 United States Court of Appeals
          FOR THE DISTRICT OF COLUMBIA CIRCUIT



Argued January 30, 2020                 Decided May 26, 2020

                         No. 18-5122

                    CHRISTOPHER J. CODE,
                        APPELLANT

                               v.

RYAN D. MCCARTHY , SECRETARY, U.S. DEPARTMENT OF THE
                       ARMY ,
                     APPELLEE


        Appeal from the United States District Court
                for the District of Columbia
                    (No. 1:15-cv-00031)



    Nathan S. Mammen argued the cause for appellant. With
him on the briefs were Hannah L. Bedard and Matthew J.
McIntee.

    John B. Wells, Raymond J. Toney, and Brian D. Schenk
were on the brief for amicus curiae Military-Veterans
Advocacy, Inc. in support of appellant.

     Jeremy A. Haugh, Special Assistant U.S. Attorney, argued
the cause for appellee. With him on the brief were Jessie K.
Liu, U.S. Attorney at the time the brief was filed, and R. Craig
                                2
Lawrence, Assistant U.S. Attorney. Roberto C. Martens Jr.,
Special Assistant U.S. Attorney, entered an appearance.

    Before: TATEL, PILLARD, and WILKINS, Circuit Judges.

    Opinion for the Court filed by Circuit Judge PILLARD.

     PILLARD , Circuit Judge: Lieutenant Christopher Code
asked the Army Board for the Correction of Military Records
(the Board or ABCMR) to expunge or amend Army
investigators’ determinations recorded in his military files.
The records at issue stated that credible information and
probable cause existed to believe that Code committed the
criminal offenses of making a false official statement with
intent to deceive and obtaining services under false pretenses.
The allegedly false statement was the expiration date of Code’s
current military orders, which he wrote in a blank on the 2007-
2008 school year registration form to re-enroll his three
children at the Fort Buchanan base school that they had
attended since 2005. The Secretary of the Army claims Code’s
provision of that date was a false pretense that he used to obtain
an additional year of schooling for his children when, the Army
alleges, Code knew they were not entitled to that service.

     When Code filled out the school form on April 30, 2007,
he was under orders assigning him to Fort Buchanan for three
years, from July 2005 to July 2008. Where the school
registration form stated “I am active duty and my current orders
will expire on _____,” Code filled in “July 2008.” Army
investigators apparently at first believed Code’s assignment
was for two years, not three; they opened a fraud investigation
on that premise. It is by now undisputed, however, that the
assignment was for three years. The investigation did not lead
to any criminal prosecution or military discipline. Yet, when
Code sought to have the allegations and charges removed from
                                3
his military records, the Board denied his application and the
district court sustained its decision. Because a basic mistake of
fact renders the Board’s decision arbitrary and capricious, we
reverse.

                       BACKGROUND

A. Legal Context

     The U.S. Department of Defense operates elementary and
secondary schools to serve families of individuals who live
and/or work on military installations where appropriate local
free public education is not available to their dependents. See
10 U.S.C. § 2164(a)(1)-(2); Department of Defense Instruction
(DoDI) 1342.26 ¶¶ 1, 6.2 (1997). The children of active duty
military members, including those who live outside such an
installation, may receive “tuition-free education at an
installation.” DoDI 1342.26 ¶¶ 6.2.1.1, 6.2.2.1. Eligibility for
tuition-free education is “based upon the permanent duty
station to which the military sponsor [e.g., the parent] is
assigned by official orders.” Id. ¶ 6.3.3. Anticipating possible
changes in a sponsor’s duty station, the governing statute and
policy provide that, “[i]f the status of the sponsor of a currently
enrolled student changes so that the child would no longer be
eligible for enrollment” at the military installation’s school,
“enrollment may continue for the remainder of the school
year.” Id. ¶ 6.3.7; see 10 U.S.C. § 2164(h)(1) (“The Secretary
of Defense shall permit a dependent of a member of the armed
forces . . . to continue enrollment in an educational program
provided by the Secretary . . . for the remainder of a school year
notwithstanding a change during such school year in the status
of the member . . . that, except for this paragraph, would
otherwise terminate the eligibility of the dependent to be
enrolled in the program.”).
                               4
     Under the Uniform Code of Military Justice (UCMJ), a
person commits the offense of making a false official statement
when he, “with intent to deceive[,] (1) signs any false record,
return, regulation, order, or other official document, knowing
it to be false; or (2) makes any other false official statement
knowing it to be false.” 10 U.S.C. § 907(a). A person commits
larceny under the UCMJ when he “wrongfully takes, obtains,
or withholds, by any means, from the possession of the owner
or of any other person any money, personal property, or article
of value . . . with intent permanently to deprive or defraud
another person of the use and benefit of property or to
appropriate it” for his own use or use by another. Id.
§ 921(a)(1). The UCMJ also makes it a criminal offense to,
“with intent to defraud, knowingly use[] false pretenses to
obtain services.” Id. § 921b. As relevant here, all three
offenses require proof of wrongful intent, and both false
statement and false pretenses specifically require intent to
defraud.

      As soon as a Department of Defense Criminal
Investigative Organization has “credible information that” the
subject of an investigation “committed a criminal offense,” it
must place the subject’s name and identifying information in
the title block of an investigative report—a step known as
“titling.” DoDI 5505.7 ¶¶ 6.1, 6.5 (2003). The Department of
Defense defines credible information as “[i]nformation
disclosed or obtained by a criminal investigator that,
considering the source and nature of the information and the
totality of the circumstances, is sufficiently believable to lead
a trained investigator to presume that the fact or facts in
question are true.” Id. ¶ E1.1.1. Concurrent with titling, the
investigative organization must list the subject’s name in the
Defense Central Index of Investigations (DCII), a searchable
database used by the Department of Defense’s security and
investigative agencies and selected other federal agencies “to
                                5
determine security clearance status and the existence/physical
location of criminal and personnel security investigative files.”
Id. ¶ E1.1.3. The subject’s identifying information “shall be
removed from the title block of a report of investigation and the
DCII” only “in the case of mistaken identity” or if it is
“determined a mistake was made at the time the titling and/or
indexing occurred in that credible information indicating that
the subject committed a crime did not exist.” Id. ¶ 6.6.

