
    George James TREPAL, Petitioner-Appellant, v. SECRETARY, FLORIDA DEPARTMENT OF CORRECTIONS, Respondent-Appellee.
    No. 10-15306.
    United States Court of Appeals, Eleventh Circuit.
    June 19, 2012.
    
      Todd Gerald Scher (Courb-Appointed), Law Office of Todd G. Scher, P.L., Dania Beach, FL, for Petitioner-Appellant.
    Carol Marie Dittmar, Atty. General’s Office, Tampa, FL, for Respondent-Appellee.
    Before CARNES, HULL and PRYOR, Circuit Judges.
   HULL, Circuit Judge:

Florida death row inmate George James Trepal appeals the district court’s denial of his 28 U.S.C. § 2254 petition for a writ of habeas corpus. After review and oral argument, we affirm.

I. BACKGROUND

A. Overview

In 1991, a Florida jury convicted Trepal, a sophisticated chemist and Mensa member, of murdering his neighbor Peggy Carr and attempting to murder six other members of Carr’s family. Trepal poisoned the victims by adding the toxic element thallium to bottles of Coca-Cola in the Carrs’ home.

Trepal’s trial lasted a month, with more than 70 witnesses together providing overwhelming evidence of Trepal’s guilt. For example, several independent witnesses chronicled Trepal’s long-running conflicts with and animosity toward the Carr family. Evidence established Trepal’s extensive knowledge of chemistry, as well as his possession of chemistry laboratory equipment, a number of toxic chemicals, and a homemade journal on poisons and poison detection in human organs. Finally, multiple experts uniformly testified that (1) the victims were poisoned by thallium, (2) thallium was found in both the empty and unopened Coca-Cola bottles in the victims’ home, and (3) thallium was found in a brown bottle in Trepaks garage. Thallium is a heavy metallic element that is both rare and toxic to humans. When dissolved, it is odorless and tasteless. A lethal dose of thallium is approximately 14 milligrams per kilogram of body weight, which for an average person is around 1 gram of thallium.

Trepaks case would be long over but for the fact that in 1997, six years after Trepaks trial, the Office of the Inspector General of the United States Department of Justice (“OIG”) issued a report (the “OIG Report”) that was critical of certain work performed by Roger Martz, a Special Agent in the Chemistry-Toxicology Unit of the FBI Laboratory, who testified against Trepal. After other witnesses had established independently that thallium was found in Trepaks garage and was put in Coca-Cola bottles to poison the victims, Agent Martz went further and tried to identify the particular chemical form of thallium that was found in Trepaks garage and in three unopened Coca-Cola bottles in the victims’ home.

Trepal filed a state postconviction motion alleging that certain parts of Martz’s trial testimony were false and thus Trepal was entitled to a new trial under Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972). The state court denied Trepaks motion, finding that although some of Martz’s trial testimony was false, it did not prejudice Trepal enough to warrant a new trial, given the strength of the unchallenged portions of Martz’s testimony, other experts’ unchallenged testimony, and all the other trial evidence of Trepaks guilt. The Florida Supreme Court affirmed.

Trepal filed his § 2254 petition, which the district court denied. A certificate of appealability (“COA”) was granted on Trepaks Giglio claim. As explained later, this case presents many thorny issues about Trepaks Giglio claim, such as the appropriate level of deference due the Florida Supreme Court’s denial of the claim, whether Martz’s testimony was false, whether Martz’s testimony can be imputed to the state prosecutor, and whether any false testimony was material under Giglio. Although we identify and discuss the issues to some extent, we ultimately need not decide them because even assuming arguendo that Trepal has shown a Giglio error, Trepal has not suffered the requisite actual prejudice and thus any Giglio error was harmless. To show why Trepal was not prejudiced, we outline in depth the evidence presented at trial and in state postconviction proceedings.

B. The Poisonings

Trepal and his wife, Dr. Diana Carr, lived in Alturas, Florida, on property adjoining the home of victim Peggy Carr and her husband Parearlyn “Pye” Carr. The two homes — Pye Carr’s and Trepaks— were located amid orange groves and were very isolated. The next nearest neighbors were about a quarter-mile away.

In June 1988, Pye Carr received an anonymous letter stating, <cYou and all your so-called family have two weeks to move out of Florida forever or else you will all die. This is no joke.” The letter was postmarked in nearby Bartow, Florida. Even though Pye’s home was in Alturas, the letter correctly listed Pye’s mailing address as being in Bartow, Florida. Pye’s and Trepal’s homes, both in Alturas, had Bartow mailing addresses because they got their mail on the Bartow post office route. Trepal would know this fact.

On October 23, 1988, Peggy Carr began to show symptoms of an unknown illness, including nausea, pain in her chest and extremities, and difficulty breathing. She was admitted to Bartow Memorial Hospital the next day and stayed for three days. Back at home, Peggy’s symptoms worsened, and the children in the Carr home, Travis and Duane, began to show similar symptoms. On October 30, 1988, Peggy, Travis, and Duane were admitted to Winter Haven Hospital.

Treating neurologist Dr. Richard Hostler suspected thallium poisoning. Within 24 hours, lab tests confirmed the presence of thallium in Peggy’s tissues.

Despite treatment, Peggy Carr’s condition deteriorated, and within a week she lapsed into a coma from which she never awoke. She died on March 3,1989.

Duane remained hospitalized for two months and Travis for six months, but both eventually recovered. Tests revealed the presence of thallium not only in Travis and Duane, but also in Pye, his daughter Gelena, and his granddaughter Kasey, who also lived with Pye and Peggy.

C. The Investigation

Following the thallium poisoning diagnosis, the Polk County Sheriffs Office and other governmental agencies searched for the source of the Carrs’ exposure. Representatives of the Polk County Health Department, the Florida Department of Health and Rehabilitative Services (“HRS”), and the EPA searched the Carrs’ home.

At the Carrs’ home, investigators recovered an 8-pack of 16-ounce glass Coca-Cola bottles from the kitchen. Three bottles were full and four were empty. The HRS and FBI Laboratories tested and found thallium in the three full bottles and thallium residue in the four empty bottles. The bottle caps from the three full bottles showed evidence of having been removed by a small tool and then placed back onto the bottles with a press or capping device. The investigation became a criminal one.

In December 1988, investigators interviewed Trepal. When asked why anyone would want to poison the Carrs, Trepal said that perhaps someone wanted them to move out of their home. Investigators found Trepal’s response eerily similar to the threatening letter. Police later learned Trepal had a college degree in chemistry and in the 1970s was the chemist of a methamphetamine laboratory, for which he served two and a half years in federal prison. Local police began an undercover investigation of Trepal that lasted more than a year.

On December 12, 1989, investigators searched Trepaks home. They found a small brown bottle in the drawer of a workbench in his garage. The bottle contained a white powder that was tested and found to contain thallium.

Trepal was arrested. On April 5, 1990, Trepal was indicted on one count of first-degree murder, six counts of attempted first-degree murder, seven counts of poisoning food or water, and one count of tampering with a consumer product.

D. Trial Evidence

Trepaks trial ran from January 7 to February 7, 1991. In the guilt phase, the State called more than 70 witnesses. Trepaks three attorneys- — J. Wofford Stidham, Jonathan Stidham, and Dabney Conner— called no witnesses, relying on the evidence elicited during cross-examination.

Below we set forth in more detail the trial evidence by which the State connected Trepal to the Carr poisonings, divided into these topics: (1) Trepaks suspicious police interview and the ensuing undercover investigation of Trepal, including the “Mensa murder weekend” event Trepal hosted; (2) the searches of Trepaks homes, in which police discovered Trepaks chemistry equipment, poison journal, poisonous chemicals, and the bottle of thallium; (3) Trepaks chemistry and criminal background; (4) Trepaks history of animosity toward the Carrs; (5) Florida HRS’s testing of the empty Coca-Cola bottles; (6) expert Havekost’s testing at the FBI Lab; (7) Martz’s testimony; and (8) testing by the Coca-Cola corporate laboratory.

1. Trepal’s Suspicious Interview and Ensuing Undercover Investigation

Detective Ernest Mincey of the Polk County Sheriffs Office led the investigation and the interview of Trepal that put him on the police’s radar. In his interview, which took place on December 22, 1988, Trepal looked very nervous. Trepal told Detective Mincey and FBI Agent Brad Brekke that he was a self-employed computer programmer and technical writer and he knew nothing of thallium.

When asked why someone might want to poison the Carr family, Trepal said perhaps someone wanted them to move out of their house, which, Trepal noted, the Carrs had done. Mincey found this response suspicious because it was different from those given by the more than 50 people Mincey had already interviewed and, as noted earlier, it was “almost identical” to the threatening letter.

In April 1989, an article in the local newspaper advertised upcoming events for the Mensa organization, of which Trepal and his wife were members. The article discussed an upcoming “Mensa murder weekend” role-playing event that Trepal and his wife were hosting. Susan Goreck, a Special Agent with the Polk County Sheriffs Department, began an undercover investigation of Trepal by attending the event under the assumed name “Sherry Guin.”

The Mensa murder weekend was held at a local hotel. There were four “murders” acted out during the weekend, which the participants, while acting out their roles, tried to solve. The story concerned voodoo. The murders were very sophisticated, and each of the four was preceded by the victim receiving a threatening note. Trepaks wife wrote the murder scenarios with Trepal’s help. In particular, Trepal himself wrote a booklet given to participants during the weekend that discussed, among other things, poisoning and threats by neighbors. It stated:

New voodooists believe they can be killed by psychic means, but no one doubts that he can be poisoned. When a death threat appears on the doorstep, prudent people throw out all their food and watch what they eat. Hardly anyone dies from magic. Most items on the doorstep are just a neighbor’s way of saying, “I don’t like you. Move or else.”

During the weekend, Trepal told Goreck that he and his wife were planning to move and that Trepal might be selling his Alturas home. Goreck told Trepal she would like to look at Trepal’s home if it were for sale.

A few days after the Mensa murder weekend, Agent Goreck, as Sherry Guin, went to Trepal’s home, ostensibly about buying it. Goreck visited Trepal several more times in May and June 1989. Goreck became friends with Trepal and his wife and learned, among other things, that Trepal was very interested in botany and knew about poisonous plants.

In November 1989, Trepal and his wife moved to Sebring, Florida. From December 1989 to January 1990, Goreck rented Trepal’s home in Alturas.

2. Searches of Trepal’s Homes and, Discovery of Thallium Bottle

While Goreck was renting Trepal’s house in Alturas, she and other law enforcement officers searched it. FBI Agent Brekke found a brown bottle inside the drawer of a workbench in Trepal’s detached garage. Agent Brekke uncapped the bottle and saw residue inside it. Goreck sent the bottle to the FBI Lab for analysis. The FBI Lab informed Goreck that the bottle contained thallium I nitrate.

Police also searched Trepal’s new home in Sebring, Florida. Police found chemistry books, including: (1) The Merck Index of Chemicals and Drugs; (2) the Handbook of Chemistry and Physics, which contained chemical information on thallium; and (3) the Fire Protection Guide on Hazardous Materials, which contained a section on thallium compounds. Police also seized from Trepal’s home: (1) a pamphlet written by Trepal called “Chemistry for the Complete Idiot, Practical Guide to all Chemistry” with pictures and index; (2) “many, many” chemicals, plus chemistry-related glassware and equipment; and (3) a homemade journal described as “a general poison guide.”

Trepal’s journal included photocopied pages from a book entitled, Poison Detection in Human Organs. One of the photocopied pages included a discussion of thallium. The journal was tested for fingerprints and was found to have Trepal’s prints on it. Trepal’s wife’s prints were not found on the journal.

Trepaks journal also contained photocopied pages from another book with a section entitled, “Death by Poison Synopsis.” One page from the journal, which was read to the jury, stated that “Determining whether a person died as a result of natural illness or as a result of poisoning is one of the most difficult types of investigation both for the officer and for the medical expert.” The page described the process by which one tries to determine if someone has been poisoned. The next page in the journal stated, among other things, “The presence of any one poison is so difficult to ascertain that it may be undetected unless the [medical] examiner has some idea as to the type of poison for which he is looking.”

