FA-100091 / Preference pair construction / Open access

Preference pairs: tied extrema are resolved by input order · case 01

tied extrema are resolved by input order.

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

ROOT CAUSE

Selecting the first maximum and minimum fabricates a strict preference despite tied ratings.

THE FAILURE

Selecting the first maximum and minimum fabricates a strict preference despite tied ratings.

Unsuccessful approach: Skipping every group containing any tie discards groups with a harmless middle tie.

Case contract

Rows are [prompt,id,score]. Emit [prompt,best_id,worst_id] only when max and min are each unique; a middle tie is allowed.

Why this case matters

A small deterministic preference-data transform makes pair semantics inspectable without a training framework.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(rows):
    groups={}
    for r in rows: groups.setdefault(r[0],[]).append(r)
    return [[p,max(g,key=lambda r:r[2])[1],min(g,key=lambda r:r[2])[1]] for p,g in groups.items() if len(g)>1]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
p='p'+str(N)
check('tied maximum skipped',solve([[p,'a',3],[p,'b',3],[p,'c',0]]),[])
check('tied minimum skipped',solve([[p,'a',3],[p,'b',0],[p,'c',0]]),[])
check('middle tie allowed',solve([[p,'a',3],[p,'b',2],[p,'c',2],[p,'d',0]]),[[p,'a','d']])
check('unique extremes',solve([[p,'a',N],[p,'b',0]]),[[p,'a','b']])
check('singleton',solve([[p,'a',N]]),[])
check('empty',solve([]),[])
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
tied maximum skipped	`[['p1', 'a', 'c']]`	`[]`	Failed
tied minimum skipped	`[['p1', 'a', 'b']]`	`[]`	Failed
middle tie allowed	`[['p1', 'a', 'd']]`	`[['p1', 'a', 'd']]`	Passed
unique extremes	`[['p1', 'a', 'b']]`	`[['p1', 'a', 'b']]`	Passed
singleton	`[]`	`[]`	Passed
empty	`[]`	`[]`	Passed

SHA-256 / 0008d44d3919651ceb4cc88fd0240beaea886a358ad83abcd87019011b60c164

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(rows):
    groups={}
    for r in rows: groups.setdefault(r[0],[]).append(r)
    return [[p,max(g,key=lambda r:r[2])[1],min(g,key=lambda r:r[2])[1]] for p,g in groups.items() if len(g)>1 and len({x[2] for x in g})==len(g)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
p='p'+str(N)
check('tied maximum skipped',solve([[p,'a',3],[p,'b',3],[p,'c',0]]),[])
check('tied minimum skipped',solve([[p,'a',3],[p,'b',0],[p,'c',0]]),[])
check('middle tie allowed',solve([[p,'a',3],[p,'b',2],[p,'c',2],[p,'d',0]]),[[p,'a','d']])
check('unique extremes',solve([[p,'a',N],[p,'b',0]]),[[p,'a','b']])
check('singleton',solve([[p,'a',N]]),[])
check('empty',solve([]),[])
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
tied maximum skipped	`[]`	`[]`	Passed
tied minimum skipped	`[]`	`[]`	Passed
middle tie allowed	`[]`	`[['p1', 'a', 'd']]`	Failed
unique extremes	`[['p1', 'a', 'b']]`	`[['p1', 'a', 'b']]`	Passed
singleton	`[]`	`[]`	Passed
empty	`[]`	`[]`	Passed

SHA-256 / 0a3662bf0da799750c2825d68ad37e67b59ed39697dca4ec7e5145597a69acc0

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

These are explicit toy record contracts; they do not claim compatibility with a trainer or improved model behavior. 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 2026-09-30T16:48:31.716800+00:00.

Case digest / f5ebfcb6d09168582f4137c09c49d94a9f840dcdadfa0baea3ec1616dbbcf595