FA-51836 / Raster clipping / Open access
Circle span scissor: right bound exclusive · case 01
The inclusive right pixel index is used as the exclusive end, dropping the last covered pixel.
ROOT CAUSE
The inclusive right pixel index is used as the exclusive end, dropping the last covered pixel.
THE FAILURE
The inclusive right pixel index is used as the exclusive end, dropping the last covered pixel.
Unsuccessful approach: Folding the half-pixel into the numerator only matches the exclusive end when the root is even.
Case contract
Each command is [cx,cy,r,scissor] for a filled disc centred on the integer pixel-corner point (cx,cy). Pixel (x,y) is covered when its center (x+1/2,y+1/2) lies within the closed disc. Rows of the half-open scissor [left,top,right,bottom) intersected with [0,size) are scanned in order, computing exact integer span bounds with half-pixel doubled coordinates and an integer square root, then clipping to scissor columns. Non-empty spans are [row,start,end).
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 math import isqrt
N = 1
observations = []
def solve(commands, size):
out=[]
for cx,cy,r,clip in commands:
l,t,rr,b=max(clip[0],0),max(clip[1],0),min(clip[2],size),min(clip[3],size)
spans=[]
for y in range(t,b):
m=4*r*r-(2*y+1-2*cy)**2
if m<0: continue
k=isqrt(m)
xa=-((1+k-2*cx)//2)
xb=(2*cx-1+k)//2
xa,xb=max(xa,l),min(xb,rr)
if xa<xb: spans.append([y,xa,xb])
out.append(spans)
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([[3, 3, 2, [0, 0, 6, 6]]], 6), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
check('explicit case 1', solve([[3, 3, 3, [0, 0, 6, 6]]], 6), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
check('explicit case 2', solve([[2, 2, 1, [0, 0, 6, 6]]], 6), [[[1, 1, 3], [2, 1, 3]]])
check('explicit case 3', solve([[3, 3, 3, [1, 1, 6, 5]]], 6), [[[1, 1, 6], [2, 1, 6], [3, 1, 6], [4, 1, 6]]])
check('explicit case 4', solve([[0, 0, 3, [0, 0, 6, 6]]], 6), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
check('explicit case 5', solve([[6, 3, 2, [0, 0, 6, 6]]], 6), [[[1, 5, 6], [2, 4, 6], [3, 4, 6], [4, 5, 6]]])
check('explicit case 6', solve([[4, 2, 4, [2, 0, 6, 4]]], 6), [[[0, 2, 6], [1, 2, 6], [2, 2, 6], [3, 2, 6]]])
check('explicit case 7', solve([[1, 3, 2, [0, 0, 6, 6]]], 6), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
check('explicit case 8', solve([[2, 4, 3, [0, 0, 6, 6]]], 6), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5]]])
check('explicit case 9', solve([[3, 2, 5, [0, 0, 6, 6]]], 6), [[[0, 0, 6], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 0, 6]]])
if N == 2:
check('explicit case 0', solve([[3, 3, 2, [0, 0, 7, 7]]], 7), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
check('explicit case 1', solve([[3, 3, 3, [0, 0, 7, 7]]], 7), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
check('explicit case 2', solve([[2, 2, 1, [0, 0, 7, 7]]], 7), [[[1, 1, 3], [2, 1, 3]]])
check('explicit case 3', solve([[3, 3, 3, [1, 1, 7, 6]]], 7), [[[1, 1, 6], [2, 1, 6], [3, 1, 6], [4, 1, 6], [5, 1, 5]]])
check('explicit case 4', solve([[0, 0, 3, [0, 0, 7, 7]]], 7), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
check('explicit case 5', solve([[7, 3, 2, [0, 0, 7, 7]]], 7), [[[1, 6, 7], [2, 5, 7], [3, 5, 7], [4, 6, 7]]])
check('explicit case 6', solve([[4, 2, 4, [2, 0, 7, 4]]], 7), [[[0, 2, 7], [1, 2, 7], [2, 2, 7], [3, 2, 7]]])
