FAILURE MAP
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FA-88756 / Mesh topology invariants / Open access

UV seam requires both endpoints to differ · case 01

Edges whose UV splits at only one endpoint are not marked as seams.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The comparison demands a mismatch at both vertices.

THE FAILURE

The comparison demands a mismatch at both vertices.

Unsuccessful approach: Comparing only the first endpoint misses splits at the other vertex.

Case contract

Input [faces, uvfaces]: each face has a parallel list of UV indices. A face whose UV list length differs returns ["uv-mismatch", face index]. A geometric edge is a seam when a later face assigns a different UV index to either endpoint than the first face did. Return sorted seam edges [min,max].

Why this case matters

Mesh processing pipelines (remeshing, export, simulation, printing) trust these topological counts and adjacency answers; a wrong invariant silently accepts broken meshes or rejects valid ones.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    faces,uvf=x
    seen={}
    seams=set()
    for fi,(f,t) in enumerate(zip(faces,uvf)):
        if len(f)!=len(t): return ['uv-mismatch',fi]
        n=len(f)
        for i in range(n):
            a,b=f[i],f[(i+1)%n]
            ua,ub=t[i],t[(i+1)%n]
            k=(min(a,b),max(a,b))
            m={a:ua,b:ub}
            if k in seen:
                if seen[k][a]!=m[a] and seen[k][b]!=m[b]: seams.add(k)
            else: seen[k]=m
    return sorted([list(k) for k in seams])
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['shared uv no seam', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [2, 1, 3]]]], []], ['one endpoint split', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [4, 1, 3]]]], [[1, 2]]], ['both endpoints split', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [5, 4, 3]]]], [[1, 2]]], ['swapped uv indices', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [1, 2, 3]]]], [[1, 2]]], ['cube with seams', [[[[0, 3, 2, 1], [4, 5, 6, 7], [0, 1, 5, 4], [1, 2, 6, 5], [2, 3, 7, 6], [3, 0, 4, 7]], [[0, 3, 2, 1], [4, 5, 6, 7], [0, 1, 9, 8], [1, 2, 10, 9], [2, 3, 11, 10], [3, 0, 8, 11]]]], [[4, 5], [4, 7], [5, 6], [6, 7]]], ['length mismatch', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [2, 1]]]], ['uv-mismatch', 1]], ['disk atlas', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], [[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [6, 5, 1]]]], [[0, 1], [0, 5]]]], [['swapped uv indices', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [1, 2, 3]]]], [[1, 2]]], ['cube with seams', [[[[0, 3, 2, 1], [4, 5, 6, 7], [0, 1, 5, 4], [1, 2, 6, 5], [2, 3, 7, 6], [3, 0, 4, 7]], [[0, 3, 2, 1], [4, 5, 6, 7], [0, 1, 9, 8], [1, 2, 10, 9], [2, 3, 11, 10], [3, 0, 8, 11]]]], [[4, 5], [4, 7], [5, 6], [6, 7]]], ['length mismatch', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [2, 1]]]], ['uv-mismatch', 1]], ['extra uv corner', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2, 7], [2, 1, 3]]]], ['uv-mismatch', 0]], ['quad strip', [[[[0, 1, 4, 3], [1, 