Some of the photocopies in the journal were made from a library book at Central Piedmont Community College in Charlotte, North Carolina. Trepal attended Central Piedmont Community College from 1974-1975.

3. Trepal’s Chemistry and Criminal Background

Several witnesses testified about Trepaks chemistry experience, which went back well over a decade, and the collection of chemistry equipment Trepal kept in his Alturas garage and Sebring home.

First, DEA Agent Richard Broughton testified that, in the mid-1970s, Trepal “was the chemist and mastermind” of a group that produced methamphetamine. David Warren, Trepaks partner in the methamphetamine production scheme, also testified to Trepaks role as chemist for the group.

Trepal’s methamphetamine production experience was particularly relevant because, as Agent Broughton testified, thallium nitrate can be used in the process. Specifically, thallium III nitrate can be used to produce phenyl-II-propanone, called “P2P,” which “is an immediate precursor used in the manufacture of both methamphetamine and amphetamine.” When the P2P is produced, a sediment drops out of solution, and that sediment is thallium I nitrate. The P2P “is then used to manufacture amphetamine, and the Thallium I Nitrate is disposed of.”

Second, a witness confirmed that Trepal kept chemicals and other chemistry equipment in the garage of his Alturas home. Calvin Adams, a builder who did some work for Trepal and his wife as they were moving into their Alturas home in 1982 and who helped them with the move, noticed that one of the items he helped move into Trepaks garage “was a plastic milk carton filled with chemical bottles.” There were at least four or five boxes of chemicals and chemical bottles and other chemistry items. Some of the chemicals were in brown bottles like the bottle police found in Trepaks garage.

Adams asked Trepal what he was doing with the chemistry items, and Trepal replied, “I’m a chemist. I intend to set up a laboratory in the garage.” Trepal also had an antique-type bottle capper, which is used to affix metal caps onto glass bottles. Trepal told Adams he sometimes made wine for himself and capped the wine bottles.

Third, Trepaks chemistry collection at the time of his arrest included many exotic and dangerous chemicals. Scott Ryland, an analytical chemist for the Florida Department of Law Enforcement, analyzed various chemicals that were seized from Trepal’s homes in Alturas and Sebring. These chemicals included sodium cyanide, barium chloride, cobalt nitrate, potassium ferricyanide, chromium trioxide, platinum oxide, lead chloride, and uranium oxide, all of which are toxic.

4. Trepal’s Animosity Toward the Carrs

Numerous witnesses recounted Trepáis years of threats, arguments, and animosity toward the Carrs. For example, Alan Adams, who did lawn care for Trepal in 1982 and 1983, saw Trepal interact with the children who lived at the Carrs’ property. Trepal “always got highly upset and usually yelled obscenities at them.” Trepal “made threats” toward the Carr children on “several occasions.” One time Trepal said, “I will get them.” Another time, Trepal “got highly upset when they rode some motorcycles through his yard and said, Tm going to kill you.’ ”

Margaret Smith, who was Pye’s first wife and the mother of Tammy and Travis, lived next door to Trepal for four years. Trepal did not like the Carrs’ dogs. Several times Smith saw Trepal “throwing sticks or stomping his foot at them trying to get them out of his yard.”

John Schaffer bought the Carrs’ home after Peggy’s death and became Trepal’s new neighbor. Trepal told Schaffer that Pye had a drinking problem and irritated Trepal by coming over to Trepaks house while drunk and banging on Trepaks door. Trepal told Schaffer that there was a “big social difference” between the Trepal and Carr families because the Trepáis were reserved and childless and kept to themselves, whereas the Carrs were “kind of redneckish and ... the children weren’t disciplined the way they should be.” The Carr children bothered Trepal by playing the radio too loudly and being disrespectful.

Pye estimated he had disagreements with Trepal at least 10 or 12 times. One time the Carrs were “working on [Travis’s] truck in the back of the workshop” and they and a visitor were listening to “a party tape” that had risque jokes and profanity on it. The tape was played pretty loudly, and Trepal came over to talk to Pye about it three times. Pye did not turn the tape down.

In March 1988, Trepal called the zoning board to complain about the Carrs converting their garage to an apartment, which Trepal claimed violated the zoning ordinance. A county codes inspector issued the Carrs a notice of violation for building without a permit, and Pye later got a permit.

One day in September 1988, Gelena’s former husband Ronald Chester was working on his truck and had the radio on. Trepal asked Chester to turn the radio down because Trepal was reading a book. Trepal was shaking and “acted like he was upset.” Chester turned the radio down, and “like two minutes later” Trepal came and again told Chester to turn the radio down, even though the radio was not playing loudly.

Both Trepaks and the Carrs’ houses had their water supplied by wells. On occasion, each home had to share water by hooking up to the other’s well. In early October 1988, at which time one of the wells was supplying water to both houses, Trepal came over to the Carrs’ home to complain about their radio playing outside. Pye told Trepal they would turn the radio off soon. Trepal left, and they did so. Later Travis turned the radio back on while washing his car, and Trepal again complained. Pye told Trepal that Travis was “just listening to the radio and washing the car.” After Pye went into the house, Trepal disconnected the water hose to the Carrs’ home.

A few days before Peggy Carr became ill, Trepal’s wife had “a discussion” with Peggy “about some loud music.” The Carr children were playing the music outside and “[i]t was extremely loud even inside [Trepal’s] house.” Trepal’s wife asked Peggy to have the Carr children turn their music down. Peggy told Trepal’s wife that Peggy “didn’t have to.” Trepal’s wife believed Trepal was home with her at the time.

Trepal’s conversations with law enforcement reflected his animosity toward the Carr family. Trepal’s comments also showed that his hostility toward the Carrs continued even after Peggy was killed and the rest of the Carrs moved away. Trepal told Agent Goreck that Pye Carr was “always trying to sell him something” and “tried to sell him everything but his wife.” Trepal continued talking and “seemed to get agitated.”

Trepal told FBI Agent Brad Brekke that the Carrs had not been friendly to him and his wife, and that Pye tried to take advantage of them by selling them a barbecue cooker Pye had made. Trepal reached an oral agreement to buy Pye’s workshop behind his house for $10,000, but Pye backed out of the deal.

Trepal complained about a lot of people coming and going out of the Carrs’ house, and their having a lot of trucks. Trepal “acted angry and exhibited animosity,” which Agent Brekke “felt was unusual since the incidents ... were seven or eight years old.”

5. Florida HRS’s Testing of Washings from Empty Coca-Cola Bottles

Although part of Martz’s testimony about the full Coca-Cola bottles is challenged here, other experts confirmed the presence of thallium in the Coca-Cola bottles at the Carrs’ home and in the brown bottle in Trepal’s garage. For example, Larry Blackwell, a Florida HRS chemist, tested the samples sent from the Carrs’ home, including the washings from the empty Coca-Cola bottles. Blackwell used two instruments, an inductively coupled plasma atomic emission spectrometer (“AES” or “ICP”) and a graphite furnace atomic absorption spectrometer (“AAS”). The AES and AAS tests indicate only the presence and concentration of the metal searched for (in this case, thallium). They chemically decompose any other ions or elements in association with the metal, so they cannot indicate what compound of thallium was present in the samples. The washings from the empty Coca-Cola bottles were positive for thallium, as were urine samples from the Carr family members.

6. Havekost’s Testing at FBI Lab

a. Full Coca-Cola Bottles— Ql, Q2, and Q3

The three full bottles of Coca-Cola were sent to the FBI Lab and labeled as sampies Ql, Q2, and Q3. Donald Havekost, an analytical chemist with the Elemental Analysis Unit of the FBI Lab, was asked to analyze the contents of the full bottles Ql, Q2, and Q3 for the presence of heavy metal poisons, including arsenic, lead, and thallium. Havekost tested the samples using AES and found the “predominant element was thallium.” Havekost found none of the other heavy metals for which he tested.

Once Havekost learned that thallium was present, he again performed an AES analysis, this time comparing the result with that from known thallium standards he prepared in the laboratory to determine the quantity of thallium present in the Coca-Cola. For the bottle labeled Ql, Havekost found 403.6 milligrams of thallium in the total volume of the bottle. For the bottle labeled Q2, Havekost found 915.3 milligrams of thallium. For the bottle labeled Q3, Havekost found 767.5 milligrams of thallium.

b. Empty Coca-Cola Bottles— Qll, Q12, Q13, and Q14

Havekost’s laboratory unit received from the Florida HRS laboratory the washings from the four empty Coca-Cola bottles, which the FBI labeled Qll, Q12, Q13, and Q14. The washings from the four empty bottles contained thallium in the following amounts: 4.32 milligrams, 3.65 milligrams, 2.08 milligrams, and .62 milligrams.

c. Trepal Garage Sample — Q206

Havekost later received the residue from the brown bottle found in Trepal’s garage, which the FBI labeled Q206. The sample consisted of 640 milligrams of “beige-colored, dirty-white crystalline material or powder.” Havekost tested the powder using scanning electron microscopy (“SEM”). Havekost found thallium in the compound.

d.Havekost Trial Testimony

At trial, Havekost testified about his testing of the full bottles Ql through Q3, the washings from the empty bottles Qll through Q14, and the powder residue in the brown bottle, Q206, from Trepal’s garage. Havekost testified that he found thallium in all of those samples. Trepal has never challenged Havekost’s findings, testing methodology, or trial testimony.

7. Martz’s Testimony

Before Martz tested any samples, thallium had already been found in all of them. Martz was asked only to determine what salt of thallium was in the samples of Coca-Cola from the full Coca-Cola bottles Ql, Q2, and Q3, and from the residue found in the brown bottle Q206. Martz did not test, and did not testify about, the washings from the empty Coca-Cola bottles Qll through Q14.

Martz first tested the Coca-Cola from the full Ql, Q2, and Q3 bottles. Martz testified that he performed a diphenylamine (“DP”) test on all three samples and “got a blue color,” which he said indicated the solution “contains a nitrate.” Martz testified: “Based on that test I concluded that thallium nitrate was added to the Coca-Cola.”

Martz also performed an ion chromatography (“IC”) test to determine whether thallium nitrate was present in the Ql, Q2, and Q3 samples. Martz testified that he tested all three samples and again concluded that all three samples contained nitrate ions. Based on the DP and IC tests, Martz opined that thallium nitrate was in the Ql, Q2, and Q3 samples.

On cross-examination, Martz admitted he did not “a hundred percent” exclude the possibility that the nitrate he found in the Coca-Cola may have come from a source other than the thallium salt that was added, but Martz “found nothing else in the Coca-Cola to indicate that anything else was present.”

Later, Martz received Q206, the brown bottle with white powder in it from Trepaks garage, and was asked to identify the white powder. Martz tested the powder using infrared and x-ray diffraction (“XRD”) and concluded the brown bottle contained thallium I nitrate. Martz did not measure quantitatively the amount of substance in the bottle, but “based on the tests [he] did, nothing else was identified.” The powder weighed .64 grams, which is about “a little more than two aspirin tablets” or one “extra strength capsule” of Tylenol.

8. Testing by Cocar-Cola Corporate Laboratory

Chemists at the Coca-Cola corporate laboratory tested the effect of adding various thallium salts to bottled Coca-Cola.

Coca-Cola chemists first added various thallium compounds to bottles of Coca-Cola to see which would dissolve. The chemists successfully dissolved thallium malonate, thallium formate, thallium phosphate, and thallium sulfate in the Coca-Cola, and re-capped the bottle. When finished, the Coca-Cola in the re-capped bottle “looked the same” as it had before.

Later the Coca-Cola chemists performed this test using thallium I nitrate and thalhum III nitrate. The thallium I nitrate dissolved and the Coca-Cola looked normal. The thallium III nitrate did not dissolve well. It “gave a ... brownish precipitant” and “[t]he Coca-Cola turned sort of a muddy color.” In time, “the muddy color settled to the bottom” of the bottle, but “the beverage looked substantially different, much lighter in color, and there was a precipitant or sort of a muddy-looking substance at the bottom of the bottle.”

