
559 F.3d 44 (2009)
ASOCIACIÓN DE EMPLEADOS DEL ESTADO LIBRE ASOCIADO DE PUERTO RICO, Plaintiff-Appellee,
v.
UNIÓN INTERNACIONAL DE TRABAJADORES DE LA INDUSTRIA DE AUTOMÓVILES, AEROESPACIO E IMPLEMENTOS AGRÍCOLAS, U.A.W. LOCAL 1850, Defendant-Appellant.
No. 07-2636.
United States Court of Appeals, First Circuit.
Heard October 27, 2008.
Decided March 6, 2009.
*46 Miguel Simonet Sierra, with whom Simonet Sierra Law Office, was on brief for appellant.
Jorge Martínez-Luciano, with whom Law Offices of Pedro Ortiz Alvarez, was on brief for appellee.
Before TORRUELLA and HOWARD, Circuit Judges, and DiCLERICO, JR.,[*] District Judge.
HOWARD, Circuit Judge.
Appellant Union Internacional de Trabajadores de la Industria de Automoviles, Aerospacio e Implementos Agricolas, U.A.W. Local 1850 ("the Union") challenges the district court's decision to vacate the portion of an arbitration award which awarded back pay and reinstatement to five employees discharged by appellee Asociacion de Empleados del Estado Libre Asociado ("AEELA"). Although the district court upheld the arbitrator's ruling that the Union employees were improperly dischargeda ruling which AEELA does not appealthe court ruled that the reinstatement and back pay awards exceeded the arbitrator's authority.[1] In our view, however, the arbitrator employed a plausible construction of the collective bargaining agreement between the parties. We therefore reverse the district court's judgment.

I.
In September 1999, AEELA terminated five employees for allegedly engaging in unauthorized financial transactions.[2] The Union subsequently initiated grievance procedures on behalf of the employees, in accordance with the collective bargaining agreement ("CBA") between AEELA and the Union, claiming that the transactions were actually the result of computer programming errors.
After all internal grievance procedures provided by the CBA had been exhausted, the matter was submitted to arbitration.[3] After eighteen days of hearings spanning the period of December 2000 to June 2003, the arbitrator ruled that the employees had been unjustly discharged. The arbitrator ordered the employees reinstated with back pay and awarded them attorneys' fees.
AEELA sought judicial review of the arbitration award in the Puerto Rico Commonwealth Court; the Union removed the action to the federal district court. There, the parties consented to the jurisdiction of a magistrate judge, who ordered them to file cross-motions for summary judgment. AEELA I, 515 F.Supp. at 212. The magistrate judge's summary judgment ruling confirmed the arbitrator's conclusion that the employees had been improperly discharged. The court also, however, concluded that the awards of back pay and *47 reinstatement were not available under the CBA, which provides that "The Arbitrator must rule in accordance to Law." Id. at 221. In particular, the court found that the arbitral award ran afoul of Puerto Rico Law 80 of 1976, 29 L.P.R.A. §§ 185a-m ("Law 80"), which provides for only severance pay and attorneys' fees in wrongful termination cases, absent findings of discrimination or other tortious acts not claimed here. Id. The Union seeks reversal of the district court's ruling, arguing that the arbitrator was not limited to Law 80's remedies because the CBA explicitly contemplates reinstatement of wrongfully discharged employees.
We review de novo the district court's decision to vacate the arbitral award on summary judgment. Wheelabrator Envirotech Operating Servs., Inc. v. Mass. Laborers Dist. Council Local 1144, 88 F.3d 40, 43 (1st Cir.1996).

II.
"It is a firm principle of federal labor law that where parties agree to submit a dispute to binding arbitration, absent unusual circumstances, they are bound by the outcome of said proceedings." Posadas de Puerto Rico Assocs., Inc. v. Asociacion de Empleados de Casino de Puerto Rico, 821 F.2d 60, 61 (1st Cir.1987) (citing United Steelworkers of America v. Enterprise Wheel & Car Corp., 363 U.S. 593, 599, 80 S.Ct. 1358, 4 L.Ed.2d 1424 (1960)). "Judicial review of an arbitration award is among the narrowest known in the law." Me. Cent. R.R. Co. v. Bhd. of Maint. of Way Employees, 873 F.2d 425, 428 (1st Cir.1989) (citing Enterprise Wheel, 363 U.S. at 596, 80 S.Ct. 1358).
