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(Bloomberg) — The pitch went like this: Good, safe drinking water has become such a scarce resource that Americans will pay to fill up jugs — 30 or 40 cents to the gallon — at dispensers all across the country.

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Hundreds of investors bought thousands of units, believing in the vision laid out by Ryan Wear, founder of a startup called WaterStation Management. They plunked down $8,500 for each vending machine and then waited for the dispensers to throw off a steady stream of cash. Among those lured in was a product manager in Oregon in 2021 and then, several months later, a dentist in Illinois. Each bought dozens of water dispensers, which Wear’s team would install and operate.

What they didn’t know is that at least one of those Hylyte-branded machines wound up being sold to both of them: serial number 101962, wedged in between a liquor store and a yoga studio in a strip mall in the Los Angeles suburb of Torrance, according to court records. To make matters worse, a machine with that same serial number was also pledged as collateral to back WaterStation bonds that were sold in April 2022 to the investment bank Jefferies Financial Group Inc.

Serial number 101962, faded and rusted in pictures submitted to court, is now gone from that strip mall, WaterStation is in bankruptcy, and Wear, 49, is the target of legal action by federal prosecutors, the Securities and Exchange Commission, a state banking regulator, Jefferies and scores of small-time investors, all of whom claim the company’s business was largely an illusion.

“This case involves a massive Ponzi scheme,” Assistant U.S. Attorney Justin Rodriguez told a federal judge in Manhattan Wednesday after Wear pleaded not guilty to criminal charges. A few feet away sat Jordan Chirico, a former Jefferies fund manager who prosecutors allege also committed fraud, directing his fund to purchase more WaterStation bonds after Wear admitted many water machines didn’t exist. He, too, pleaded not guilty. Lawyers for both declined to comment.

Voluminous legal filings describe a business that drew in military veterans, stock traders, pharmacists, salespeople and retirees by leveraging growing fears about contaminated tap water and microplastics and offering a lucrative solution that’d churn out annual returns as high as 20%, year after year. That desire to make easy money, coupled with clever marketing and alleged diligence lapses, kept the sputtering business going until the money finally stopped flowing around June 2023, according to court documents.

“These schemes never arise in a vacuum,” said John Bender, a lawyer who is representing a committee of WaterStation creditors. “The tragic consequences of the WaterStation affair could have been avoided had it not been for a cabal of insiders and institutions that prioritized their greed over doing the right thing even if it meant devastating the lives of a lot of people.”

Earlier this month, the committee asked a judge overseeing the proceedings to rule that Wear’s business meets the legal definition of a Ponzi scheme — a type of operation that uses new money to pay returns of existing investors or other creditors, with promoters usually promising high returns for little risk. If granted, franchisees would likely get tax relief and advisers would have an easier time clawing back funds from entities that profited off WaterStation’s business, which “will lay the groundwork for future recoveries on behalf of victims of this Ponzi,” according to the committee’s filing.”

Machine Mismatch

Formed in 2016 in Everett, Washington, WaterStation Management sold upwards of 21,000 machines and raised more than $380 million over the course of some seven years. Growth was fueled by a handful of banks that issued loans backed by the US Small Business Administration, as well as about $100 million in bonds bought by a fund run by Jefferies. Wear claimed in a 2023 deposition that his business had more than 500 employees.

In actuality, Wear’s firm only deployed roughly 2,100 machines, many likely never existed at all and most of the money WaterStation raised paid other costs or payments to existing franchisees, according to court records. Many dispensers that do exist were sold to multiple buyers — like the one that was in Torrance — or were promised as Jefferies’ collateral. Serial numbers on other machines don’t correspond with addresses investors were given by the company, court papers indicate. Determining who owns each machine and who bears responsibility for the alleged scheme is being fought over in federal court.

To locate machines that were sold more than once, Bloomberg News analyzed thousands of serial numbers submitted in court by creditors with claims to WaterStation machines and more than a dozen investor lawsuits that have piled up. Restructuring advisers say in court papers that more than 10,000 water machines were sold to multiple purchasers.

Falling Behind

WaterStation had trouble paying franchisees for years before monthly payments stopped completely two years ago, according to Becky Yang O’Malley, a GlassRatner Advisory Services managing director and certified fraud examiner retained by a committee representing WaterStation franchisees and other creditors. Franchisees have sued WaterStation and Wear, who along with Chirico, was sued by the Jefferies fund, while banks have sued franchisees who have fallen behind on business loans, according to court records. Jefferies has also sued one lender, First Fed Bank, alleging it helped keep WaterStation afloat after becoming aware of the alleged fraud in order to prioritize repayment of debt it was owed.