     When and if investigation “adequately substantiate[s]” the
commission of a criminal offense such that investigators have
“probable cause supported by corroborating evidence” to
believe that the subject in fact committed the crime, the
military investigative organization may issue an investigative
report supporting its determination that the offense is
“founded.” Army Regulation 190-45, ¶ 4-3(a) (2007); id.
Glossary § II, “Founded offense”; see Appellee’s Br. 26. If
investigators determine that no crime was committed, the
offense is reported as “unfounded.” See Army Regulation
190-45 Glossary § II, “Unfounded offense.”

     Individuals who believe their military file contains an error
may request that the Secretary of the military department that
created the record make corrections to it. See 10 U.S.C. § 1552.
Secretaries generally rely on civilian boards to review and act
on requests for correction. Id. § 1552(a)(1). The Secretary of
the Army reviews correction applications through the Army
Board for the Correction of Military Records, a board of
civilians “vested with broad authority to ‘correct any military
record when it considers it necessary to correct an error or
remove an injustice.’” Wolfe v. Marsh, 835 F.2d 354, 357
(D.C. Cir. 1987) (alterations omitted) (quoting 10 U.S.C.
§ 1552). The Board must “[r]eview all applications that are
properly before [it] to determine the existence of error or
injustice,” 32 C.F.R. § 581.3(b)(4)(i); “direct or recommend
                              6
changes” where needed to correct an error or injustice, id.
§ 581.3(b)(4)(ii); recommend hearings “when appropriate in
the interest of justice,” id. § 581.3(b)(4)(iii); and “[d]eny
applications when the alleged error or injustice is not
adequately supported by the evidence,” id. § 581.3(b)(4)(iv).
The burden rests with the applicant to “prov[e] an error or
injustice by a preponderance of the evidence.”              Id.
§ 581.3(e)(2). When a titling/indexing decision is under
review, the reviewing body “shall consider the investigative
information available at the time the initial titling/indexing
decision was made.” DoDI 5505.7 ¶ 6.9.

B. Factual Record

     Christopher Code was an officer in the U.S. Navy and is
now a member of the Navy Reserve. On July 25, 2005, Code
began a three-year tour of duty at Fort Buchanan Army Base in
San Juan, Puerto Rico. See Navy Personnel Command,
Official Change Duty Orders for Lt Christopher John Code
(Jan. 24, 2005) (J.A. 421); Memorandum from the Dep’t of
Def., San Juan Military Entrance Processing Station, to Fort
Buchanan Family Hous. (July 25, 2005) (J.A. 471); Code v.
Esper, 285 F. Supp. 3d 58, 61-62 (D.D.C. 2017); Appellee’s
Br. 10. During that tour of duty, Code and his family lived in
off-base housing and his three children attended the
Department of Defense school at the Fort Buchanan base.

     Sometime between January and March of 2007, Code
learned that he was likely to receive new “permanent change of
station” orders assigning him somewhere else before his
current orders assigning him to Puerto Rico expired in July
2008. Fla. Fraud Resident Agency, Army CID, Agent’s
Investigation Report (Jan. 25, 2008) (J.A. 405); Code Decl. ¶ 6
(J.A. 455). Because his elderly father had only recently moved
to live with Code’s family in Puerto Rico, Code’s preference
                               7
was to remain at Fort Buchanan for the full three years if
possible. With the support of his superiors, Code applied on
March 12, 2007, for a one-month extension of his then-current
orders which, if granted, would keep him at Fort Buchanan
through August 2008.

     In a letter dated Thursday, April 26, 2007, the Navy’s
department of human resources denied the extension request,
describing it as a request for a “thirteen-month extension.”
Letter from Head, Human Res. Cmty., to Lt. Christopher Code
(Apr. 26, 2007) (J.A. 430). Code asserts, and the Secretary
does not dispute, that he did not receive the denial letter until
Tuesday, May 8, 2007, as evidenced by a faxed copy of the
letter with a heading showing the date of May 8, 2007.

     Meanwhile, Code’s three children were attending the Fort
Buchanan school, where they had been enrolled since Code’s
tour in Puerto Rico began in 2005. Registration for the
upcoming school year was in progress. See Oral Arg. Rec.
22:13-37; see also DoDI 1342.26 ¶ 6.3.4.3 (referencing May
enrollment deadline). On Monday, April 30, 2007, Code
submitted an application to reenroll the children for the 2007-
2008 school year. Where the enrollment form stated: “I am
active duty and my current orders will expire on _____,” Code
filled in “July 2008,” as he presumably had done each of the
prior two years. Suppl. DoDEA Form 600 – School Year
2007-2008 (Apr. 30, 2007) (J.A. 223). The form also stated
that “if my orders change/terminate before the start of the SY
2007-2008, I will notify the registrar immediately.” Id.
Although Code did not sign his name on the line appearing next
to that statement, he signed the bottom of the form, under a
statement averring the veracity of information provided.

    As Code later explained under oath, “[a]t the time I
submitted the paperwork, I did not yet know that my request
                               8
for extension had been denied and still believed that my
extension request would be granted.” Code Decl. ¶ 7 (J.A.
456). But school enrollment forms were due, and there is no
contention that the Code family was rushing to submit theirs
early. See Oral Arg. Rec. 22:13-37. As of April—the same
time of year the Code family had applied the prior year—the
school was urging parents of currently enrolled children to
submit any 2007 reenrollment forms. Code’s wife told the
school’s Registrar of the possibility that Code would receive
early change orders, in advance of his current orders’ July 2008
expiration date. Code attests that the Registrar “advised my
wife that my children’s eligibility to attend the [Fort] Buchanan
school for the 2007-2008 term was tied to my current orders,
which at that point still had me stationed in San Juan through
July 2008.” Code Decl. ¶ 8 (J.A. 456).

