Well, there is this little called "proof" which is evidence or facts needs to prove something. I'll quote from the Congressional Research Service:
Proof, Burden of Proof, and Presumptions.
It had long been presumed that “reasonable doubt” was the proper standard for criminal cases,1174 but, because the standard was so widely accepted, it was only relatively recently that the Court had the opportunity to pronounce it guaranteed by due process. In 1970, the Court held in In re Winship that the Due Process Clauses of the Fifth and Fourteenth Amendments “[protect] the accused against conviction except upon proof beyond a reasonable doubt of every fact necessary to constitute the crime with which he is charged.”1175
The standard is closely related to the presumption of innocence, which helps to ensure a defendant a fair trial,1176 and requires that a jury consider a case solely on the evidence.1177 “The reasonable doubt standard plays a vital role in the American scheme of criminal procedure. It is a prime instrument for reducing the risk of convictions resting on factual error. The standard provides concrete substance for the presumption of innocence—that bedrock ‘axiomatic and elementary’ principle whose ‘enforcement lies at the foundation of the administration of our criminal law.’ ”1178
The Court had long held that, under the Due Process Clause, it would set aside convictions that are supported by no evidence at all.1179 The holding of the Winship case, however, left open the question as to whether appellate courts should weigh the sufficiency of trial evidence. Thus, in Jackson v. Virginia,1180 the Court held that federal courts, on direct appeal of federal convictions or collateral review of state convictions, must satisfy themselves that the evidence on the record could reasonably support a finding of guilt beyond a reasonable doubt. The question the reviewing court is to ask itself is not whether it believes the evidence at the trial established guilt beyond a reasonable doubt, but whether, after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.1181
Because due process requires the prosecution to prove beyond a reasonable doubt every fact necessary to constitute the crime charged,1182 the Court held in Mullaney v. Wilbur1183 that it was unconstitutional to require a defendant charged with murder to prove that he acted “in the heat of passion on sudden provocation” in order to reduce the homicide to manslaughter. The Court indicated that a balancing-of-interests test should be used to determine when the Due Process Clause required the prosecution to carry the burden of proof and when some part of the burden might be shifted to the defendant. The decision, however, called into question the practice in many states under which some burdens of persuasion1184 were borne by the defense, and raised the prospect that the prosecution must bear all burdens of persuasion—a significant and weighty task given the large numbers of affirmative defenses.
The Court, however, summarily rejected the argument that Mullaney means that the prosecution must negate an insanity defense,1185 and, later, in Patterson v. New York,1186 upheld a state statute that required a defendant asserting “extreme emotional disturbance” as an affirmative defense to murder1187 to prove such by a preponderance of the evidence. According to the Court, the constitutional deficiency in Mullaney was that the statute made malice an element of the offense, permitted malice to be presumed upon proof of the other elements, and then required the defendant to prove the absence of malice. In Patterson, by contrast, the statute obligated the state to prove each element of the offense (the death, the intent to kill, and the causation) beyond a reasonable doubt, while allowing the defendant to prove an affirmative defense by preponderance of the evidence that would reduce the degree of the offense.1188 This distinction has been criticized as formalistic, as the legislature can shift burdens of persuasion between prosecution and defense easily through the statutory definitions of the offenses.1189
Despite the requirement that states prove each element of a criminal offense, criminal trials generally proceed with a presumption that the defendant is sane, and a defendant may be limited in the evidence that he may present to challenge this presumption. In Clark v. Arizona,1190 the Court considered a rule adopted by the Supreme Court of Arizona that prohibited the use of expert testimony regarding mental disease or mental capacity to show lack of mens rea, ruling that the use of such evidence could be limited to an insanity defense. In Clark, the Court weighed competing interests to hold that such evidence could be “channeled” to the issue of insanity due to the controversial character of some categories of mental disease, the potential of mental-disease evidence to mislead, and the danger of according greater certainty to such evidence than experts claim for it.1191
Another important distinction that can substantially affect a prosecutor’s burden is whether a fact to be established is an element of a crime or instead is a sentencing factor. Although a criminal conviction is generally established by a jury using the “beyond a reasonable doubt” standard, sentencing factors are generally evaluated by a judge using few evidentiary rules and under the more lenient “preponderance of the evidence” standard. The Court has taken a formalistic approach to this issue, allowing states to designate essentially which facts fall under which of these two categories. For instance, the Court has held that whether a defendant “visibly possessed a gun” during a crime may be designated by a state as a sentencing factor, and determined by a judge based on the preponderance of evidence.1192
Although the Court has generally deferred to the legislature’s characterizations in this area, it limited this principle in Apprendi v. New Jersey. In Apprendi the Court held that a sentencing factor cannot be used to increase the maximum penalty imposed for the underlying crime.1193 This led, in turn, to the Court’s overruling conflicting prior case law that had held constitutional the use of aggravating sentencing factors by judges when imposing capital punishment.1194 These holdings are subject to at least one exception, however,1195 and the decisions might be evaded by legislatures revising criminal provisions to increase maximum penalties, and then providing for mitigating factors within the newly established sentencing range.
