FA-56576 / Auction allocation rules / Open access

Activity eligibility: stage ceiling · case 01

Stage transition uses the initial ceiling or increases existing eligibility.

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ROOT CAUSE

Stage transition uses the initial ceiling or increases existing eligibility.

VERIFIED REPAIR

Apply the current stage ceiling without restoring eligibility.

Unsuccessful approach: The attempted repair uses min(x["previous"],x["stage_limits"][0]); the explicit regression cases demonstrate that this still violates the stipulated auction rule.

Case contract

A stipulated ascending multiround auction records eligibility in activity points. Submitted lots contribute fixed points, withdrawn lots contribute none, a waiver preserves previous eligibility once, and frozen eligibility cannot grow. These rules are pedagogical and independent of real spectrum-auction regulations. Named decision stage-ceiling: Apply the current stage ceiling without restoring eligibility.

Why this case matters

Offline administrative auction model for software failure analysis.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(x):
    v0 = sum(x["points"][i] for i in set(x["active"])-set(x["withdrawn"]))
    v1 = sum(x["points"][i] for i in set(x["active"])|set(x["standing"]))
    v2 = x["use_waiver"] and x["waivers"]>0
    v3 = x["waivers"]-int(x["use_waiver"] and x["waivers"]>0)
    v4 = min(x["previous"],sum(x["points"][i] for i in x["active"]))
    v5 = x["previous"] if x["use_waiver"] and x["waivers"]>0 else min(x["previous"],x["required"])
    v6 = x["history"] if x["round"]<=x["last_round"] else x["history"]+[x["previous"]]
    v7 = x["stage_limits"][min(x["stage"],len(x["stage_limits"])-1)]
    v8 = min(x["qualification"],x["previous"]+x["transferred"])
    v9 = 0 if x["revoked"] else min(x["previous"],x["qualification"])
    return {'withdrawn-activity':v0,'standing-credit-dedup':v1,'waiver-availability':v2,'waiver-consumption':v3,'eligibility-monotonicity':v4,'waiver-preservation':v5,'round-advance':v6,'stage-ceiling':v7,'transfer-cap':v8,'revocation':v9}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [('stage entry', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 0, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [8, 16, 24, 32, 40]), ('late stage', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 3, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [3, 6, 9, 12, 15]), ('normal contract', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('waiver round', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': True, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('no waiver left', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 0, 'use_waiver': True, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('all withdrawn', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['A', 'B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('standing overlaps activity', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['A'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('replayed round', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 1, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('small qualification', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 2, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('qualification revoked', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': True}, [4, 8, 12, 16, 20])]
def vary(value):
 if type(value) is int: return value*N
 if isinstance(value,list): return [vary(v) for v in value]
 if isinstance(value,dict): return {k:(v if k in ['count', 'delivery_index', 'disputed', 'maximum_set', 'minimum_set', 'stage', 'threshold', 'waived'] else vary(v)) for k,v in value.items()}
 return value
for label, request, expected in fixtures:
 check(label, solve(vary(request))['stage-ceiling'], expected[N-1])
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
stage entry	`10`	`8`	Failed
late stage	`4`	`3`	Failed
normal contract	`4`	`4`	Passed
waiver round	`4`	`4`	Passed
no waiver left	`4`	`4`	Passed
all withdrawn	`4`	`4`	Passed
standing overlaps activity	`4`	`4`	Passed
replayed round	`4`	`4`	Passed
small qualification	`4`	`4`	Passed
qualification revoked	`4`	`4`	Passed

SHA-256 / 4a6c9fab552e4a82ec2eaa233e66b4130dbfd54aed9af1b46f6d9ed3b2d7d232

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(x):
    v0 = sum(x["points"][i] for i in set(x["active"])-set(x["withdrawn"]))
    v1 = sum(x["points"][i] for i in set(x["active"])|set(x["standing"]))
    v2 = x["use_waiver"] and x["waivers"]>0
    v3 = x["waivers"]-int(x["use_waiver"] and x["waivers"]>0)
    v4 = min(x["previous"],sum(x["points"][i] for i in x["active"]))
    v5 = x["previous"] if x["use_waiver"] and x["waivers"]>0 else min(x["previous"],x["required"])
    v6 = x["history"] if x["round"]<=x["last_round"] else x["history"]+[x["previous"]]
    v7 = min(x["previous"],x["stage_limits"][0])
    v8 = min(x["qualification"],x["previous"]+x["transferred"])
    v9 = 0 if x["revoked"] else min(x["previous"],x["qualification"])
    return {'withdrawn-activity':v0,'standing-credit-dedup':v1,'waiver-availability':v2,'waiver-consumption':v3,'eligibility-monotonicity':v4,'waiver-preservation':v5,'round-advance':v6,'stage-ceiling':v7,'transfer-cap':v8,'revocation':v9}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [('stage entry', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 0, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [8, 16, 24, 32, 40]), ('late stage', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 3, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [3, 6, 9, 12, 15]), ('normal contract', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('waiver round', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': True, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('no waiver left', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 0, 'use_waiver': True, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('all withdrawn', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['A', 'B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('standing overlaps activity', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['A'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('replayed round', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 1, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('small qualification', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 2, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('qualification revoked', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': True}, [4, 8, 12, 16, 20])]
def vary(value):
 if type(value) is int: return value*N
 if isinstance(value,list): return [vary(v) for v in value]
 if isinstance(value,dict): return {k:(v if k in ['count', 'delivery_index', 'disputed', 'maximum_set', 'minimum_set', 'stage', 'threshold', 'waived'] else vary(v)) for k,v in value.items()}
 return value
for label, request, expected in fixtures:
 check(label, solve(vary(request))['stage-ceiling'], expected[N-1])
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
stage entry	`8`	`8`	Passed
late stage	`3`	`3`	Passed
normal contract	`8`	`4`	Failed
waiver round	`8`	`4`	Failed
no waiver left	`8`	`4`	Failed
all withdrawn	`8`	`4`	Failed
standing overlaps activity	`8`	`4`	Failed
replayed round	`8`	`4`	Failed
small qualification	`8`	`4`	Failed
qualification revoked	`8`	`4`	Failed