     On May 23, 2007, Code received change-of-station orders
directing him to report for duty in Kingsville, Texas, in June
2007. Code attests that, “[i]mmediately upon receipt” of his
new orders, he notified the Registrar, who assured him that the
children could stay at the Fort Buchanan school, because
“eligibility was based on my Orders at the time of enrollment.”
Id. ¶ 9; Suppl. Code Decl. ¶ 2 (J.A. 497). Pursuant to his
orders, Code reported to Kingsville in June 2007. His wife and
children, together with Code’s father, remained in Puerto Rico
for the time being, and the children attended the Fort Buchanan
school during the 2007-2008 school year.

     In November 2007, base police in Puerto Rico became
aware that the Code children were attending the Fort Buchanan
school while Code was stationed elsewhere. In January 2008,
the Florida Fraud Resident Agency of the U.S. Army Criminal
Investigation Command (known as the “CID” because it was
formerly called the Criminal Investigation Division) opened an
investigation into whether Code’s children were fraudulently
                                 9
enrolled in the Fort Buchanan school. The Army CID first
interviewed an unnamed First Sergeant at the Military Entrance
and Processing Station at Fort Buchanan. The First Sergeant
erroneously informed the CID that the orders assigning Code
to Fort Buchanan, which were in effect when Code completed
the school enrollment form, expired “sometime during the
summer months” of 2007. Fla. Fraud Resident Agency, Army
CID, Agent’s Investigation Report (Jan. 25, 2008) (J.A. 405).
As noted above, it is undisputed that Code’s current orders at
the time he submitted the form assigned him to Fort Buchanan
until July 2008.

     Without yet having contacted Code, the Army CID
interviewed the Fort Buchanan school Registrar on January 25,
2008. There is no record whether the investigator asked about
the Registrar’s actual conversations with Code or his wife. The
interview report reflects only that the Army CID presented to
the Registrar hypothetically “the scenario involving Lt. Code.”
Fla. Fraud Resident Agency, Army CID, Agent’s Investigation
Report (Jan. 25, 2008) (J.A. 404). The Registrar responded
with her then-current understanding that (in retrospect) she
believed Code’s children would have been ineligible to register
for or attend the school “since the sponsor, Lt. Code was no
longer assigned or stationed in Puerto Rico.” Id. She then
stated that Code did not fit any applicable exceptions, including
an exception that she described as allowing children to “finish
the school year, if the school year was in progress (Sep[tember]
through May)” when the sponsor received new orders. Id. She
appears to have been referring to the rule providing that “[i]f
the status of the sponsor of a currently enrolled student changes
so that the child would no longer be eligible for enrollment . . . ,
enrollment may continue for the remainder of the school year.”
DoDI 1342.26 ¶ 6.3.7; see 10 U.S.C. § 2164(h)(1).
                               10
     In late July 2009, the Army CID also queried by email the
Navy human resources officer who had sent Code the April 26,
2007, letter notifying him that his extension request had been
denied. The Army CID wished to know “the date Lt. Code
received the letter of denial,” given “the closeness on the dates
of the false statement (30 Apr 07) and the date of the letter of
denial of extension (26 Apr 07).” Fla. Fraud Resident Agency,
Army CID, Agent’s Investigation Report (July 30, 2009) (J.A.
441). The officer responded:

    If you are trying to prove that he intentionally
    defrauded the local school by saying he thought his
    extension was approved, I can affirm with absolute
    confidence that I personally told him otherwise
    within no more than a few days after the date on
    letter, and certainly we issued him transfer orders,
    which presumably he executed, which once again
    would indicate that he knew he was no longer
    eligible to use the school.

Id. (J.A. 441-42).

     At some point during the investigation, the Army CID
obtained a copy of Code’s orders assigning him to Fort
Buchanan in July 2005. Those orders, as confirmed by Code’s
commanding officer when he signed in for duty, authoritatively
established that Code was assigned to Fort Buchanan from July
25, 2005, until July 25, 2008. See Navy Personnel Command,
Official Change Duty Orders for Lt Christopher John Code
(Jan. 24, 2005) (J.A. 421); Memorandum from the Dep’t of
Def., San Juan Military Entrance Processing Station, to Fort
Buchanan Family Hous. (July 25, 2005) (J.A. 471) (copy of
memorandum from Code’s commanding officer certifying that
Code’s “tour is from July 25, 2005, to July 25, 2008”). The
district court found that that the Army CID’s description of
                               11
Code’s tour as a “twenty-four month tour, ending in the
summer of 2007 . . . does not appear to have been an accurate
description of [Code’s] orders” because his “tour in Puerto
Rico was initially scheduled to last for three years, concluding
in the summer of 2008,” and specifically noted that Code’s
orders expired in July 2008. Code, 285 F. Supp. 3d at 62. The
Secretary’s own brief tells us that Code’s “tour of duty in
Puerto Rico was to be from August 2005 until July 2008” and
that Navy personnel advised Code he would receive new
change of station orders before his “current orders expired in
July 2008.” Appellee’s Br. 10 (quoting J.A. 471). At oral
argument, counsel for the Secretary confirmed that Code’s
orders “expired on [their] face, by [their] terms . . . in 2008,”
and that the Secretary did not “contest[] that, in fact, Lt. Code
was given orders to be at Fort Buchanan, Puerto Rico, initially
. . . [until] 2008.” Oral Arg. Rec. 16:26-35, 17:27-42. Those
were Code’s “current orders” until his tour of duty was cut
short by issuance on May 23, 2007, of Permanent Change of
Station orders sending him to the Naval Air Station at
Kingsville, Texas.

     Nonetheless, as the Army CID later summed up its
reasoning, “Mr. Code was aware, or should have been aware
that his dependents were not authorized [sic] the services,
which is why he would have provided the false date to ensure
his dependents could enroll.” Memorandum from the Army
CID to Director, Army Review Bds. Agency, at 2 (May 26,
2016) (J.A. 314). The Army CID stressed that this was “re-
iterated” by the CID at its February 2008 interview with Code.
Id.

