1]),Fraction(k))
    out=[]
    for poly in commands:
        src=[(Fraction(x),Fraction(y)) for x,y in poly]
        pts=stage(src,lambda p:p[0]>=0,at_x(0))
        pts=stage(pts,lambda p:p[0]<=size,at_x(size))
        pts=stage(pts,lambda p:p[1]>=0,at_y(0))
        pts=stage(pts,lambda p:p[1]<=size,at_y(size))
        clean=[p for i,p in enumerate(pts) if p!=pts[i-1]]
        if not clean: clean=[]
        out.append([[str(x),str(y)] for x,y in clean])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
    check('explicit case 0', solve([[[1, 1], [5, 1], [5, 5], [1, 5]]], 6), [[['1', '1'], ['5', '1'], ['5', '5'], ['1', '5']]])
    check('explicit case 1', solve([[[-2, 1], [3, 1], [3, 4]]], 6), [[['0', '11/5'], ['0', '1'], ['3', '1'], ['3', '4']]])
    check('explicit case 2', solve([[[1, 1], [8, 2], [2, 4]]], 6), [[['1', '1'], ['6', '12/7'], ['6', '8/3'], ['2', '4']]])
    check('explicit case 3', solve([[[-2, -2], [8, -2], [8, 8], [-2, 8]]], 6), [[['0', '6'], ['0', '0'], ['6', '0'], ['6', '6']]])
    check('explicit case 4', solve([[[2, -3], [4, 2], [1, 3]]], 6), [[['3/2', '0'], ['16/5', '0'], ['4', '2'], ['1', '3']]])
    check('explicit case 5', solve([[[-3, 1], [-1, 1], [-2, 3]]], 6), [[]])
    check('explicit case 6', solve([[[0, 1], [0, 3], [-2, 2]]], 6), [[]])
    check('explicit case 7', solve([[[0, 0], [-1, -2], [-2, -1]]], 6), [[]])
    check('explicit case 8', solve([[[1, 1], [7, 1], [1, 9]]], 6), [[['1', '6'], ['1', '1'], ['6', '1'], ['6', '7/3'], ['13/4', '6']]])
    check('explicit case 9', solve([[['1/2', 2], [6, 2], [6, 5]]], 6), [[['1/2', '2'], ['6', '2'], ['6', '5']]])
    check('explicit case 10', solve([[[-2, 2], [2, 1], [0, 3]]], 6), [[['0', '3/2'], ['2', '1'], ['0', '3']]])
    check('explicit case 11', solve([[[3, 1], [8, 3], [6, 4], [5, 1]]], 6), [[['3', '1'], ['6', '11/5'], ['6', '4'], ['5', '1']]])
if N == 2:
    check('explicit case 0', solve([[[1, 1], [6, 1], [6, 6], [1, 6]]], 7), [[['1', '1'], ['6', '1'], ['6', '6'], ['1', '6']]])
    check('explicit case 1', solve([[[-2, 1], [3, 1], [3, 4]]], 7), [[['0', '11/5'], ['0', '1'], ['3', '1'], ['3', '4']]])
    check('explicit case 2', solve([[[1, 1], [9, 2], [2, 4]]], 7), [[['1', '1'], ['7', '7/4'], ['7', '18/7'], ['2', '4']]])
    check('explicit case 3', solve([[[-2, -2], [9, -2], [9, 9], [-2, 9]]], 7), [[['0', '7'], ['0', '0'], ['7', '0'], ['7', '7']]])
    check('explicit case 4', solve([[[2, -3], [4, 2], [1, 3]]], 7), [[['3/2', '0'], ['16/5', '0'], ['4', '2'], ['1', '3']]])
    check('explicit case 5', solve([[[-3, 1], [-1, 1], [-2, 3]]], 7), [[]])
    check('explicit case 6', solve([[[0, 1], [0, 3], [-2, 2]]], 7), [[]])
