MATHESON, Circuit Judge.
The district court denied state prisoner Michael Leatherwood’s 28 U.S.C. § 2241 habeas application. It granted him a certificate of appealability (“COA”) on his claim that revocation of his suspended sentence for violation of a probation condition violated his procedural and substantive due process rights. It denied a COA on his other claims. Exercising jurisdiction under 28 U.S.C. §§ 1291 and 2253(a), we affirm the district court’s denial of his due process claim. We also deny his request for additional COAs and his motion to supplement the record.
I. BACKGROUND
A. State Court Proceedings
1. Sentence
In 2009, Mr. Leatherwood pled guilty in Oklahoma state court to two counts of Rape in the First Degree and four counts of Rape in the First Degree by Instrumentation. Judge Kenneth Watson sentenced him to six concurrent 20-year terms and suspended the sentence except for 90 days in jail.
Upon completion' of his jail time, Mr. Leatherwood was supposed to serve “the remainder of [his] sentence(s) ... under the terms set forth in the probation guidelines,” including a list of Special Probation Conditions for Sex Offenders (“Special Probation Conditions”). Record on Appeal (“ROA”) at 1700, 1703. He would therefore serve a suspended sentence and also be under probationary supervision. See Okla. Stat. tit. 22 § 991(a)(A)(1).1
Mr. Leatherwood agreed to the Special Probation Conditions “as consideration for the imposition of a probated sentence, in whole or in part” and acknowledged that “[fjailure to comply with any of these con[1040]*1040ditions may result in the revocation ... of [his] probated sentence.” ROA at 1703.
One of the Special Probation Conditions, Rule 17, required that Mr. Leatherwood “[n]ot date, socialize, or enter into a romantic or sexual relationship with any person who has children under the age of eighteen (18) years present in their residence or custody at any time.” Id. Judge Watson ordered Mr. Leatherwood to report to jail on January 8, 2010.
2. First Revocation — Five Years
On September 23, 2009, before the scheduled start of Mr. Leatherwood’s jail term, the State applied to revoke his suspended sentence, alleging he had violated several probation conditions. Mr. Leather-wood was put in jail before his revocation hearing. Judge Watson, who had imposed the original sentence, held a revocation hearing on January 8, 2010. During the hearing, Mr. Leatherwood’s counsel stipulated to five of the alleged probation violations, including a violation of Rule 17 based on Mr. Leatherwood’s relationship with Regina Wood, the mother of two minor children. Judge Watson chastised Mr. Leatherwood for refusing to follow the rules, stating, “And now they put you in jail and you’re doing the same thing over there.... I gave you all the rope in the world and you hung yourself with it.” Id. at 891. Judge Watson revoked five years of Mr. Leatherwood’s suspended sentence.
3. Second Revocation — 15 Years
On April 14, 2010, while Mr. Leather-wood was serving his five-year prison term,2 the State filed a second application to revoke, alleging Mr. Leatherwood had continued to violate Rule 17 while he was incarcerated. Judge Watson recused himself. Judge Tammy Bass-LeSure presided over.a second revocation hearing on August 3, 2010. She noted that despite Judge Watson’s admonitions “not to have any relationship ... with a person that has children in their custody,” Mr. Leather-wood had gone to “great lengths to hide the fact” that he continued his relationship with Ms. Wood. Id. at 1032-33. Mr. Leath-erwood acknowledged that he “would not do anything to intentionally or willfully violate the conditions of my probation except for [Rule] 17 and I take responsibility for that.” Id. at 1065. “[L]ooking at the totality” of the circumstances, including Mr. Leatherwood’s own statements and deceptive behavior, Judge Bass-LeSure concluded he knew he had violated Rule 17. Id. at 1033. Consequently, she revoked the remaining 15 years of his suspended sentence.
4.Direct Appeal and Post-Conviction Review
Mr. Leatherwood appealed to the Oklahoma Court of Criminal Appeals (“OCCA”), raising three issues that are relevant here: (1) the revocation violated his procedural and substantive due process rights because (a) Rule 17 failed to warn him that he could violate it while incarcerated, and (b) the revocation was so arbitrary as to be fundamentally unfair; (2) Judge' Bass-LeSure’s bias violated due process; and (3) cumulative error in the second revocation proceeding required reversal. The OCCA affirmed.