    The children openly attended the Fort Buchanan school
throughout the 2007-2008 school year. The school is run by
the Department of Defense, which manages its enrollment
according to priorities established by Department of Defense
                               12
regulation. See DoDI 1342.26 ¶ 6.2.2. The February 2008
interview was the first that Code learned about any potential
problem with his children’s enrollment. See Code Decl. ¶ 10
(J.A. 456). There is no evidence that the school at any point—
either before or after the CID’s February 2008 interview with
Code—asked the family to remove the children from the school
or otherwise took steps to exclude them.

     In its earliest report in the record, the Army CID stated on
July 30, 2009, that it had what it believed was both “credible
information” and “probable cause” to believe that Code made
a false statement on April 30, 2007, when he submitted the
application form to the Fort Buchanan school for his three
children for the 2007-2008 school year. Based on Domestic
Dependent Elementary and Secondary School (DDESS)-
Puerto Rico tuition rates, the Army CID calculated that the
“monetary loss to the U.S. Government [was] $44,200.” Army
CID, Report of Investigation - 3rd Status, at 2 (July 30, 2009)
(J.A. 227). The investigators referred the putative debt to the
Defense Finance and Accounting Service for collection. On
September 30, 2010, the Accounting Service initiated debt
collection against Code.

    The Army CID concluded its investigation on January 12,
2011, issuing a final report that determined there was

    [p]robable cause to believe Lt. Code committed the
    offense of False Official Statement and Larceny
    when he falsified documentation by registering his
    three children in the DDESS for a year while he was
    not assigned to the geographic area. Lt. Code
    knowingly falsified these DDESS documents 4 days
    after his Permanent Change of Station (PCS),
    extension request was denied, transferring him from
    Puerto Rico to Kingsville, TX.
                               13
Army CID, Report of Investigation - Final, at 2 (Jan. 12, 2011)
(J.A. 398-99). The Army CID noted that it had referred the
case to the U.S. Attorney’s Office in San Juan but that the U.S.
Attorney had declined to prosecute, leaving to the Department
of Defense and Code’s chain of command whether to take any
action against him. Defense Department personnel declined to
take any prosecutorial or disciplinary action.

C. Procedural History

     Code applied first to the Army CID itself, then to the Army
Board for Correction of Military Records, for expungement or
correction of the Report of Investigation—that is, to vacate the
CID’s titling and probable-cause determinations. Code
explained that he could not have made a false official statement
because the registration form asked specifically and
exclusively for the date of expiration of his “current orders,”
which, when he signed the registration form, he accurately
stated were set to expire in July 2008.

     The Army CID and Board nonetheless denied relief, and
Code timely sought review in district court. The district court
identified several inadequacies in the Board’s decision,
including the Board’s application of the wrong regulation to
determine the eligibility of Code’s children and its failure to
address Code’s challenge to the Army CID’s referral of the
investigative report to the Defense Finance and Accounting
Service to initiate collection. Over Code’s objection, the
district court granted the Secretary’s motion for voluntary
remand to allow the Board to “address the inadequacies” raised
by Code’s complaint. Code v. McHugh, 139 F. Supp. 3d 465,
472 (D.D.C. 2015).

    The Board issued a second decision reinstating and
bolstering its initial decision of almost three years earlier. The
Board denied any relief in Code’s favor, instead taking the
                               14
occasion to recommend that the Army CID amend the Report
of Investigation to substitute a charge of obtaining services
under false pretenses for the inapposite larceny charge. See
ABCMR, Record of Proceedings (Jan. 31, 2017) (J.A. 110).
The Board determined that, while the behavior the CID
ascribed to Code did not amount to larceny, Code could instead
be re-titled with, and have founded against him, an offense of
obtaining     services under false pretenses, which
“contemplate[s] the wrongful obtaining of services rather than
tangible property.” Id. ¶ 19 (J.A. 141).

     Code returned to the district court to pursue his claim that
the Board’s denial of relief from the titling and probable-cause
determinations was arbitrary and capricious. He continued to
contend that the Army CID lacked any evidence of a false
statement, given that “the information [Code] submitted on the
application was completely true and accurate.” Am. Compl.
¶ 2, Code v. Speer, No. 15-cv-31 (D.D.C. Apr. 13, 2017), ECF
No. 17.

     Ruling on cross-motions for summary judgment, the
district court held “that there was nothing arbitrary, capricious
or contrary to law about the [Board]’s conclusion that there was
sufficient evidence to support the CID’s decision to title [Code]
with the charges of Obtaining Services under False Pretenses
and Making a False Official Statement.” Code, 285 F. Supp.
3d at 61. The district court emphasized that both the CID and
the Board had concluded that Code’s statement “that ‘I am
active duty and my current orders will expire on July 2008’”
was “a purposeful misrepresentation of the true nature of
[Code’s] orders because, at the time he made this statement,
[Code] knew that his ‘current orders’ were actually going to
‘expire’ in the near future, and that he was going to be required
to leave Puerto Rico long before 2008.” Id. at 67. The district
                               15
court did not separately address Code’s challenge to the
probable-cause determination.

     On appeal, Code renews his contention that he made no
false statement because, at the time he filled out and signed the
school enrollment form asking him for the date his “current
orders will expire,” his current orders assigned him to Fort
Buchanan until July 2008. He contends that the Board’s failure
to expunge or amend the titling, indexing, and probable-cause
finding was therefore arbitrary and capricious under the
Administrative Procedure Act (APA).              See 5 U.S.C.
§ 706(2)(A).

                        DISCUSSION

     Three principles control our review. First, “[o]n review of
a district court’s grant of summary judgment in connection
with the appeal of a decision of the ABCMR [Army Board for
Correction of Military Records], we review the ABCMR’s
decision de novo, applying the same standards as the district
court” and with “no particular deference to the judgment of the
district court.” Coburn v. McHugh, 679 F.3d 924, 929 (D.C.
Cir. 2012) (citations and internal quotation marks omitted).