SHA-256 / fd9ad1e9c68c356bc12b06ed8f917cb94ee27ba4266220f7f76fa6b635f680f7

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(x):
    v0 = sum(x["points"][i] for i in set(x["active"])-set(x["withdrawn"]))
    v1 = sum(x["points"][i] for i in set(x["active"])|set(x["standing"]))
    v2 = x["use_waiver"] and x["waivers"]>0
    v3 = x["waivers"]-int(x["use_waiver"] and x["waivers"]>0)
    v4 = min(x["previous"],sum(x["points"][i] for i in x["active"]))
    v5 = x["previous"] if x["use_waiver"] and x["waivers"]>0 else min(x["previous"],x["required"])
    v6 = x["history"] if x["round"]<=x["last_round"] else x["history"]+[x["previous"]]
    v7 = min(x["previous"],x["stage_limits"][min(x["stage"],len(x["stage_limits"])-1)])
    v8 = min(x["qualification"],x["previous"]+x["transferred"])
    v9 = 0 if x["revoked"] else min(x["previous"],x["qualification"])
    return {'withdrawn-activity':v0,'standing-credit-dedup':v1,'waiver-availability':v2,'waiver-consumption':v3,'eligibility-monotonicity':v4,'waiver-preservation':v5,'round-advance':v6,'stage-ceiling':v7,'transfer-cap':v8,'revocation':v9}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [('stage entry', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 0, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [8, 16, 24, 32, 40]), ('late stage', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 3, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [3, 6, 9, 12, 15]), ('normal contract', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('waiver round', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': True, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('no waiver left', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 0, 'use_waiver': True, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('all withdrawn', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['A', 'B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('standing overlaps activity', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['A'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('replayed round', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 1, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('small qualification', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 2, 'transferred': 2, 'revoked': False}, [4, 8, 12, 16, 20]), ('qualification revoked', {'points': {'A': 3, 'B': 2, 'C': 1}, 'active': ['A', 'B'], 'withdrawn': ['B'], 'standing': ['C'], 'previous': 8, 'waivers': 2, 'use_waiver': False, 'required': 5, 'round': 2, 'last_round': 1, 'history': [8, 6, 5], 'stage': 2, 'stage_limits': [10, 7, 4], 'qualification': 9, 'transferred': 2, 'revoked': True}, [4, 8, 12, 16, 20])]
def vary(value):
 if type(value) is int: return value*N
 if isinstance(value,list): return [vary(v) for v in value]
 if isinstance(value,dict): return {k:(v if k in ['count', 'delivery_index', 'disputed', 'maximum_set', 'minimum_set', 'stage', 'threshold', 'waived'] else vary(v)) for k,v in value.items()}
 return value
for label, request, expected in fixtures:
 check(label, solve(vary(request))['stage-ceiling'], expected[N-1])
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
stage entry	`8`	`8`	Passed
late stage	`3`	`3`	Passed
normal contract	`4`	`4`	Passed
waiver round	`4`	`4`	Passed
no waiver left	`4`	`4`	Passed
all withdrawn	`4`	`4`	Passed
standing overlaps activity	`4`	`4`	Passed
replayed round	`4`	`4`	Passed
small qualification	`4`	`4`	Passed
qualification revoked	`4`	`4`	Passed

SHA-256 / 02b91eee9a9cc917d868c89a9acbb08d10fd85a78e79716dcd5091e4b42311d0

Verification & scope

Stipulated toy auction rules, not a venue specification, financial advice, optimization claim, or live trading implementation. Nonnegative integer inputs and internally aligned list fields only. 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 2026-09-29T14:46:08.336765+00:00.

Case digest / de0294070f65e9ac3f33273994fac9e83e3b62c9577a92a71f2c7ab3b1f54dc7