    check('explicit case 7', solve([[[0, 0], [-1, -2], [-2, -1]]], 7), [[]])
    check('explicit case 8', solve([[[1, 1], [8, 1], [1, 10]]], 7), [[['1', '7'], ['1', '1'], ['7', '1'], ['7', '16/7'], ['10/3', '7']]])
    check('explicit case 9', solve([[['1/2', 2], [7, 2], [7, 5]]], 7), [[['1/2', '2'], ['7', '2'], ['7', '5']]])
    check('explicit case 10', solve([[[-2, 2], [2, 1], [0, 3]]], 7), [[['0', '3/2'], ['2', '1'], ['0', '3']]])
    check('explicit case 11', solve([[[3, 1], [9, 3], [7, 4], [6, 1]]], 7), [[['3', '1'], ['7', '7/3'], ['7', '4'], ['6', '1']]])
if N == 3:
    check('explicit case 0', solve([[[1, 1], [7, 1], [7, 7], [1, 7]]], 8), [[['1', '1'], ['7', '1'], ['7', '7'], ['1', '7']]])
    check('explicit case 1', solve([[[-2, 1], [3, 1], [3, 4]]], 8), [[['0', '11/5'], ['0', '1'], ['3', '1'], ['3', '4']]])
    check('explicit case 2', solve([[[1, 1], [10, 2], [2, 4]]], 8), [[['1', '1'], ['8', '16/9'], ['8', '5/2'], ['2', '4']]])
    check('explicit case 3', solve([[[-2, -2], [10, -2], [10, 10], [-2, 10]]], 8), [[['0', '8'], ['0', '0'], ['8', '0'], ['8', '8']]])
    check('explicit case 4', solve([[[2, -3], [4, 2], [1, 3]]], 8), [[['3/2', '0'], ['16/5', '0'], ['4', '2'], ['1', '3']]])
    check('explicit case 5', solve([[[-3, 1], [-1, 1], [-2, 3]]], 8), [[]])
    check('explicit case 6', solve([[[0, 1], [0, 3], [-2, 2]]], 8), [[]])
    check('explicit case 7', solve([[[0, 0], [-1, -2], [-2, -1]]], 8), [[]])
    check('explicit case 8', solve([[[1, 1], [9, 1], [1, 11]]], 8), [[['1', '8'], ['1', '1'], ['8', '1'], ['8', '9/4'], ['17/5', '8']]])
    check('explicit case 9', solve([[['1/2', 2], [8, 2], [8, 5]]], 8), [[['1/2', '2'], ['8', '2'], ['8', '5']]])
    check('explicit case 10', solve([[[-2, 2], [2, 1], [0, 3]]], 8), [[['0', '3/2'], ['2', '1'], ['0', '3']]])
    check('explicit case 11', solve([[[3, 1], [10, 3], [8, 4], [7, 1]]], 8), [[['3', '1'], ['8', '17/7'], ['8', '4'], ['7', '1']]])
if N == 4:
    check('explicit case 0', solve([[[1, 1], [8, 1], [8, 8], [1, 8]]], 9), [[['1', '1'], ['8', '1'], ['8', '8'], ['1', '8']]])
    check('explicit case 1', solve([[[-2, 1], [3, 1], [3, 4]]], 9), [[['0', '11/5'], ['0', '1'], ['3', '1'], ['3', '4']]])
    check('explicit case 2', solve([[[1, 1], [11, 2], [2, 4]]], 9), [[['1', '1'], ['9', '9/5'], ['9', '22/9'], ['2', '4']]])
    check('explicit case 3', solve([[[-2, -2], [11, -2], [11, 11], [-2, 11]]], 9), [[['0', '9'], ['0', '0'], ['9', '0'], ['9', '9']]])
    check('explicit case 4', solve([[[2, -3], [4, 2], [1, 3]]], 9), [[['3/2', '0'], ['16/5', '0'], ['4', '2'], ['1', '3']]])
    check('explicit case 5', solve([[[-3, 1], [-1, 1], [-2, 3]]], 9), [[]])