     Second, “under section 706(2) of the [APA], this court
shall ‘set aside’ the ABCMR’s ‘action, findings, and
conclusions’ regarding the correction of military records if they
are ‘arbitrary, capricious, an abuse of discretion, or otherwise
not in accordance with law.’” Haselwander v. McHugh, 774
F.3d 990, 996 (D.C. Cir. 2014) (quoting 5 U.S.C. § 706(2)(A)).
The Secretary’s “broad discretion in administering the
correction of military records” does not obviate the APA’s
requirement that administrative actions “be supported by
‘reasoned decisionmaking.’” Id. (quoting Allentown Mack
Sales & Serv., Inc. v. NLRB, 522 U.S. 359, 374 (1998)); see
                                16
also Kreis v. Sec’y of the Air Force, 866 F.2d 1508, 1514 (D.C.
Cir. 1989).

     Third, we have recognized that, “when a military records
correction board fails to correct an injustice clearly presented
in the record before it, it is acting in violation of its statutory
mandate under 10 U.S.C. § 1552. And such a violation,
contrary to the evidence, is arbitrary and capricious.”
Haselwander, 774 F.3d at 996 (alterations omitted) (quoting
Yee v. United States, 512 F.2d 1383, 1387 (Ct. Cl. 1975)).

     We also have noted that “[a] Correction Board can only
exercise its discretion for the benefit of the individual
member.” Wolfe, 835 F.2d at 358. In view of that constraint,
it is not clear that the Board acted within the scope of its
authority when it suggested that Code could be re-titled with a
new offense. But because Code does not press that argument,
see Oral Arg. Rec. 10:42-58, and prevails on other grounds, we
do not resolve it now.

A. Probable Cause

     The Secretary has forfeited any defense of the Army CID’s
probable-cause determination. In neither its initial review nor
its review on remand from the district court did the Board
separately address Code’s contentions that the CID lacked
probable cause to conclude that he had committed fraud.
Rather than account for the Board’s omissions, counsel for the
Secretary asserts that it was Code who failed to preserve his
challenge to probable cause on summary judgment in the
district court. Oral Arg. Rec. 12:57-13:29. That is wrong. Not
only at summary judgment, but also at every other opportunity,
Code has asked for the probable cause determination to be
reversed or expunged—and has challenged as arbitrary and
capricious the Board’s failure to do so. See Appellant’s
                              17
Br. 33-34; Pl.’s Req. for Recons. at 1, Code v. Speer, No. 15-
cv-31 (D.D.C. Jan. 16, 2018), ECF No. 29; Pl.’s Mem. in
Support of His Cross-Mot. for Summ. J. & in Opp’n to Def.’s
Mot. for Summ. J. at 13, Code v. Speer, No. 15-cv-31 (D.D.C.
Jan. 16, 2018), ECF No. 20-1; Am. Compl. ¶ 113, Code v.
Speer, No. 15-cv-31 (D.D.C. Apr. 13, 2017), ECF No. 17;
Compl. ¶¶ 77-78, Code v. McHugh, No. 15-cv-31 (D.D.C. Jan.
9, 2015), ECF No. 1; Letter from Andrew K. Wible, Cohen
Mohr LLP, to Army Review Bds. Agency, at 1 (Sept. 26, 2013)
(J.A. 369); Letter from Andrew K. Wible, Cohen Mohr LLP,
to U.S. Army Crime Records Ctr., at 1 (Jan. 24, 2013) (J.A.
389). We reverse the district court’s decision insofar as it
declines to hold arbitrary and capricious the Board’s failure to
engage with Code’s challenge to the probable-cause
determination.

    In any case, for essentially the same reasons explained
below in connection with the titling and indexing decision, the
Board’s determination of probable cause to believe that Code
defrauded the Department of Defense cannot stand.

B. Titling and Indexing

     We hold arbitrary and capricious the Board’s decision
affirming the Army CID’s titling and indexing decision.

     1. Review of a titling and indexing decision is unusual,
but it is called for here by several circumstances particular to
this case.

      First, the case appears before us without a record that
separately identifies whatever initial, presumably limited, body
of evidence the Army CID relied on to decide to title and index
Code for criminal fraud. Applicable regulations suggest that
titling is akin to a threshold reason-to-believe or reasonable-
suspicion standard, typically made at the very outset of an
                               18
investigation. As Department of Defense rules explain,
“[t]itling and indexing . . . shall be done as early in the
investigation as it is determined that credible information exists
that the subject committed a criminal offense.” DoDI 5505.7
¶ 6.1. The earliest determination in the record before us,
however, is reflected in the July 30, 2009, Report of
Investigation, in which the titling and probable cause
determinations are merged. That Report was “generated to
correct identifying on the subject [sic], change the offenses
from U.S. Code to UCMJ, and list the offenses as founded.”
Army CID, Report of Investigation - 3rd Status, at 2 (July 30,
2009) (J.A. 225). We have no record of any threshold titling
and indexing determination apart from and in advance of the
Report that also found probable cause, nor has the Secretary
explained how we might otherwise isolate the information that
was available to the investigators at the investigative threshold.
In fact, we lack any distinct evidentiary record underpinning
the 2009 titling, indexing, or founding decisions; this appeal
came to us on the record supporting the 2011 final Report of
Investigation. See Army CID, Report of Investigation - Final
(Jan. 12, 2011) (J.A. 398-445).

     Another unusual twist in this case is that the decision
appears to be having an impermissible continuing effect on
Code. As conceded by the Secretary and reflected in the
record, the Army appears to be relying exclusively on the
challenged titling decision to seek to collect from him the value
of the education that it asserts Code obtained for his children
under false pretenses. Ordinarily, a titling decision is
superseded and largely mooted by a finding of probable cause.
Reporting an offense as “founded” reflects that investigation
has “adequately substantiated” the charge, giving law
enforcement “probable cause supported by corroborating
evidence” to believe the crime was committed. If the
investigation yields a determination of no probable cause to
                               19
believe that a crime was committed, the offense is reported as
“unfounded.” See Army Regulation 190-45, ¶ 4-3(a); id.
Glossary § II (defining “Founded offense” and “Unfounded
offense”). Titling and indexing, on the other hand, “are
administrative procedures and shall not connote any degree of
guilt or innocence.” DoDI 5505.7 ¶ 6.5. Department of
Defense policy therefore confines the use of titling and
indexing to “law enforcement or security purposes” and forbids
“[j]udicial or adverse administrative actions . . . against
individuals or entities based solely on the fact that they have
been titled or indexed due to a criminal investigation.” Id.
¶¶ 6.2, 6.5.2.