check('explicit case 7', solve([[1, 3, 2, [0, 0, 7, 7]]], 7), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
check('explicit case 8', solve([[2, 4, 3, [0, 0, 7, 7]]], 7), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 4]]])
check('explicit case 9', solve([[3, 2, 5, [0, 0, 7, 7]]], 7), [[[0, 0, 7], [1, 0, 7], [2, 0, 7], [3, 0, 7], [4, 0, 7], [5, 0, 7], [6, 1, 5]]])
if N == 3:
check('explicit case 0', solve([[3, 3, 2, [0, 0, 8, 8]]], 8), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
check('explicit case 1', solve([[3, 3, 3, [0, 0, 8, 8]]], 8), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
check('explicit case 2', solve([[2, 2, 1, [0, 0, 8, 8]]], 8), [[[1, 1, 3], [2, 1, 3]]])
check('explicit case 3', solve([[4, 4, 4, [1, 1, 8, 7]]], 8), [[[1, 1, 7], [2, 1, 8], [3, 1, 8], [4, 1, 8], [5, 1, 8], [6, 1, 7]]])
check('explicit case 4', solve([[0, 0, 3, [0, 0, 8, 8]]], 8), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
check('explicit case 5', solve([[8, 3, 2, [0, 0, 8, 8]]], 8), [[[1, 7, 8], [2, 6, 8], [3, 6, 8], [4, 7, 8]]])
check('explicit case 6', solve([[4, 2, 4, [2, 0, 8, 4]]], 8), [[[0, 2, 8], [1, 2, 8], [2, 2, 8], [3, 2, 8]]])
check('explicit case 7', solve([[1, 3, 2, [0, 0, 8, 8]]], 8), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
check('explicit case 8', solve([[2, 4, 3, [0, 0, 8, 8]]], 8), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 4]]])
check('explicit case 9', solve([[3, 2, 5, [0, 0, 8, 8]]], 8), [[[0, 0, 8], [1, 0, 8], [2, 0, 8], [3, 0, 8], [4, 0, 7], [5, 0, 7], [6, 1, 5]]])
if N == 4:
check('explicit case 0', solve([[3, 3, 2, [0, 0, 9, 9]]], 9), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
check('explicit case 1', solve([[3, 3, 3, [0, 0, 9, 9]]], 9), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
check('explicit case 2', solve([[2, 2, 1, [0, 0, 9, 9]]], 9), [[[1, 1, 3], [2, 1, 3]]])
check('explicit case 3', solve([[4, 4, 4, [1, 1, 9, 8]]], 9), [[[1, 1, 7], [2, 1, 8], [3, 1, 8], [4, 1, 8], [5, 1, 8], [6, 1, 7], [7, 2, 6]]])
check('explicit case 4', solve([[0, 0, 3, [0, 0, 9, 9]]], 9), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
check('explicit case 5', solve([[9, 3, 2, [0, 0, 9, 9]]], 9), [[[1, 8, 9], [2, 7, 9], [3, 7, 9], [4, 8, 9]]])
check('explicit case 6', solve([[4, 2, 4, [2, 0, 9, 4]]], 9), [[[0, 2, 8], [1, 2, 8], [2, 2, 8], [3, 2, 8]]])
check('explicit case 7', solve([[1, 3, 2, [0, 0, 9, 9]]], 9), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
check('explicit case 8', solve([[2, 4, 3, [0, 0, 9, 9]]], 9), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 4]]])
check('explicit case 9', solve([[3, 2, 5, [0, 0, 9, 9]]], 9), [[[0, 0, 8], [1, 0, 8], [2, 0, 8], [3, 0, 8], [4, 0, 7], [5, 0, 7], [6, 1, 5]]])
if N == 5:
check('explicit case 0', solve([[3, 3, 2, [0, 0, 10, 10]]], 10), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
check('explicit case 1', solve([[3, 3, 3, [0, 0, 10, 10]]], 10), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
check('explicit case 2', solve([[2, 2, 1, [0, 0, 10, 10]]], 10), [[[1, 1, 3], [2, 1, 3]]])
check('explicit case 3', solve([[5, 5, 5, [1, 1, 10, 9]]], 10), [[[1, 1, 9], [2, 1, 9], [3, 1, 10], [4, 1, 10], [5, 1, 10], [6, 1, 10], [7, 1, 9], [8, 1, 9]]])
check('explicit case 4', solve([[0, 0, 3, [0, 0, 10, 10]]], 10), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
check('explicit case 5', solve([[10, 3, 2, [0, 0, 10, 10]]], 10), [[[1, 9, 10], [2, 8, 10], [3, 8, 10], [4, 9, 10]]])