    check('explicit case 6', solve([[[0, 1], [0, 3], [-2, 2]]], 9), [[]])
    check('explicit case 7', solve([[[0, 0], [-1, -2], [-2, -1]]], 9), [[]])
    check('explicit case 8', solve([[[1, 1], [10, 1], [1, 12]]], 9), [[['1', '9'], ['1', '1'], ['9', '1'], ['9', '20/9'], ['38/11', '9']]])
    check('explicit case 9', solve([[['1/2', 2], [9, 2], [9, 5]]], 9), [[['1/2', '2'], ['9', '2'], ['9', '5']]])
    check('explicit case 10', solve([[[-2, 2], [2, 1], [0, 3]]], 9), [[['0', '3/2'], ['2', '1'], ['0', '3']]])
    check('explicit case 11', solve([[[3, 1], [11, 3], [9, 4], [8, 1]]], 9), [[['3', '1'], ['9', '5/2'], ['9', '4'], ['8', '1']]])
if N == 5:
    check('explicit case 0', solve([[[1, 1], [9, 1], [9, 9], [1, 9]]], 10), [[['1', '1'], ['9', '1'], ['9', '9'], ['1', '9']]])
    check('explicit case 1', solve([[[-2, 1], [3, 1], [3, 4]]], 10), [[['0', '11/5'], ['0', '1'], ['3', '1'], ['3', '4']]])
    check('explicit case 2', solve([[[1, 1], [12, 2], [2, 4]]], 10), [[['1', '1'], ['10', '20/11'], ['10', '12/5'], ['2', '4']]])
    check('explicit case 3', solve([[[-2, -2], [12, -2], [12, 12], [-2, 12]]], 10), [[['0', '10'], ['0', '0'], ['10', '0'], ['10', '10']]])
    check('explicit case 4', solve([[[2, -3], [4, 2], [1, 3]]], 10), [[['3/2', '0'], ['16/5', '0'], ['4', '2'], ['1', '3']]])
    check('explicit case 5', solve([[[-3, 1], [-1, 1], [-2, 3]]], 10), [[]])
    check('explicit case 6', solve([[[0, 1], [0, 3], [-2, 2]]], 10), [[]])
    check('explicit case 7', solve([[[0, 0], [-1, -2], [-2, -1]]], 10), [[]])
    check('explicit case 8', solve([[[1, 1], [11, 1], [1, 13]]], 10), [[['1', '10'], ['1', '1'], ['10', '1'], ['10', '11/5'], ['7/2', '10']]])
    check('explicit case 9', solve([[['1/2', 2], [10, 2], [10, 5]]], 10), [[['1/2', '2'], ['10', '2'], ['10', '5']]])
    check('explicit case 10', solve([[[-2, 2], [2, 1], [0, 3]]], 10), [[['0', '3/2'], ['2', '1'], ['0', '3']]])
    check('explicit case 11', solve([[[3, 1], [12, 3], [10, 4], [9, 1]]], 10), [[['3', '1'], ['10', '23/9'], ['10', '4'], ['9', '1']]])
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
explicit case 0	`[[['1', '1'], ['5', '1'], ['5', '5'], ['1', '5']]]`	`[[['1', '1'], ['5', '1'], ['5', '5'], ['1', '5']]]`	Passed
explicit case 1	`[[['0', '11/5'], ['0', '1'], ['3', '1'], ['3', '4']]]`	`[[['0', '11/5'], ['0', '1'], ['3', '1'], ['3', '4']]]`	Passed
explicit case 2	`[[['1', '1'], ['6', '12/7'], ['6', '8/3'], ['2', '4']]]`	`[[['1', '1'], ['6', '12/7'], ['6', '8/3'], ['2', '4']]]`	Passed
explicit case 3	`[[['0', '6'], ['0', '0'], ['6', '0'], ['6', '6']]]`	`[[['0', '6'], ['0', '0'], ['6', '0'], ['6', '6']]]`	Passed