      Notwithstanding the prohibition against sole reliance on a
titling decision as grounds for “adverse administrative actions,”
counsel for the Secretary asserts that the Defense Finance and
Accounting Service may continue to seek to collect from Code
the cost of his three children’s year of schooling at Fort
Buchanan based on the titling decision alone. See Oral Arg.
Rec. 36:55-37:37 (counsel for the Secretary stating that “[t]he
titling decision would still be adequate” to support the
Department’s claim of entitlement to recoup tuition costs from
Code), 38:36-57; see also Def. Fin. & Accounting Serv.,
Advisory Opinion: Department of Defense Education Activity
(DoDEA) Debt Situation Involving Navy Lt Code, at 3 (Oct.
13, 2016) (J.A. 213) (“The fact that [Code] was not charged
with a crime does not negate this debt to the US
Government.”). The record suggests that the Department of
Defense does indeed plan to continue to seek to collect in
excess of $40,000 from Code based on the mere suspicion that
he obtained those services by fraud. The Defense Finance and
Accounting Service notified Code of the putative tuition debt
only because the Army CID forwarded to the Accounting
Service the Report of Investigation reflecting both the titling
and probable cause determinations. See ABCMR, Record of
                                20
Proceedings ¶ 6 (Jan. 31, 2017) (J.A. 112). The Accounting
Service did not distinguish between titling and probable cause
when it insisted that it would not cancel the debt or cease efforts
to recoup it unless the Army CID “overturned” its prior
determination. Letter from Bridgette Chrisman, Customer
Care Representative, Def. Fin. & Accounting Serv., to
Christopher J. Code (Apr. 20, 2012) (J.A. 201); see also Def.
Fin. & Accounting Serv., Advisory Opinion: Department of
Defense Education Activity (DoDEA) Debt Situation
Involving Navy Lt Code, at 1 (Oct. 13, 2016) (J.A. 211); Email
from Leonard Cooley, Def. Fin. & Accounting Serv., to Maria
Sanchez, Army Review Bds. Agency (May 3, 2016, 12:21
EDT) (J.A. 244); but see Memorandum from the Army CID to
Director, Army Review Bds. Agency, at 1 (May 26, 2016) (J.A.
313) (stating that the Defense Finance and Accounting Service,
“not CID, is the determining body responsible for recouping
funds”).

     2. Because of the evident continuing harm to Code from
the Board’s refusal to correct the record titling and indexing
him for crimes of making a false official statement and
procuring services under false pretenses, we review those
decisions and hold that they were arbitrary and capricious. The
record of titling and indexing presented to the Board and
reviewed by the district court did not credibly suggest that
Code falsified the Fort Buchanan school enrollment form, nor
that he did so as a ruse to get his children school access they
did not deserve. We therefore cannot agree with the district
court that the Board “provided a reasoned explanation of its
decision that is rationally related to the evidence before it”
when it held that credible information supported the Army
CID’s titling and indexing determinations that Code knowingly
submitted a false enrollment form, thereby committing crimes
of fraud and obtaining services by false pretenses. Code, 285
F. Supp. 3d at 68.
                              21
     The record submitted in support of titling and indexing
reflects the Army CID’s determination that Code fraudulently
“certified his date of departure” as July 2008 on the enrollment
form, and that it rested those threshold determinations on
interviews and “examination of records and military orders”
showing that Code “was assigned” to his post at the Fort
Buchanan Military Entrance and Processing Station (MEPS)
on August 3, 2005, and “the tour at MEPS was twenty-four
months.” Army CID, Report of Investigation - 3rd Status, at
3-4 (July 30, 2009) (J.A. 226-27). Investigators purported to
have determined that, “[a]t the time Lt. Code signed the
DoDEA Form 600 on 30 Apr 07, he knew that his P[ermanent]
C[hange of] S[tation] was in June 07, and as such his dependent
children were not eligible for attendance at the DOD school on
[Fort] Buchanan.” Id. at 4 (J.A. 227). The Army CID’s final
report likewise announced that “Code falsified documentation
by registering his three children in the DDESS for a year while
he was not assigned to the geographic area,” basing its
inference of fraudulent intent on its conclusion that Code did
so “4 days after his Permanent Change of Station (PCS)[]
extension request was denied, transferring him from Puerto
Rico to Kingsville, TX.” Army CID, Report of Investigation -
Final, at 2 (Jan. 12, 2011) (J.A. 399).

     The Army CID’s investigators made a simple but
consequential mistake at the outset and then compounded their
error when they should have corrected course. It is apparently
not unusual for a tour of duty at the Military Entrance and
Processing Station to last only two years. The Army CID’s
first error was to accept—apparently without checking the
records—the statement of the First Sergeant at the Military
Entrance and Processing Station that Code’s 2005 assignment
to Fort Buchanan was due to expire in the summer of 2007. See
Fla. Fraud Resident Agency, Army CID, Agent’s Investigation
Report (Jan. 25, 2008) (J.A. 405). Accepting the First
                                 22
Sergeant’s accusation, the Army CID concluded that Code was
seeking at the tail end of his assignment to enroll his children
in the Fort Buchanan School for an additional year—a year
during which he already knew (according to the Army CID) he
would no longer be assigned to Fort Buchanan. Second, failing
to discern that, even without extension, Code’s then-current
orders lasted until July 2008, not July 2007, the Army CID
jumped to further erroneous conclusions: that Code already
knew when he submitted the school enrollment form that his
request for extension had been denied, and that he also knew,
even before his reassignment to Texas, that he would have to
leave Fort Buchanan in 2007.

