FA-99501 / Vector retrieval ranking / Open access

Vector retrieval: A radius query includes points beyond the radius · case 01

A radius query includes points beyond the radius.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The radius test selects outside points or expands the boundary.

THE FAILURE

The radius test selects outside points or expands the boundary.

Unsuccessful approach: An expanded radius admits an out-of-range point.

Case contract

Given [id,distance] and radius, retain distance <= radius in nearest-first order.

Why this case matters

An offline vector retrieval toy model isolates one ranking contract from embedding generation, storage, and serving.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(rows, radius):
    return [r[0] for r in sorted(rows,key=lambda r:r[1]) if r[1]>=radius]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('inside and outside',solve([['in',N-1],['out',N+1]],N),['in'])
check('boundary included',solve([['edge',N]],N),['edge'])
check('origin',solve([['zero',0],['far',N+2]],0),['zero'])
check('none',solve([['x',N+1]],N),[])
check('multiple sorted',solve([['b',N-1],['a',N-2],['c',N+2]],N),['a','b'])
check('empty',solve([],N),[])
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
inside and outside	`['out']`	`['in']`	Failed
boundary included	`['edge']`	`['edge']`	Passed
origin	`['zero', 'far']`	`['zero']`	Failed
none	`['x']`	`[]`	Failed
multiple sorted	`['c']`	`['a', 'b']`	Failed
empty	`[]`	`[]`	Passed

SHA-256 / 0ad5b109c81bf0ac4e9866139cfb8b285e2a677848c78539cb7c005c9ed506b0

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(rows, radius):
    return [r[0] for r in sorted(rows,key=lambda r:r[1]) if r[1]<radius]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('inside and outside',solve([['in',N-1],['out',N+1]],N),['in'])
check('boundary included',solve([['edge',N]],N),['edge'])
check('origin',solve([['zero',0],['far',N+2]],0),['zero'])
check('none',solve([['x',N+1]],N),[])
check('multiple sorted',solve([['b',N-1],['a',N-2],['c',N+2]],N),['a','b'])
check('empty',solve([],N),[])
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
inside and outside	`['in']`	`['in']`	Passed
boundary included	`[]`	`['edge']`	Failed
origin	`[]`	`['zero']`	Failed
none	`[]`	`[]`	Passed
multiple sorted	`['a', 'b']`	`['a', 'b']`	Passed
empty	`[]`	`[]`	Passed

SHA-256 / 8bf954a0afd94f5b2aa46d1274fc38c7cc3d213ce79b357b8e122d6b7ede5ec6

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 6 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

Inputs are small exact toy vectors and scores. No production index, ANN recall, embedding quality, or latency claim 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 2026-09-30T16:48:24.912892+00:00.

Case digest / 9b6b02b57153e70e3b19c42e2257f7942af066b280261e233c57c6ce8c82ceb1