explicit case 4	`[[['3/2', '0'], ['16/5', '0'], ['4', '2'], ['1', '3']]]`	`[[['3/2', '0'], ['16/5', '0'], ['4', '2'], ['1', '3']]]`	Passed
explicit case 5	`[[]]`	`[[]]`	Passed
explicit case 6	`[[['0', '1'], ['0', '3']]]`	`[[]]`	Failed
explicit case 7	`[[]]`	`[[]]`	Passed
explicit case 8	`[[['1', '6'], ['1', '1'], ['6', '1'], ['6', '7/3'], ['13/4', '6']]]`	`[[['1', '6'], ['1', '1'], ['6', '1'], ['6', '7/3'], ['13/4', '6']]]`	Passed
explicit case 9	`[[['1/2', '2'], ['6', '2'], ['6', '5']]]`	`[[['1/2', '2'], ['6', '2'], ['6', '5']]]`	Passed
explicit case 10	`[[['0', '3/2'], ['2', '1'], ['0', '3']]]`	`[[['0', '3/2'], ['2', '1'], ['0', '3']]]`	Passed
explicit case 11	`[[['3', '1'], ['6', '11/5'], ['6', '4'], ['5', '1']]]`	`[[['3', '1'], ['6', '11/5'], ['6', '4'], ['5', '1']]]`	Passed

SHA-256 / 850df3c8f803f193abeffb7a7cc51da867ba0175d07404bee8a41606c2d5115b

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(commands, size):
    def stage(poly,inside,cross):
        res=[]
        for i in range(len(poly)):
            cur=poly[i]
            prev=poly[i-1]
            if inside(cur):
                if not inside(prev): res.append(cross(prev,cur))
                res.append(cur)
            elif inside(prev):
                res.append(cross(prev,cur))
        return res
    def at_x(k):
        return lambda p,c: (Fraction(k),p[1]+(c[1]-p[1])*(k-p[0])/(c[0]-p[0]))
    def at_y(k):
        return lambda p,c: (p[0]+(c[0]-p[0])*(k-p[1])/(c[1]-p[1]),Fraction(k))
    out=[]
    for poly in commands:
        src=[(Fraction(x),Fraction(y)) for x,y in poly]
        pts=stage(src,lambda p:p[0]>=0,at_x(0))
        pts=stage(pts,lambda p:p[0]<=size,at_x(size))
        pts=stage(pts,lambda p:p[1]>=0,at_y(0))
        pts=stage(pts,lambda p:p[1]<=size,at_y(size))
        clean=[p for i,p in enumerate(pts) if p!=pts[i-1]]
        if len(clean)<2: clean=[]
        out.append([[str(x),str(y)] for x,y in clean])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
    check('explicit case 0', solve([[[1, 1], [5, 1], [5, 5], [1, 5]]], 6), [[['1', '1'], ['5', '1'], ['5', '5'], ['1', '5']]])
    check('explicit case 1', solve([[[-2, 1], [3, 1], [3, 4]]], 6), [[['0', '11/5'], ['0', '1'], ['3', '1'], ['3', '4']]])
    check('explicit case 2', solve([[[1, 1], [8, 2], [2, 4]]], 6), [[['1', '1'], ['6', '12/7'], ['6', '8/3'], ['2', '4']]])
    check('explicit case 3', solve([[[-2, -2], [8, -2], [8, 8], [-2, 8]]], 6), [[['0', '6'], ['0', '0'], ['6', '0'], ['6', '6']]])
    check('explicit case 4', solve([[[2, -3], [4, 2], [1, 3]]], 6), [[['3/2', '0'], ['16/5', '0'], ['4', '2'], ['1', '3']]])
    check('explicit case 5', solve([[[-3, 1], [-1, 1], [-2, 3]]], 6), [[]])
    check('explicit case 6', solve([[[0, 1], [0, 3], [-2, 2]]], 6), [[]])