Mr. Leatherwood then sought post-conviction relief, alleging: (1) ineffective assistance of counsel; (2) judicial bias and conflict;3 and (3) cumulative error. The state [1041]*1041trial court denied relief, and the OCCA affirmed.
B. Federal Habeas Proceedings
In October 2013, Mr. Leatherwood applied for habeas relief under 28 U.S.C. § 2241 in the United States District Court for the Western District of Oklahoma. He asserted seven grounds for relief: (1) violation of due process; (2) insufficient evidence; (3) improper admission of evidence; (4) judicial bias; (5) judicial conflict; (6) ineffective assistance of counsel; and (7) cumulative error. As on direct appeal, his first claim alleged violation of procedural and substantive due process because (1) Rule 17 failed to warn that he could violate it while incarcerated, and (2) the revocation arbitrarily deprived him of his liberty. Mr. Leatherwood filed motions to supplement his application with affidavits from Justin Jones, the former Director of the Oklahoma Department of Corrections, and from Judge Watson.
The magistrate judge recommended denial of Mr. Leatherwood’s habeas application. Over Mr. Leatherwood’s objection, the federal district court agreed. It also denied his request for an evidentiary hearing and his motions to supplement the record. The court issued a COA on the claim alleging a violation of procedural and substantive due process but declined any other COAs.
Mr. Leatherwood filed a timely notice of appeal on his due process claim. He also requests COAs on his judicial bias/conflict4 and cumulative error claims, and he has moved to supplement the record on appeal with an affidavit from Judge Watson.
II. LEGAL BACKGROUND
A. Section 2241 Challenge to Revocation and Standard of Review
1. 28 U.S.C. § 2241 and Revocation
A habeas application under 28 U.S.C. § 2241 generally attacks the execution of a sentence rather than its validity. See Straley v. Utah Bd. of Pardons, 582 F.3d 1208, 1213 (10th Cir. 2009) (“[State prisoner’s] § 2241 habeas petition can only challenge the execution of his sentence, not the validity of his conviction and the original sentence.”); Yellowbear v. Wyoming Att’y Gen., 525 F.3d 921, 924 (10th Cir. 2008) (“Section [ ] 2241 is a vehicle for [a state prisoner] ... attacking the execution of a sentence.” (citations omitted)). It challenges “the fact or duration of a prisoner’s confinement and seeks the remedy of immediate release or a shortened period of confinement.” McIntosh v. U.S. Parole Comm’n, 115 F.3d 809, 812 (10th Cir. 1997) (quotations omitted).
A state prisoner’s challenge to the revocation of a suspended sentence is properly brought under § 2241 based on our circuit precedent. Montez v. McKinna, 208 F.3d 862, 865 (10th Cir. 2000) (stating that a habeas application challenging where a state sentence will be served “seems to fit better under the rubric of § 2241”); Stoltz v. Sanders, Nos. 00-6188 & 00-6288, 242 F.3d 390, 2000 WL 1730894, [1042]*1042at *1 (10th Cir. 2000) (unpublished table decision) (“To the extent [petitioner] is challenging the revocation of his [suspended] sentence, we construe his petition as filed under 28 U.S.C. § 2241 because it challenges the execution of his sentence, rather than its validity.”).5 By contrast, a state prisoner’s federal habeas challenge to the validity of an underlying conviction or sentence must typically be brought under § 2254. Montez, 208 F.3d at 865.
Mr. Leatherwood challenges the execution of his sentence — whether he will serve 15 years in prison or as a suspended sentence. See id. He does not challenge the validity of his rape conviction or his sentence of six concurrent 20-year terms. He therefore properly brought a § 2241 habeas application.6
2. Standard of Review
“When reviewing the denial of a habeas petition under § 2241, we review the district court’s legal conclusions de novo and accept its factual findings unless clearly erroneous.” al-Marri v. Davis, 714 F.3d 1183, 1186 (10th Cir. 2013). In doing so, we employ the same deference the district court must apply in reviewing the state proceedings. Curtis v. Chester, 626 F.3d 540, 544 (10th Cir. 2010).