check('explicit case 6', solve([[4, 2, 4, [2, 0, 10, 4]]], 10), [[[0, 2, 8], [1, 2, 8], [2, 2, 8], [3, 2, 8]]])
check('explicit case 7', solve([[1, 3, 2, [0, 0, 10, 10]]], 10), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
check('explicit case 8', solve([[2, 4, 3, [0, 0, 10, 10]]], 10), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 4]]])
check('explicit case 9', solve([[3, 2, 5, [0, 0, 10, 10]]], 10), [[[0, 0, 8], [1, 0, 8], [2, 0, 8], [3, 0, 8], [4, 0, 7], [5, 0, 7], [6, 1, 5]]])
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, 2, 3], [2, 1, 4], [3, 1, 4], [4, 2, 3]]] | [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]] | Failed |
| explicit case 1 | [[[0, 1, 4], [1, 0, 5], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 1, 4]]] | [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]] | Failed |
| explicit case 2 | [[[1, 1, 2], [2, 1, 2]]] | [[[1, 1, 3], [2, 1, 3]]] | Failed |
| explicit case 3 | [[[1, 1, 5], [2, 1, 5], [3, 1, 5], [4, 1, 5]]] | [[[1, 1, 6], [2, 1, 6], [3, 1, 6], [4, 1, 6]]] | Failed |
| explicit case 4 | [[[0, 0, 2], [1, 0, 2], [2, 0, 1]]] | [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]] | Failed |
| explicit case 5 | [[[1, 5, 6], [2, 4, 6], [3, 4, 6], [4, 5, 6]]] | [[[1, 5, 6], [2, 4, 6], [3, 4, 6], [4, 5, 6]]] | Passed |
| explicit case 6 | [[[0, 2, 6], [1, 2, 6], [2, 2, 6], [3, 2, 6]]] | [[[0, 2, 6], [1, 2, 6], [2, 2, 6], [3, 2, 6]]] | Passed |
| explicit case 7 | [[[1, 0, 1], [2, 0, 2], [3, 0, 2], [4, 0, 1]]] | [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]] | Failed |
| explicit case 8 | [[[1, 0, 3], [2, 0, 4], [3, 0, 4], [4, 0, 4], [5, 0, 4]]] | [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5]]] | Failed |
| explicit case 9 | [[[0, 0, 6], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 0, 6]]] | [[[0, 0, 6], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 0, 6]]] | Passed |
SHA-256 / 539f28c95f685bd3b2aecabb58aedec9809b0f610c896cf2a146b6b1a630caa6
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from math import isqrt
N = 1
observations = []
def solve(commands, size):
out=[]
for cx,cy,r,clip in commands:
l,t,rr,b=max(clip[0],0),max(clip[1],0),min(clip[2],size),min(clip[3],size)
spans=[]
for y in range(t,b):
m=4*r*r-(2*y+1-2*cy)**2
if m<0: continue
k=isqrt(m)
xa=-((1+k-2*cx)//2)
xb=(2*cx+k)//2
xa,xb=max(xa,l),min(xb,rr)
if xa<xb: spans.append([y,xa,xb])
out.append(spans)
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([[3, 3, 2, [0, 0, 6, 6]]], 6), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
check('explicit case 1', solve([[3, 3, 3, [0, 0, 6, 6]]], 6), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
check('explicit case 2', solve([[2, 2, 1, [0, 0, 6, 6]]], 6), [[[1, 1, 3], [2, 1, 3]]])
check('explicit case 3', solve([[3, 3, 3, [1, 1, 6, 5]]], 6), [[[1, 1, 6], [2, 1, 6], [3, 1, 6], [4, 1, 6]]])
check('explicit case 4', solve([[0, 0, 3, [0, 0, 6, 6]]], 6), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
check('explicit case 5', solve([[6, 3, 2, [0, 0, 6, 6]]], 6), [[[1, 5, 6], [2, 4, 6], [3, 4, 6], [4, 5, 6]]])
check('explicit case 6', solve([[4, 2, 4, [2, 0, 6, 4]]], 6), [[[0, 2, 6], [1, 2, 6], [2, 2, 6], [3, 2, 6]]])
check('explicit case 7', solve([[1, 3, 2, [0, 0, 6, 6]]], 6), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
check('explicit case 8', solve([[2, 4, 3, [0, 0, 6, 6]]], 6), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5]]])