"We do not sit as a court of appeal to hear claims of factual or legal error by an arbitrator or to consider the merits of the award." Challenger Caribbean Corp. v. Union General de Trabajadores de Puerto Rico, 903 F.2d 857, 860 (1st Cir.1990). "So far as the arbitrator's decision concerns construction of the [CBA], the courts have no business overruling him because their interpretation of the contract is different from his." Dorado Beach Hotel Corp. v. Union de Trabajadores de la Industria Gastronomica de Puerto Rico, 959 F.2d 2, 4 (1st Cir.1992) (citations and quotation marks omitted). Furthermore, we may not set aside the award even if we are convinced that the arbitrator committed a serious error of fact or law. UMass Mem'l Med. Ctr., Inc. v. United Food & Commercial Workers Union, Local 1445, 527 F.3d 1, 5 (1st Cir.2008), (citing Cytyc Corp. v. DEKA Prods. Ltd. P'ship, 439 F.3d 27, 32 (1st Cir.2006)).
Nonetheless, as deferential as the standard of review is, we are not required to give an arbitrator "carte blanche approval" for every decision. Challenger, 903 F.2d at 860 (citation omitted). An arbitrator's decision will not stand if it is "unfounded in reason and fact, is based on reasoning so palpably faulty that no judge or group of judges could ever conceivably have made such a ruling, or is mistakenly based on a crucial assumption which is decidedly a non-fact." Id. at 861 (citation and quotation marks omitted). We have encapsulated the standard for review of arbitral awards by inquiring whether an award was in "manifest disregard of the law." McCarthy v. Citigroup Global Mkts., Inc., 463 F.3d 87, 91 (1st Cir.2006). Such a manifest disregard is found where the record shows that the arbitrator recognized applicable law, but wilfully ignored it. Id. at 91 (citing Wonderland Greyhound Park, Inc. v. Autotote Sys. Inc., 274 F.3d 34, 35 (1st Cir.2001)).

III.
The battle lines in this case are clear. AEELA arguesand the district *48 court ruledthat the "in accordance to Law" language of the CBA forbids any remedy beyond those listed in Law 80. The Union, however, says that Article 10 of the CBA, entitled "Seniority," supports the arbitrator's chosen remedy. In relevant part, Article 10 states that "[e]mployees shall lose their rights to seniority and employment, due to any of the following reasons: ... [d]ismissal due to just cause and such dismissal is not revoked through the complaints and grievance procedure." According to the Union, Article 10's requirement of just cause for dismissal, when read together with the reference to revoking such dismissals, suggests that reinstatement is a remedy contemplated by the CBA. The Union has the better of the argument.
We addressed the interplay among reinstatement, Law 80 and a CBA containing the "according to law" language in Challenger, in which we upheld the portion of an arbitral award that granted reinstatement to certain employees whom the arbitrator found had been improperly laid off. 903 F.2d at 870. In so doing, we noted the importance of the fact that the arbitrator had found that the employer had violated terms of the CBA that were independent of other provisions in the CBA that limited remedies to Law 80. See id. at 868 ("[I]f the arbitrator found no more than a violation of Law 80, an award of reinstatement and back pay would be improper."). Similarly, in In re Hotel Da Vinci, 797 F.2d 33 (1st Cir.1986), we upheld an arbitration remedy that exceeded the bounds of Puerto Rico's Workmen's Accident Compensation Act because the arbitrator found violations of both the Act and the applicable CBA.
Here, it is not entirely clear whether the arbitrator's decision to overturn the dismissals was based on the CBA or Law 80, the distinction we relied upon in Challenger. Indeed, the portion of the sixty-four page decision addressing the dismissals mentions neither the CBA nor Law 80 in concluding that AEELA failed to prove that the dismissals were justified. We also note, however, that in its submission to the arbitrator,[4] AEELA framed the issue as whether the dismissals were "justified in accordance with the Collective Bargaining Agreement & applicable law." (emphasis added). The arbitrator ultimately ruled that the task was to "determine whether complaining parties dismissal was justified or not. If ruled non-justified, the arbitrator provide for the adequate remedy therein."
When the arbitrator's decision is viewed through the prism of the "just cause" language of Article 10 and the arbitral submission,[5] the arbitrator's substantive ruling (that the dismissals were not justified) could conceivably have drawn "its essence" from the CBA. Enterprise Wheel, 363 U.S. at 597, 80 S.Ct. 1358.