The standard of federal habeas review of state court decisions depends on which habeas statute applies. For § 2254 habeas applications, relief may not be granted unless the state court’s decision “was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States,” 28 U.S.C. § 2254(d)(1), or “was based on an unreasonable determination of the fáets in light of the evidence presented in the State court proceeding,” id. § 2254(d)(2). Congress imposed these standards when it enacted the Antiterrorism and Effective Death Penalty Act (“AEDPA”), and it intended they be “difficult to meet.” Harrington v. Richter, 562 U.S. 86, 102, 131 S.Ct. 770, 178 L.Ed.2d 624 (2011).
The standard of review for a § 2241 application is less demanding. In Walck v. Edmondson, we stated, “The def[1043]*1043erential standard of review contained within § 2254 is ... only properly invoked when an individual in state custody collaterally attacks the validity of a state conviction and/or sentence.” 472 F.3d 1227, 1234 (10th Cir. 2007). Accordingly, “we review habeas claims made pursuant to § 2241 ... de novo.” Id. at 1235; see also Phillips v. Court of Common Pleas, Hamilton Cty., 668 F.3d 804, 810 (6th Cir. 2012) (“[Habeas petitions governed by § 2241 are not subject to the heightened standards contained in § 2254(d)”); Martinez v. Caldwell, 644 F.3d 238, 242 (5th Cir. 2011) (“The deferential standard afforded to state court decisions, which is specifically articulated in § 2254, is not included in the text of § 2241.”). Thus, we review the state court’s denial of Mr. Leatherwood’s § 2241 application de novo. See Walck, 472 F.3d at 1235.
B. Scope of Habeas Review: State Law and Federal Due Process
Federal habeas relief is not available to correct state law errors. Estelle v. McGuire, 502 U.S. 62, 67-68, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991); Eizember v. Trammell, 803 F.3d 1129, 1145 (10th Cir. 2015). “[T]his court’s role on collateral review isn’t to second-guess state courts about the application of their own laws but to vindicate federal rights.” Eizember, 803 F.3d at 1145. A prisoner may seek relief, however, if a state law decision is so fundamentally unfair that it implicates federal due process. Estelle, 502 U.S. at 67-68, 75, 112 S.Ct. 475; Hicks v. City of Watonga, 942 F.2d 737, 746 n.4 (10th Cir. 1991). “[Wjhether a state has afforded sufficient process to protect a [federal] constitutional right is not a question of state law.” Guttman v. Khalsa, 669 F.3d 1101, 1115 (10th Cir. 2012) (quotations omitted).
A habeas applicant cannot transform a state law claim into a federal one merely by attaching a due process label. See Gryger v. Burke, 334 U.S. 728, 731, 68 S.Ct. 1256, 92 L.Ed. 1683 (1948). Otherwise, “every erroneous decision by a state court on state law would come [to federal court] as a federal constitutional question.” Id.; see Onyx Props. LLC v. Bd. of Cty. Comm’rs, 838 F.3d 1039, 1044 (10th Cir. 2016); Johnson v. Rosemeyer, 117 F.3d 104, 110 (3d Cir. 1997) (“Errors of state law cannot be repackaged as federal errors simply by citing the Due Process Clause.”). Rather, the habeas applicant should “include reference to a specific federal constitutional guarantee, as well as a statement of the facts that entitle [him] to relief.” Gray v. Netherland, 518 U.S. 152, 162-63, 116 S.Ct. 2074, 135 L.Ed.2d 457 (1996); Perruquet v. Briley, 390 F.3d 505, 512 (7th Cir. 2004) (explaining the applicant must “draw[ ] enough of a connection” between the right to due process and the sentencing court’s alleged errors “to render his claim cognizable on habeas review”). Examples of state law decisions that may violate due process include erroneous jury instructions7 and improper admission or exclusion of evidence.8 See Bri[1044]*1044an R. Means, Postconviction Remedies, Ch. 41 (2016 ed.).
