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FA-17506 / Time representation / Open access

Projection center loses elapsed-time direction · case 01

The decoded time state disagrees with the explicit regression oracle for center.

Verified by executionVariant 1 · 11 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Projection center loses elapsed-time direction.

THE FAILURE

Projection center loses elapsed-time direction.

Unsuccessful approach: The partial correction still substitutes r['anchor'] - r['elapsed'] at the same fault site.

Case contract

Project a center with asymmetric early/late error through signed elapsed ticks. Error growth uses elapsed magnitude and independent parts-per-thousand bounds rounded outward. Return projected [low,high], full width, zero containment, earliest/latest signed query duration and strict certainty of preceding query.

Why this case matters

Clock transfer and timestamp consumers require preserved coordinate, phase, validity and elapsed-time semantics.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(r):
    age = abs(r['elapsed'])
    early_growth = (age * r['early_rate'] + 999) // 1000
    late_growth = (age * r['late_rate'] + 999) // 1000
    center = r['anchor'] + age
    low = center - r['early'] - early_growth
    high = center + r['late'] + late_growth
    width = high - low
    contains_zero = low <= 0 <= high
    earliest = r['query'] - high
    latest = r['query'] - low
    return [[low,high],width,contains_zero,[earliest,latest],high < r['query']]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1', solve({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 20}), [[8, 15], 7, False, [5, 12], True])
check('fixture 2', solve({'anchor': 0, 'elapsed': -5, 'early': 0, 'late': 1, 'early_rate': 200, 'late_rate': 1, 'query': 0}), [[-6, -3], 3, False, [3, 6], True])
check('fixture 3', solve({'anchor': -1, 'elapsed': 1, 'early': 0, 'late': 0, 'early_rate': 0, 'late_rate': 0, 'query': -3}), [[0, 0], 0, True, [-3, -3], False])
check('fixture 4', solve({'anchor': 20, 'elapsed': 1000, 'early': 3, 'late': 5, 'early_rate': 2, 'late_rate': 7, 'query': 100}), [[1015, 1032], 17, False, [-932, -915], False])
check('fixture 5', solve({'anchor': -10, 'elapsed': 0, 'early': 2, 'late': 3, 'early_rate': 0, 'late_rate': 0, 'query': -20}), [[-12, -7], 5, False, [-13, -8], False])
check('fixture 6', solve({'anchor': 0, 'elapsed': 2, 'early': 5, 'late': 0, 'early_rate': 1, 'late_rate': 2000, 'query': 0}), [[-4, 6], 10, True, [-6, 4], False])
check('fixture 7', solve({'anchor': 10, 'elapsed': -1001, 'early': 0, 'late': 1, 'early_rate': 2, 'late_rate': 1, 'query': 8}), [[-994, -988], 6, False, [996, 1002], True])
check('fixture 8', solve({'anchor': 0, 'elapsed': 0, 'early': 0, 'late': 0, 'early_rate': 0, 'late_rate': 0, 'query': 0}), [[0, 0], 0, True, [0, 0], False])
check('fixture 9', solve({'anchor': 2, 'elapsed': -1, 'early': 0, 'late': 0, 'early_rate': 1000, 'late_rate': 1000, 'query': 2}), [[0, 2], 2, True, [0, 2], False])
check('fixture 10', solve({'anchor': 0, 'elapsed': 10, 'early': 1, 'late': 10, 'early_rate': 90, 'late_rate': 150, 'query': 20}), [[8, 22], 14, False, [-2, 12], False])
variant = [({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 21}, [[8, 15], 7, False, [6, 13], True]), ({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 22}, [[8, 15], 7, False, [7, 14], True]), ({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 23}, [[8, 15], 7, False, [8, 15], True]), ({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 24}, [[8, 15], 7, False, [9, 16], True]), ({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 25}, [[8, 15], 7, False, [10, 17], True])]
check("variant capture", solve(variant[N-1][0]), variant[N-1][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 fixtureActualExpectedOutcome
fixture 1[[8, 15], 7, False, [5, 12], True][[8, 15], 7, False, [5, 12], True]Passed
fixture 2[[4, 7], 3, False, [-7, -4], False][[-6, -3], 3, False, [3, 6], True]Failed
fixture 3[[0, 0], 0, True, [-3, -3], False][[0, 0], 0, True, [-3, -3], False]Passed
fixture 4[[1015, 1032], 17, False, [-932, -915], False][[1015, 1032], 17, False, [-932, -915], False]Passed
fixture 5[[-12, -7], 5, False, [-13, -8], False][[-12, -7], 5, False, [-13, -8], False]Passed
fixture 6[[-4, 6], 10, True, [-6, 4], False][[-4, 6], 10, True, [-6, 4], False]Passed
fixture 7[[1008, 1014], 6, False, [-1006, -1000], False][[-994, -988], 6, False, [996, 1002], True]Failed
fixture 8[[0, 0], 0, True, [0, 0], False][[0, 0], 0, True, [0, 0], False]Passed
fixture 9[[2, 4], 2, False, [-2, 0], False][[0, 2], 2, True, [0, 2], False]Failed
fixture 10[[8, 22], 14, False, [-2, 12], False][[8, 22], 14, False, [-2, 12], False]Passed
variant capture[[8, 15], 7, False, [6, 13], True][[8, 15], 7, False, [6, 13], True]Passed

