FA-12186 / Astronomical coordinate conventions / Open access
Optical barycentric velocity correction omits the redshift cross term · case 01
Optical barycentric velocity correction omits the redshift cross term.
ROOT CAUSE
A correction expressed as optical velocity is added as if independent velocities were additive.
VERIFIED REPAIR
Compose the redshift factors, retaining measured*correction/c in addition to their sum.
Unsuccessful approach: Relativistic velocity addition belongs to a different velocity convention and gives a different result.
Case contract
Toy exact optical-velocity correction: positive rational speed constant c, measured m and correction b. Return rational string m+b+m*b/c; inputs avoid the singular denominator in the deliberately wrong relativistic attempt. No barycentric correction is computed here.
Why this case matters
Astronomical coordinate adapters must preserve convention semantics. Primary background: https://docs.astropy.org/en/stable/coordinates/velocities.html
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(m, b, c):
return str(Fraction(m+b))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('both redshift terms', solve(N,2*N,10*N), str(Fraction(16*N,5)))
check('opposing terms', solve(N,-2*N,10*N), str(Fraction(-6*N,5)))
check('zero correction', solve(N,0,10*N), str(N))
check('zero measured', solve(0,N,10*N), str(N))
check('both zero', solve(0,0,10*N), '0')
check('both negative', solve(-N,-2*N,10*N), str(Fraction(-14*N,5)))
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 |
|---|---|---|---|
| both redshift terms | 3 | 16/5 | Failed |
| opposing terms | -1 | -6/5 | Failed |
| zero correction | 1 | 1 | Passed |
| zero measured | 1 | 1 | Passed |
| both zero | 0 | 0 | Passed |
| both negative | -3 | -14/5 | Failed |
SHA-256 / 531971eae01bd3c45988824213f10d1501da44f94838dffb3ca4ee9b69ce9414
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(m, b, c):
return str(Fraction(m+b)/(1+Fraction(m*b,c*c)))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('both redshift terms', solve(N,2*N,10*N), str(Fraction(16*N,5)))
check('opposing terms', solve(N,-2*N,10*N), str(Fraction(-6*N,5)))
check('zero correction', solve(N,0,10*N), str(N))
check('zero measured', solve(0,N,10*N), str(N))
check('both zero', solve(0,0,10*N), '0')
check('both negative', solve(-N,-2*N,10*N), str(Fraction(-14*N,5)))
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 |
|---|---|---|---|
| both redshift terms | 50/17 | 16/5 | Failed |
| opposing terms | -50/49 | -6/5 | Failed |
| zero correction | 1 | 1 | Passed |
| zero measured | 1 | 1 | Passed |
| both zero | 0 | 0 | Passed |
| both negative | -50/17 | -14/5 | Failed |
SHA-256 / 3596b816860805a8c6b94a126a08700737368987c9a4c30eed5053caf2fe021d
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(m, b, c):
return str(Fraction(m+b)+Fraction(m*b,c))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('both redshift terms', solve(N,2*N,10*N), str(Fraction(16*N,5)))
check('opposing terms', solve(N,-2*N,10*N), str(Fraction(-6*N,5)))
check('zero correction', solve(N,0,10*N), str(N))
check('zero measured', solve(0,N,10*N), str(N))
check('both zero', solve(0,0,10*N), '0')
check('both negative', solve(-N,-2*N,10*N), str(Fraction(-14*N,5)))
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 |
|---|---|---|---|
| both redshift terms | 16/5 | 16/5 | Passed |
| opposing terms | -6/5 | -6/5 | Passed |
| zero correction | 1 | 1 | Passed |
| zero measured | 1 | 1 | Passed |
| both zero | 0 | 0 | Passed |
| both negative | -14/5 | -14/5 | Passed |
SHA-256 / f621373de8476e3bbe3d39a4d982dce262c5ef0c95e928b63f4b5650bd67ad18
Verification & scope
Reduced deterministic algebraic model only; no ephemeris, full sky projection, or physical accuracy claims. 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 2026-09-29T14:38:54.671032+00:00.
Case digest / 8f571b0461bd42c55a5017846fa5731f6b9a67a0dc468e0db355c2efdd493c35