2, 5, 4]], [[0, 1, 4, 3], [1, 2, 5, 4]]]], []], ['quad strip split', [[[[0, 1, 4, 3], [1, 2, 5, 4]], [[0, 1, 4, 3], [6, 2, 5, 7]]]], [[1, 4]]], ['disk atlas', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], [[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [6, 5, 1]]]], [[0, 1], [0, 5]]]], [['shared uv no seam', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [2, 1, 3]]]], []], ['one endpoint split', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [4, 1, 3]]]], [[1, 2]]], ['quad strip', [[[[0, 1, 4, 3], [1, 2, 5, 4]], [[0, 1, 4, 3], [1, 2, 5, 4]]]], []], ['quad strip split', [[[[0, 1, 4, 3], [1, 2, 5, 4]], [[0, 1, 4, 3], [6, 2, 5, 7]]]], [[1, 4]]], ['disk atlas', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], [[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [6, 5, 1]]]], [[0, 1], [0, 5]]], ['mismatch after seams', [[[[0, 1, 2], [2, 1, 3], [3, 1, 4]], [[0, 1, 2], [5, 1, 3], [3, 1]]]], ['uv-mismatch', 2]], ['same uv sum collision', [[[[0, 3, 1], [1, 3, 2]], [[0, 3, 1], [1, 3, 2]]]], []]], [['shared uv no seam', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [2, 1, 3]]]], []], ['one endpoint split', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [4, 1, 3]]]], [[1, 2]]], ['both endpoints split', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [5, 4, 3]]]], [[1, 2]]], ['swapped uv indices', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [1, 2, 3]]]], [[1, 2]]], ['disk atlas', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], [[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [6, 5, 1]]]], [[0, 1], [0, 5]]], ['mismatch after seams', [[[[0, 1, 2], [2, 1, 3], [3, 1, 4]], [[0, 1, 2], [5, 1, 3], [3, 1]]]], ['uv-mismatch', 2]], ['same uv sum collision', [[[[0, 3, 1], [1, 3, 2]], [[0, 3, 1], [1, 3, 2]]]], []]], [['one endpoint split', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [4, 1, 3]]]], [[1, 2]]], ['swapped uv indices', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [1, 2, 3]]]], [[1, 2]]], ['cube with seams', [[[[0, 3, 2, 1], [4, 5, 6, 7], [0, 1, 5, 4], [1, 2, 6, 5], [2, 3, 7, 6], [3, 0, 4, 7]], [[0, 3, 2, 1], [4, 5, 6, 7], [0, 1, 9, 8], [1, 2, 10, 9], [2, 3, 11, 10], [3, 0, 8, 11]]]], [[4, 5], [4, 7], [5, 6], [6, 7]]], ['length mismatch', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [2, 1]]]], ['uv-mismatch', 1]], ['extra uv corner', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2, 7], [2, 1, 3]]]], ['uv-mismatch', 0]], ['quad strip', [[[[0, 1, 4, 3], [1, 2, 5, 4]], [[0, 1, 4, 3], [1, 2, 5, 4]]]], []], ['disk atlas', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], [[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [6, 5, 1]]]], [[0, 1], [0, 5]]]]]
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 fixtureActualExpectedOutcome
shared uv no seam[][]Passed
one endpoint split[][[1, 2]]Failed
both endpoints split[[1, 2]][[1, 2]]Passed
swapped uv indices[[1, 2]][[1, 2]]Passed
cube with seams[[4, 5], [4, 7], [5, 6], [6, 7]][[4, 5], [4, 7], [5, 6], [6, 7]]Passed
length mismatch['uv-mismatch', 1]['uv-mismatch', 1]Passed
disk atlas[][[0, 1], [0, 5]]Failed