The State contends that Mr. Leatherwood raises only a question of state law: whether his suspended sentence could be revoked under Oklahoma law for a violation of Rule 17 while incarcerated. But Mr. Leatherwood’s habeas application alleged: (1) “Rule 17 failed to give fair warning that [he] could violate the rule” even though he was incarcerated, Dist. Ct. Doc. 2 at 48; and (2) the district court’s enforcement of a probation condition (i.e., Rule 17) during his incarceration “arbitrarily deprived him of his liberty and constituted a denial of his right to substantive due process,” id. at 28. The foregoing arguments go beyond labeling a state claim as a due process claim by referencing the “specific federal constitutional guarantee” and the “statement of the facts” that Mr. Leatherwood contends warrant relief. See Gray, 518 U.S. gt 162-63, 116 S.Ct. 2074. We thus proceed to consider the merits of his claim.
C. Due Process Protections for Revocation of a Suspended Sentence
Mr. Leatherwood’s due process claim on appeal includes his (1) procedural due process claim alleging lack of fair warning, and (2) substantive due process claim alleging arbitrary government action. We provide legal background information below.
1. Procedural Due Process
Procedural due process protections apply to the revocation of a suspended sentence. See United States v. Ferguson, 624 F.2d 81, 83 (9th Cir. 1980) (holding revocation of suspended sentence violated due process when court refused to consider mitigating circumstances); Bumgarner v. Middleton, No. 94-7003, 54 F.3d 787, 1995 WL 275718, *1 (10th Cir. 1995) (unpublished table case) (“Requirements of due process with regard to .revocation of a suspended sentence are ... not as broad as those provided a defendant in. a criminal trial.”). These protections are the same as those afforded to revocation of probation, parole, or supervised release. See Gagnon v. Scarpelli, 411 U.S. 778, 786, 93 S.Ct. 1756, 36 L.Ed.2d 656 (1973); United States v. Gallo, 20 F.3d 7, 11 (1st Cir. 1994); Bumgarner, 1995 WL 275718, at *1.9 We therefore rely on cases about revocation of probation, parole, and supervised release in analyzing the due process issue here.
One of the due process protections is the void-for-vagueness doctrine. “It is a basic principle of due process that an enactment is void for vagueness if its prohibitions are not clearly defined.” Grayned v. City of Rockford, 408 U.S. 104, 108, 92 S.Ct. 2294, 33 L.Ed.2d 222 (1972) (explaining that “laws [must] give [a] person of ordinary intelligence a reasonable opportunity to know what is prohibited, so that he may act accordingly”). Courts — including this one — have applied this doctrine in the revocation context. See, e.g., United States [1045]*1045v. Muñoz, 812 F.3d 809, 818 (10th Cir. 2016) (supervised release condition); United States v. Jordan, 890 F.2d 247, 255 (10th Cir. 1989) (probation condition).10
Mr. Leatherwood labels his claim as a vagueness challenge, see Aplt. Br. at 37 (“[Rule 17] w[as] unconstitutionally vague”), but he does not argue that the language of Rule 17 itself is impermissibly vague. Instead, he argues he lacked fair warning — from any source — about the circumstances under which Rule 17 could be enforced. See id. at 39. Courts have recognized such a due process fair warning argument in the revocation context. See, e.g., Gallo, 20 F.3d at 11.
In Gallo, a probationer claimed he lacked fair warning that he could violate his probation by refusing to submit to inpatient medical care when his probation condition required him to submit to care “upon his release from i[n]patient hospitalization[.]” Id. at 9, 12 (emphasis added). The First Circuit found the probationer had adequate warning based on, among other things, the probation officer’s and the court’s “repeated[ ] explanations]” that the probationer’s conduct risked revocation. Id. at 13. Similarly, in Green v. Abrams, the Second Circuit rejected a fair warning challenge to a probation condition, holding that although the written probation condition “did not designate a particular time for payment,” the probation officer’s “constant urging to pay the fine should have put [the defendant] on notice” that the probation condition required “immediate attempts at payment.” 984 F.2d 41, 46-47 (2d Cir. 1993).