    check('explicit case 7', solve([[[0, 0], [-1, -2], [-2, -1]]], 6), [[]])
    check('explicit case 8', solve([[[1, 1], [7, 1], [1, 9]]], 6), [[['1', '6'], ['1', '1'], ['6', '1'], ['6', '7/3'], ['13/4', '6']]])
    check('explicit case 9', solve([[['1/2', 2], [6, 2], [6, 5]]], 6), [[['1/2', '2'], ['6', '2'], ['6', '5']]])
    check('explicit case 10', solve([[[-2, 2], [2, 1], [0, 3]]], 6), [[['0', '3/2'], ['2', '1'], ['0', '3']]])
    check('explicit case 11', solve([[[3, 1], [8, 3], [6, 4], [5, 1]]], 6), [[['3', '1'], ['6', '11/5'], ['6', '4'], ['5', '1']]])
if N == 2:
    check('explicit case 0', solve([[[1, 1], [6, 1], [6, 6], [1, 6]]], 7), [[['1', '1'], ['6', '1'], ['6', '6'], ['1', '6']]])
    check('explicit case 1', solve([[[-2, 1], [3, 1], [3, 4]]], 7), [[['0', '11/5'], ['0', '1'], ['3', '1'], ['3', '4']]])
    check('explicit case 2', solve([[[1, 1], [9, 2], [2, 4]]], 7), [[['1', '1'], ['7', '7/4'], ['7', '18/7'], ['2', '4']]])
    check('explicit case 3', solve([[[-2, -2], [9, -2], [9, 9], [-2, 9]]], 7), [[['0', '7'], ['0', '0'], ['7', '0'], ['7', '7']]])
    check('explicit case 4', solve([[[2, -3], [4, 2], [1, 3]]], 7), [[['3/2', '0'], ['16/5', '0'], ['4', '2'], ['1', '3']]])
    check('explicit case 5', solve([[[-3, 1], [-1, 1], [-2, 3]]], 7), [[]])
    check('explicit case 6', solve([[[0, 1], [0, 3], [-2, 2]]], 7), [[]])
    check('explicit case 7', solve([[[0, 0], [-1, -2], [-2, -1]]], 7), [[]])
    check('explicit case 8', solve([[[1, 1], [8, 1], [1, 10]]], 7), [[['1', '7'], ['1', '1'], ['7', '1'], ['7', '16/7'], ['10/3', '7']]])
    check('explicit case 9', solve([[['1/2', 2], [7, 2], [7, 5]]], 7), [[['1/2', '2'], ['7', '2'], ['7', '5']]])
    check('explicit case 10', solve([[[-2, 2], [2, 1], [0, 3]]], 7), [[['0', '3/2'], ['2', '1'], ['0', '3']]])
    check('explicit case 11', solve([[[3, 1], [9, 3], [7, 4], [6, 1]]], 7), [[['3', '1'], ['7', '7/3'], ['7', '4'], ['6', '1']]])
if N == 3:
    check('explicit case 0', solve([[[1, 1], [7, 1], [7, 7], [1, 7]]], 8), [[['1', '1'], ['7', '1'], ['7', '7'], ['1', '7']]])
    check('explicit case 1', solve([[[-2, 1], [3, 1], [3, 4]]], 8), [[['0', '11/5'], ['0', '1'], ['3', '1'], ['3', '4']]])
    check('explicit case 2', solve([[[1, 1], [10, 2], [2, 4]]], 8), [[['1', '1'], ['8', '16/9'], ['8', '5/2'], ['2', '4']]])
    check('explicit case 3', solve([[[-2, -2], [10, -2], [10, 10], [-2, 10]]], 8), [[['0', '8'], ['0', '0'], ['8', '0'], ['8', '8']]])
    check('explicit case 4', solve([[[2, -3], [4, 2], [1, 3]]], 8), [[['3/2', '0'], ['16/5', '0'], ['4', '2'], ['1', '3']]])
    check('explicit case 5', solve([[[-3, 1], [-1, 1], [-2, 3]]], 8), [[]])