check('explicit case 9', solve([[3, 2, 5, [0, 0, 6, 6]]], 6), [[[0, 0, 6], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 0, 6]]])
if N == 2:
check('explicit case 0', solve([[3, 3, 2, [0, 0, 7, 7]]], 7), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
check('explicit case 1', solve([[3, 3, 3, [0, 0, 7, 7]]], 7), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
check('explicit case 2', solve([[2, 2, 1, [0, 0, 7, 7]]], 7), [[[1, 1, 3], [2, 1, 3]]])
check('explicit case 3', solve([[3, 3, 3, [1, 1, 7, 6]]], 7), [[[1, 1, 6], [2, 1, 6], [3, 1, 6], [4, 1, 6], [5, 1, 5]]])
check('explicit case 4', solve([[0, 0, 3, [0, 0, 7, 7]]], 7), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
check('explicit case 5', solve([[7, 3, 2, [0, 0, 7, 7]]], 7), [[[1, 6, 7], [2, 5, 7], [3, 5, 7], [4, 6, 7]]])
check('explicit case 6', solve([[4, 2, 4, [2, 0, 7, 4]]], 7), [[[0, 2, 7], [1, 2, 7], [2, 2, 7], [3, 2, 7]]])
check('explicit case 7', solve([[1, 3, 2, [0, 0, 7, 7]]], 7), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
check('explicit case 8', solve([[2, 4, 3, [0, 0, 7, 7]]], 7), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 4]]])
check('explicit case 9', solve([[3, 2, 5, [0, 0, 7, 7]]], 7), [[[0, 0, 7], [1, 0, 7], [2, 0, 7], [3, 0, 7], [4, 0, 7], [5, 0, 7], [6, 1, 5]]])
if N == 3:
check('explicit case 0', solve([[3, 3, 2, [0, 0, 8, 8]]], 8), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
check('explicit case 1', solve([[3, 3, 3, [0, 0, 8, 8]]], 8), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
check('explicit case 2', solve([[2, 2, 1, [0, 0, 8, 8]]], 8), [[[1, 1, 3], [2, 1, 3]]])
check('explicit case 3', solve([[4, 4, 4, [1, 1, 8, 7]]], 8), [[[1, 1, 7], [2, 1, 8], [3, 1, 8], [4, 1, 8], [5, 1, 8], [6, 1, 7]]])
check('explicit case 4', solve([[0, 0, 3, [0, 0, 8, 8]]], 8), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
check('explicit case 5', solve([[8, 3, 2, [0, 0, 8, 8]]], 8), [[[1, 7, 8], [2, 6, 8], [3, 6, 8], [4, 7, 8]]])
check('explicit case 6', solve([[4, 2, 4, [2, 0, 8, 4]]], 8), [[[0, 2, 8], [1, 2, 8], [2, 2, 8], [3, 2, 8]]])
check('explicit case 7', solve([[1, 3, 2, [0, 0, 8, 8]]], 8), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
check('explicit case 8', solve([[2, 4, 3, [0, 0, 8, 8]]], 8), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 4]]])
check('explicit case 9', solve([[3, 2, 5, [0, 0, 8, 8]]], 8), [[[0, 0, 8], [1, 0, 8], [2, 0, 8], [3, 0, 8], [4, 0, 7], [5, 0, 7], [6, 1, 5]]])
if N == 4:
check('explicit case 0', solve([[3, 3, 2, [0, 0, 9, 9]]], 9), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
check('explicit case 1', solve([[3, 3, 3, [0, 0, 9, 9]]], 9), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
check('explicit case 2', solve([[2, 2, 1, [0, 0, 9, 9]]], 9), [[[1, 1, 3], [2, 1, 3]]])
check('explicit case 3', solve([[4, 4, 4, [1, 1, 9, 8]]], 9), [[[1, 1, 7], [2, 1, 8], [3, 1, 8], [4, 1, 8], [5, 1, 8], [6, 1, 7], [7, 2, 6]]])
check('explicit case 4', solve([[0, 0, 3, [0, 0, 9, 9]]], 9), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
check('explicit case 5', solve([[9, 3, 2, [0, 0, 9, 9]]], 9), [[[1, 8, 9], [2, 7, 9], [3, 7, 9], [4, 8, 9]]])
check('explicit case 6', solve([[4, 2, 4, [2, 0, 9, 4]]], 9), [[[0, 2, 8], [1, 2, 8], [2, 2, 8], [3, 2, 8]]])
check('explicit case 7', solve([[1, 3, 2, [0, 0, 9, 9]]], 9), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
