
380 B.R. 375 (2007)
The CADLE COMPANY, Plaintiff-Appellant
v.
David E. ZOFKO, Defendant-Appellee.
No. 1:06cv170, Bankruptcy No. 04-11758, Adversary No. 04-1157.
United States District Court, W.D. Pennsylvania.
January 23, 2007.
*376 *377 Mark G. Claypool, Erie, PA, for Plaintiff-Appellant.
Michael A. Agresti, Erie, PA, for Defendant-Appellee.

MEMORANDUM OPINION
SEAN J. McLAUGHLIN, District Judge.
This appeal involves a dispute originating in the underlying bankruptcy case as to whether the Debtor, David E. Zofko, is entitled to a discharge of his debts. Debtor's primary creditor is the Plaintiff/Appellant, the Cadle Company ("Cadle"). On September 29, 2004, Cadle filed a complaint in the Bankruptcy Court requesting that the Debtor be denied a discharge for, among other things, allegedly making false oaths in connection with his bankruptcy petition. Following a bench trial, the Bankruptcy Court entered an order dismissing Cadle's complaint. This appeal followed. The dispute involves a core proceeding pursuant to 28 U.S.C. § 157(b)(2)(J), and we have jurisdiction under 28 U.S.C. § 158(a)(1) and (c)(1)(A).

I. BACKGROUND
The Debtor is a licensed professional engineer. By 1992 he and his then wife, Marian Zofko, had enjoyed substantial financial success, having accumulated a net worth of approximately $4,000,000. Their assets included a residence in Warren, Ohio and a hunting camp in Tidioute, Pennsylvania which had been purchased, together with its contents, in 1977. On December 7, 1992, Debtor and his wife created The David E. Zofko and Marian L. Zofko Children's Trust ("Children's Trust") for the benefit of their two daughters. The Warren, Ohio residence and the Tidioute Property were gifted to the Children's Trust that same year.
Thereafter, Debtor's fortunes began in decline. It appears his present financial problems stem largely from his involvement in an unsuccessful construction project known as the "Surrey Point Condominiums." This project was financed by National City Bank under a note in the amount of $500,000. In 1994, National City Bank called the note, which was subsequently acquired by Cadle. Cadle eventually obtained a judgment against the Debtor in the amount of $569,229.71. Cadle pursued the judgment and ultimately obtained a settlement which included a payment from the Children's Trust, certain of Debtor's oil and gas interests, and Debtor's IRA accounts. When Cadle foreclosed on a vacant lot in Tidioute and attempted to garnish the Debtor's wages, Debtor filed for protection under Chapter 7 of the Bankruptcy Code.
On July 22, 2004, Debtor filed his Bankruptcy Schedules and Statement of Financial Affairs. Cadle alleges that these filings contained numerous false statements. A trial was held on January 26, 2006 and, on February 3, 2006, the Bankruptcy Court dismissed the complaint. On June 27, 2006, the Bankruptcy Court issued an opinion setting forth its rationale for the February 3 ruling. At issue are the Bankruptcy Court's findings of fact and conclusions of law as they relate to the Debtor's alleged nondisclosure of several items, which we discuss seriatim.
*378 1. The Zofko Family Trust
In 1993, Debtors' parents, Andrew (now deceased) and Anna Mae Zofko, created a trust (the "Zofko Family Trust") for the purpose of providing for Anna Zofko's health and welfare. Debtor's sister, Mary Jeanine Pipino, is the named Trustee. As of the date of the trial in this matter, the Trust assets were valued at approximately $400,000. Upon Anna Zofko's death, the remaining assets will be divided between the Debtor, Mrs. Pipino, and a third sibling. On April 12, 2004, Debtor borrowed $4,000 from the Zofko Family Trust. There are no records indicating that the loan has been repaid.