Another closely related issue is statutory presumptions, where proof of a “presumed fact” that is a required element of a crime, is established by another fact, the “basic fact.”1196 In Tot v. United States,1197 the Court held that a statutory presumption was valid under the Due Process Clause only if it met a “rational connection” test. In that case, the Court struck down a presumption that a person possessing an illegal firearm had shipped, transported, or received such in interstate commerce. “Under our decisions, a statutory presumption cannot be sustained if there be no rational connection between the fact proved and the ultimate fact presumed, if the inference of the one from the proof of the other is arbitrary because of lack of connection between the two in common experience.”
In Leary v. United States,1198 this due process test was stiffened to require that, for such a “rational connection” to exist, it must “at least be said with substantial assurance that the presumed fact is more likely than not to flow from the proved fact on which it is made to depend.” Thus, the Court voided a provision that permitted a jury to infer from a defendant’s possession of marijuana his knowledge of its illegal importation. A lengthy canvass of factual materials established to the Court’s satisfaction that, although the greater part of marijuana consumed in the United States is of foreign origin, there was still a good amount produced domestically and there was no way to assure that the majority of those possessing marijuana have any reason to know whether their marijuana is imported.1199 The Court left open the question whether a presumption that survived the “rational connection” test “must also satisfy the criminal ‘reasonable doubt’ standard if proof of the crime charged or an essential element thereof depends upon its use.”1200
In a later case, a closely divided Court drew a distinction between mandatory presumptions, which a jury must accept, and permissive presumptions, which may be presented to the jury as part of all the evidence to be considered. With respect to mandatory presumptions, “since the prosecution bears the burden of establishing guilt, it may not rest its case entirely on a presumption, unless the fact proved is sufficient to support the inference of guilt beyond a reasonable doubt.”1201 But, with respect to permissive presumptions, “the prosecution may rely on all of the evidence in the record to meet the reasonable doubt standard. There is no more reason to require a permissive statutory presumption to meet a reasonable-doubt standard before it may be permitted to play any part in a trial than there is to require that degree of probative force for other relevant evidence before it may be admitted. As long as it is clear that the presumption is not the sole and sufficient basis for a finding of guilt, it need only satisfy the test described in Leary.”1202 Thus, due process was not violated by the application of the statute that provides that “the presence of a firearm in an automobile is presumptive evidence of its illegal possession by all persons then occupying the vehicle.”1203 The division of the Court in these cases and in the Mullaney v. Wilbur line of cases clearly shows the unsettled nature of the issues they concern.
Well, there is this little called "proof" which is evidence or facts needs to prove something. I'll quote from the Congressional Research Service:
Proof, Burden of Proof, and Presumptions.
It had long been presumed that “reasonable doubt” was the proper standard for criminal cases,1174 but, because the standard was so widely accepted, it was only relatively recently that the Court had the opportunity to pronounce it guaranteed by due process. In 1970, the Court held in In re Winship that the Due Process Clauses of the Fifth and Fourteenth Amendments “[protect] the accused against conviction except upon proof beyond a reasonable doubt of every fact necessary to constitute the crime with which he is charged.”1175
The standard is closely related to the presumption of innocence, which helps to ensure a defendant a fair trial,1176 and requires that a jury consider a case solely on the evidence.1177 “The reasonable doubt standard plays a vital role in the American scheme of criminal procedure. It is a prime instrument for reducing the risk of convictions resting on factual error. The standard provides concrete substance for the presumption of innocence—that bedrock ‘axiomatic and elementary’ principle whose ‘enforcement lies at the foundation of the administration of our criminal law.’ ”1178
The Court had long held that, under the Due Process Clause, it would set aside convictions that are supported by no evidence at all.1179 The holding of the Winship case, however, left open the question as to whether appellate courts should weigh the sufficiency of trial evidence. Thus, in Jackson v. Virginia,1180 the Court held that federal courts, on direct appeal of federal convictions or collateral review of state convictions, must satisfy themselves that the evidence on the record could reasonably support a finding of guilt beyond a reasonable doubt. The question the reviewing court is to ask itself is not whether it believes the evidence at the trial established guilt beyond a reasonable doubt, but whether, after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.1181
Because due process requires the prosecution to prove beyond a reasonable doubt every fact necessary to constitute the crime charged,1182 the Court held in Mullaney v. Wilbur1183 that it was unconstitutional to require a defendant charged with murder to prove that he acted “in the heat of passion on sudden provocation” in order to reduce the homicide to manslaughter. The Court indicated that a balancing-of-interests test should be used to determine when the Due Process Clause required the prosecution to carry the burden of proof and when some part of the burden might be shifted to the defendant. The decision, however, called into question the practice in many states under which some burdens of persuasion1184 were borne by the defense, and raised the prospect that the prosecution must bear all burdens of persuasion—a significant and weighty task given the large numbers of affirmative defenses.