A Coca-Cola representative came to the FBI Lab and tested the three full bottles of Coca-Cola (Ql, Q2, and Q3) for carbonization and pressure. The three bottles had lower than Coca-Cola’s normal levels of carbonization and pressure. This was evidence that the Coca-Cola bottles had been uncapped so that thallium could be added to them, and then recapped. Notably too, a witness had seen Trepal with a device used to recap bottles.

E. Verdict, Penalty Phase, and Sentence

After deliberating for six hours, the jury found Trepal guilty of one count of first-degree murder, six counts of attempted first-degree murder, seven counts of poisoning food or water with intent to kill or injure, and one count of tampering with a consumer product.

In the penalty phase, the State called Dr. Richard Hostler, the neurologist who treated Peggy Carr, to testify about the pain Peggy Carr experienced from the thallium poisoning, including her complaints of an intense burning sensation in her feet and the fact she was in pain for several days, until she became comatose. The State called no other witnesses.

The parties entered into two stipulations. First, they stipulated that Trepal (1) “was arrested and convicted of the offense of conspiracy to manufacture methamphetamine in 1975,” (2) “was incarcerated for this offense for a period of two- and-one-half years,” and (3) had “no record of other criminal convictions.” Second, the parties stipulated that Trepal “does not have a history of violent behavior.”

The defense called no witnesses and, apart from the stipulations, presented no evidence. After deliberating for about one hour, the jury, by a 9 to 3 vote, recommended that the court impose the death penalty.

The state trial court followed the jury’s recommendation and imposed the death penalty on the first-degree murder conviction.

The state trial court sentenced Trepal to concurrent 90-year sentences on the remaining convictions.

F. Direct Appeal

Trepal appealed to the Florida Supreme Court. Trepal argued, inter alia, that the evidence was insufficient to support his first-degree murder conviction. The Florida Supreme Court affirmed Trepal’s convictions and death sentence. Trepal v. State, 621 So.2d 1361 (Fla.1993) (‘‘Trepal I”). The Supreme Court denied Trepal’s certiorari petition. Trepal v. Florida, 510 U.S. 1077, 114 S.Ct. 892, 127 L.Ed.2d 85 (1994).

G. Initial State Postconviction Proceedings

On June 16, 1995, Trepal filed a Florida Rule of Criminal Procedure 3.850 motion to vacate his convictions and death sentence, which he later amended. Trepal’s amended 3.850 motion raised 30 claims, including ineffective assistance of counsel. On November 6, 1996, after an evidentiary hearing, the 3.850 court issued a 40-page order denying relief on all of Trepal’s claims. Trepal appealed.

H.1997 OIG Report

In April 1997, while Trepal’s 3.850 appeal was pending in the Florida Supreme Court, the OIG Report issued. Among other things, the OIG Report criticized some of Martz’s testimony about Ql, Q2, and Q3 in the Trepal case.

The OIG’s main criticism was that Martz’s testimony as to Ql through Q3 was “stronger than his analytical results would support.” The OIG Report admitted “Martz could have properly opined that certain samples were consistent with thallium nitrate having been added to them.” However, the OIG Report criticized Martz for testifying that “thallium nitrate was added to the Coca-Cola” and that, in his opinion, thallium nitrate was in the Ql, Q2, and Q3 samples.

The OIG Report also pointed out that Martz had run DP tests on Ql, Q2, and Q3 but IC tests on only Ql and Q2. Because Martz did not run an IC test on Q3 (contrary to his trial testimony), the OIG Report opined that Martz did not have an analytical basis for stating Q3 was even consistent with the addition of nitrate.

Third, the OIG Report faulted Martz’s trial testimony about the number of tests he performed. Martz was asked whether he had performed any tests other than the DP test to determine if there was thallium nitrate in the Coca-Cola samples, and Martz answered that he had done “one other test,” IC. But in fact Martz ran other tests besides DP and IC, which he did not mention at trial. Fourth, the OIG Report criticized Martz for not performing certain additional tests such as (1) the “validation experiment of adding thallium nitrate to known unadulterated Coca-Cola” and running the DP and IC tests on this known sample, and (2) quantifying the nitrate he identified in Ql through Q3 and comparing the amount of nitrate to the amount of thallium that Havekost found in those samples. Additionally, the OIG Report indicated that Martz’s notes were lacking in detail and in some instances inaccurate.

The OIG Report concluded that Martz’s work on the Trepal case demonstrated “a lower threshold of scientific proof than is generally accepted in forensic science” and a “lack [of] appropriate scientific rigor in [Martz’s] approach to examinations.”

I. Remand and Another 3.850 Evidentiary Hearing in Trial Court

After the OIG Report was issued, and upon Trepal’s motion, the Florida Supreme Court stayed Trepal’s appeal and relinquished jurisdiction to the 3.850 court. Trepal then amended his Rule 3.850 motion to raise, among other things, a Giglio claim as to his convictions. The 3.850 court held an evidentiary hearing.

1. Roger Martz

Trepal’s first witness was Martz. Martz discussed his methodology and testimony and acknowledged some errors, but ultimately held fast to his opinion at trial that thallium nitrate had been added to Ql, Q2, and Q3, the full Coca-Cola bottles.

Martz believed the OIG Report contained three major criticisms of his work in the Trepal case: (1) Martz gave a stronger opinion than the OIG believed was warranted when he opined the thallium nitrate “was added” to the samples instead of the results being “consistent with thallium nitrate having been added”; (2) Martz’s notes were incomplete and in places inaccurate; and (3) Martz said all three samples Ql through Q3 were tested for nitrate, but Q3 was not tested using the IC.

Martz acknowledged he could have done a better job of taking notes, and he erred in not mentioning that he did not run the IC test on Q3. But neither failure affected his final report or final opinion. Martz’s opinion was still that thallium nitrate was added to the Coca-Cola. Martz testified that “in hindsight, [he] probably should have” tested all three samples using the IC test, but “a lot of time if we have multiple samples, we wouldn’t test all of them. We would test a representative sample for the confirmatory test just to speed things up.”

As to Q3, Martz did no other tests besides the DP test. Martz justified his conclusion that Q3 had nitrate in it, despite only running one test on that sample:

I have 25 years of experience testing samples that are associated with the case and doing representative samples from those cases, that if you take two out of three of the samples, they both have thallium in it, two of the three have nitrate, and the third one has a presumptive test for nitrate, I used my 25 years — or 20 years of experience working these type of cases to conclude that the third sample, even though I didn’t do the confirmative test, the only logical explanation would be nitrate.

Martz also explained that the DP test is a presumptive screening test for oxidizing agents, such as nitrates. The DP test was positive for Ql, Q2, and Q3, and negative for an unadulterated Coca-Cola sample. A positive result is indicated by a blue color.

At Trepal’s trial, Martz testified that when you pour DP into a solution that contains a nitrate, “you get a blue color.” However, that testimony failed to acknowledge that “there’s other chemicals that will give a blue color” in a DP test. Although Martz had first testified at trial that his conclusion that thallium nitrate was added to the Coca-Cola was based on the DP test, later in his trial testimony he clarified that he had also relied on the IC test results in reaching that conclusion.

Martz testified that the IC is used as a “confirmatory test” to confirm the results of the DP test. However, without a positive result on both tests, Martz “would not call it a positive nitrate.”

Martz acknowledged that neither the DP nor the IC tests alone provide positive identification for nitrate (by themselves, each test can at best produce results “consistent with” nitrate). But Martz stated that if both tests are positive, then in his opinion you have proven the presence of nitrate. Amd, both the DP and IC tests were positive for the Coca-Cola in Ql and Q2. Martz stated that “generally in forensic science, you do a multiple of tests, at least two, in order to prove something is present because of the fact that you can get false positives.”

In the State’s cross-examination, Martz pointed out that the OIG never said Martz’s actual testing of the samples in the Trepal case was done improperly. The OIG merely questioned the documentation and testimony.

Martz also opined that “based on the data [he] provided,” he did not believe anyone could say thallium nitrate was not added to the Coca-Cola samples. That is because thallium is present and there are elevated levels of nitrate.

2. Marland Dulaney, Jr.

Trepal’s main witness in the state collateral proceeding was Marland Dulaney, Jr., a consulting toxicologist. Dulaney opined that he could not rely on the IC charts to a “reasonable scientific certainty” because Martz did not run proper standards and blanks. Martz did not run chloride or sulfate standards to confirm where chloride and sulfate ions appeared on the charts. Martz ran a nitrate standard, but did so by adding known nitrate to water, not to Coca-Cola.

Dulaney did not dispute that thallium was present in the Coca-Cola samples. But Dulaney opined that all one can say with reasonable scientific certainty about Ql, Q2, and Q3 is that they contain thallium. Dulaney could not rule out the possibility that thallium nitrate was added to the Coca-Cola samples. Moreover, Dulaney could not testify that the thallium salt present in the Q samples was something other than thallium I nitrate, because he had insufficient information. Dulaney testified that Martz’s “approach is so bad, ... it has so many holes that anybody can say anything that they want, because they have to make assumptions, and if you assume this and this and this, then this is true.” But the data provided no way to test the assumptions.

Based on his review of the data, Dulaney opined that the conclusion that thallium nitrate was added to Ql and Q2 cannot be made to a reasonable degree of scientific certainty. According to Dulaney, adding nitrate to Coca-Cola and running an IC on it was “the fundamental step that would allow us to say that thallium nitrate was added to Coca-Cola,” and that was not done.

3. Frederic Whitehurst

Frederic Whitehurst, the former FBI Lab examiner whose complaints began the OIG investigation, worked in the FBI Lab from 1986 to 1998. Whitehurst’s area of expertise was explosives, but he was familiar with the tests and equipment used in the Trepal case.

Whitehurst opined that the IC testing in the Trepal case did not meet acceptable scientific standards. Whitehurst agreed with Dulaney that Martz should have run a standard in Coca-Cola instead of water “to see what effect the Coke and the instrument has on the chromatography.”

Nonetheless, Whitehurst had no doubt that thallium was found in the Coca-Cola. But Whitehurst believed there were “too many unknowns” to conclude which form of thallium was added. However, Whitehurst admitted that, based on the test results he reviewed, Ql and Q2 are consistent with thallium nitrate having been added to them, and neither he nor anyone else could, based on the data available, rule out thallium nitrate having been added to the samples. In Whitehurst’s opinion, there was not enough data to say one way or another.

J. Denial of Trepal’s Amended Rule 3.850 Motion

On October 26, 2000, the 3.850 court issued a 36-page order denying Trepal’s amended Rule 3.850 motion. The 3.850 court found that “[n]o real attack [was] made on the findings of Q206,” the brown bottle from Trepal’s garage. Thus, the court limited its discussion on the testing of Q206 to the relationship of Q206 to Ql, Q2, and Q3, the samples from the full Coca-Cola bottles.

As to Ql, Q2, and Q3, the 3.850 court found the following instances of false testimony by Martz at Trepal’s trial: (1) Martz stated a positive DP test indicates the presence of a nitrate (instead of saying the presence of an oxidizing ion, of which nitrate is an example); (2) Martz stated nitrate was not present in the unadulterated Coca-Cola (whereas the IC results indicated a nitrate could be present, although the DP test was negative); (3) Martz stated he ran IC tests on Ql, Q2, and Q3 (when he only tested Ql and Q2); (4) Martz did not reveal he performed additional testing on the Q samples (beyond the DP and IC tests he discussed at trial); and (5) Martz stated that the tests indicated thallium nitrate was added to Ql, Q2, and Q3 (instead of that the test results were consistent with thallium nitrate having been added to Ql and Q2, and consistent with an oxidizing ion being present in 03).

The 3.850 court called Martz’s trial conduct “outrageous and shocking,” but noted that regardless, to prevail on any of his claims, Trepal must show he was prejudiced. Thus, “the court must look to the effect the evidence would have on the jury verdict, both in the guilt phase and the penalty phase.”