Cadle complains that Debtor failed to mention this trust anywhere on his Bankruptcy Schedules and Statement of Financial Affairs. Specifically, under Item 19 of his Schedule B-Personal Property, relating to "contingent and non-contingent interests in estate of a decedent . . . or trust," Debtor represented he had no such interest by checking the box marked "None." The Bankruptcy Court found that Debtor was unaware of his interest in this trust at the time of the bankruptcy filing and therefore had no intent to knowingly and fraudulently make a false oath in failing to list the interest on his schedules. The Bankruptcy Court found that even Mrs. Pipino, the trustee, did not believe that Debtor was a contingent beneficiary of the trust because it was thought that the Trust had been amended to exclude Debtor while his divorce from Marian Zofko was pending.[1]
2. The Tidioute Property and Contents
As a result of Debtor's divorce settlement, the Children's Trust retained ownership of the Warren, Ohio residence and the Tidioute property. Debtor obtained the right to occupy the Tidioute property for up to 23 years at a rental rate equivalent to the real estate taxes, the real estate insurance premiums, and the, cost of maintenance. He also acquired the right to purchase the Tidioute property from the Children's Trust during the term of his tenancy for fair market value. A lease agreement dated June 1, 2000 set a specified monthly rental rate of $500 until June 1, 2020 and required Debtor to make a $500 security deposit. Debtor's federal income tax return for the year 2002 indicates that he took an itemized deduction for real estate taxes paid on the property even though Debtor was apparently not obligated by the lease to pay real estate taxes on the dwelling. Debtor conceded at trial that this deduction probably was not proper but would have been proper if he had owned the property. Cadle complains that nowhere in Debtor's Bankruptcy Schedules and Statement of Financial Affairs did Debtor mention: his right to occupy the property for 16 years at a fixed rate of $500/month; the $500 security deposit paid; his option to purchase the property during the term of the lease; or the fact that he had taken deductions on his prior federal income tax returns for real estate taxes paid on the property.
With respect to the contents of the Tidioute Property, Cadle notes that, as of July 2004, the Property contained a washer and dryer, stove, refrigerator, microwave, VCR, DVD, stereo, four beds, a 36-inch television, and some lamps. The contents of the Property were insured for losses up to $25,000. Notably, in April of 2001 the Tidioute property was burglarized, resulting in damage to the dwelling and the loss *379 of personal property. Several months later, Debtor received $25,686 under a renter's insurance policy in his name. Cadle complains that the only "household goods and furnishings" listed by Debtor on his Schedule B-Personal Property were "old computer ($0)" and "miscellaneous outdoor furniture ($100)" relative to the Tidioute Property. Although Debtor contends that it was his intent that all the personal items within the Tidioute Property be conveyed to the Children's Trust, Cadle notes that Debtor had full use of those items and his children were living elsewhere.
The Bankruptcy Court found that, with respect to the Tidioute Property itself, Debtor's option to purchase the property was "immaterial and of no value" because it was merely the right to purchase the property at fair market value. Since the Trustee of the Children's Trust is the Marian Zofko's (i.e. Debtor's ex-wife's) brother, the Bankruptcy Court found there is no reason to believe that Debtor could obtain ownership of the Property for anything less than fair market value.
As for the contents of the Tidioute Property, the Bankruptcy Court credited the Debtor's testimony that it had been Debtor's intent to convey both the real property and its contents to the Children's Trust, just as the property had originally been purchased together with its contents included. The Bankruptcy Court further credited the Debtor's estimation that the market value of the personalty within the property was $2,000 to $2,500. The Bankruptcy Court concluded that, even if Debtor erroneously considered the personalty to be property of the Children's Trust, all of the property would have been within the allowable exemptions and would have therefore made no difference to creditors.
3. The Rhodes Property and Contents
At times relevant to this appeal, the Debtor also occupied a property located on North Rhodes Avenue in Niles, Ohio (the "Rhodes" property). That property is owned by the Debtor's sister, Mary Jeanine Pipino, and her husband, James D. Pipino. Mr. and Mrs. Pipino lived at the Rhodes Property until October, 2000, when they purchased a new home. Thereafter, Debtor entered into a 20-year rental agreement commencing on January 1, 2001 and terminating December 31, 2021. Pursuant to this agreement, Debtor, as tenant, paid a $5,000 security deposit and also paid $2,000 per month in rent as well as all utilities. In 2000 or 2001, Debtor gave Mrs. Pipino a lump sum of $35,000 and made additional payments to Mrs. Pipino totaling $13,600 in 2001, $14,000 in 2002, $16,768.50 in 2003, and $8,719.09 in 2004. On his 2002 federal income tax return, Debtor took itemized deductions for the mortgage interest and real estate taxes paid on the property. Debtor had credit card statements mailed to the residence and listed the property as his address on a 2005 employment application.