      At the time of their initial titling and indexing decision, the
Army CID investigators presumably had it within their power
to verify the premise of their fraud theory. The record of the
titling and indexing decisions includes Code’s official orders.
It is uncontested that Code’s orders assigned him to Fort
Buchanan from 2005 to 2008.                    The Secretary now
acknowledges that official records authoritatively contradict
any information that might have led the Army CID to think that
Code’s assignment to Puerto Rico was for only 24 months. See
Oral Arg. Rec. 16:10-38. Code never denied that the
assignment was subject to change. But the Secretary also does
not contest that Code’s superiors supported his application to
serve out—and even slightly extend—his assignment at Fort
Buchanan through August 2008, giving Code grounds for
optimism that he might stay. In any event, it is clear and
undisputed that no changed orders had yet issued when Code
filled out the school’s application form in April 2007.
Therefore, the only factually accurate way for Code to fill out
the form when he did was to write “July 2008” in the blank
where the form states “My current orders will expire on
_______.”         Suppl. DoDEA Form 600 – School Year
2007-2008 (Apr. 30, 2007) (J.A. 223). Code’s request for
                               23
correction of the titling decision is therefore “supported by
uncontested, creditable evidence,” and the Board’s decision
otherwise “defies reason and is devoid of any evidentiary
support.” Haselwander, 774 F.3d at 992-93.

     Code has consistently acknowledged that, at the time he
signed the application, he had heard that his orders were likely
to be changed. Indeed, by Code’s uncontradicted account, the
family informed the school’s Registrar in April that Code
anticipated early reassignment elsewhere, and, after his
Permanent Change of Station order came through in late May,
Code contacted the Registrar again to verify the children’s
eligibility. See Code Decl. ¶¶ 8-9 (J.A. 456). The Registrar
assured him, Code attested, that the children could stay at the
Fort Buchanan school, because “eligibility was based on my
Orders at the time of enrollment.” Suppl. Code. Decl. ¶ 2 (J.A.
497). The way the application form is worded is not to the
contrary.

     The Board did not deem Code’s account unworthy of
belief for any reason, but rejected it for want of corroboration,
“such as a statement from the Registrar,” which, the Board
opined, “would appear to be easily obtained.” ABCMR,
Record of Proceedings ¶ 4 (Aug. 12, 2014) (J.A. 364). But it
is not at all apparent how Code could have obtained such a
statement. Tellingly, the Army CID’s own interview of the
Registrar—at which the investigator in 2008 hypothetically
posed to her the “situation” involving Code’s children—failed
to contradict Code’s account of his actual conversation with her
in 2007. Fla. Fraud Resident Agency, Army CID, Agent’s
Investigation Report (Jan. 25, 2008) (J.A. 404). If she had told
Code that children are ineligible once their parent is reassigned
elsewhere, or if the Codes had in fact never asked her about
their children’s eligibility, one would expect the Registrar to
have said so. The omission from the Army CID’s interview
                               24
report of any statement on the Registrar’s part regarding her
actual communications—or lack thereof—with the Code
family tends to corroborate Code’s declaration.

C. The Alternative, Failure-to-Disenroll Theory

     The Secretary has fleetingly suggested that the charged
offense of obtaining services under false pretenses is separately
supported by Code’s action in keeping the children enrolled in
school at Fort Buchanan after his Permanent Change of Station
orders sent him to Texas. Oral Arg. Rec. 30:05-31:06; see also
ABCMR, Record of Proceedings ¶ 19 (Jan. 31, 2017) (J.A.
141). But the only falsehood or fraud the Army CID identified
was that Code submitted a school application for the 2007-
2008 school year listing July 2008 as the date his assignment
to Fort Buchanan was due to expire. The Board itself described
the sole issue before it as whether to expunge records of the
CID investigators’ determination that “there was credible
evidence to believe [Code] fraudulently obtained education
services from the government and did so by means of a false
official statement.” ABCMR, Record of Proceedings ¶ 28
(Jan. 31, 2017) (J.A. 144). We cannot sustain the Board’s
decision on a different ground, neither charged nor litigated in
this case.

     As explained above, the sole falsehood anywhere in the
record of the Army CID’s investigation was the statement Code
made on the school application form on April 30, 2007, that his
“current orders” expired on “July 2008.” In its interim and
final titling decisions, the CID found that Code “falsely listed
his [order expiry date] of July 2008,” Army CID, Report of
Investigation - 3rd Status, at 2 (July 30, 2009) (J.A. 225), and
concluded that there was “probable cause to believe Lt. Code
committed the offense of False Official Statement and Larceny
when he falsified documentation by registering his three
                               25
children in the DDESS for a year while he was not assigned to
the geographic area,” Army CID, Report of Investigation -
Final, at 2 (Jan. 12, 2011) (J.A. 399).

      Even if the Army had made, the Board upheld, and
briefing preserved a charge of fraudulent failure to disenroll, a
titling and indexing decision made on that theory must fail
because it is unsupported by any credible information that
Code acted with fraudulent intent when he persisted in sending
his children to the Fort Buchanan school. This alternative
theory assumes that the application itself was not fraudulent
and that the children were permissibly re-registered at the Fort
Buchanan school, but that Code knew that his children became
ineligible once his new Permanent Change of Station orders
came through yet failed at that time to withdraw them from the
school.

     Because state of mind is what differentiates mere error
from criminal fraud, a charge of fraudulent failure to withdraw
could not be made without credible information that the suspect
acted with fraudulent intent. See generally United States v.
Project on Gov’t Oversight, 616 F.3d 544, 552 & n.9 (D.C. Cir.
2010) (collecting cases). But the Army CID never identified
any credible information on which to conclude that Code knew
that his children lost their school eligibility simultaneously
with his change of orders, and hence that he knowingly violated
an obligation to take them out of school. The Board only gets
part of the way with its contention that Code’s “change of
station orders taking him to Texas had the obvious effect of
making him and his family ineligible for tuition-free education
at the Fort Buchanan school.”           ABCMR, Record of
Proceedings ¶ 27 (Jan. 31, 2017) (J.A. 144). We assume that
the Board is correct that, under Department of Defense policy,
Code’s reassignment rendered his children ineligible. But that
does not mean Code knew they were ineligible. And, contrary
                                26
to the Board’s characterization, the eligibility rules for children
of a servicemember who moves are far from “obvious.” Id.