As to Trepal’s Giglio claim, the 3.850 court discussed the materiality standard, as follows:

[Trepal] claims a violation of Giglio for use of false testimony at trial. Giglio v. United States, 405 U.S. 150 [92 S.Ct. 763, 31 L.Ed.2d 104] (1972) .... Giglio holds that a conviction based on false or perjured testimony, which the prosecution knew or should have known was false, violates due process when such information is material. The materiality prong is the same as that used in Brady. See Rose v. State, 2000 WL 1508576 (Fla.2000). False information is material if “there is a reasonable likelihood that it could have [a]ffected the jury verdict.” Id.

The 3.850 court determined that the materiality question “implies a comparison” between Martz’s “actual testimony” at trial and “what Martz could have truthfully testified to at trial.”

Denying relief, the 3.850 court concluded that Trepal could not show prejudice. The 3.850 court found that “given the test re-suits that Martz could have rightfully testified about and considering all the other evidence in the case,” there was “no reasonable likelihood that the verdict would have been different.”

K. Rule 3.850 Appeal

Trepal appealed the denial of his Rule 3.850 motion to the Florida Supreme Court, which affirmed. Trepal v. State, 846 So.2d 405 (Fla.2003) (“Trepal II”), receded from in part by Guzman v. State, 868 So.2d 498, 506 (Fla.2003).

, As to Trepal’s Giglio claim, the Florida Supreme Court quoted at length the 3.850 court’s order. Trepal II, 846 So.2d at 410-26. In particular, the Florida Supreme Court quoted the 3.850 court’s statements that: (1) the Giglio “materiality prong is the same as that used in Brady”-, (2) “[fjalse information is material if ‘there is a reasonable likelihood that it could have affected the jury verdict’ (3) in conducting the Giglio analysis, Martz’s “actual testimony should be compared to what Martz could have truthfully testified to at trial”; (4) in the guilt phase, “there is no reasonable likelihood that the verdict would have been different”; and (5) in the penalty phase, “there is no reasonable likelihood that the verdict would have been different.” Trepal II, 846 So.2d at 425-26 (emphasis added and omitted).

The Florida Supreme Court then set forth its own analysis. Id. at 426-28. The Florida Supreme Court agreed with the 3.850 court’s conclusion “that Trepal was not impermissibly prejudiced by the testimony of Martz.” Id. at 426.

To explain why, the Florida Supreme Court reviewed the 3.850 court’s findings on specific false or misleading statements Martz made at Trepal’s trial:

In the present case, the circuit court found that the following statements made at trial by Martz were improper for the following reasons:
— Martz stated: “And when you pour that [i.e., diphenylamine or DP] into a solution which contains a nitrate you get a blue color.” (The circuit court, however, found as follows: when you pour DP into a solution that contains an oxidizing ion — which may or may not be a nitrate — you get a blue color.)
• — ■ Martz stated: “Based on that test [i.e., the DP test] I concluded that thallium nitrate was added to the Coca-Cola.” (The circuit court, however, found as follows: all that could be concluded based on the DP test — in conjunction with the other tests — was that the test results were consistent with the presence of thallium nitrate.)
— Martz stated: “No nitrates were present in the unadulterated Coca-Cola.” (The circuit court, however, found as follows: ion chromatography or IC testing showed the presence of a substance that could have been a nitrate in the unadulterated Coke.)
— “In this particular case, when I tested the Coca-Cola [via IC] the results were positive for the nitrate ion.” (The circuit court, however, found as follows: the IC test can show only the presence of an oxidizing ion — which may or may not be a nitrate.)
— Martz was asked: “Did you test each of the samples on the ion chromatograph to determine whether nitrate was present?” He responded: “Yes, I did.” (The circuit court, however, found as follows: Martz did not test each sample. He did not test the third sample, i.e., Q3, on the ion chromatograph.)
— Martz stated: “On three samples that I tested, all three contained nitrate ions.” (The circuit court, however, found as follows: on two samples that Martz tested, all that he appropriately could have attested to was that the tests were consistent with the presence of a nitrate; and that on the third sample, the tests were consistent with the presence of an oxidizing ion — which may or may not have been a nitrate.)
— Martz was asked: “Based on those two tests [i.e., DP and IC], is it your opinion that what was in those three Coca-Colas, sir, was thallium nitrate?” He responded: “That is correct.” (The circuit court, however, found — as noted above — that all that Martz appropriately could have attested to was that the tests were consistent with the presence of thallium nitrate.)

Id. at 427 (brackets in original). The Florida Supreme Court then noted unchallenged, incriminating facts that existed regardless of Martz’s false testimony:

Regardless of the above improprieties in the testimony of Martz (and regardless of the improprieties in his testing practices and omissions in his testimony), the following conclusions nevertheless can properly be drawn from the present record:
[1.] Peggy Carr died from ingesting thallium (of an undetermined type).
[2.] Of the various forms of thallium, only thallium sulfate and thallium nitrate (sub-group I) dissolve in Coca-Cola without changing the appearance of the Coke or foaming out of the bottle.
[3.] The brown bottle found in Trepáis garage contained (a) thallium, and (b) an oxidizing ion consistent with the presence of a nitrate.
[4.] Five empty Coca-Cola bottles found in the Carr household contained thallium (of an undetermined type).
[5.] Tests on two unopened bottles of Coca-Cola found in the Carr household (a) showed the presence of thallium, and (b) yielded results that were consistent with the presence of a nitrate.
[6.] Tests on a third unopened bottle of Coca-Cola found in the Carr household (a) showed the presence of thallium, and (b) yielded results that were consistent with the presence of an oxidizing ion (which may or may not have been a nitrate).

Id. at 427-28.

The Florida Supreme Court concluded that the 3.850 court’s “factual findings are supported by competent, substantial evidence in the record, and the court properly concluded — based on those findings — that the prejudice suffered by Trepal was insufficient to warrant a new trial. We find no error.” Id. at 428. The Florida Supreme Court’s majority opinion did not state explicitly what materiality standard it was applying, and did not comment upon (whether to approve or disapprove) the materiality standard applied by the 3.850 court.

In a special concurrence, two Florida Supreme Court justices clarified the different prejudice standards relating to Brady and Giglio claims. Trepal II, 846 So.2d at 437 (Pariente, J., concurring). The concurrence explained its view that the 3.850 court incorrectly stated that the Brady and Giglio materiality standards were identical. Id. at 438-39. Nevertheless, the justices concurred because, even if Martz’s false testimony satisfied the other elements of the Giglio test, the testimony “could not have led the jury to find other than that Trepal intentionally poisoned his neighbors with thallium, resulting in the death of Peggy Carr.” Id. at 439.

Several months after Trepal II, the Florida Supreme Court, in a unanimous decision, noted its precedent lacked clarity and explained that the Brady and Giglio materiality standards are different. Guzman v. State, 868 So.2d 498, 505-06 (Fla.2003). Under Brady, one must show “a reasonable probability that the undisclosed evidence would have produced a different verdict,” whereas under Giglio, one must show that “there is any reasonable likelihood that the false testimony could have affected the judgment of the jury.” Guzman, 868 So.2d at 506 (emphasis added).

After Guzman, Trepal moved the Florida Supreme Court to reopen his appeal. Trepal argued that he was entitled to a new trial or, at least, a remand to the 3.850 court for a proper Giglio analysis.

On December 6, 2004, in an unpublished decision, the Florida Supreme Court summarily denied relief “on the merits.”

L. Federal Habeas Proceedings

On August 17, 2005, Trepal filed in the district court his 28 U.S.C. § 2254 petition for a writ of habeas corpus. Trepal’s § 2254 petition claimed, inter alia, that Martz’s false testimony violated Giglio.

On June 15, 2010, the district court issued a 75-page order denying Trepal’s § 2254 petition. The district court concluded Trepal did not show that the Florida Supreme Court’s Trepal II decision was contrary to or based on an unreasonable application of Giglio.

The district court granted Trepal a COA on “[w]hether the decision in Trepal II, 846 So.2d at 428 — that ‘the prejudice suffered by Trepal as a result of Martz’s improprieties was insufficient to warrant a new trial’ — is objectively unreasonable.” Trepal appealed to this Court.

II. STANDARD OF REVIEW

The Antiterrorism and Effective Death Penalty Act of 1996 (“AEDPA”), Pub.L. No. 104-132, 110 Stat. 1214, “imposes a highly deferential standard for evaluating state-court rulings and demands that state-court decisions be given the benefit of the doubt.” Hardy v. Cross, 565 U.S. -, 132 S.Ct. 490, 491, 181 L.Ed.2d 468 (2011) (quoting Felkner v. Jackson, 562 U.S. -, 131 S.Ct. 1305, 1307, 179 L.Ed.2d 374 (2011)). Section 2254, as amended by AEDPA, provides that a federal court shall not grant federal habeas relief to a state prisoner on a claim adjudicated on the merits in state court unless the state court’s adjudication of the claim: (1) “resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States”; or (2) “resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.” 28 U.S.C. § 2254(d).

“We review de novo the district court’s decision about whether the state court acted contrary to clearly established federal law, unreasonably applied federal law, or made an unreasonable determination of fact.” Johnson v. Upton, 615 F.3d 1318, 1330 (11th Cir .2010) (quotation marks omitted), cert. denied, — U.S. —, 131 S.Ct. 3041, 180 L.Ed.2d 859 (2011).

III. DISCUSSION

In order to discuss the issue of whether the Florida courts contravened or unreasonably applied controlling federal law here, we first set forth the governing Giglio materiality standard.

A. Giglio Standard

In Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972), the Supreme Court held that when the prosecution solicits or fails to correct known false evidence, due process requires a new trial where “the false testimony could in any reasonable likelihood have affected the judgment of the jury.” 405 U.S. at 154, 92 S.Ct. at 766 (ellipsis omitted). Giglio error, which “is a species of Brady error,” exists “when ‘the undisclosed evidence demonstrates that the prosecution’s case included perjured testimony and that the prosecution knew, or should have known, of the perjury.’ ” Ventura v. Att’y Gen., 419 F.3d 1269, 1276-77 (11th Cir.2005) (quoting United States v. Agurs, 427 U.S. 97, 103, 96 S.Ct. 2392, 2397, 49 L.Ed.2d 342 (1976)).

“To establish a Giglio claim, a habeas petitioner must prove: (1) the prosecutor knowingly used perjured testimony or failed to correct what he subsequently learned was false testimony; and (2) such use was material, i.e., that there is any reasonable likelihood that the false testimony could have affected the judgment.” Guzman v. Sec’y, Dep’t of Corr., 663 F.3d 1336, 1348 (11th Cir.2011) (“Guzman II”) (quotation marks and ellipsis omitted).

The Giglio materiality standard is “different and more defense-friendly” than the Brady materiality standard, as we have explained:

Where there has been a suppression of favorable evidence in violation of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), the nondisclosed evidence is material: “if there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different. A ‘reasonable probability’ is a probability sufficient to undermine confidence in the outcome.” United States v. Bagley, 473 U.S. 667, 682, 105 S.Ct. 3375, 3383, 87 L.Ed.2d 481 (1985). A different and more defense-friendly standard of materiality applies where the prosecutor knowingly used perjured testimony, or failed to correct what he subsequently learned was false testimony. Where either of those events has happened, the falsehood is deemed to be material “if there is any reasonable likelihood that the false testimony could have affected the judgment of the jury.” United States v. Agurs, 427 U.S. 97, 103, 96 S.Ct. 2392, 2397, 49 L.Ed.2d 342 (1976) (emphasis added); accord Giglio v. United States, 405 U.S. 150, 154, 92 S.Ct. 763, 766, 31 L.Ed.2d 104 (1972); Napue v. Illinois, 360 U.S. 264, 271, 79 S.Ct. 1173, 1178, 3 L.Ed.2d 1217 (1959).