Cadle complains that Debtor made no mention of the Rhodes Property in his Schedule G (pertaining to unexpired leases) or his Schedule J (pertaining to current rental expenditures). He made no mention of the security deposit payment in his Schedule B (pertaining to personal property). Further, Debtor made no mention of the property in his Statement of Financial Affairs, Item 15, which required him to list all premises occupied within the previous two years, and he failed to list Mrs. Pipino as a creditor to whom a debt had been paid within the 90 days prior to commencement of the bankruptcy case. Despite the fact that Debtor had been the named insured on a renter's insurance policy covering personal property at the Rhodes Property for losses up to $75,000, Debtor failed to list any of those personalty items in his *380 statement of financial affairs. As of March 2001, these items included bar stools, bunks, miscellaneous furniture, drapes and window dressings, a refrigerator, stoves, a microwave, a washer and a dryer.
The Bankruptcy Court found that Debtor had no intent to knowingly and fraudulently make a false oath in these regards. The Bankruptcy Court found that Debtor originally desired to purchase the Rhodes Property and, toward that end, paid an advance rental payment of $35,000 and treated his payments as a purchase for tax purposes in 2002. After that year, however, Debtor did not treat the rental as a purchase for tax purposes, and there is no evidence that a purchase arrangement was ever discussed or agreed to by Mrs. Pipino. Though the lease agreement called for a $5,000 security deposit, the Bankruptcy Court found that it was not clear on the record whether such deposit was ever actually paid.
The Bankruptcy Court further found that, during the term of the lease, the primary resident of the Rhodes property was Rebecca Woodford, then Debtor's girlfriend (now his wife). The Bankruptcy Court found that Debtor occasionally stayed at the Rhodes property during this time but that he primarily resided at the Tidioute property. The Bankruptcy Court further found that, while Mrs. Pipino had left a few pieces of furniture and some window treatments behind in the property, most of the personal property at the residence (including appliances) belonged to Ms. Woodford. It was her belongings that were insured under the renter's policy (albeit, evidently in Debtor's name).
4. The Travel Allowance/ Professional Business Earnings
From 2001 through at least 2004, Debtor was employed by Aerotech Mechanical Contractors, Inc. He received a salary and a travel allowance for work related expenses. Debtor received a travel allowance of $18,000 in 2002 and also received allowances in 2003 and 2004. On his Bankruptcy Schedule I  Current Monthly Income, Debtor stated that he was a Professional Engineer and had been employed by Aerotech for five years. He reported his current "monthly gross wages, salary and commissions" to be $5,400. He reported "$0.00" earnings as to "regular income from operation of business or profession," "interests and dividends," and "other monthly income." At the bottom of the form, Debtor wrote:
In the past (excluding the past year), Debtor has performed limited engineering services as an independent consultant. At the present time, no such work is being performed as there is no demand. It is possible that such work will be present in the future should the economy continue to grow.
Debtor reported his gross wages from Aerotech to be $62,400 in 2002; $62,400 in 2003; and $30,000 as of June 30, 2004.
Cadle objects that Debtor did not include the amounts received for travel allowances as part of his gross wages for the years 2002 through 2004. This is in contrast to Debtor's actions when completing a 2005 employment application in which he calculated his gross salary from Aerotech by including the travel allowance as part of his earnings. In fact, Cadle notes, Debtor did not mention the travel allowance anywhere on his Bankruptcy Schedules and Statement of Financial Affairs, although he did report certain transportation expenses and auto payments on his Schedule J  Current Expenditures. Cadle further objects that, although Debtor's federal income tax returns reflect earnings from his professional consulting business totaling $19,170 in 2002 and $6,350 in 2004, Debtor *381 made no mention of these receipts in his Statement of Financial Affairs.
The Bankruptcy Court found that any omissions in these respects did not reflect an intent on the Debtor's part to knowingly and fraudulently make a false oath in connection with his bankruptcy proceedings. The Bankruptcy Court acknowledged that Debtor was inconsistent with respect to his treatment of the travel allowance on his income tax returns.[2] As for Debtor's failure to report the travel allowance in his bankruptcy schedules, the Bankruptcy Court credited the Debtor's representation that his travel expenses exceeded the allowances. The court therefore concluded that any omission of the allowance was immaterial and did not reflect an intent to deceive.