SHA-256 / dcf131a726d689bfaca404544b8b52758d202859cbb2c1acec980eece1fa448a

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(r):
    age = abs(r['elapsed'])
    early_growth = (age * r['early_rate'] + 999) // 1000
    late_growth = (age * r['late_rate'] + 999) // 1000
    center = r['anchor'] - r['elapsed']
    low = center - r['early'] - early_growth
    high = center + r['late'] + late_growth
    width = high - low
    contains_zero = low <= 0 <= high
    earliest = r['query'] - high
    latest = r['query'] - low
    return [[low,high],width,contains_zero,[earliest,latest],high < r['query']]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1', solve({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 20}), [[8, 15], 7, False, [5, 12], True])
check('fixture 2', solve({'anchor': 0, 'elapsed': -5, 'early': 0, 'late': 1, 'early_rate': 200, 'late_rate': 1, 'query': 0}), [[-6, -3], 3, False, [3, 6], True])
check('fixture 3', solve({'anchor': -1, 'elapsed': 1, 'early': 0, 'late': 0, 'early_rate': 0, 'late_rate': 0, 'query': -3}), [[0, 0], 0, True, [-3, -3], False])
check('fixture 4', solve({'anchor': 20, 'elapsed': 1000, 'early': 3, 'late': 5, 'early_rate': 2, 'late_rate': 7, 'query': 100}), [[1015, 1032], 17, False, [-932, -915], False])
check('fixture 5', solve({'anchor': -10, 'elapsed': 0, 'early': 2, 'late': 3, 'early_rate': 0, 'late_rate': 0, 'query': -20}), [[-12, -7], 5, False, [-13, -8], False])
check('fixture 6', solve({'anchor': 0, 'elapsed': 2, 'early': 5, 'late': 0, 'early_rate': 1, 'late_rate': 2000, 'query': 0}), [[-4, 6], 10, True, [-6, 4], False])
check('fixture 7', solve({'anchor': 10, 'elapsed': -1001, 'early': 0, 'late': 1, 'early_rate': 2, 'late_rate': 1, 'query': 8}), [[-994, -988], 6, False, [996, 1002], True])
check('fixture 8', solve({'anchor': 0, 'elapsed': 0, 'early': 0, 'late': 0, 'early_rate': 0, 'late_rate': 0, 'query': 0}), [[0, 0], 0, True, [0, 0], False])
check('fixture 9', solve({'anchor': 2, 'elapsed': -1, 'early': 0, 'late': 0, 'early_rate': 1000, 'late_rate': 1000, 'query': 2}), [[0, 2], 2, True, [0, 2], False])
check('fixture 10', solve({'anchor': 0, 'elapsed': 10, 'early': 1, 'late': 10, 'early_rate': 90, 'late_rate': 150, 'query': 20}), [[8, 22], 14, False, [-2, 12], False])
variant = [({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 21}, [[8, 15], 7, False, [6, 13], True]), ({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 22}, [[8, 15], 7, False, [7, 14], True]), ({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 23}, [[8, 15], 7, False, [8, 15], True]), ({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 24}, [[8, 15], 7, False, [9, 16], True]), ({'anchor': 10, 'elapsed': 1, 'early': 2, 'late': 3, 'early_rate': 1, 'late_rate': 500, 'query': 25}, [[8, 15], 7, False, [10, 17], True])]
check("variant capture", solve(variant[N-1][0]), variant[N-1][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 fixtureActualExpectedOutcome
fixture 1[[6, 13], 7, False, [7, 14], True][[8, 15], 7, False, [5, 12], True]Failed
fixture 2[[4, 7], 3, False, [-7, -4], False][[-6, -3], 3, False, [3, 6], True]Failed
fixture 3[[-2, -2], 0, False, [-1, -1], False][[0, 0], 0, True, [-3, -3], False]Failed
fixture 4[[-985, -968], 17, False, [1068, 1085], True][[1015, 1032], 17, False, [-932, -915], False]Failed
fixture 5[[-12, -7], 5, False, [-13, -8], False][[-12, -7], 5, False, [-13, -8], False]Passed
fixture 6[[-8, 2], 10, True, [-2, 8], False][[-4, 6], 10, True, [-6, 4], False]Failed
fixture 7[[1008, 1014], 6, False, [-1006, -1000], False][[-994, -988], 6, False, [996, 1002], True]Failed
fixture 8[[0, 0], 0, True, [0, 0], False][[0, 0], 0, True, [0, 0], False]Passed
fixture 9[[2, 4], 2, False, [-2, 0], False][[0, 2], 2, True, [0, 2], False]Failed
fixture 10[[-12, 2], 14, True, [18, 32], True][[8, 22], 14, False, [-2, 12], False]Failed
variant capture[[6, 13], 7, False, [8, 15], True][[8, 15], 7, False, [6, 13], True]Failed

SHA-256 / 5e5d5f784c23d43d401622ae5ca7a77fc894577ff53fcaf4c5ead256bb57accb

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 11 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

Deterministic integer reference model with stipulated units and policies; not a complete clock, wire standard or platform implementation. 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 2026-09-29T14:39:47.485287+00:00.

Case digest / 0aaf9b42c5dded67db4caaf0dbcbc17629f96dd7ba81c06bc4ade085ece83a10