Given this conclusion, and sticking to the course laid in Challenger, it follows that the arbitrator was not limited to the remedies specified in Law 80. Moreover, our reading of Article 10 supports the arbitrator's reinstatement remedy. As previously noted, Article 10 explicitly limits an employee's risk of losing his "rights to ... *49 employment" to situations where he is "dismiss[ed] due to just cause" and the dismissal is not "revoked" through the grievance procedure, of which arbitration is the final step. As a result "for which [each] party could have bargained," reinstatement is a permissible outcome under the CBA. See Local 1445, United Food and Commercial Workers Int'l Union v. Stop & Shop Cos., Inc., 776 F.2d 19, 20 (1st Cir.1985) ("parties not entitled to judicial review unless it can be shown that the arbitrator acted in a way for which neither party could have bargained.") (citing Enterprise Wheel, 363 U.S. at 599, 80 S.Ct. 1358.)[6]
In the end, we are unable to conclude that the arbitrator acted with "manifest disregard of the law." McCarthy, 463 F.3d at 91. Although Law 80 ultimately was not applied, the arbitrator's discussion of both Law 80 and the meaning of the "accordance to Law" language occupied approximately seven pages of her decision. Included within that discussion were citations to, and analyses of, various Puerto Rico Supreme Court cases, which served as guidance for the ultimate remedial award. We are not permitted to "conduct our own analysis" of the law to determine whether the arbitrator ruled correctly. See id. at 95 ("instead of finding manifest disregard of the law ... [the district court impermissibly] found an application of the [] Law with which it disagreed"); Poland Spring Corp. v. United Food & Commercial Int'l Union, 314 F.3d 29, 33 (1st Cir. 2002) ("We do not sit as a court of appeal to hear claims of factual or legal error....").
The arbitrator's analysiswhether we agree with it or notdemonstrates that this was not a case where the arbitrator "`knew the law and expressly disregarded it.'" McCarthy, 463 F.3d at 92 (quoting Advest, Inc. v. McCarthy, 914 F.2d 6, 10 (1st Cir.1990)). Instead, because the arbitrator was "arguably construing the [CBA]," we will not overturn the remedy, even if we believe that the decision not to apply Law 80 may have been improper, a point on which we express no view. Challenger, 903 F.2d at 869 n. 15 (quoting Bayamon Can Co., Inc. v. Congreso de Uniones Industriales de Puerto Rico, 843 F.2d 65, 67 (1st Cir.1988)); Enterprise Wheel, 363 U.S. at 598, 80 S.Ct. 1358 ("A mere ambiguity in the opinion accompanying an award, which permits the inference that the arbitrator may have exceeded his authority is not a reason for refusing to enforce the award.")[7]
The district court's judgment vacating the arbitrator's award of reinstatement and back pay is reversed. The case is remanded to the district court for the purpose of entering summary judgment in the Union's favor. Costs to appellant.
NOTES
[*]  Of the District of New Hampshire, sitting by designation.
[1]  Asociacion de Empleados del Estado Libre Asociado de Puerto Rico v. Union Internacional de Trabajadores de la Industria de Automoviles, 515 F.Supp.2d 209 (D.P.R.2007) ("AEELA I").
[2]  AEELA is a non-profit savings and loan association. The five employees were essentially accused of erasing records of loans made to them.
[3]  The CBA contains a four-step grievance procedure. Step I is a report to a supervisor. If the employee is dissatisfied with the response, Step II is an appeal to the Industrial Relations and Human Resources Director. Step III is a further appeal to a Grievance Committee consisting of both Union and AEELA representatives. The final step is submission of the matter to arbitration. Where, as here, the discipline at issue is termination, the first two steps are skipped.
[4]  The CBA requires the parties to provide a written submission to the arbitrator to outline the controversy to be resolved, and calls for the arbitrator to fashion a submission if the parties do not agree. The Union had proposed that the Arbitrator rule "whether the dismissals ... were justified or not. If ruled unjustified, that any remedy deemed to be appropriate be ordered therein, including, but not limited to, fees, among others."
[5]  Reviewing courts must consider both the CBA and arbitral submissions in their analyses. Challenger, 903 F.2d at 860-61.
[6]  Our conclusion here is consistent with Puerto Rico Department of Labor and Human Resources Guidelines, which state that parties have the power in collective bargaining to contract for remedies above and beyond those specified in Law 80. See Otero-Burgos v. Inter American University, 558 F.3d 1, 5, 2009 WL 416647, at *7 (1st Cir.2009).
[7]  AEELA asks us to rely on a case from the Puerto Rico Supreme Court involving the same parties which overturned an arbitral award of reinstatement. However, this unreported judgment is non-binding and carries no precedential value beyond the intrinsic persuasive value of its rationale. Baralt v. Nationwide Mut. Ins. Co., 251 F.3d 10, 20 n. 12 (1st Cir.2001). Given the deference owed to the arbitrator's decision, we decline to accept AEELA's invitation.
