FA-50991 / Raster clipping / Open access
Homogeneous segment clip: inside shortcut · case 01
The all-inside fast path accepts a segment with one exterior endpoint.
ROOT CAUSE
The all-inside fast path accepts a segment with one exterior endpoint.
VERIFIED REPAIR
Apply the documented state transition at inside shortcut. Clip ordered segments in homogeneous (x,w,u) coordinates against requested left x+w>=0, right w-x>=0 and eye w>=1 halfspaces. Interpolate every component at intersections before perspective division; retain endpoint order. Output exact rational strings, or null for rejected segments. The integer surface size scales horizontal halfspaces.
Unsuccessful approach: Stopping after one satisfied plane skips later planes that may reject the segment.
Case contract
Clip ordered segments in homogeneous (x,w,u) coordinates against requested left x+w>=0, right w-x>=0 and eye w>=1 halfspaces. Interpolate every component at intersections before perspective division; retain endpoint order. Output exact rational strings, or null for rejected segments. The integer surface size scales horizontal halfspaces.
Why this case matters
Raster clip state can leak coverage across draws even when every individual region is valid.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(commands, size):
from fractions import Fraction
out=[]
for first,last,planes in commands:
a=list(map(Fraction,first)); b=list(map(Fraction,last))
original_a=list(a); original_b=list(b)
rejected=False
for plane in planes:
def distance(p):
if plane=='left': return p[0]+size*p[1]
if plane=='right': return size*p[1]-p[0]
return p[1]-1
da=distance(a); db=distance(b)
ia=da>=0; ib=db>=0
if not ia and not ib: rejected=True; break
if ia or ib: continue
t=da/(da-db)
point=[a[i]+t*(b[i]-a[i]) for i in range(3)]
if not ia: a=point
else: b=point
out.append(None if rejected else [[str(v) for v in a],[str(v) for v in b]])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 4), [[['-4', '1', '8'], ['0', '1', '12']]])
check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 4), [[['0', '1', '0'], ['4', '1', '4']]])
check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 4), [None])
check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 4), [[['-4', '1', '0'], ['-8', '2', '8']]])
check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 4), [[['0', '1', '5'], ['0', '2', '10']]])
check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 4), [[['-4', '1', '8'], ['4', '1', '16']]])
check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 4), [[['0', '1', '0'], ['4', '1', '4']]])
check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 4), [[['0', '1', '0'], ['1', '1', '1']]])
check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 4), [[['0', '1', '12'], ['6', '3/2', '18']]])
check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 4), [None])
check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 4), [[['0', '1', '1'], ['0', '1', '1']]])
check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 4), [[['0', '1', '12'], ['40/9', '10/9', '40/3']]])
if N == 2:
check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 5), [[['-5', '1', '7'], ['0', '1', '12']]])
check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 5), [[['0', '1', '0'], ['5', '1', '5']]])
check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 5), [None])
check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 5), [[['-4', '1', '0'], ['-8', '2', '8']]])
check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 5), [[['0', '1', '5'], ['0', '2', '10']]])
check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 5), [[['-5', '1', '7'], ['5', '1', '17']]])
check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 5), [[['0', '1', '0'], ['5', '1', '5']]])
check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 5), [[['0', '1', '0'], ['1', '1', '1']]])
check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 5), [[['0', '1', '12'], ['60/7', '12/7', '144/7']]])
check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 5), [None])
check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 5), [[['0', '1', '1'], ['0', '1', '1']]])
check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 5), [[['0', '1', '12'], ['40/7', '8/7', '96/7']]])
if N == 3:
check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 6), [[['-6', '1', '6'], ['0', '1', '12']]])
check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 6), [[['0', '1', '0'], ['6', '1', '6']]])
check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 6), [None])
check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 6), [[['-4', '1', '0'], ['-8', '2', '8']]])
check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 6), [[['0', '1', '5'], ['0', '2', '10']]])
check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 6), [[['-6', '1', '6'], ['6', '1', '18']]])
check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 6), [[['0', '1', '0'], ['6', '1', '6']]])
check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 6), [[['0', '1', '0'], ['1', '1', '1']]])