United States v. Alzate, 47 F.3d 1103, 1109-10 (11th Cir.1995). Thus, for Brady violations, the defendant must show a reasonable probability the result would have been different, but for Giglio violations, the defendant has the lighter burden of showing that there is any reasonable likelihood that the false testimony could have affected the jury’s judgment. Alzate, 47 F.3d at 1109-10. The Brady materiality standard “is substantially more difficult for a defendant to meet than the ‘could have affected’ standard” under Giglio. Id. at 1110 n. 7.

B. Whether Trepal has Satisfied § 2254(d)

A threshold issue is the proper standard of deference that applies to the Florida Supreme Court’s denial of Trepal’s Giglio claim — that is, whether Trepal has shown that the Florida Supreme Court’s denial of his claim in Trepal II was contrary to or based on an unreasonable application of clearly established Supreme Court precedent. See 28 U.S.C. § 2254(d)(1). Here, the relevant Supreme Court precedent is Giglio, for “no Supreme Court case since Giglio itself has squarely addressed a Giglio claim.” Ventura, 419 F.3d at 1279.

Trepal argues that we should review the merits of his claim de novo because the Florida Supreme Court’s Trepal II decision was contrary to Giglio in that it applied the wrong materiality standard. Trepal is correct that a state court decision falls under the “contrary to” prong of § 2254(d)(1) if it “applies a rule that contradicts the governing law set forth” in a prior Supreme Court holding. Price v. Vincent, 538 U.S. 634, 640, 123 S.Ct. 1848, 1853, 155 L.Ed.2d 877 (2003) (quotation marks omitted). However, it is less than clear whether the Florida Supreme Court in Trepal II applied a materiality rule that contradicts Giglio’s.

The Florida Supreme Court, for its part, did not expressly state what materiality standard it applied. Instead, the Florida Supreme Court quoted nearly the entire analysis of the 3.850 court, and then stated that it agreed Trepal was not prejudiced by Martz’s testimony:

After evaluating the conflicting testimony of the witnesses, the [3.850] court concluded that Trepal was not impermissibly prejudiced by the testimony of Martz. We agree.
... [W]e agree that the prejudice suffered by Trepal as a result of Martz’s improprieties was insufficient to warrant a new trial .... [W]e conclude that the [3.850] court’s factual findings are supported by competent, substantial evidence in the record, and the [3.850] court properly concluded — based on those findings — that the prejudice suffered by Trepal was insufficient to warrant a new trial. We And no error.

Trepal II, 846 So.2d at 426-28 (footnote omitted).

As to the quoted portions of the 3.850 court’s analysis, even those are not entirely clear as to whether the 3.850 court misapplied Giglio’s materiality standard. Although the 3.850 court stated — incorrectly — that the “materiality prong [of Giglio ] is the same as that used in Brady,” its very next sentence correctly sets forth the Giglio standard: “False information is material if ‘there is a reasonable likelihood that it could have affected the jury verdict.’ ” Trepal II, 846 So.2d at 425.

We need not resolve the question of the proper standard of deference to the Florida Supreme Court’s adjudication of Trepal’s claim of Giglio error. Instead, we adopt an approach the United States Supreme Court itself has employed when a petitioner fails to show prejudice even under de novo review:

Even if the state court used an incorrect legal standard, we need not determine whether AEDPA’s deferential standard of review, 28 U.S.C. § 2254(d), applies in this situation. Cf. Williams v. Taylor, 529 U.S. 362, 397-398, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). That is because, even if AEDPA deference does not apply, Thompkins cannot show prejudice under de novo review, the more favorable standard of review for Thompkins. Courts cannot grant writs of habeas corpus under § 2254 by engaging only in de novo review when it is unclear whether AEDPA deference applies, § 2254(d). In those situations, courts must resolve whether AEDPA deference applies, because if it does, a habeas petitioner may not be entitled to a writ of habeas corpus under § 2254(d). Courts can, however, deny writs of habeas corpus under § 2254 by engaging in de novo review when it is unclear whether AEDPA deference applies, because a habeas petitioner will not be entitled to a writ of habeas corpus if his or her claim is rejected on de novo review, see § 2254(a).

Berghuis v. Thompkins, 560 U.S. -, 130 S.Ct. 2250, 2265, 176 L.Ed.2d 1098 (2010) (emphasis added). As was the case for the Supreme Court in Thompkins, we need not determine whether the state supreme court used an incorrect legal standard, for we conclude that Trepal cannot prevail even under de novo review.

To prevail here, Trepal must show that a Giglio error resulted in “actual prejudice” to him under the standard set forth in Brecht v. Abrahamson, 507 U.S. 619, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993). See Guzman II, 663 F.3d at 1347; see also Mansfield v. Sec’y, Dep’t of Corr., 679 F.3d 1301, 1307 (11th Cir.2012) (“On collateral review, a federal constitutional error is harmless unless there is ‘actual prejudice,’ meaning that the error had a ‘substantial and injurious effect or influence’ on the jury’s verdict.” (quoting Brecht, 507 U.S. at 637, 113 S.Ct. at 1722)). Even if Trepal shows part of Martz’s testimony was false about some things, and even assuming ar~ guendo that Martz’s false testimony (1) can be imputed to the state prosecutor, and (2) was material under Giglio, Trepal has not shown that he suffered the actual prejudice required under Brecht. We explain below.

C. Brecht “Actual Prejudice” Standard for Federal Habeas Relief

In Brecht, the Supreme Court began by discussing its prior decision in Chapman v. California, 386 U.S. 18, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967). See Brecht, 507 U.S. at 622, 630, 113 S.Ct. at 1713, 1717. The Brecht Court pointed out that Chapman “rejected the argument that the Constitution requires a blanket rule of automatic reversal in the case of constitutional error, and concluded instead that ‘there may be some constitutional errors which in the setting of a particular case are so unimportant and insignificant that they may, consistent with the Federal Constitution, be deemed harmless.’ ” Brecht, 507 U.S. at 630, 113 S.Ct. at 1717 (quoting Chapman, 386 U.S. at 22, 87 S.Ct. at 827). Accordingly, constitutional defects in criminal trials fall into two classes: (1) “structural defects,” which require automatic reversal of a conviction, and (2) “trial errors,” which are subject to harmless error analysis. See id. at 629-30, 113 S.Ct. at 1717. The standard Chapman set for harmlessness of constitutional trial error was whether the reviewing court was “able to declare a belief that [the error] was harmless beyond a reasonable doubt.” Id. at 630, 113 S.Ct. at 1717 (quoting Chapman, 386 U.S. at 24, 87 S.Ct. at 828).

Chapman was a direct-appeal case, and until Brecht, the Supreme Court had not had occasion to squarely address whether the Chapman “harmless beyond a reasonable doubt” standard applied to cases on collateral review. Brecht, 507 U.S. at 630, 113 S.Ct. at 1718. Brecht determined that Chapman’s harmless error standard did not apply on collateral review. Id. at 623, 630-38, 113 S.Ct. at 1714, 1718-22.

Instead, the Brecht Court concluded that the appropriate harmless-error standard for habeas review of criminal convictions was whether the constitutional error “had substantial and injurious effect or influence in determining the jury’s verdict.” Id. at 623, 113 S.Ct. at 1714 (quoting Kotteakos v. United States, 328 U.S. 750, 776, 66 S.Ct. 1239, 1253, 90 L.Ed. 1557 (1946)). The Supreme Court reasoned that “granting habeas relief merely because there is a ‘reasonable possibility1 that trial error contributed to the verdict is at odds with the historic meaning of habeas corpus — to afford relief to those whom society has ‘grievously wronged’ ”— and also imposes social costs and infringes on the states’ sovereignty and interest in finality of judgments. Id. at 637, 113 S.Ct. at 1721 (quotation marks and citations omitted). Moreover, “[s]tate courts are fully qualified to identify constitutional error and evaluate its prejudicial effect on the trial process under Chapman, and state courts often occupy a superior vantage point from which to evaluate the effect of trial error,” and thus “it scarcely seems logical to require federal habeas courts to engage in the identical approach to harmless-error review that Chapman requires state courts to engage in on direct review.” Id. at 636, 113 S.Ct. at 1721.

Consequently, the Brecht Court concluded that the Kotteakos standard— which derived from the federal harmless-error statute, 28 U.S.C. § 2111 — -was “better tailored” than the Chapman standard “to the nature and purpose of collateral review and [was] more likely to promote the considerations underlying [the Supreme Court’s] recent habeas cases.” Brecht, 507 U.S. at 638, 113 S.Ct. at 1722. Thus, to grant habeas relief based on constitutional trial error, the federal habeas court must find not only that the error occurred, but that it “resulted in ‘actual prejudice,’ ” that is, “the error had ‘substantial and injurious effect or influence in determining the jury’s verdict.’ ” Id. at 637, 113 S.Ct. 1710 (quoting Kotteakos, 328 U.S. at 776, 66 S.Ct. at 1253; citing United States v. Lane, 474 U.S. 438, 449, 106 S.Ct. 725, 732, 88 L.Ed.2d 814 (1986)). The Brecht standard “is more favorable to and less onerous on the state, and thus less favorable to the defendant, than the Chapman harmless beyond a reasonable doubt standard.” Mansfield, 679 F.3d at 1307 (quotation marks omitted).

Giglio error is trial error, not a structural defect. Ventura, 419 F.3d at 1278 n. 3. Therefore, when considering a Giglio claim on federal habeas review, we can grant relief on that claim only if (1) the petitioner establishes that a Giglio error occurred, and (2) that error had “substantial and injurious effect or influence in determining the jury’s verdict.” Brecht, 507 U.S. at 637, 113 S.Ct. at 1722; see Guzman II, 663 F.3d 1336, 1355 (11th Cir.2011) (“Having found the state court’s decision was an unreasonable application of clearly established federal law, we further find that Guzman’s claim is meritorious for all the reasons discussed above. But this does not end our inquiry. We must next consider whether Guzman’s Giglio claim had a substantial and injurious effect on the outcome of his trial.”). Because we consider the Brecht question in the first instance on federal habeas review, there is no state court Brecht actual-prejudice finding to review or to which we should defer. See Mansfield, 679 F.3d at 1307 (noting that federal habeas courts “apply a different harmless error analysis” than the Chapman standard applied by state courts and that “[h]armlessness under the Brecht standard is a question of law that we review de novo ”). Of course, we still would defer to the state court’s other fact findings derived from testimony, documents, and what happened at trial and the 3.850 hearing.

Having determined that the Brecht standard applies, we now consider how it compares with, and relates to, Giglio’s materiality standard. We note that no Brecht analysis is needed for Brady violations, for the Supreme Court has held that a showing of materiality under Brady necessarily establishes actual prejudice under Brecht, Kyles v. Whitley, 514 U.S. 419, 435, 115 S.Ct. 1555, 1566, 131 L.Ed.2d 490 (1995). In Kyles, the Supreme Court explained that the Brady materiality standard “impose[s] a higher burden on • the [criminal] defendant” than the Kotteakos standard that the Court adopted for habeas review in Brecht. Kyles, 514 U.S. at 436, 115 S.Ct. at 1567; see also id. (noting that materiality test for Brady claims “would recognize reversible constitutional error only when the harm to the defendant was greater than the harm sufficient for reversal under Kotteakos ”). In other words, a Brady error cannot be harmless under Brecht because “ ‘a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different’ necessarily entails the conclusion that the suppression must have had ‘substantial and injurious effect or influence in determining the jury’s verdict.’ ” Id. at 435, 115 S.Ct. at 1566 (quotation marks and citation omitted).

But the more lenient Giglio materiality standard leaves room for the possibility that perjured testimony may be material under Giglio but still be harmless under Brecht. See Guzman II, 663 F.3d at 1355-56 (finding Giglio violation and then applying Brecht standard to determine whether error was harmless); see also Rosencrantz v. Lafler, 568 F.3d 577, 584 (6th Cir.2009) (“[W]hile a traditional Brady materiality analysis obviates a later harmless-error review under Brecht v. Abrahamson, courts may excuse [ ]Giglio violations involving known and materially false statements as harmless error.”); Gilday v. Callahan, 59 F.3d 257, 268 (1st Cir.1995) (“Applying [the Giglio materiality] standard in most cases involving perjury or its equivalent will likely result in a finding of constitutional error. Scaling that lower materiality hurdle, however, still will leave the petitioner facing the Brecht harmless error inquiry into whether the perjured testimony in fact had a substantial and injurious effect or influence on the jury’s verdict. In other words, ... it is quite possible to find a constitutional violation, but to conclude that it was harmless.” (footnote omitted)).