check('explicit case 8', solve([[2, 4, 3, [0, 0, 9, 9]]], 9), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 4]]])
check('explicit case 9', solve([[3, 2, 5, [0, 0, 9, 9]]], 9), [[[0, 0, 8], [1, 0, 8], [2, 0, 8], [3, 0, 8], [4, 0, 7], [5, 0, 7], [6, 1, 5]]])
if N == 5:
check('explicit case 0', solve([[3, 3, 2, [0, 0, 10, 10]]], 10), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
check('explicit case 1', solve([[3, 3, 3, [0, 0, 10, 10]]], 10), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
check('explicit case 2', solve([[2, 2, 1, [0, 0, 10, 10]]], 10), [[[1, 1, 3], [2, 1, 3]]])
check('explicit case 3', solve([[5, 5, 5, [1, 1, 10, 9]]], 10), [[[1, 1, 9], [2, 1, 9], [3, 1, 10], [4, 1, 10], [5, 1, 10], [6, 1, 10], [7, 1, 9], [8, 1, 9]]])
check('explicit case 4', solve([[0, 0, 3, [0, 0, 10, 10]]], 10), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
check('explicit case 5', solve([[10, 3, 2, [0, 0, 10, 10]]], 10), [[[1, 9, 10], [2, 8, 10], [3, 8, 10], [4, 9, 10]]])
check('explicit case 6', solve([[4, 2, 4, [2, 0, 10, 4]]], 10), [[[0, 2, 8], [1, 2, 8], [2, 2, 8], [3, 2, 8]]])
check('explicit case 7', solve([[1, 3, 2, [0, 0, 10, 10]]], 10), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
check('explicit case 8', solve([[2, 4, 3, [0, 0, 10, 10]]], 10), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 4]]])
check('explicit case 9', solve([[3, 2, 5, [0, 0, 10, 10]]], 10), [[[0, 0, 8], [1, 0, 8], [2, 0, 8], [3, 0, 8], [4, 0, 7], [5, 0, 7], [6, 1, 5]]])
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, 2, 4], [2, 1, 4], [3, 1, 4], [4, 2, 4]]] | [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]] | Failed |
| explicit case 1 | [[[0, 1, 4], [1, 0, 5], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 1, 4]]] | [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]] | Failed |
| explicit case 2 | [[[1, 1, 2], [2, 1, 2]]] | [[[1, 1, 3], [2, 1, 3]]] | Failed |
| explicit case 3 | [[[1, 1, 5], [2, 1, 5], [3, 1, 5], [4, 1, 5]]] | [[[1, 1, 6], [2, 1, 6], [3, 1, 6], [4, 1, 6]]] | Failed |
| explicit case 4 | [[[0, 0, 2], [1, 0, 2], [2, 0, 1]]] | [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]] | Failed |
| explicit case 5 | [[[1, 5, 6], [2, 4, 6], [3, 4, 6], [4, 5, 6]]] | [[[1, 5, 6], [2, 4, 6], [3, 4, 6], [4, 5, 6]]] | Passed |
| explicit case 6 | [[[0, 2, 6], [1, 2, 6], [2, 2, 6], [3, 2, 6]]] | [[[0, 2, 6], [1, 2, 6], [2, 2, 6], [3, 2, 6]]] | Passed |
| explicit case 7 | [[[1, 0, 2], [2, 0, 2], [3, 0, 2], [4, 0, 2]]] | [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]] | Failed |
| explicit case 8 | [[[1, 0, 3], [2, 0, 4], [3, 0, 4], [4, 0, 4], [5, 0, 4]]] | [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5]]] | Failed |
| explicit case 9 | [[[0, 0, 6], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 0, 6]]] | [[[0, 0, 6], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 0, 6]]] | Passed |
SHA-256 / 9e21717e39ab798909cecc48c059e994021d26b5c1d6f775611ecd6845f2d5f8
HELD IN THE MEMBER ARCHIVE
The verified repair and its recorded checks are member-only.
This mechanism has 10 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.
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Sign in to the archive ↗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 2026-09-29T14:45:23.034758+00:00.
Case digest / 49f22d7076c4a7e2ac8a31b2896690eca89b5dd86d561cf93544d982fce7efb1