With regard to Debtor's earnings from his independent consulting business, the Bankruptcy Court examined Debtor's federal income tax returns and found that, while Debtor reported a total income of $59,950 for the year 2002, the net income from his personal engineering business totaled only $12,894. In 2003, Debtor had no gross income from the operation of his business but did incur expenses resulting in a net loss of $9,338. In 2004, the Debtor reported gross income of $6,350 from his personal business, with a net income of $2,258. Based on these figures, the Bankruptcy Court concluded that the Debtor's income from his personal consulting business was "minuscule." The court found that the income disclosed by Debtor fairly represented his earnings and that Debtor had no intention to knowingly and fraudulently make a false oath regarding his business income.
5. Evenflow Eastern Partners
Also reported on the Debtor's 2002-2004 tax returns is a "working interest investment" in Evenflow Eastern Partners showing income in the amount of $662 (2002), $531 (2003), and $1,881 (2004). Cadle complains that this income is not reported anywhere on Debtor's statement of financial affairs or on his Schedule B relating to partnerships and joint ventures.
The Bankruptcy Court noted that, as part of his settlement agreement with Cadle and the Children's Trust in 1999, Debtor had assigned all of his rights in the Kleese Development Partnership and gas and oil well partnership interests to Cadle. Thereafter, despite the assignment, Debtor continued to receive certain royalty checks and also accepted a $2,000 payment that was offered from Kleese for his interest in the partnership. The Bankruptcy Court found that, while Debtor may have received royalty checks and the $2,000 payment from. Kleese, Debtor believed that Cadle had the right to take those interests at any time by virtue of the prior assignment and, therefore, he did not knowingly and fraudulently make a false oath when indicating on his bankruptcy filings that he had no interests in partnerships or joint ventures.
6. The Crawford Judgment
At the time he filed his Bankruptcy Schedules and Statement of Financial Affairs, Debtor owned an outstanding judgment against one Tracey Crawford for $7,600. Ms. Crawford was a prior tenant and Debtor had obtained the judgment in $2,000 for damages incurred in 1997 and 1998. Cadle objects that Debtor failed to mention the judgment anywhere on his *382 Schedules and Statement of Financial Affairs.
The Bankruptcy Court found that the judgment is uncollectible and of no value. It further found that Debtor did not knowingly or fraudulently make a false oath with respect to the judgment.

II. STANDARD OF REVIEW
We review the Bankruptcy Court's legal determinations de novo, its factual findings for clear error, and its exercises of discretion for abuse. See In re Engel, 124 F.3d 567, 571 (3d Cir.1997); In re J. Allan Steel Co., 336 B.R. 226, 228 (W.D.Pa. 2005).

III. DISCUSSION
Cadle contends that, under § 727(a)(4)(A) of the Bankruptcy Code, the Debtor should not be entitled to a discharge of his debt.[3] That provision states, in pertinent part, that the bankruptcy court "shall grant the debtor a discharge, unless . . . the debtor knowingly and fraudulently, in or in connection with the case[,] made a false oath or account." 11 U.S.C. § 727(a)(4)(A). A debtor's failure to list all assets owned in his Bankruptcy Schedule and Statement of Financial Affairs can constitute a false oath or account for purposes of § 727(a)(4)(A), since these are statements made under oath. See In re Spitko, 357 B.R. 272, 312 (Bankr. E.D.Pa.2006); In re Strickland, 350 B.R. 158, 163 (Bankr.D.Del.2006) (citing cases).
As a general matter, the Code's discharge provision is to be construed liberally in favor of the debtor and against the creditor. See Rosen v. Bezner, 996 F.2d 1527, 1534 (3d Cir.1993); In re Pelkowski, 990 F.2d 737, 744 (3d Cir.1993). Consequently, a creditor opposing discharge has the burden of establishing by a preponderance of the evidence that the obligation is not dischargeable. See Boston University v. Mehta, 310 F.3d 308, 311 (3d Cir.2002) (citing Grogan v. Garner, 498 U.S. 279, 111 S.Ct. 654, 112 L.Ed.2d 755 (1991)). To successfully challenge a debtor's discharge under § 727(a)(4)(A), a creditor must prove that:
(1) the debtor made a statement under oath;
(2) the statement was false;
(3) the debtor knew the statement was false;
(4) the debtor made the statement with the intent to deceive; and
(5) the statement related materially to the bankruptcy case.
