Question: Gates v. Collier and Illinois v. Gates, are cases regarding which numbered portions type of the Constitution?

Context paragraphs:
Gates v. Collier: Gates v. Collier, 501 F.2d 1291 (5th Cir.  1974), was a landmark case decided in U.S. federal court that brought an end to the Trusty system and the flagrant inmate abuse that accompanied it at Mississippi State Penitentiary (Parchman) in Sunflower County, Mississippi.  It was the first case in a body of law developed in the Fifth Circuit Court of Appeals holding that a variety of forms of corporal punishment against prisoners constituted cruel and unusual punishment and a violation of Eighth Amendment rights.  This case was also the first broad-scale intervention by a court in the supervision of prison practices.

Randall Boe: Randall Boe (born 1962) was General Counsel for AOL and has been involved in many ground breaking cases regarding internet law.  He was born in Ohio and grew up in Iowa City, Iowa.  He attended the University of Wisconsin–Madison and graduated in 1983 with majors in political science and economics.  He graduated from the University of Pennsylvania Law School in 1987.  After graduation, he went to work at Arent, Fox, Kintner, Plotkin & Kahn in Washington, D.C. While at Arent Fox, Boe specialized in complex litigation and tried a wide variety of matters, including antitrust cases, white collar criminal matters and product liability matters.

Aguilar v. Texas: Aguilar v. Texas, 378 U.S. 108 (1964) , was a decision by the United States Supreme Court, which held that “[a]lthough an affidavit supporting a search warrant may be based on hearsay information and need not reflect the direct personal observations of the affiant, the magistrate must be informed of some of the underlying circumstances relied on by the person providing the information and some of the underlying circumstances from which the affiant concluded that the informant, whose identity was not disclosed, was credible or his information reliable.”  Along with "Spinelli v. United States" (1969), "Aguilar" established the Aguilar–Spinelli test, a judicial guideline for evaluating the validity of a search warrant based on information provided by a confidential informant or an anonymous tip.  The test developed in this case was subsequently rejected and replaced in "Illinois v. Gates", 462 U.S. 213 (1983).

Illinois v. Gates: Illinois v. Gates, 462 U.S. 213 (1983) , is a Fourth Amendment case.  "Gates" overruled "Aguilar v. Texas", 378 U.S. 108 (1964) and "Spinelli v. United States", 393 U.S. 410 (1969) , thereby replacing the Aguilar–Spinelli test for probable cause with the "totality of the circumstances" test.

Dale v Trustbank Waikato Ltd: Dale v Trustbank Waikato Ltd is an often cited case in New Zealand cases regarding promissory estoppel, requiring that the promise must be unequivocal for this doctrine to be successful.

Elmwood Cemetery Gates: The Elmwood Cemetery Gates mark the east and north entrances to the Elmwood Cemetery in Sycamore, Illinois.  The cast iron gates were likely built in 1865, the year the cemetery opened and the one emblazoned on the gates, though records of their construction have been lost.  While cast iron was commonly used for building facades at the time, the gates are a rare example of its use in landscape architecture.  The gates have a Serlian design with a wide central road entry and narrower pedestrian gates on either side; square columns separate the gates.  An arch bearing the cemetery's name rises above the center entrance, while lintels span the side entrances; both the arch and the lintels feature ornamental designs.  The Illinois Historic Structures Survey described the gates as the best extant example of iron cemetery gate design in the state.

Trusty system (prison): The "trustee system" (sometimes homophonically though perhaps incorrectly called "trusty system") was a strict system of discipline and security in the United States made compulsory under Mississippi state law (but also used in other states, such as Arkansas, Alabama, Louisiana, New York and Texas) as the method of controlling and working inmates at Mississippi State Penitentiary at Parchman, Mississippi's only prison.  It was designed to replace convict leasing.  Under this system, designated inmates were used by staff to control and administer physical punishment to other inmates according to a strict prison-determined inmate hierarchy of power.  The case of "Gates v. Collier" (Gates v. Collier Prison Reform Case, 1970–1971) ended the flagrant abuse of inmates under the trusty system and other prison abuses which had continued essentially unchanged since the building of the prison in 1903 in Mississippi.  Other states using the trusty system were also forced to give it up under this ruling.

Trevor Ivory Ltd v Anderson: Trevor Ivory Ltd v Anderson is one of the leading New Zealand cases regarding the personal liability of company directors.  The case concerns the personal liability of a director of a one-man company for negligent misstatement and applied the principle of "Tesco Supermarkets Ltd v Nattrass "that where a director is the "directing mind" of a company, his actions are legally those of the company.  The application of the case by New Zealand courts during the leaky homes crisis has been described as a "barrier to litigants recovering from directors of these companies".

Aguilar–Spinelli test: The Aguilar–Spinelli test was a judicial guideline set down by the U.S. Supreme Court for evaluating the validity of a search warrant or a warrantless arrest based on information provided by a confidential informant or an anonymous tip.  The Supreme Court abandoned the "Aguilar"–"Spinelli" test in "Illinois v. Gates", 462 U.S. 213 (1983), in favor of a rule that evaluates the reliability of the information under the "totality of the circumstances."  However, Alaska, Massachusetts, New York, Tennessee, Vermont, and Washington have retained the "Aguilar–Spinelli" test, based on their own state constitutions.

Criminal law in the Waite Court: During the tenure of Morrison Waite as Chief Justice of the Supreme Court of the United States (March 4, 1874 through March 23, 1888), the Supreme Court heard an unprecedented volume and frequency of criminal cases.  In just fourteen years, the Court heard 106 criminal cases, almost as many cases as the Supreme Court had heard in the period from its creation to the appointment of Waite as Chief Justice.  Notable cases include "United States v. Cruikshank" (1875), "United States v. Reese" (1875), "Reynolds v. United States" (1878), "Wilkerson v. Utah" (1879), the "Trade-Mark Cases" (1879), "Strauder v. West Virginia" (1880), "Pace v. Alabama" (1883), "United States v. Harris" (1883), "Ex parte Crow Dog" (1883), "Hurtado v. California" (1884), "Clawson v. United States" (1885), "Yick Wo v. Hopkins" (1886), "United States v. Kagama" (1886), "Ker v. Illinois" (1886), and "Mugler v. Kansas" (1887).

Supporting paragraphs: Gates v. Collier Illinois v. Gates
Answer: Amendment