We have held that the Giglio materiality standard is equivalent to the Chapman “harmless beyond a reasonable doubt” test. Ventura, 419 F.3d at 1279 n. 4. And, as the Supreme Court made clear in Brecht, the “substantial and injurious effect or influence” test is more onerous (from the criminal defendantyhabeas petitioner’s point of view), than the Chapman standard. Brecht, 507 U.S. at 623, 113 S.Ct. at 1714. Thus, while a Brady error can never be harmless under Brecht because of Brady’s higher materiality standard, a Giglio error can be harmless under Brecht because the Giglio materiality standard is lower than that of Brecht.

In short, we cannot grant federal habeas relief to Trepal unless (1) he shows that Martz’s false testimony violated Giglio, and (2) we find that the Giglio error was not harmless under Brecht. Because the Brecht harmlessness standard is more strict from a habeas petitioner’s perspective than the Giglio materiality standard, federal courts confronted with colorable Giglio claims in § 2254 petitions in many cases may choose to examine the Brecht harmlessness issue first. We choose to do so here.

We therefore ask whether, assuming Martz’s false testimony violated Giglio, was the Giglio error harmless under the standard set forth in Brecht.

D. Brecht Analysis

Again, the Brecht test for actual prejudice is whether the constitutional error “had substantial and injurious effect or influence in determining the jury’s verdict.” Brecht, 507 U.S. at 623, 113 S.Ct. at 1714. “To show prejudice under Brecht, there must be more than a reasonable possibility that the error contributed to the conviction or sentence.” Mansfield, 679 F.3d at 1313 (quoting Mason v. Allen, 605 F.3d 1114, 1123 (11th Cir.2010)). To determine the effect on the verdict of a constitutional error, the Court must consider the error “in relation to all else that happened” at trial. Kotteakos, 328 U.S. at 764, 66 S.Ct. at 1248. The question turns on whether the Court can “say, with fair assurance,” that the verdict “was not substantially swayed by the error”:

If, when all is said and done, the [court’s] conviction is sure that the error did not influence the jury, or had but very slight effect, the verdict and the judgment should stand .... But if one cannot say, with fair assurance, after pondering all that happened without stripping the erroneous action from the whole, that the judgment was not substantially swayed by the error, it is impossible to conclude that substantial rights were not affected. The inquiry cannot be merely whether there was enough to support the result, apart from the phase affected by the error. It is rather, even so, whether the error itself had substantial influence. If so, or if one is left in grave doubt, the conviction cannot stand.

O’Neal, 513 U.S. at 437-38, 115 S.Ct. at 995 (quoting Kotteakos, 328 U.S. at 764-65, 66 S.Ct. at 1248) (brackets and ellipsis in O’Neal) (emphasis omitted).

The Brecht standard “does not require a showing that but for the error the jury would have rendered a verdict in favor of the defendant.” Duest v. Singletary, 997 F.2d 1336, 1338 (11th Cir.1993). Nor does it matter whether the reviewing court believes the petitioner is guilty, for the “crucial thing is the impact of the thing done wrong on the minds of [the jurors] ... in the total setting.” Id. (quoting Kotteakos, 328 U.S. at 764, 66 S.Ct. at 1247-48). But although the Brecht harmless error analysis “is necessarily fact-specific and must be performed on a case-by-case basis, the erroneous admission of evidence is likely to be harmless under the Brecht standard where there is significant corroborating evidence, or where other evidence of guilt is overwhelming.” Mansfield, 679 F.3d at 1313 (citations omitted).

With this framework in mind, we consider the impact of Martz’s false testimony on the verdict. When we do so, we readily conclude that the challenged portions of Martz’s testimony did not have a substantial and injurious effect or influence in determining the jury’s guilty verdict. Thus, any assumed Giglio error was harmless.

First, we note that Trepal’s is not a typical Giglio claim. Usually (indeed, in every Giglio case in the Supreme Court or in this Court of which we are aware), a witness at trial gives testimony that is later shown to be demonstrably factually false. Here, by contrast, Trepal’s core Giglio allegation is that Martz gave his opinion at trial — that thallium nitrate was added to the Coca-Cola in samples Ql, Q2, and Q3 — and that opinion was held and testified to with more strength than what his data supported, but it has not been shown to be incorrect as a matter of fact. No one has shown either at trial or in postconviction proceedings that thallium nitrate was not added to the Coca-Colas, or that some form of thallium other than thallium nitrate was added to the Coca-Colas. At the 3.850 evidentiary hearing, Martz held fast to his opinion that thallium nitrate was added, and Trepal’s own 3.850 experts Dulaney and Whitehurst could not rule out that possibility, but merely stated there was insufficient data to identify which thallium salt was added. And it was undisputed that thallium in any salt is a deadly poison and that the Carrs were poisoned with thallium. Accordingly, here the contention is just that Martz could not truthfully have testified that thallium nitrate is the form of thallium that was added, but only that his test results were consistent with thallium nitrate being the form that was added.

Because the question we must answer is the influence on the jury of the false testimony, we focus on the nature of the falsity — here, the difference between what Martz’s testimony was and what it should have been. Specifically, as the Florida courts correctly found, Martz: (1) testified that a positive result on the DP test (that is, when added DP turns a solution blue) indicates the presence of a nitrate, when Martz should have said that it indicates the presence of an oxidizing ion, of which nitrate is an example; (2) testified that he ran IC tests on Ql, Q2, and Q3, when he actually ran the IC test only on Ql and Q2; (3) testified there was no nitrate present in unadulterated Coca-Cola, when he should have said that the DP test was negative but the IC indicated a nitrate could be present; (4) testified only as to the DP and IC tests, when actually he performed additional testing on the samples, though he did not rely on the other tests in forming his conclusion; and (5) testified that, as a result of his testing, he concluded that thallium nitrate was added to Ql, Q2, and Q3, when he should have testified that the tests results for Ql and Q2 were consistent with the presence of thallium nitrate and the results for Q3 were consistent with the presence of thallium and an oxidizing ion, which could be a nitrate. Notably, Martz’s conclusion about the brown bottle Q206 that was found in Trepal’s garage — that it contained thallium I nitrate — is not challenged.

The gap between what Martz did testify and what everyone agrees he truthfully could have testified is narrow. For the most part, the difference is that Martz’s testimony should have been more nuanced, more guarded, less absolute or certain. The exception is Martz’s positive assertion that he ran the IC test on all three samples Ql through Q3, when in fact he did not run the IC test on Q3. But even so, the DP result on Q3 was still consistent with the proposition that thallium nitrate was added to Q3; it just made that proposition less certain. And it hardly matters whether thallium nitrate was the form of thallium that was added to Ql, Q2, and Q3, as opposed to just Ql and Q2.

Furthermore, Martz’s testimony as a whole was just one small part of the State’s evidence against Trepal. Among other things, the State established with other witnesses, whose testimony stands unchallenged, that: (1) the Carr family was poisoned with thallium; (2) thallium was found in the full and empty Coca-Cola bottles in the Carrs’ home; (3) thallium is a rare and toxic element, and is difficult to obtain because the chemical companies that sell it do not sell to individuals; (4) a brown glass bottle containing thallium was found in Trepal’s Alturas garage; (5) when moving into his Alturas home in 1982, Trepal had chemicals in brown glass bottles and said he intended to set up a chemistry laboratory in his garage; (6) Trepal had an extensive knowledge of chemistry and a collection of chemistry paraphernalia, including glassware, bottles of toxic chemicals, and books that discussed thallium; (7) Trepal had a homemade journal on poisons and poison detection; (8) Trepal’s poison journal bore his fingerprints and contained photocopies from a library book belonging to the college Trepal attended in the 1970s, suggesting the journal pre-dated the Carr poisonings; (9) Trepal was the chemist for a methamphetamine production ring, and thallium is sometimes used in methamphetamine production; (10) Trepal did not get along with any of the members of the Carr family, and he still exhibited anger and animosity after the poisonings about incidents that had happened years earlier; (11) Trepal repeatedly threatened the Carr children, and once said he would kill them; (12) Trepal’s conflicts with the Carrs continued well into 1988, the year of the poisonings; (13) in the middle of 1988, the Carrs received an anonymous letter warning the whole Carr family that they would all die unless they moved away; (14) Trepal and his wife were the Carrs’ only neighbors; (15) Trepal wrote a Mensa “murder mystery weekend” pamphlet that discussed poisoning and a “move-or-else” note left on a neighbor’s doorstep; and (16) Trepal’s explanation for the Carr poisonings was “to get them to move out, like they did.”

Amid the breadth and depth of this evidence, Martz (who was one of more than 70 witnesses during the State’s case) testified to one discrete issue: the comparison of (1) the substance added to the full Coca-Cola bottles Q1 through Q3, with (2) the substance found in the brown bottle Q206. The State had already established through expert Havekost (whose work and testimony has not been challenged or disparaged in any way) that both substances were thallium compounds — that is, that thallium was found in Q1-Q3 and in Q206. Thallium in any form is rare enough, as the State pointed out to the jury in its closing argument. Martz just further added to an already tight link by opining that the Q1-Q3 bottles and the Q206 bottle all contained the same form of thallium— which was thallium nitrate. There was no evidence at all from any witness or source that the Q1-Q3 samples and the Q206 bottle contained different forms of thallium.

To be sure, Martz was an important witness for the State’s case, as his testimony went to the identification of the potential murder weapon (the substance in Q206), which was the piece of physical evidence linking Trepal to thallium. But Martz’s testimony that Q206 contained thallium I nitrate is not challenged. And the other permissible testimony from Martz was highly incriminating, such as that the Q1 and Q2 samples were consistent with the presence of thallium nitrate.

In any event, Martz’s testimony about the samples from the Q1 through Q3 Coca-Cola bottles — even to the extent it was overly strong in its conclusions — did not, and could not, establish conclusively that the substance that had been added to the Carrs’ Coca-Colas had come from the Q206 bottle. Even without Martz’s testimony, Q206’s linkage of Trepal to thallium was just as strong, for Martz neither found the Q206 bottle in Trepal’s garage (Brekke did) nor found that it contained thallium (Havekost did). As we have pointed out, thallium in any form is a rare and deadly poison.

The portion of Martz’s testimony that was challenged was just one narrow part of the State’s strong case against Trepal, and any falsities in Martz’s testimony were narrower still. Although Trepal belittles the abundant evidence against him at trial, the Florida courts properly characterized the totality of the evidence as “strong.” See Trepal II, 846 So.2d at 426 (“Although this is a circumstantial evidence case, the evidence was strong.” (quoting 3.850 court)).

In sum, we are convinced that, if any falsities in Martz’s testimony had any effect at all upon the jury’s verdict, it was very slight. Martz’s improper testimony certainly did not have, as the Brecht test requires, “a substantial and injurious effect or influence in determining the jury’s verdict.” Brecht, 507 U.S. at 623, 113 S.Ct. at 1714. We are convinced of that. Thus, even assuming arguendo that Trepal could establish a Giglio violation, we conclude that it was harmless. Accordingly, Trepal is not entitled to habeas relief.

IV. CONCLUSION

We affirm the district court’s denial of Trepal’s § 2254 petition.

AFFIRMED.