See In re Spitko, supra, at 312 (Bankr. E.D.Pa. Oct. 23, 2006); In re Strickland, 350 B.R. at 163; In re Dolata, 306 B.R. 97, 148 (Bankr.W.D.Pa.2004).
"`The requirement that a false statement" be knowingly and fraudulently made is satisfied for purposes of 11 U.S.C. § 727(a)(4)(A) if the debtor knows the truth and nonetheless willfully and intentionally swears to what is false,'" In re Dolata, 306 B.R. at 148-49 (quoting In re Ingle, 70 B.R. 979, 984 (Bankr.E.D.N.C. 1987)) (additional citation omitted), or if the debtor exhibits "reckless indifference to the truth." Id., at 149 (quoting In re Dubrowsky, 244 B.R. 560, 576 (E.D.N.Y. 2000)) (additional citations omitted). See also In re Spitko, supra, at 312 (reckless indifference to the truth will fall within the scope of § 727(a)(4)(A) if the subject matter is material to the administration of the bankruptcy case) (citing Matter of Beaubouef 966 F.2d 174, 178 (5th Cir.1992)). *383 Moreover, the necessary fraudulent intent may be proved through circumstantial evidence, or may be inferred from a course of conduct such as a "pattern of concealment and nondisclosure." Dolata, 306 B.R. at 149 (quoting In re Hatton, 204 B.R. 477, 484 (E.D.Va.1997)).
In this case, there is no real dispute that the Debtor's Schedules and Statement of Financial Affairs contain many inaccuracies. Thus, the dispute before the Bankruptcy Court centered primarily on whether the Debtor's misstatements had been made with the requisite fraudulent intent and whether they related materially to the bankruptcy case. The Bankruptcy Court found against Cadle on both of these issues. It concluded, among other things, that:
[m]ost of the asserted falsities relate to items of trivial value. In numerous cases, the inaccurate answers were disclosed elsewhere on the Schedules.
* * *
While certain statements made by the Debtor were inaccurate, they are immaterial and of no effect on creditors. Further, the Debtor did not knowingly and fraudulently make a false oath. There was no intent on the part of the Debtor to hinder, delay and defraud his creditors.
(Op., dated 6/27/06 [Doc. # 1], at p. 20.)
Cadle argues that the Bankruptcy Court failed to apply the law correctly and made clearly erroneous findings when it ruled that the Debtor did not violate § 727(a)(4)(A). While we render no opinion on the ultimate merits of Cadle's "nondischargeability argument," we believe that a remand for further fact finding is appropriate.
First, it appears that the Bankruptcy Court applied the wrong legal standard in determining the materiality of the Debtor's misstatements. In its written opinion, which constituted its findings of fact and conclusions of law, the Bankruptcy Court addressed seriatim the various assets which Cadle had complained were not properly reported on Debtor's Bankruptcy Schedules and Statement of Financial Affairs. As to several items, the Bankruptcy Court's analysis focused on the pecuniary value of the asset in question and whether its omission from the Debtor's Bankruptcy Schedules and Statement of Financial Affairs substantially impacted the creditors' recovery from the estate. In this respect the Bankruptcy Court's legal analysis was flawed.
In determining whether an omission is material for purposes of § 727(a)(4)(A), "the issue is not merely the value of the omitted assets or whether the omission was detrimental to creditors." 4 Collier on Bankruptcy, ¶ 727.04[1], at 727-59. Rather, for purposes of § 727(a)(4)(A), the test for "materiality" is whether the subject matter of the false oath "bears a relationship to the bankrupt's business transactions or estate, or concerns the discovery of assets, business dealings, or the existence and disposition of his property." In re Chalik, 748 F.2d 616, 618 (11th Cir. 1984). See also; In re Spitko, supra, at 312; In re Dolata, 306 B.R. at 148 (quoting In re Wilson, 290 B.R. 333, 337 (Bankr. C.D.Ill.2002)). As one court has noted:
. . . undergirding this analysis of 11 U.S.C. § 727(a)(4)(A) is that section's purpose of insuring that the chapter 7 debtor has made honest and accurate disclosure of his financial circumstances so the bankruptcy trustee and creditors have sufficient information' for the proper administration of the chapter 7 case, without having to conduct costly investigations. See In re Aubrey, 111 B.R. 268 (274 B.A.P. 9th Cir.1990); In re Burnley, *384 1999 WL 717215, at *3 (E.D.Pa. 1994). The bankruptcy process depends upon the complete and candid disclosure of assets, income, expenses and liabilities of the debtor. See generally Oneida Motor Freight, Inc. v. United Jersey Bank, 848 F.2d 414 (3d Cir.1988) (failure to disclose a claim in a bankruptcy case may estop the debtor from later asserting that claim).