Courts generally look to the list of probation conditions to determine whether a defendant had adequate notice of proscribed activities. See, e.g., United States v. Grant, 816 F.2d 440, 442 (9th Cir. 1987). “Of course, where the warning is not contained in a formal [probation] condition, the record must be closely scrutinized to determine whether the defendant did, in fact, receive the requisite warning.” Id. (quotations omitted). In this regard, “the inquiry into fair warning is not necessarily confined to the four corners of the probation order.” Gallo, 20 F.3d at 13. “The meaning of a probation order may be illuminated by the judge’s statements ... or other events, any or all of which may ... aid[] the court to determine whether a probationer has been forewarned....” Id.
2. Substantive Due Process
As relevant to Mr. Leather-wood’s arguments on appeal, the Due Process Clause also imposes “substantive limits on the revocation of [] conditional liberty....” Black v. Romano, 471 U.S. 606, 610, 105 S.Ct. 2254, 85 L.Ed.2d 636 (1985); see, e.g., Bearden v. Georgia, 461 U.S. 660, 666, 103 S.Ct. 2064, 76 L.Ed.2d 221 (1983) (recognizing substantive limit on the automatic revocation of probation where an indigent defendant is unable to pay a fine); Douglas v. Buder, 412 U.S. 430, 432, 93 S.Ct. 2199, 37 L.Ed.2d 52 (1973) (recognizing substantive limit on revocation of probation absent evidence the probationer violated probation). A revocation violates due process when it is “fundamentally unfair or arbitrary.” Bearden, 461 U.S. at 666, 103 S.Ct. 2064; see Cummings v. Sirmons, 506 F.3d 1211, [1046]*10461237 (10th Cir. 2007) (“[I]n rare circumstances, a determination of state law can be so arbitrary or capricious as to constitute an independent due process violation.” (alterations and quotations omitted)). “[T]he deprivation occasioned by the state’s failure to follow its own law must be arbitrary in the constitutional sense; that is, it must shock the judicial conscience.” Aycox v. Lytle, 196 F.3d 1174, 1179-80 (10th Cir. 1999) (quotations omitted).11
D. Analysis
As the following analysis shows, Mr. Leatherwood’s procedural and substantive due process arguments fail for much the same reasons.
I. Mr. Leatherwood’s Procedural Due Process Argument Fails
Mr. Leatherwood’s procedural due process/fair warning argument does not challenge the content of Rule 17 but rather its scope. Under the section of his opening brief titled “The Special Probation Conditions ... were unconstitutionally vague,” he contends Rule 17 did not provide fair warning that his suspended sentence'could be revoked for violating the rule when he was incarcerated.' Aplt. Br. at 37-38. He further argues that no other source — not his probation documents, the revocation hearing, Oklahoma law, or otherwise — provided fair warning. Id. at 39 (contending “Mr. Leatherwood received no notice whatsoever from any source that [Rule 17] would apply while in prison”).12 Because Mr. Leatherwood had ample warning, his procedural due process claim fails.
a. Mr. Leatherwood had fair warning that Rule 17 applied while he was in prison
Mr. Leatherwood had fair warning regarding the consequences of engaging in a relationship with Ms. Wood based on Judge Watson’s statements during the January 8, 2010 revocation hearing. See Maynard v. Cartwright, 486 U.S. 356, 361, 108 S.Ct. 1853, 100 L.Ed.2d 372 (1988) (“Objections to vagueness under the Due Process Clause rest on the lack of notice, and hence may be overcome in any specific case where reasonable persons would know that their conduct is at risk.”); Gallo, [1047]*104720 F.3d at 12 (“[T]he fair warning doctrine does not provide a safe harbor for probationers who' choose to ignore the obvious”).
The judge informed Mr. Leatherwood that continuing his relationship with Ms. Wood while incarcerated could result in further revocation of his suspended sentence:
Good lawyering ... convinced me [to impose the original suspended sentence] .... And noiv they put you in jail and you’re doing the same thing over there.... And you may not even be a threat but the law says that as a sex offender you cannot have a relationship with a person who has minor children. ... I gave you all the rope in the world and you hung yourself with it.