check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 6), [[['0', '1', '12'], ['12', '2', '24']]])
check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 6), [None])
check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 6), [[['0', '1', '1'], ['0', '1', '1']]])
check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 6), [[['0', '1', '12'], ['120/17', '20/17', '240/17']]])
if N == 4:
check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 7), [[['-7', '1', '5'], ['0', '1', '12']]])
check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 7), [[['0', '1', '0'], ['7', '1', '7']]])
check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 7), [None])
check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 7), [[['-4', '1', '0'], ['-8', '2', '8']]])
check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 7), [[['0', '1', '5'], ['0', '2', '10']]])
check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 7), [[['-7', '1', '5'], ['7', '1', '19']]])
check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 7), [[['0', '1', '0'], ['7', '1', '7']]])
check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 7), [[['0', '1', '0'], ['1', '1', '1']]])
check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 7), [[['0', '1', '12'], ['12', '2', '24']]])
check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 7), [None])
check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 7), [[['0', '1', '1'], ['0', '1', '1']]])
check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 7), [[['0', '1', '12'], ['280/33', '40/33', '160/11']]])
if N == 5:
check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 8), [[['-8', '1', '4'], ['0', '1', '12']]])
check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 8), [[['0', '1', '0'], ['8', '1', '8']]])
check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 8), [None])
check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 8), [[['-4', '1', '0'], ['-8', '2', '8']]])
check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 8), [[['0', '1', '5'], ['0', '2', '10']]])
check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 8), [[['-8', '1', '4'], ['8', '1', '20']]])
check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 8), [[['0', '1', '0'], ['8', '1', '8']]])
check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 8), [[['0', '1', '0'], ['1', '1', '1']]])
check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 8), [[['0', '1', '12'], ['12', '2', '24']]])
check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 8), [None])
check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 8), [[['0', '1', '1'], ['0', '1', '1']]])
check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 8), [[['0', '1', '12'], ['10', '5/4', '15']]])
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 sequence 0 | [[['-12', '1', '0'], ['0', '1', '12']]] | [[['-4', '1', '8'], ['0', '1', '12']]] | Failed |
| explicit sequence 1 | [[['0', '1', '0'], ['12', '1', '12']]] | [[['0', '1', '0'], ['4', '1', '4']]] | Failed |
| explicit sequence 2 | [None] | [None] | Passed |
| explicit sequence 3 | [[['-4', '1', '0'], ['-8', '2', '8']]] | [[['-4', '1', '0'], ['-8', '2', '8']]] | Passed |
| explicit sequence 4 | [[['0', '0', '0'], ['0', '2', '10']]] | [[['0', '1', '5'], ['0', '2', '10']]] | Failed |
| explicit sequence 5 | [[['-12', '1', '0'], ['12', '1', '24']]] | [[['-4', '1', '8'], ['4', '1', '16']]] | Failed |
| explicit sequence 6 | [[['0', '1', '0'], ['12', '1', '12']]] | [[['0', '1', '0'], ['4', '1', '4']]] | Failed |
| explicit sequence 7 | [[['0', '1', '0'], ['1', '1', '1']]] | [[['0', '1', '0'], ['1', '1', '1']]] | Passed |
| explicit sequence 8 | [[['-12', '0', '0'], ['12', '2', '24']]] | [[['0', '1', '12'], ['6', '3/2', '18']]] | Failed |
| explicit sequence 9 | [None] | [None] | Passed |
| explicit sequence 10 | [[['0', '0', '0'], ['0', '1', '1']]] | [[['0', '1', '1'], ['0', '1', '1']]] | Failed |
| explicit sequence 11 | [[['-40', '0', '0'], ['40', '2', '24']]] | [[['0', '1', '12'], ['40/9', '10/9', '40/3']]] | Failed |
SHA-256 / 59973e7d19f8896506e69298932980b271244ca88f776ef2551a3a16f70086b7
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(commands, size):
from fractions import Fraction
out=[]
for first,last,planes in commands:
a=list(map(Fraction,first)); b=list(map(Fraction,last))
original_a=list(a); original_b=list(b)
rejected=False
for plane in planes:
def distance(p):
if plane=='left': return p[0]+size*p[1]
if plane=='right': return size*p[1]-p[0]
return p[1]-1
da=distance(a); db=distance(b)
ia=da>=0; ib=db>=0
if not ia and not ib: rejected=True; break
if ia and ib: break
t=da/(da-db)
point=[a[i]+t*(b[i]-a[i]) for i in range(3)]
if not ia: a=point
else: b=point
out.append(None if rejected else [[str(v) for v in a],[str(v) for v in b]])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 4), [[['-4', '1', '8'], ['0', '1', '12']]])
check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 4), [[['0', '1', '0'], ['4', '1', '4']]])
check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 4), [None])