In re Spitko, supra, at 312. Thus, the omission even of assets having little value can be material. In re Strickland, 350 B.R. at 165. Proof of actual harm to creditors is unnecessary, and the debtor cannot excuse the omission merely by claiming that the undisclosed property was of little value to the estate. In re Spitko, supra, at 312 (citing cases). Accord In re Strickland, 350 B.R. at 165 (even if debtor's interest in hair stylist business had nominal value, it would be material since it related to the debtor's business dealings; therefore disclosure on debtor's Schedules and Statement of Financial Affairs was required).
Second, it is not clear from the Bankruptcy Court's analysis whether it applied the correct legal standard relative to intent. It appears to be a widely accepted principle that the relevant fraudulent intent under § 727(a)(4)(A) can be established by a showing of the Debtor's "reckless indifference to the truth," which may include a pattern of nondisclosure. See In re Dolata, 306 B.R. at 149 (quoting In re Dubrowsky, 244 B.R. at 576) (additional citations omitted); In re Spitko, supra, at 312 (reckless indifference to the truth will fall within the scope of § 727(a)(4)(A) if the subject matter is material to the administration of the bankruptcy case) (citing Matter of Beaubouef 966 F.2d at 178). See also In re Mitchell, 102 Fed.Appx. 860 (5th Cir.2004) (reckless indifference to truth supports denial of discharge under § 727(a)(4)); In re Keeney, 227 F.3d 679, 685-86 (6th Cir.2000) (same); In re Chavin, 150 F.3d 726, 728 (7th Cir.1998) (same); In re Hatton, 204 B.R. 477, 484 (E.D.Va.1997) (same). Because the Bankruptcy Court did not reference this standard in its memorandum opinion, it is not clear to us whether the Bankruptcy Court applied this standard in finding that Debtor lacked the requisite intent to defraud.
We recognize that the § 727 discharge provision has been described by Congress as "the heart of the fresh start of the bankruptcy law provisions." In re Katz, 203 B.R. 227, 231 (Bankr.E.D.Pa. 1996) (quoting Rosen, 996 F.2d at 1531). Consequently, denial of a discharge is considered "an extreme step . . . not to be taken lightly." Id. (citation omitted) (ellipsis in the original). Moreover, as we have noted, the discharge provision is to be construed liberally in favor of the debtor, requiring the creditor challenging discharge to carry the burden of proof by a preponderance of the evidence. Notwithstanding these principles, however, and the great deference normally accorded a bankruptcy court's findings of fact, we cannot affirm the decision where it appears the Bankruptcy Court's findings may have been premised on an errant application of the law.

IV. CONCLUSION
In sum, we agree with Cadle that the Bankruptcy Court committed certain legal errors which require us to reverse its February 3 ruling and remand the matter for further fact finding in light of the legal standards of materiality and intent discussed above. In light of our conclusion, we do not pass upon the ultimate merits of Cadle's argument that Debtor should be denied a discharge under § 727(a)(4)(A).
An appropriate order follows.


*385 ORDER

AND NOW, this 23rd day of January, 2007, for the reasons set forth in the accompanying Memorandum Opinion,
IT IS HEREBY ORDERED AND ADJUDGED that the Order entered by the Bankruptcy Court on February 3, 2006 be and hereby is REVERSED and the case REMANDED for further proceedings consistent with this opinion.
NOTES
[1]  In 1996, Marian Zofko initiated a divorce proceeding, which resulted in protracted litigation.
[2]  In 2002, the Debtor reported the travel allowance for federal income tax purposes and deducted expenses against it, but in years 2003 and 2004, he neither reported the travel allowance nor deducted work-related travel expenses.
[3]  In its complaint opposing discharge of Debtor's debt, Cadle initially invoked §§ 523 and 727(a)(5) of the Bankruptcy Code, in addition to § 727(a)(4)(A). Because those provisions are not at issue in this appeal, we do not address them further.