PRYOR, Circuit Judge,

concurring:

I concur in the panel opinion because I agree that George Trepal is not entitled to habeas relief and that any error under Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972), that occurred during Trepal’s trial was harmless. I write separately to explain why the adjudication of Trepal’s Giglio claim by the Supreme Court of Florida is also entitled to deference under Antiterrorism and Effective Death Penalty Act, 28 U.S.C. § 2254(d). The Supreme Court of Florida did not apply an incorrect standard in its adjudication of Trepal’s Giglio claim. Nor did the Florida circuit court apply an incorrect standard in its adjudication of Trepal’s Giglio claim. Either decision is entitled to deference under section 2254(d), and neither decision involves an unreasonable application of clearly established federal law.

A Nothing in the Analysis by the Supreme Court of Florida Suggests that the Court Incorrectly Identified the Standard Applicable to Trepal’s Giglio Claim or Applied the Incorrect Standard in Its Adjudication of Trepal’s Giglio Claim.

Trepal argues that the Supreme Court of Florida conflated the Giglio and Brady standards of materiality in evaluating his Giglio claim, but there is nothing in the analysis of his claim by that court to support his assertion. See Trepal v. State, 846 So.2d 405, 426-28 (Fla.2003) (Trepal II). The Supreme Court of Florida never articulated the materiality standard that it purported to apply in its adjudication of Trepal’s claim, and its analysis gives little insight into which standard it actually applied in its adjudication of that claim. See id. “Where the standards utilized by the state court are not articulated,” we “may properly assume that the state [court] applied correct standards of federal law ... in the absence of evidence ... that an incorrect standard was in fact applied.” Demps v. Wainwright, 805 F.2d 1426, 1434 (11th Cir.1986) (internal quotation marks omitted). The only discussion of the Giglio and Brady standards in the opinion by the Supreme Court of Florida appears in a section labeled “Circuit Court’s Analysis” and is a direct quote from the opinion by the state circuit court. See Trepal II, 846 So.2d at 423-25. The Supreme Court of Florida neither repeated nor otherwise adopted, in the section of its opinion labeled “This Court’s Analysis,” the statements by the circuit court regarding the Giglio and Brady standards. See id. at 426-28. The Supreme Court of Florida approved the factual findings of the circuit court and agreed with the conclusion by the circuit court “that Trepal was not impermissibly prejudiced by the testimony of Martz,” see id., but the Supreme Court of Florida never stated its standard for determining prejudice.

Nor do statements that the Supreme Court of Florida made in other opinions that adjudicated other petitioners’ Giglio claims prove that the court applied the wrong standard in adjudicating Trepal’s Giglio claim. The relevant decision for our analysis under section 2254(d) is the decision that adjudicated Trepal’s claim, not the decisions in other appeals. See 28 U.S.C. § 2254(d) (precluding federal habeas relief based upon “any claim that was adjudicated on the merits in State court proceedings unless the adjudication of the claim ” satisfies certain requirements) (emphasis added). The relevance to our inquiry of any decision by the Supreme Court of Florida before that court adjudicated Trepal’s claim is not readily apparent, especially when that court did not cite any of those decisions in its analysis of Trepal’s claim, see Trepal II, 846 So.2d at 426-28. Cf. Ventura, 419 F.3d at 1283 (considering the conclusions of law articulated in decisions cited by a state court in its own opinion). Although the Supreme Court of Florida erroneously suggested that the Brady and Giglio standards were equivalent in several opinions issued between 1991 and 2000, see, e.g., Rose v. State, 774 So.2d 629, 635 (Fla.2000), the opinion in Ventura v. State reveals that the Supreme Court of Florida was aware of the distinction between the Brady and Giglio standards in 2001 — well before it adjudicated Trepal’s claim in 2003. See Ventura v. State, 794 So.2d 553, 563 (Fla.2001) (quoting United States v. Alzate, 47 F.3d 1103, 1109-10 (11th Cir.1995)). It is likewise of little relevance to our inquiry that the Supreme Court of Florida “reeede[d]” from Trepal II in a later decision, “to the extent” that Trepal II stood “for the incorrect legal principle that the ‘materiality’ prongs of Brady and Giglio are the same,” because the court neither overruled Trepal II nor declared that Trepal II was intended to — or did in fact — stand for that principle. See Guzman v. State, 868 So.2d 498, 505-06 (Fla.2003).

B. Nothing in the Analysis by the Florida Circuit Court Suggests that the Court Incorrectly Identified the Standard Applicable to TrepaVs Giglio Claim or Applied the Incorrect Standard in Its Adjudication of TrepaVs Giglio Claim.

Even if the Supreme Court of Florida had adopted the analysis that appears in the section of its opinion labeled “Circuit Court’s Analysis,” the Supreme Court of Florida would not have applied the incorrect standard in its adjudication of Trepaks Giglio claim. The Supreme Court of the United States has made clear that we must “presum[e] that state courts know and follow the law,” and give state court decisions “the benefit of the doubt,” Woodford v. Visciotti, 537 U.S. 19, 24, 123 S.Ct. 357, 360, 154 L.Ed.2d 279 (2002). Nothing in the portion of the analysis by the circuit court that appears in the opinion by the Supreme Court of Florida is sufficient to overcome the presumption that the Florida courts applied the correct standard in their adjudication of Trepaks Giglio claim.

The circuit court correctly articulated the Giglio standard for materiality in its explanation of Trepaks Giglio claim. See Trepal II, 846 So.2d at 425. The formulation of the standard by the circuit court deviated only slightly from the formulation favored by the Supreme Court in that the circuit court used “a” instead of “any” and “jury verdict” instead of “judgment of the jury,” but neither of those minor inconsistencies could have had any effect on the analysis of Trepaks claim. This Court has held that the substitution of “a” for “any” is “of no consequence” in the articulation of the Giglio standard. See Ventura, 419 F.3d at 1282. There also is no relevant distinction between “jury verdict” and “judgment of the jury,” as both refer to the jury’s “decision” on the issue of the defendant’s guilt. See Oxford English Dictionary (2d ed. 1989); accord Black’s Law Dictionary (9th ed. 2009).

Although the circuit court incorrectly stated that “[t]he materiality prong [used in Giglio ] is the same as that used in Brady,” Trepal II, 846 So.2d at 425, this single misstatement is “insufficient” to support the conclusion that the circuit court applied the wrong standard in its adjudication of Trepaks claim. Cf. Ventura, 419 F.3d at 1285-86. The circuit court offered no explanation of the Brady materiality standard, but articulated the Giglio materiality standard in terms that closely approximate those used by the United States Supreme Court. Compare id. (observing that false testimony is “material if there is a reasonable likelihood that it could have affected the jury verdict”) (internal quotation marks omitted), with United States v. Agurs, 427 U.S. 97, 103, 96 S.Ct. 2392, 2397, 49 L.Ed.2d 342 (1976) (observing that false testimony is material “if there is any reasonable likelihood that the false testimony could have affected the judgment of the jury”). That the circuit court explained the Giglio standard and not the Brady standard suggests that, if the circuit court believed that the same standard applied to both Giglio and Brady claims, then that so-called “same” standard was the Giglio standard. In that case, the circuit court applied the correct standard to Trepaks Giglio claim.

The circuit court also applied the Giglio standard using correct terminology. After the circuit court correctly articulated the Giglio standard at the beginning of its discussion of Trepaks Giglio claim, see Trepal II, 846 So.2d at 425, the circuit court ruled “that there [was] no reasonable likelihood that the verdict would have been different” in either the guilt phase or the penalty phase of Trepaks trial had Martz not testified falsely, id. at 426. Trepal contends that the circuit court misapplied the Giglio standard when it used the term “would” instead of “could,” but that argument fails. The conclusion of the circuit court that “there [was] no reasonable likelihood that the verdict would have been different” in the absence of Martz’s false testimony, id. at 426, is a satisfactory response to the question whether there was “any reasonable likelihood that the false testimony could have affected the judgment of the jury,” Agurs, 427 U.S. at 103, 96 S.Ct. at 2397. As a matter of logic, when answering the question posed by the Giglio standard, saying that there is no reasonable likelihood that the verdict would have been different is the same as saying that there is no reasonable likelihood that the verdict could have been different. This Court too has used the term “would” in applying the Giglio standard to reach the conclusion that false testimony did not satisfy that standard. Sitting en banc in McCleskey v. Kemp, an appeal from a grant of habeas corpus relief, this Court correctly stated that false testimony is material under the Giglio standard if “it could ‘in any reasonable likelihood have affected the judgment of the jury.’ ” 753 F.2d 877, 885 (11th Cir.1985) (en banc) (quoting Giglio v. United States, 405 U.S. 150, 154, 92 S.Ct. 763, 766, 31 L.Ed.2d 104 (1972)). We then applied the standard and, like the Florida circuit court that adjudicated Trepal’s claim, concluded that the false testimony at issue was not material because it “would have had no effect on the jury’s decision.” Id. (emphasis added). We reversed the grant of habeas corpus relief as to the petitioner’s Giglio claim. Id. We cannot fault the circuit court for applying the Giglio standard using the same language that we have used when we have applied it.

C. Neither the Supreme Court of Florida Nor the Florida Circuit Court Unreasonably Applied Clearly Established Federal Law in Its Adjudication of Trepal’s Giglio Claim.

Neither the Supreme Court of Florida nor the Florida circuit court unreasonably applied the Giglio standard of materiality to Trepaks Giglio claim when those courts determined that there was no reasonable likelihood that Martz’s false testimony could have affected the judgment of the jury at Trepaks trial, see Trepal II, 846 So.2d at 425-28. Martz’s testimony was useful only to establish the particular type of thallium in the three full bottles of Coca-Cola taken from the Carr residence and the glass bottle taken from Trepaks garage. The government established through other witnesses that thallium in any form is rare and unavailable to the general public and that thallium in some form had been added to the three bottles taken from the Carr residence and was contained in the glass bottle taken from Trepaks garage. Fairminded jurists considering this unchallenged testimony in combination with the wealth of unchallenged circumstantial evidence of Trepaks guilt presented at trial could disagree whether Martz’s false testimony could have affected the judgment of the jury at Trepaks trial. Cf. Yarborough v. Alvarado, 541 U.S. 652, 664, 124 S.Ct. 2140, 2149, 158 L.Ed.2d 938 (2004). That “fairminded jurists could disagree on the correctness of the state eourt[s’] decision[s]” means that we cannot grant Trepal federal habeas relief on the basis of his Giglio claim. Harrington v. Richter, 562 U.S. -, 131 S.Ct. 770, 786, 178 L.Ed.2d 624 (2011). 
      
      . Mensa is a society of persons aged 14 and older who are in the top 2% of intelligence, as shown by test scores.
     
      
      . Dr. Carr, a medical doctor, is no relation to Pye or Peggy Carr and their family. When we refer to the "Carr family,” we mean Pye and Peggy Carr and their relatives living on their property (whether or not those relatives bear the surname Carr), not Trepal’s wife or any of her relatives. To avoid confusion, we will refer to Dr. Carr as "Trepaks wife.”
     
      
      . Peggy Carr and her teenaged son Duane Dubberly moved into Pye's home after Peggy and Pye’s March 1988 wedding. Pye's teenaged son, Travis Carr, lived in the home as well.
     
      
      . Pure thallium metal is not absorbed appreciably into the human body. However, there are a number of thallium salts (including thallium nitrate) that are water soluble. When dissolved, thallium forms an ion that, in human tissues, interferes with the body’s ability to use oxygen and generate energy.
      Thallium is used in certain manufacturing processes and in chemical laboratories, but it is not commonly available to the public. Thallium was used as an ingredient in rodenticides and pesticides in the United States until 1972, when the Environmental Protection Agency ("EPA”) banned its use in such products.
     
      
      . In March 1988, Pye converted a detached garage on his property into an apartment for his daughters, Tammy Carr and Gelena Bell, and Pye’s two-year old granddaughter, Kasey Bell. The residents of the apartment spent time in the "main” house, too.
     
      
      . Local officials searched Peggy and Pye’s places of employment and found no thallium.
     
      
      . The eighth bottle consisted of broken pieces of glass.
     