SHA-256 / 17958d86891e80d44cdcd88bebb3e162a22f3dfd5823c0875f06bb4a974a600a

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    faces,uvf=x
    seen={}
    seams=set()
    for fi,(f,t) in enumerate(zip(faces,uvf)):
        if len(f)!=len(t): return ['uv-mismatch',fi]
        n=len(f)
        for i in range(n):
            a,b=f[i],f[(i+1)%n]
            ua,ub=t[i],t[(i+1)%n]
            k=(min(a,b),max(a,b))
            m={a:ua,b:ub}
            if k in seen:
                if seen[k][a]!=m[a]: seams.add(k)
            else: seen[k]=m
    return sorted([list(k) for k in seams])
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['shared uv no seam', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [2, 1, 3]]]], []], ['one endpoint split', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [4, 1, 3]]]], [[1, 2]]], ['both endpoints split', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [5, 4, 3]]]], [[1, 2]]], ['swapped uv indices', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [1, 2, 3]]]], [[1, 2]]], ['cube with seams', [[[[0, 3, 2, 1], [4, 5, 6, 7], [0, 1, 5, 4], [1, 2, 6, 5], [2, 3, 7, 6], [3, 0, 4, 7]], [[0, 3, 2, 1], [4, 5, 6, 7], [0, 1, 9, 8], [1, 2, 10, 9], [2, 3, 11, 10], [3, 0, 8, 11]]]], [[4, 5], [4, 7], [5, 6], [6, 7]]], ['length mismatch', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [2, 1]]]], ['uv-mismatch', 1]], ['disk atlas', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], [[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [6, 5, 1]]]], [[0, 1], [0, 5]]]], [['swapped uv indices', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [1, 2, 3]]]], [[1, 2]]], ['cube with seams', [[[[0, 3, 2, 1], [4, 5, 6, 7], [0, 1, 5, 4], [1, 2, 6, 5], [2, 3, 7, 6], [3, 0, 4, 7]], [[0, 3, 2, 1], [4, 5, 6, 7], [0, 1, 9, 8], [1, 2, 10, 9], [2, 3, 11, 10], [3, 0, 8, 11]]]], [[4, 5], [4, 7], [5, 6], [6, 7]]], ['length mismatch', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [2, 1]]]], ['uv-mismatch', 1]], ['extra uv corner', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2, 7], [2, 1, 3]]]], ['uv-mismatch', 0]], ['quad strip', [[[[0, 1, 4, 3], [1, 2, 5, 4]], [[0, 1, 4, 3], [1, 2, 5, 4]]]], []], ['quad strip split', [[[[0, 1, 4, 3], [1, 2, 5, 4]], [[0, 1, 4, 3], [6, 2, 5, 7]]]], [[1, 4]]], ['disk atlas', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], [[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [6, 5, 1]]]], [[0, 1], [0, 5]]]], [['shared uv no seam', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [2, 1, 3]]]], []], ['one endpoint split', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [4, 1, 3]]]], [[1, 2]]], ['quad strip', [[[[0, 1, 4, 3], [1, 2, 5, 4]], [[0, 1, 4, 3], [1, 2, 5, 4]]]], []], ['quad strip split', [[[[0, 1, 4, 3], [1, 2, 5, 4]], [[0, 1, 4, 3], [6, 2, 5, 7]]]], [[1, 4]]], ['disk atlas', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], [[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [6, 5, 1]]]], [[0, 1], [0, 5]]], ['mismatch after seams', [[[[0, 1, 2], [2, 1, 3], [3, 1, 4]], [[0, 1, 2], [5, 1, 3], [3, 1]]]], ['uv-mismatch', 2]], ['same uv sum collision', [[[[0, 3, 1], [1, 3, 2]], [[0, 3, 1], [1, 3, 2]]]], []]], [['shared uv no seam', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [2, 1, 3]]]], []], ['one endpoint split', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [4, 1, 3]]]], [[1, 2]]], ['both endpoints split', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [5, 4, 3]]]], [[1, 2]]], ['swapped uv indices', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [1, 2, 3]]]], [[1, 2]]], ['disk atlas', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], [[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [6, 5, 1]]]], [[0, 1], [0, 5]]], ['mismatch after seams', [[[[0, 1, 2], [2, 1, 3], [3, 1, 4]], [[0, 1, 2], [5, 1, 3], [3, 1]]]], ['uv-mismatch', 2]], ['same uv sum collision', [[[[0, 3, 1], [1, 3, 2]], [[0, 3, 1], [1, 3, 2]]]], []]], [['one endpoint split', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [4, 1, 3]]]], [[1, 2]]], ['swapped uv indices', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [1, 2, 3]]]], [[1, 2]]], ['cube with seams', [[[[0, 3, 2, 1], [4, 5, 6, 7], [0, 1, 5, 4], [1, 2, 6, 5], [2, 3, 7, 6], [3, 0, 4, 7]], [[0, 3, 2, 1], [4, 5, 6, 7], [0, 1, 9, 8], [1, 2, 10, 9], [2, 3, 11, 10], [3, 0, 8, 11]]]], [[4, 5], [4, 7], [5, 6], [6, 7]]], ['length mismatch', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2], [2, 1]]]], ['uv-mismatch', 1]], ['extra uv corner', [[[[0, 1, 2], [2, 1, 3]], [[0, 1, 2, 7], [2, 1, 3]]]], ['uv-mismatch', 0]], ['quad strip', [[[[0, 1, 4, 3], [1, 2, 5, 4]], [[0, 1, 4, 3], [1, 2, 5, 4]]]], []], ['disk atlas', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], [[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [6, 5, 1]]]], [[0, 1], [0, 5]]]]]
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 fixtureActualExpectedOutcome
shared uv no seam[][]Passed
one endpoint split[[1, 2]][[1, 2]]Passed
both endpoints split[[1, 2]][[1, 2]]Passed
swapped uv indices[[1, 2]][[1, 2]]Passed
cube with seams[[4, 5], [4, 7], [5, 6], [6, 7]][[4, 5], [4, 7], [5, 6], [6, 7]]Passed
length mismatch['uv-mismatch', 1]['uv-mismatch', 1]Passed
disk atlas[[0, 5]][[0, 1], [0, 5]]Failed

SHA-256 / 529cf8a83a554ec1de58a4c5c0973891c6c5616769c72872a42dc92016a36c18

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 7 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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Verification & scope

Pure combinatorial teaching model over integer face lists with a stipulated contract; no geometry kernel or file format is implied. 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 2026-09-29T14:51:11.029490+00:00.

Case digest / 1ce9fc152dc113fc1bb7ac00f64e562dca3b225aab8deaf922b2c779ee7eaeb1