check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 4), [[['-4', '1', '0'], ['-8', '2', '8']]])
check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 4), [[['0', '1', '5'], ['0', '2', '10']]])
check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 4), [[['-4', '1', '8'], ['4', '1', '16']]])
check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 4), [[['0', '1', '0'], ['4', '1', '4']]])
check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 4), [[['0', '1', '0'], ['1', '1', '1']]])
check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 4), [[['0', '1', '12'], ['6', '3/2', '18']]])
check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 4), [None])
check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 4), [[['0', '1', '1'], ['0', '1', '1']]])
check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 4), [[['0', '1', '12'], ['40/9', '10/9', '40/3']]])
if N == 2:
check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 5), [[['-5', '1', '7'], ['0', '1', '12']]])
check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 5), [[['0', '1', '0'], ['5', '1', '5']]])
check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 5), [None])
check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 5), [[['-4', '1', '0'], ['-8', '2', '8']]])
check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 5), [[['0', '1', '5'], ['0', '2', '10']]])
check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 5), [[['-5', '1', '7'], ['5', '1', '17']]])
check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 5), [[['0', '1', '0'], ['5', '1', '5']]])
check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 5), [[['0', '1', '0'], ['1', '1', '1']]])
check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 5), [[['0', '1', '12'], ['60/7', '12/7', '144/7']]])
check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 5), [None])
check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 5), [[['0', '1', '1'], ['0', '1', '1']]])
check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 5), [[['0', '1', '12'], ['40/7', '8/7', '96/7']]])
if N == 3:
check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 6), [[['-6', '1', '6'], ['0', '1', '12']]])
check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 6), [[['0', '1', '0'], ['6', '1', '6']]])
check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 6), [None])
check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 6), [[['-4', '1', '0'], ['-8', '2', '8']]])
check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 6), [[['0', '1', '5'], ['0', '2', '10']]])
check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 6), [[['-6', '1', '6'], ['6', '1', '18']]])
check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 6), [[['0', '1', '0'], ['6', '1', '6']]])
check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 6), [[['0', '1', '0'], ['1', '1', '1']]])
check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 6), [[['0', '1', '12'], ['12', '2', '24']]])
check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 6), [None])
check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 6), [[['0', '1', '1'], ['0', '1', '1']]])
check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 6), [[['0', '1', '12'], ['120/17', '20/17', '240/17']]])
if N == 4:
check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 7), [[['-7', '1', '5'], ['0', '1', '12']]])
check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 7), [[['0', '1', '0'], ['7', '1', '7']]])
check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 7), [None])
check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 7), [[['-4', '1', '0'], ['-8', '2', '8']]])
check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 7), [[['0', '1', '5'], ['0', '2', '10']]])
check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 7), [[['-7', '1', '5'], ['7', '1', '19']]])
check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 7), [[['0', '1', '0'], ['7', '1', '7']]])
check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 7), [[['0', '1', '0'], ['1', '1', '1']]])
check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 7), [[['0', '1', '12'], ['12', '2', '24']]])
check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 7), [None])
check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 7), [[['0', '1', '1'], ['0', '1', '1']]])
check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 7), [[['0', '1', '12'], ['280/33', '40/33', '160/11']]])
if N == 5:
check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 8), [[['-8', '1', '4'], ['0', '1', '12']]])
check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 8), [[['0', '1', '0'], ['8', '1', '8']]])
check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 8), [None])
check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 8), [[['-4', '1', '0'], ['-8', '2', '8']]])
check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 8), [[['0', '1', '5'], ['0', '2', '10']]])
check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 8), [[['-8', '1', '4'], ['8', '1', '20']]])
check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 8), [[['0', '1', '0'], ['8', '1', '8']]])