      
      . In January 1990, Goreck met with Trepal and brought up the Carr poisonings. Goreck testified that Trepal was usually very talkative, but was quiet and thoughtful during this conversation. Similarly, Patricia Boatright, who was a friend and confidante of Trepal, testified she asked Trepal about the poisonings and he "didn't meet [her] eyes, and the subject was then dropped.” For some weeks afterward, there "was a strained quality” to Boatright's relationship with Trepal, and she never discussed the poisonings again because "[i]t always just fell like a thud and the subject was changed.”
     
      
      . Two forms of thallium nitrate exist: thallium I nitrate and thallium III nitrate. The two forms of thallium nitrate have different chemical structures and properties, though both are toxic to humans.
     
      
      . Although there was no evidence Trepal himself used or obtained thallium nitrate during his methamphetamine-production days (Warren supplied Trepal with his P2P), as chemist for the group Trepal may well have been aware of thallium nitrate’s role in making P2P.
     
      
      . The empty bottles, which contained nothing visible in them, were tested to see if there was any thallium residue in the bottle that could not be seen. This was done by adding to the bottle "a concentration of distilled water and nitric acid, which would dissolve any metals,” swirling the distilled water/nitric acid mixture around in the bottle for about a minute, and then pouring the resulting "washing” into a sample bottle to be tested using AES and/or AAS.
     
      
      . The AES measures the intensity and wavelength of light emitted by a sample when it is heated, while the AAS measures the intensity and wavelength of light absorbed by the sample when it is heated. Each test then compares the light intensity and wavelength to that from a known standard.
     
      
      . There was no way from those tests to determine whether the thallium nitrate was thallium I nitrate or thallium III nitrate. And as to Ql, Q2, and Q3, Martz did not testify whether it was I or III, but only that it was thallium nitrate.
     
      
      . Martz testified that thallium I nitrate and thallium III nitrate "have different crystalline structures, and the x-ray equipment is able to differentiate those particular two compounds.”
     
      
      . Martz conducted four other tests on the Coca-Cola bottle samples: mass spectrometry ("MS”), x-ray diffraction ("XRD”), scanning electron microscopy ("SEM”), and liquid chromatography ("LC”). Martz's MS testing of the samples "wasn’t successful,” and he did not rely on it for any of his conclusions. Martz tested the Ql sample, but not Q2 or Q3, using XRD and SEM. The tests other than DP "were to give [Martz] negative results, and [he] didn’t need to repeat them on the other samples.” In short, Martz did not mention the testing other than DP and IC because his "opinion was basically ... from the [DP] test and the [IC].”
     
      
      . At the 3.850 hearing, two other FBI toxicology experts testified: (1) Thomas Jourdan, who worked in the FBI Lab’s Chemistry and Toxicology Unit from 1992 to 1997 and served as chief of the Materials and Devices Unit since 1997; and (2) Steven Burmeister, the chief of the FBI Lab’s Chemistry and Toxicology Unit. Both agreed that to a reasonable scientific certainty, thallium nitrate was added to Ql and Q2, and they gave reasons for their opinions. Both could not testify as to Q3 because no IC test was run on Q3. In its ruling, the 3.850 court discounted the testimony of Jourdan and Burmeister, so we do not rely on it.
     
      
      . Trepal’s trial attorneys Jonathan Stidham and Dabney Conner testified at the 3.850 evidentiary hearing. Stidham and Conner testified that the comparison of the contents of the Q206 bottle to the Ql through Q3 Coca-Cola bottles was important to the case, and thus defense counsel hired their own chemistry expert to try to disprove that the thallium in the Coca-Cola bottles came from Q206. However, the defense expert was not able to do so, and so they did not call him to testify. The defense expert's analysis did not replicate Martz's work and proceeded along completely different lines.
     
      
      . In full, the 3.850 court said:
      As to the guilt phase, the court finds ... that there is no reasonable likelihood that the verdict would have been different. This case was based almost entirely on circumstantial evidence. The testing results of the Coke samples and Q206 were the only direct evidence of Trepal’s guilt. Even so, given the test results that Martz could have rightfully testified about and considering all the other evidence in the case, the court finds no reasonable likelihood that the guilt phase results would have been different. Although this is a circumstantial evidence case, the evidence was strong.
      Turning to the penalty phase, .... [t]he court finds that there is no reasonable likelihood that the verdict would have been different____
     
      
      . The Florida Supreme Court noted that the Martz testimony claim involved a mixed question of law and fact. Trepal II, 846 So.2d at 426. Thus, the Florida Supreme Court reviewed the 3.850 court’s “ultimate ruling” de novo but its factual findings based on whether they were "supported by competent substantial evidence.” Id. at 427.
     
      
      . The district court also granted Trepal a COA as to "[w]hether the decision in Trepal II, 846 So.2d at 428—that the [3.850] court's factual findings are supported by competent, substantial evidence in the record’ — is objectively unreasonable.” In his initial brief on appeal, however, Trepal does not argue that the state 3.850 court's findings were not supported by the record. In any event, the record amply supports all the state 3.850 court’s fact findings and we conclude the Florida Supreme Court’s decision was not unreasonable. See 28 U.S.C. § 2254(d)(2).
     
      
      . We refer to our December 7, 2011 Guzman decision as "Guzman II" to distinguish it from the Florida Supreme Court’s 2003 decision in Guzman v. State, 868 So.2d 498, 505-06 (Fla.2003), discussed earlier, which we refer to as "Guzman."
      
     
      
      . "[T]he reason the lower materiality burden applies where there is knowing use of perjured testimony is that such a situation involves prosecutorial misconduct and a corruption of the truth-seeking function of the trial.” Alzate, 47 F.3d at 1110; accord Agurs, 427 U.S. at 103-04, 96 S.Ct. at 2397.
     
      
      . We are aware that the Supreme Court has instructed us that, on federal habeas review, we are to give state court decisions "the benefit of the doubt.” Cullen v. Pinholster, 563 U.S. -, 131 S.Ct. 1388, 1398, 179 L.Ed.2d 557 (2011) (quoting Woodford v. Visciotti, 537 U.S. 19, 24, 123 S.Ct. 357, 360, 154 L.Ed.2d 279 (2002)). Our concurring colleague points out good reasons why we should conclude the Florida Supreme Court did not apply an incorrect standard in its adjudication of Trepáis Giglio claim. But Trepáis claim fails even under de novo review.
     
      
      . There is a substantial issue as to whether FBI Agent Martz's knowing false testimony can be imputed to the Florida State Attorney who prosecuted the Trepal case. See, e.g., Moon v. Head, 285 F.3d 1301, 1309-10 (11th Cir.2002) (noting that (1) a prosecutor has a duty to learn of any favorable evidence known to others acting on the government’s behalf, including law enforcement officers, and (2) thus knowledge possessed by any member of the “prosecution team” is imputed to the prosecutor, but (3) whether knowledge held by members of one governmental entity can be imputed to a prosecutor working for a different governmental entity is determined using "a case-by-case analysis of the extent of interaction and cooperation between the two governments” (quoting United States v. Antone, 603 F.2d 566, 570 (5th Cir.1979))).
      The State contends that Martz was not a part of the "prosecution team,” that he was simply serving as an expert witness called to testify about his testing of the evidence, and that his overstatement of his opinions was neither known nor countenanced by anyone in the State Attorney’s office. We need not reach this issue to decide this case.
     
      
      . The Brecht Court explained the distinction between trial error and structural defects:
      Trial error occurs during the presentation of the case to the jury, and is amenable to harmless-error analysis because it may be quantitatively assessed in the context of other evidence presented in order to determine the effect it had on the trial. At the other end of the spectrum of constitutional errors lie structural defects in the constitution of the trial mechanism, which defy analysis by harmless-error standards. The existence of such defects — deprivation of the right to counsel, for example — requires automatic reversal of the conviction because they infect the entire trial process.
      
        Brecht, 507 U.S. at 629-30, 113 S.Ct. at 1717 (citations, quotation marks, footnotes, brackets, and ellipsis omitted).
     
      
      . We do not phrase the Brecht requirement as a burden of proof, for it is not. In O’Neal v. McAninch, 513 U.S. 432, 435, 115 S.Ct. 992, 994, 130 L.Ed.2d 947 (1995), the Supreme Court held that if a federal habeas court has “grave doubt” about whether a constitutional error is harmless under the Brecht standard, which the Court defined as situations in which “the matter is so evenly balanced that [the judge) feels himself in virtual equipoise as to the harmlessness of the error,” then "the uncertain judge should treat the error, not as if it were harmless, but as if it affected the verdict (i.e., as if it has a 'substantial and injurious effect or influence in determining the jury’s verdict’).” Id. The Supreme Court further explained:
      [ W]e deliberately phrase the issue in this case in terms of a judge's grave doubt, instead of in terms of "burden of proof.” The case before us does not involve a judge who shifts a "burden” to help control the presentation of evidence at a trial, but rather involves a judge who applies a legal standard (harmlessness) to a record that the presentation of evidence is no longer likely to affect. In such a case, we think it conceptually clearer for the judge to ask directly, "Do I, the judge, think that the error substantially influenced the jury's decision?” than for the judge to try to put the same question in terms of proof burdens (e.g., "Do I believe the party has borne its burden of showing ...?”).
      
        Id. at 436-37, 115 S.Ct. at 994-95.
     
      
      .We emphasize that the Brecht standard is a harmless error test that applies to federal habeas review of state convictions. Brecht, 507 U.S. at 634-38, 113 S.Ct. at 1720-22; Ventura, 419 F.3d at 1279 n. 4. It does not apply to state courts' review of their own convictions. Instead, the Florida courts apply the more petitioner-friendly Chapman standard of whether the constitutional error is "harmless beyond a reasonable doubt.” See Pittman v. State, 90 So.3d 794, 2011 WL 2566325, at *9 (Fla. June 30, 2011); Guzman v. State, 868 So.2d 498, 507-08 (Fla.2003).
     
      
      . Moreover, Brecht applies in federal habeas regardless of whether or not the state court recognized the constitutional error and applied a Chapman analysis. Fry v. Pliler, 551 U.S. 112, 121-22, 127 S.Ct. 2321, 2328, 168 L.Ed.2d 16 (2007).
     
      
      . As mentioned above, Giglio error is a species of Brady error. But when we refer here to “Brady violations,” we mean Brady violations that are not Giglio violations. These non-Giglio Brady violations are sometimes referred to as Bagley violations or Brady/Bagley 
        violations, after United States v. Bagley, 473 U.S. 667, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985), which established the "reasonable probability that the result of the proceeding would have been different” materiality standard used for Brady violations that do not involve the knowing use of or failure to correct perjured testimony. See Kyles v. Whitley, 514 U.S. 419, 432-43, 115 S.Ct. 1555, 1565-66, 131 L.Ed.2d 490 (1995) (discussing Brady and its progeny, including Bagley).
     
      
      . As explained above, Trepal must also show that the Florida Supreme Court's denial of his Giglio claim in Trepal II was contrary to Giglio, involved an unreasonable application of Giglio, or was based on an unreasonable determination of the facts in light of the evidence presented in state court. See 28 U.S.C. § 2254(d). But we assume, but do not decide, for purposes of this opinion that Trepal has satisfied those threshold requirements of § 2254(d).
     
      
      . To illustrate, if this case were a hit-and-run by a rare automobile instead of murder by a rare poison, Havekost established, say, that the victims were hit by, and the defendant owned, a red Ferrari. Martz narrowed it down to a 1982 red Ferrari, but still no one could match the license plates.
     
      
      . The State acknowledged this point in its closing argument, stating, "Nobody can tell you that this thallium nitrate is the thallium nitrate that was in those bottles because it's just thallium nitrate.” The State analogized to table salt dropped on a rug, noting that no crime scene technician in the world could tell whether a grain of table salt on the rug came from a particular bottle of salt or if it was already on the floor. Trepal’s attorney Wofford Stidham also made this point in his closing argument for Trepal, arguing, "[D]id the thallium in the Coca-Colas come from this little bottle? The innuendo was there that it did. You heard the witness this very morning that was asked that question, could he say the thallium in the Coca-Cola came from that little bottle and he said no. You have to speculate.”
     