    check('explicit case 6', solve([[[0, 1], [0, 3], [-2, 2]]], 8), [[]])
    check('explicit case 7', solve([[[0, 0], [-1, -2], [-2, -1]]], 8), [[]])
    check('explicit case 8', solve([[[1, 1], [9, 1], [1, 11]]], 8), [[['1', '8'], ['1', '1'], ['8', '1'], ['8', '9/4'], ['17/5', '8']]])
    check('explicit case 9', solve([[['1/2', 2], [8, 2], [8, 5]]], 8), [[['1/2', '2'], ['8', '2'], ['8', '5']]])
    check('explicit case 10', solve([[[-2, 2], [2, 1], [0, 3]]], 8), [[['0', '3/2'], ['2', '1'], ['0', '3']]])
    check('explicit case 11', solve([[[3, 1], [10, 3], [8, 4], [7, 1]]], 8), [[['3', '1'], ['8', '17/7'], ['8', '4'], ['7', '1']]])
if N == 4:
    check('explicit case 0', solve([[[1, 1], [8, 1], [8, 8], [1, 8]]], 9), [[['1', '1'], ['8', '1'], ['8', '8'], ['1', '8']]])
    check('explicit case 1', solve([[[-2, 1], [3, 1], [3, 4]]], 9), [[['0', '11/5'], ['0', '1'], ['3', '1'], ['3', '4']]])
    check('explicit case 2', solve([[[1, 1], [11, 2], [2, 4]]], 9), [[['1', '1'], ['9', '9/5'], ['9', '22/9'], ['2', '4']]])
    check('explicit case 3', solve([[[-2, -2], [11, -2], [11, 11], [-2, 11]]], 9), [[['0', '9'], ['0', '0'], ['9', '0'], ['9', '9']]])
    check('explicit case 4', solve([[[2, -3], [4, 2], [1, 3]]], 9), [[['3/2', '0'], ['16/5', '0'], ['4', '2'], ['1', '3']]])
    check('explicit case 5', solve([[[-3, 1], [-1, 1], [-2, 3]]], 9), [[]])
    check('explicit case 6', solve([[[0, 1], [0, 3], [-2, 2]]], 9), [[]])
    check('explicit case 7', solve([[[0, 0], [-1, -2], [-2, -1]]], 9), [[]])
    check('explicit case 8', solve([[[1, 1], [10, 1], [1, 12]]], 9), [[['1', '9'], ['1', '1'], ['9', '1'], ['9', '20/9'], ['38/11', '9']]])
    check('explicit case 9', solve([[['1/2', 2], [9, 2], [9, 5]]], 9), [[['1/2', '2'], ['9', '2'], ['9', '5']]])
    check('explicit case 10', solve([[[-2, 2], [2, 1], [0, 3]]], 9), [[['0', '3/2'], ['2', '1'], ['0', '3']]])
    check('explicit case 11', solve([[[3, 1], [11, 3], [9, 4], [8, 1]]], 9), [[['3', '1'], ['9', '5/2'], ['9', '4'], ['8', '1']]])
if N == 5:
    check('explicit case 0', solve([[[1, 1], [9, 1], [9, 9], [1, 9]]], 10), [[['1', '1'], ['9', '1'], ['9', '9'], ['1', '9']]])
    check('explicit case 1', solve([[[-2, 1], [3, 1], [3, 4]]], 10), [[['0', '11/5'], ['0', '1'], ['3', '1'], ['3', '4']]])
    check('explicit case 2', solve([[[1, 1], [12, 2], [2, 4]]], 10), [[['1', '1'], ['10', '20/11'], ['10', '12/5'], ['2', '4']]])
    check('explicit case 3', solve([[[-2, -2], [12, -2], [12, 12], [-2, 12]]], 10), [[['0', '10'], ['0', '0'], ['10', '0'], ['10', '10']]])
    check('explicit case 4', solve([[[2, -3], [4, 2], [1, 3]]], 10), [[['3/2', '0'], ['16/5', '0'], ['4', '2'], ['1', '3']]])