ROA at 1616-17 (emphasis added). The judge told Mr. Leatherwood that he had been “doing the same thing” — that is, “hav[ing] a relationship with a person who has minor children” — after “they put [him] in jail” awaiting his revocation hearing. Id. at 1617. These statements clearly informed Mr. Leatherwood that maintaining such a relationship was prohibited even while he was incarcerated.
The following additional statements from Judge Watson to Mr. Leatherwood reinforce this point:
• “You know, I can’t tell you how to live your life.... But it’s the children and that Sex Offender Registration Act says you can’t be around them. Now, that’s not going to change. That is the rule.” Id. at 1616.
• “But if you’ve got some questions you better ask it now. And I hope [Ms. Wood] gets it. I mean, she’s going to havé to abandon her children, completely abandon her children for her to be with you.” Id. at 1618.13
At the second revocation hearing on August 3, 2010, Mr. Leatherwood’s statements to Judge Bass-LeSure showed he had understood the potential ramifications of his behavior yet chose to accept the risk and pursue the relationship:
• I’m not trying to make an excuse. I understand the Rule [17] was in place.... However, at the s[a]me time I would ask the Court to consider the fact that this was a relationship that I was in well before I was ever sentenced .... When I was sentenced on May 18th of 2009 I could not just stop being in that relationship with the person that I was committed to for my future. And obviously I made the decision, Your Honor to do that. I take full responsibility^ Id. at 1653-64.
• I would not do anything to intentionally or willfully violate the conditions of my probation except for Number 17 and I take responsibility for that. Id. at 1684.
These statements demonstrate that Mr. Leatherwood knew that Rule 17 “was in place” when he was in prison, and he took “full responsibility” for violating it. Indeed, he said he would “intentionally’ and “willfully violate” Rule 17 to maintain his relationship with Ms. Wood.14
[1048]*1048Even if his probation documents did not expressly state that Rule 17 could be enforced while Mr. Leatherwood was in prison, Judge Watson’s statements about the impropriety of the relationship and his imposition of the five-year revocation should have put Mr. Leatherwood on notice. See Gallo, 20 F.3d at 13; Green, 984 F.2d at 46-47. Yet Mr. Leatherwood continued the relationship with Ms. Wood after he was sent to prison, and he admitted at his second revocation hearing that he knew about and was responsible for violating Rule 17 while in prison. The 15-year revocation did not violate his due process right to fair warning.
b. Oklahoma statute did not render revocation unforeseeable
Mr. Leatherwood argues the state court imposed an “unforeseeable application” of the probation statute in violation of due process. Aplt. Br. at 37. By revoking his suspended sentence for violation of a probation condition while incarcerated, the court, he says, effectively held that “incarceration was the equivalent of probation.” Id. He points out that the Oklahoma code defines probation as “a procedure by which a defendant found guilty of a crime ... is released by the court subject to conditions imposed by the court and subject to supervision of the Department of Corrections.” Okla. Stat. tit. 22 § 991a(E) (emphasis added); see Aplt. Br. at 32-33. Because he was imprisoned, he argues, he could not be on probation, and thus conditions of probation like Rule 17 could not apply to him. In light of this statute, it was unforeseeable, he contends, that the court would enforce a Rule 17 violation during his incarceration.
To the extent the foregoing presents a potentially viable due process argument, it lacks merit. The Oklahoma probation statute does not tell the whole story. As noted previously, after conviction, a defendant’s sentence can include probation, a suspended sentence, or both. Okla. Stat. tit. 22 § 991a(A)(l). In Mr. Leatherwood’s case, his revocation concerned his suspended sentence, not his probation. He has pointed to no Oklahoma law providing that a suspended sentence may not be revoked for violation of a probation condition irrespective of whether the violation occurred when incarcerated. And even if Oklahoma law is not clear on this point, Judge Watson gave him fair warning that having a relationship with Ms. Wood while incarcerated could result in revocation of his suspended sentence.