The Court, however, summarily rejected the argument that Mullaney means that the prosecution must negate an insanity defense,1185 and, later, in Patterson v. New York,1186 upheld a state statute that required a defendant asserting “extreme emotional disturbance” as an affirmative defense to murder1187 to prove such by a preponderance of the evidence. According to the Court, the constitutional deficiency in Mullaney was that the statute made malice an element of the offense, permitted malice to be presumed upon proof of the other elements, and then required the defendant to prove the absence of malice. In Patterson, by contrast, the statute obligated the state to prove each element of the offense (the death, the intent to kill, and the causation) beyond a reasonable doubt, while allowing the defendant to prove an affirmative defense by preponderance of the evidence that would reduce the degree of the offense.1188 This distinction has been criticized as formalistic, as the legislature can shift burdens of persuasion between prosecution and defense easily through the statutory definitions of the offenses.1189
Despite the requirement that states prove each element of a criminal offense, criminal trials generally proceed with a presumption that the defendant is sane, and a defendant may be limited in the evidence that he may present to challenge this presumption. In Clark v. Arizona,1190 the Court considered a rule adopted by the Supreme Court of Arizona that prohibited the use of expert testimony regarding mental disease or mental capacity to show lack of mens rea, ruling that the use of such evidence could be limited to an insanity defense. In Clark, the Court weighed competing interests to hold that such evidence could be “channeled” to the issue of insanity due to the controversial character of some categories of mental disease, the potential of mental-disease evidence to mislead, and the danger of according greater certainty to such evidence than experts claim for it.1191
Another important distinction that can substantially affect a prosecutor’s burden is whether a fact to be established is an element of a crime or instead is a sentencing factor. Although a criminal conviction is generally established by a jury using the “beyond a reasonable doubt” standard, sentencing factors are generally evaluated by a judge using few evidentiary rules and under the more lenient “preponderance of the evidence” standard. The Court has taken a formalistic approach to this issue, allowing states to designate essentially which facts fall under which of these two categories. For instance, the Court has held that whether a defendant “visibly possessed a gun” during a crime may be designated by a state as a sentencing factor, and determined by a judge based on the preponderance of evidence.1192
Although the Court has generally deferred to the legislature’s characterizations in this area, it limited this principle in Apprendi v. New Jersey. In Apprendi the Court held that a sentencing factor cannot be used to increase the maximum penalty imposed for the underlying crime.1193 This led, in turn, to the Court’s overruling conflicting prior case law that had held constitutional the use of aggravating sentencing factors by judges when imposing capital punishment.1194 These holdings are subject to at least one exception, however,1195 and the decisions might be evaded by legislatures revising criminal provisions to increase maximum penalties, and then providing for mitigating factors within the newly established sentencing range.
Another closely related issue is statutory presumptions, where proof of a “presumed fact” that is a required element of a crime, is established by another fact, the “basic fact.”1196 In Tot v. United States,1197 the Court held that a statutory presumption was valid under the Due Process Clause only if it met a “rational connection” test. In that case, the Court struck down a presumption that a person possessing an illegal firearm had shipped, transported, or received such in interstate commerce. “Under our decisions, a statutory presumption cannot be sustained if there be no rational connection between the fact proved and the ultimate fact presumed, if the inference of the one from the proof of the other is arbitrary because of lack of connection between the two in common experience.”
In Leary v. United States,1198 this due process test was stiffened to require that, for such a “rational connection” to exist, it must “at least be said with substantial assurance that the presumed fact is more likely than not to flow from the proved fact on which it is made to depend.” Thus, the Court voided a provision that permitted a jury to infer from a defendant’s possession of marijuana his knowledge of its illegal importation. A lengthy canvass of factual materials established to the Court’s satisfaction that, although the greater part of marijuana consumed in the United States is of foreign origin, there was still a good amount produced domestically and there was no way to assure that the majority of those possessing marijuana have any reason to know whether their marijuana is imported.1199 The Court left open the question whether a presumption that survived the “rational connection” test “must also satisfy the criminal ‘reasonable doubt’ standard if proof of the crime charged or an essential element thereof depends upon its use.”1200
In a later case, a closely divided Court drew a distinction between mandatory presumptions, which a jury must accept, and permissive presumptions, which may be presented to the jury as part of all the evidence to be considered. With respect to mandatory presumptions, “since the prosecution bears the burden of establishing guilt, it may not rest its case entirely on a presumption, unless the fact proved is sufficient to support the inference of guilt beyond a reasonable doubt.”1201 But, with respect to permissive presumptions, “the prosecution may rely on all of the evidence in the record to meet the reasonable doubt standard. There is no more reason to require a permissive statutory presumption to meet a reasonable-doubt standard before it may be permitted to play any part in a trial than there is to require that degree of probative force for other relevant evidence before it may be admitted. As long as it is clear that the presumption is not the sole and sufficient basis for a finding of guilt, it need only satisfy the test described in Leary.”1202 Thus, due process was not violated by the application of the statute that provides that “the presence of a firearm in an automobile is presumptive evidence of its illegal possession by all persons then occupying the vehicle.”1203 The division of the Court in these cases and in the Mullaney v. Wilbur line of cases clearly shows the unsettled nature of the issues they concern.
Impressive length