    check('explicit case 5', solve([[[-3, 1], [-1, 1], [-2, 3]]], 10), [[]])
    check('explicit case 6', solve([[[0, 1], [0, 3], [-2, 2]]], 10), [[]])
    check('explicit case 7', solve([[[0, 0], [-1, -2], [-2, -1]]], 10), [[]])
    check('explicit case 8', solve([[[1, 1], [11, 1], [1, 13]]], 10), [[['1', '10'], ['1', '1'], ['10', '1'], ['10', '11/5'], ['7/2', '10']]])
    check('explicit case 9', solve([[['1/2', 2], [10, 2], [10, 5]]], 10), [[['1/2', '2'], ['10', '2'], ['10', '5']]])
    check('explicit case 10', solve([[[-2, 2], [2, 1], [0, 3]]], 10), [[['0', '3/2'], ['2', '1'], ['0', '3']]])
    check('explicit case 11', solve([[[3, 1], [12, 3], [10, 4], [9, 1]]], 10), [[['3', '1'], ['10', '23/9'], ['10', '4'], ['9', '1']]])
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
explicit case 0	`[[['1', '1'], ['5', '1'], ['5', '5'], ['1', '5']]]`	`[[['1', '1'], ['5', '1'], ['5', '5'], ['1', '5']]]`	Passed
explicit case 1	`[[['0', '11/5'], ['0', '1'], ['3', '1'], ['3', '4']]]`	`[[['0', '11/5'], ['0', '1'], ['3', '1'], ['3', '4']]]`	Passed
explicit case 2	`[[['1', '1'], ['6', '12/7'], ['6', '8/3'], ['2', '4']]]`	`[[['1', '1'], ['6', '12/7'], ['6', '8/3'], ['2', '4']]]`	Passed
explicit case 3	`[[['0', '6'], ['0', '0'], ['6', '0'], ['6', '6']]]`	`[[['0', '6'], ['0', '0'], ['6', '0'], ['6', '6']]]`	Passed
explicit case 4	`[[['3/2', '0'], ['16/5', '0'], ['4', '2'], ['1', '3']]]`	`[[['3/2', '0'], ['16/5', '0'], ['4', '2'], ['1', '3']]]`	Passed
explicit case 5	`[[]]`	`[[]]`	Passed
explicit case 6	`[[['0', '1'], ['0', '3']]]`	`[[]]`	Failed
explicit case 7	`[[]]`	`[[]]`	Passed
explicit case 8	`[[['1', '6'], ['1', '1'], ['6', '1'], ['6', '7/3'], ['13/4', '6']]]`	`[[['1', '6'], ['1', '1'], ['6', '1'], ['6', '7/3'], ['13/4', '6']]]`	Passed
explicit case 9	`[[['1/2', '2'], ['6', '2'], ['6', '5']]]`	`[[['1/2', '2'], ['6', '2'], ['6', '5']]]`	Passed
explicit case 10	`[[['0', '3/2'], ['2', '1'], ['0', '3']]]`	`[[['0', '3/2'], ['2', '1'], ['0', '3']]]`	Passed
explicit case 11	`[[['3', '1'], ['6', '11/5'], ['6', '4'], ['5', '1']]]`	`[[['3', '1'], ['6', '11/5'], ['6', '4'], ['5', '1']]]`	Passed

SHA-256 / 2bb92b859e439ab3394fc9e6504627c58d4a859a3c2879ba717929411e6d2bfb

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 12 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

Verification & scope

Exact integer/rational arithmetic on small stipulated fixtures models the clipping decision only; no memory layout, GPU pipeline, graphics API or standards conformance 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 2026-09-29T14:45:20.884083+00:00.

Case digest / b5cb16d88b0e65027d2b77f3169d6660c1bbef065e4faf77769f88da28cdc1e2