c. Oklahoma case law supports revocation
The parties dispute the impact of two Oklahoma cases on the due process issue. The State relies on Crowds v. State, 675 P.2d 451 (Okla. Crim. App. 1984), and Demry v. State, 986 P.2d 1145 (Okla. Crim. App. 1999), to argue that the court could revoke Mr. Leatherwood’s suspended sentence even while he was incarcerated. Aplee. Br. at 16-17. In Crowels, the OCCA held a suspended sentence “imposes the inherent condition that the defendant [1049]*1049should not commit any felony during the period of that sentence.” 675 P.2d at 453 (affirming the revocation of an inmate’s suspended sentence after he committed a felony while incarcerated). In Demry, the OCCA held “a suspended sentence for a misdemeanor contains the inherent condition that the person shall not commit the same misdemeanor during the period of suspension.” 986 P.2d at 1148.
The State concedes Oklahoma courts have never squarely held that a probation rule can be applicable to someone who is incarcerated, see Oral Arg. 16:55-17:08, but it argues that these cases placed Mr. Leatherwood on notice that he was subject to revocation for violating Rule 17 while incarcerated, Aplee. Br. at 19. Mr. Leatherwood argues the cases “are wholly ditinguishable” from his case. Aplt. Br. at 26.
Although the circumstances of Mr. Leatherwood’s revocation were different from those in either Crowels or Demry, his revocation was at least a plausible extension of the general principle from those cases that a suspended sentence can be revoked for acts committed during incarceration. And as with the probation statute, Judge Watson’s warnings cured any ambiguity in the case law as far as fair warning is concerned.
2. Mr. Leatherwood’s Substantive Due Process Argument Fails
Mr. Leatherwood argues the court’s “arbitrary disregard of Oklahoma sentencing law ... is shocking to the judicial conscience,” id. at 31, a substantive due process claim.15 But it was not fundá-mentally unfair or arbitrary for the State to revoke his suspended sentence for violating Rule 17 during incarceration.
Mr. Leatherwood’s argument fails based on our previous discussion about the Oklahoma probation statute and the Oklahoma cases. If the statute and the cases do not support Mr. Leatherwood’s argument that he lacked fair warning, it follows that the revocation of his suspended sentence for conduct while in prison cannot be deemed arbitrary, much less fundamentally unfair. The district court, in denying his § 2241 application, said it well: “[E]ven if the state court’s interpretation and application of state law was incorrect, it was not obviously so or so egregious as to shock the judicial conscience in the circumstances existing here.” Leatherwood v. Allbaugh, No. CIV-13-1149-HE, 2016 WL 4006029, at *3 (W.D. Okla. July 25, 2016). This is particularly true in light of Oklahoma law providing that a sentencing court may order the defendant “at the time of sentencing or at any time during the suspended sentence to do one or more” enumerated actions, Okla. Stat. tit. 22 § 991a(A)(1)(a)-(gg), as well as comply with “any other provision specifically ordered by the court,” id. § 991a(A)(1)(hh).
Mr. Leatherwood already had received a five-year revocation for continuing his relationship with Ms. Wood, including while he was in jail. The ensuing 15-year revocation for continuing the relationship was a heavy blow, but Mr. Leatherwood does not argue an Eighth Amendment violation and, as explained above, his substantive due process argument fails.16
[1050]*1050⅜ * * ⅝
We affirm the district court’s denial of relief on Mr. Leatherwood’s § 2241 habeas application.
E. Certificates of Appealability
Mr. Leatherwood seeks COAs on the issues of (1) judicial bias/conflict and (2) cumulative error. We deny these requests.