check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 8), [[['0', '1', '0'], ['1', '1', '1']]])
check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 8), [[['0', '1', '12'], ['12', '2', '24']]])
check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 8), [None])
check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 8), [[['0', '1', '1'], ['0', '1', '1']]])
check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 8), [[['0', '1', '12'], ['10', '5/4', '15']]])
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 sequence 0 | [[['-4', '1', '8'], ['0', '1', '12']]] | [[['-4', '1', '8'], ['0', '1', '12']]] | Passed |
| explicit sequence 1 | [[['0', '1', '0'], ['4', '1', '4']]] | [[['0', '1', '0'], ['4', '1', '4']]] | Passed |
| explicit sequence 2 | [None] | [None] | Passed |
| explicit sequence 3 | [[['-4', '1', '0'], ['-8', '2', '8']]] | [[['-4', '1', '0'], ['-8', '2', '8']]] | Passed |
| explicit sequence 4 | [[['0', '1', '5'], ['0', '2', '10']]] | [[['0', '1', '5'], ['0', '2', '10']]] | Passed |
| explicit sequence 5 | [[['-4', '1', '8'], ['4', '1', '16']]] | [[['-4', '1', '8'], ['4', '1', '16']]] | Passed |
| explicit sequence 6 | [[['0', '1', '0'], ['12', '1', '12']]] | [[['0', '1', '0'], ['4', '1', '4']]] | Failed |
| explicit sequence 7 | [[['0', '1', '0'], ['1', '1', '1']]] | [[['0', '1', '0'], ['1', '1', '1']]] | Passed |
| explicit sequence 8 | [[['0', '1', '12'], ['6', '3/2', '18']]] | [[['0', '1', '12'], ['6', '3/2', '18']]] | Passed |
| explicit sequence 9 | [None] | [None] | Passed |
| explicit sequence 10 | [[['0', '1', '1'], ['0', '1', '1']]] | [[['0', '1', '1'], ['0', '1', '1']]] | Passed |
| explicit sequence 11 | [[['0', '1', '12'], ['40/9', '10/9', '40/3']]] | [[['0', '1', '12'], ['40/9', '10/9', '40/3']]] | Passed |
SHA-256 / 88fc5cc6dfdb326115223b40bd1248e5cdc97e802edef49911a6bdadfbb2cfe2
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(commands, size):
from fractions import Fraction
out=[]
for first,last,planes in commands:
a=list(map(Fraction,first)); b=list(map(Fraction,last))
original_a=list(a); original_b=list(b)
rejected=False
for plane in planes:
def distance(p):
if plane=='left': return p[0]+size*p[1]
if plane=='right': return size*p[1]-p[0]
return p[1]-1
da=distance(a); db=distance(b)
ia=da>=0; ib=db>=0
if not ia and not ib: rejected=True; break
if ia and ib: continue
t=da/(da-db)
point=[a[i]+t*(b[i]-a[i]) for i in range(3)]
if not ia: a=point
else: b=point
out.append(None if rejected else [[str(v) for v in a],[str(v) for v in b]])
return out
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 4), [[['-4', '1', '8'], ['0', '1', '12']]])
check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 4), [[['0', '1', '0'], ['4', '1', '4']]])
check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 4), [None])
check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 4), [[['-4', '1', '0'], ['-8', '2', '8']]])
check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 4), [[['0', '1', '5'], ['0', '2', '10']]])
check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 4), [[['-4', '1', '8'], ['4', '1', '16']]])
check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 4), [[['0', '1', '0'], ['4', '1', '4']]])
check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 4), [[['0', '1', '0'], ['1', '1', '1']]])
check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 4), [[['0', '1', '12'], ['6', '3/2', '18']]])
check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 4), [None])
check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 4), [[['0', '1', '1'], ['0', '1', '1']]])
check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 4), [[['0', '1', '12'], ['40/9', '10/9', '40/3']]])
if N == 2:
check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 5), [[['-5', '1', '7'], ['0', '1', '12']]])
check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 5), [[['0', '1', '0'], ['5', '1', '5']]])
check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 5), [None])
check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 5), [[['-4', '1', '0'], ['-8', '2', '8']]])
check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 5), [[['0', '1', '5'], ['0', '2', '10']]])
check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 5), [[['-5', '1', '7'], ['5', '1', '17']]])
check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 5), [[['0', '1', '0'], ['5', '1', '5']]])
check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 5), [[['0', '1', '0'], ['1', '1', '1']]])
check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 5), [[['0', '1', '12'], ['60/7', '12/7', '144/7']]])
check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 5), [None])
check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 5), [[['0', '1', '1'], ['0', '1', '1']]])
check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 5), [[['0', '1', '12'], ['40/7', '8/7', '96/7']]])
if N == 3:
check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 6), [[['-6', '1', '6'], ['0', '1', '12']]])
check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 6), [[['0', '1', '0'], ['6', '1', '6']]])