    Department of Defense law and rules tying eligibility to
where the servicemember is stationed include an exception
allowing “currently enrolled students” to remain throughout a
school year, even after their parent-sponsor has been assigned
elsewhere. The statute states that

      [t]he Secretary of Defense shall permit a dependent
      of a member of the armed forces . . . to continue
      enrollment in an educational program provided by
      the Secretary . . . for the remainder of a school year
      notwithstanding a change during such school year
      in the status of the member . . . that, except for this
      paragraph, would otherwise terminate the eligibility
      of the dependent to be enrolled in the program.

10 U.S.C. § 2164(h)(1). In similar terms, the implementing
rule provides that, “[i]f the status of the sponsor of a currently
enrolled student changes so that the child would no longer be
eligible for enrollment,” the student’s enrollment nonetheless
“may continue for the remainder of the school year.” DoDI
1342.26 ¶ 6.3.7.

      The record contains no credible information that Code
knew no such exception applied to his children. Indeed, Code’s
unrebutted declaration attests to the contrary: When Code
informed the Fort Buchanan school Registrar that he had been
reassigned to Texas, she assured him that the children could
complete the year at the Fort Buchanan school because they
had validly enrolled based on his prior assignment. See Suppl.
Code Decl. ¶ 2 (J.A. 497). Even if that view misapprehends
the relevant rule, as the Secretary now argues and we assume,
it is entirely plausible that the Registrar so understood it when
she spoke to Code.
                               27
     Indeed, the plausibility of Code’s account of his
understanding based on his exchange with the Registrar gains
powerful support from the Army’s own inconsistent usage of
the term “enrolled.” The Secretary now argues that children
are only “enrolled” within the meaning of the currently-
enrolled-student exception once classes are underway in the
corresponding school year, whereas Code was reassigned
during the summer before school had resumed for the fall term,
making his children ineligible to “continue enrollment” under
the exception. Appellee’s Br. 42; see Oral Arg. Rec. 31:07-35.
The Registrar’s post-hoc response to the hypothetical posed by
the Army CID also narrowly construed enrollment to refer only
to attendance while “the school year was in progress
(Sep[tember] through May).” Fla. Fraud Resident Agency,
Army CID, Agent’s Investigation Report (Jan. 25, 2008) (J.A.
404). But the Board and counsel for the Secretary on this
appeal themselves all repeatedly used the term “enrollment” to
refer to registration, without regard to whether classes were yet
underway. See, e.g., Memorandum from the Army CID to
Director, U.S. Army Crime Records Ctr. (Apr. 4, 2013)
(J.A. 383) (“Code committed the offenses [of] False Official
Statement and Larceny when he enrolled his children prior to
the start of the 2007-2008 school year . . . .”); ABCMR, Record
of Proceedings ¶¶ 19, 27 (Jan. 31, 2017) (J.A. 141) (noting that
Code “is accused of fraudulently enrolling his children into the
Fort Buchanan school”); Appellee’s Br. 9, 11; Oral Arg. Rec.
30:48-54 (“They had only been enrolled. So they hadn’t
actually started school.”) (all emphases added). The Board’s
and government counsel’s equation of registration and
enrollment is inconsistent with the Department of Defense’s
reading of its own rule, but it reinforces the plausibility of
Code’s understanding, avowedly on the Registrar’s advice, that
despite his reassignment his children were “enrolled” and so
eligible to remain at the Fort Buchanan School under the
exception for currently enrolled students.
                               28
     Ultimately, the Secretary’s case for fraudulent failure-to-
disenroll rests on the “presumption of administrative
regularity” the ABCMR accords official actions. 32 C.F.R.
§ 581.3(e)(2); see Appellee’s Br. 43-44 (citing Roberts v.
United States, 741 F.3d 152, 158 (D.C. Cir. 2014)). The
Secretary contends that a presumption that government
personnel “properly discharge[] their official duties”
establishes that, had Code or his wife called the Registrar, she
necessarily would have informed them of their children’s
ineligibility. Roberts, 741 F.3d at 158 (quoting 32 C.F.R.
§ 723.3(e)(2)); Army Board for Correction of Military
Records, Record of Proceedings (Aug. 12, 2014) (J.A. 365).
The Secretary reasons that Code’s affidavits cannot overcome
such a presumption without “corroborating evidence”—in
particular, a signed statement from the Registrar affirming
Code’s own declarations that she told him his children could
remain at the school through the 2007-2008 school year.
Appellee’s Br. 43; see also ABCMR, Record of Proceedings
¶¶ 4, 8 (Aug. 12, 2014) (J.A. 364-65). To the contrary, once
Code identified the absence of evidence supporting the Army
CID’s actions, it was not his obligation to disprove fraudulent
intent. Rather, the issue was that the Army investigators had
never met their burden to show it—first with “credible
information” for titling and indexing, and then with probable
cause to deem the charge “founded.” Neither the Army CID,
the Board, nor counsel for the Secretary have pointed to any
evidence that Code intended to defraud the government—
whether when he submitted the enrollment form accurately
stating the expiration date of his current orders, or when, after
his orders changed, his children continued to attend the Fort
Buchanan school where they were enrolled. We reject the
extraordinary position that a background presumption of
regularity can alone prove criminal intent to defraud, and that
a suspect’s statement to the contrary under oath cannot rebut
such “proof” unless independently corroborated by the very
                              29
official benefiting from the presumption—especially where, as
here, the administrative process does not appear to provide for
any opportunity to question or obtain a statement from the
official under oath. See 32 C.F.R. § 581.3(c)(2)(iii), (f).

                      CONCLUSION

     We reverse the judgment of the district court, vacate the
decision of the Army Board for the Correction of Military
Records, and remand the case to the district court with
instructions to remand to the Board for further proceedings
consistent with this opinion.

                                                   So ordered.