1. COA and Standard of Review
A COA is a jurisdictional prerequisite to this court’s review of a habeas application. 28 U.S.C. § 2253(c)(1)(A); Dulworth v. Jones, 496 F.3d 1133, 1135 (10th Cir. 2007). To receive a COA, the prisoner must make “a substantial showing of the denial of a constitutional right.” 28 U.S.C. § 2253(c)(2); Clark v. Oklahoma, 468 F.3d 711, 713 (10th Cir. 2006). The COA inquiry “is not coextensive with a merits analysis.” Buck v. Davis, — U.S. -, 137. S.Ct. 759, 773, 197 L.Ed.2d 1 (2017). “At the COA stage, .the only question is whether the applicant has shown that ‘jurists of reason could disagree with the district court’s resolution of his constitutional claims or that jurists could conclude the issues presented are adequate to deserve encouragement to proceed further.’ ” Id. (quoting Miller-El v. Cockrell, 537 U.S. 322, 327, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003)).17
2. Judicial Bias/Conflict
Mr. Leatherwood claims he was denied his due process right to an impartial tribunal. He attempts to combine separate claims of judicial bias and judicial conflict into one claim. As to the judicial bias part of the claim, due process requires a “neutral and detached hearing body.” Gagnon, 411 U.S. at 786, 93 S.Ct. 1756 (quotations omitted). Judicial rulings alone are almost always insufficient to establish bias, see Liteky v. United States, 510 U.S. 540, 555, 114 S.Ct. 1147, 127 L.Ed.2d 474 (1994), as are mere “speculation, beliefs, conclusions, innuendo, suspicion, opinion, and similar non-factual matters,” United States v. Cooley, 1 F.3d 985, 993 (10th Cir. 1993).
Mr. Leatherwood argues Judge Bass-LeSure was biased because she believed the initial sentence imposed by Judge Watson was too lenient. During the second revocation hearing, Mr. Leather-wood said that “[t]he State was clearly not happy with the sentence that I received from Judge Watson.” ROA at 595. Judge Bass-LeSure replied, “I agree.” Id. This comment, he argues, shows bias. But Mr. Leatherwood offers nothing to support his claim other than Judge Bass-LeSure’s statement, which provides, at most, her opinion as to the appropriateness of Judge Watson’s original sentence. It is not a valid basis for a claim of judicial bias. See Liteky, 510 U.S. at 555, 114 S.Ct. 1147; Cooley, 1 F.3d at 993-94. Reasonable jurists could not debate the district court’s denial of this claim, and we thus deny COA.
As to judicial conflict, Mr. Leath-erwood argues the same D.A.’s office that [1051]*1051was prosecuting his revocation was also investigating Judge Bass-LeSure, and she thus would have been inclined to side with the D.A. who was prosecuting Mr. Leath-erwood and revoke Mr. Leatherwood’s suspended sentence. Mr. Leatherwood’s conflict claim overstates the record evidence. The D.A.’s office notified Judge Bass-LeSure about its investigation of her five months after she had revoked the remaining 15 years of Mr. Leatherwood’s suspended sentence. Mr. Leatherwood offers nothing beyond speculation that the judge was aware of the D.A.’s investigation into her misconduct at the time of his second revocation hearing. Nor does he offer any evidence that any such contemporary investigation may have influenced her decision. The district court properly rejected this claim, and we again deny a COA.
3. Cumulative Error
Mr. Leatherwood claims that even if none of his alleged errors in isolation justify relief, “the combined effect of the errors deprived him of due process and a fundamentally fair proceeding.” Aplt. Br. at 59. Mr. Leatherwood lacks the minimum of two errors necessary to sustain a cumulative error claim. Hanson v. Sherrod, 797 F.3d 810, 852 (10th Cir. 2015); Stouffer v. Trammell, 738 F.3d 1205, 1229 (10th Cir. 2013). We therefore decline to issue a COA.
F. Motion to Supplement
Mr. Leatherwood asks us to supplement the record with an affidavit from Judge Watson. We will not consider material outside the record that was not before the district court unless it is necessary to “truly disclose[ ] what occurred in the district court.” Fed. R. App. P. 10(e)(1); United States v. Kennedy, 225 F.3d 1187, 1192 (10th Cir. 2000) (noting exceptions to Rule 10(e) are “rare”). The affidavit does not satisfy this rule. We therefore deny the motion to supplement.
III. CONCLUSION
We affirm the district court’s denial of the application for habeas relief. We also deny the requests for additional COAs and the motion to supplement the record.