check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 6), [None])
check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 6), [[['-4', '1', '0'], ['-8', '2', '8']]])
check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 6), [[['0', '1', '5'], ['0', '2', '10']]])
check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 6), [[['-6', '1', '6'], ['6', '1', '18']]])
check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 6), [[['0', '1', '0'], ['6', '1', '6']]])
check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 6), [[['0', '1', '0'], ['1', '1', '1']]])
check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 6), [[['0', '1', '12'], ['12', '2', '24']]])
check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 6), [None])
check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 6), [[['0', '1', '1'], ['0', '1', '1']]])
check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 6), [[['0', '1', '12'], ['120/17', '20/17', '240/17']]])
if N == 4:
check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 7), [[['-7', '1', '5'], ['0', '1', '12']]])
check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 7), [[['0', '1', '0'], ['7', '1', '7']]])
check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 7), [None])
check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 7), [[['-4', '1', '0'], ['-8', '2', '8']]])
check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 7), [[['0', '1', '5'], ['0', '2', '10']]])
check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 7), [[['-7', '1', '5'], ['7', '1', '19']]])
check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 7), [[['0', '1', '0'], ['7', '1', '7']]])
check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 7), [[['0', '1', '0'], ['1', '1', '1']]])
check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 7), [[['0', '1', '12'], ['12', '2', '24']]])
check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 7), [None])
check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 7), [[['0', '1', '1'], ['0', '1', '1']]])
check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 7), [[['0', '1', '12'], ['280/33', '40/33', '160/11']]])
if N == 5:
check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 8), [[['-8', '1', '4'], ['0', '1', '12']]])
check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 8), [[['0', '1', '0'], ['8', '1', '8']]])
check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 8), [None])
check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 8), [[['-4', '1', '0'], ['-8', '2', '8']]])
check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 8), [[['0', '1', '5'], ['0', '2', '10']]])
check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 8), [[['-8', '1', '4'], ['8', '1', '20']]])
check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 8), [[['0', '1', '0'], ['8', '1', '8']]])
check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 8), [[['0', '1', '0'], ['1', '1', '1']]])
check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 8), [[['0', '1', '12'], ['12', '2', '24']]])
check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 8), [None])
check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 8), [[['0', '1', '1'], ['0', '1', '1']]])
check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 8), [[['0', '1', '12'], ['10', '5/4', '15']]])
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 sequence 0 | [[['-4', '1', '8'], ['0', '1', '12']]] | [[['-4', '1', '8'], ['0', '1', '12']]] | Passed |
| explicit sequence 1 | [[['0', '1', '0'], ['4', '1', '4']]] | [[['0', '1', '0'], ['4', '1', '4']]] | Passed |
| explicit sequence 2 | [None] | [None] | Passed |
| explicit sequence 3 | [[['-4', '1', '0'], ['-8', '2', '8']]] | [[['-4', '1', '0'], ['-8', '2', '8']]] | Passed |
| explicit sequence 4 | [[['0', '1', '5'], ['0', '2', '10']]] | [[['0', '1', '5'], ['0', '2', '10']]] | Passed |
| explicit sequence 5 | [[['-4', '1', '8'], ['4', '1', '16']]] | [[['-4', '1', '8'], ['4', '1', '16']]] | Passed |
| explicit sequence 6 | [[['0', '1', '0'], ['4', '1', '4']]] | [[['0', '1', '0'], ['4', '1', '4']]] | Passed |
| explicit sequence 7 | [[['0', '1', '0'], ['1', '1', '1']]] | [[['0', '1', '0'], ['1', '1', '1']]] | Passed |
| explicit sequence 8 | [[['0', '1', '12'], ['6', '3/2', '18']]] | [[['0', '1', '12'], ['6', '3/2', '18']]] | Passed |
| explicit sequence 9 | [None] | [None] | Passed |
| explicit sequence 10 | [[['0', '1', '1'], ['0', '1', '1']]] | [[['0', '1', '1'], ['0', '1', '1']]] | Passed |
| explicit sequence 11 | [[['0', '1', '12'], ['40/9', '10/9', '40/3']]] | [[['0', '1', '12'], ['40/9', '10/9', '40/3']]] | Passed |
SHA-256 / 551181ac5740f2507d9332ca503db85d2645c36fd736ab690694549542774375
Verification & scope
Finite one-dimensional integer sample sets model coverage state only; no geometric intersection, memory layout, GPU or graphics-standard 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 2026-09-29T14:45:14.507105+00:00.
Case digest / 4696852ef93b68c2be570dd47ed48aa3255e9335ea13fe6e07f9cf67c3966498