Wear in a sworn statement in April 2024 said franchisees’ allegations that machines don’t exist were untrue and their claims of fraud “are baseless, inflammatory and false.” Although WaterStation had occasionally experienced cash-flow issues, the business was legitimate and profits derived from water machines “were historically paid to plaintiffs,” Wear said at the time.

A First Fed spokesman said the bank isn’t able to comment on specific aspects of Jefferies’ lawsuit “as this is an ongoing legal matter,” but that the lender did nothing wrong. The bank will be submitting a formal response to Jefferies’ complaint next month, “which will provide additional clarity at that time,” he said.

‘Financially Devastated’

Chirico, 41, has also denied wrongdoing. His lawyer has said Chirico is also a victim of the WaterStation fraud and that Jefferies has “tried to scapegoat our client for an alleged scheme that deceived him along with hundreds of other investors and major institutions.”

Jefferies’ 352 Capital fund, once managed by Chirico, filed a civil lawsuit against Chirico in New York state court after a federal judge in May dismissed an earlier complaint. The bond transactions and their risks “were no secret” to the firm and other institutions, Chirico’s lawyers said in a motion to dismiss the latest lawsuit. Chirico sought to protect the fund by removing Wear as manager and attempted “to stabilize the collateral so the possibility of a restructuring or refinancing could be explored,” according to his Aug. 14 motion.

Restructuring advisers face a daunting task of trying to return money to franchisees who face substantial losses after Wear’s businesses went bankrupt last year. The situation is worse for those who took out loans to buy machines because even though the business was an alleged fraud, franchisees are still responsible for the debt and certain banks have sued borrowers who have fallen behind on payments. Some investors contend banks that partnered with Wear’s business should have uncovered the alleged scheme earlier because they had access to machine lists with duplicate serial numbers.

“My family has been financially devastated by the WaterStation scheme,” one Indiana franchisee noted in a sworn statement. He said he spent $3.3 million on machines and took out loans from two banks to fund his investment, pushing his monthly loan payments to $35,000. He said WaterStation’s assurances that it would buy back machines and that the financing was “SBA-approved” made him believe the business was more profitable and secure than it actually was.

Bank Loans

WaterStation was listed on the SBA’s database of franchises eligible for agency-approved loans starting in 2018. It gained momentum two years later, when Wear hired former bank-loan officer Kevin Nooney to help forge ties with banks and build a financing program to boost machine sales. The arrangement brought in new investor cash as the pandemic triggered a plunge in interest rates that motivated Americans to pile into a raft of alternative investments during lockdowns.

First Fed and fellow regional lenders Unibank and Celtic Bank were among the institutions that provided the most financing to investors, according to papers filed by a committee representing WaterStation creditors. Nooney said in a 2024 court filing that one of his former colleagues knew First Fed’s vice president of commercial lending, and that he also had “long-standing personal relationships” with Unibank’s former chief credit officer and a former loan officer.

Unibank and Celtic participate in the SBA’s preferred lending program which lets private banks administer SBA-backed loans with minimal agency review. Preferred lenders approved 28,875 SBA loans worth nearly $30 billion in fiscal 2021, roughly 55% of all loans approved in the SBA’s flagship lending program, according to a 2022 congressional report.

Unibank and Celtic didn’t respond to requests for comment.

From the start, though, the machines that Wear’s business was built on never made enough money to pay investors or cover WaterStation’s other costs. Instead, Wear relied on investors’ money and other loans to pay returns he promised franchisees “and to perpetuate the illusion of a legitimate business,” according to Yang O’Malley’s report.

As new money rolled in, people who already purchased machines got payouts they thought were their cut of the money generated from the vending business, according to court documents. WaterStation paid out $31.5 million in investor returns in 2021, about double what it paid in 2020, and more than $44 million in 2022, according to Yang O’Malley’s report.

But cracks were already forming as soon as August 2021, when Nooney learned that WaterStation purchases could constitute a security, according to a complaint brought by Washington’s banking regulator in May. The company responded by altering how it pitched the opportunity and paid returns, and these changes had the effect of curtailing new purchases, the complaint said. A lawyer for Nooney didn’t return messages seeking comment.

There was another problem with Wear’s business. The company pitched its machines as a way to make passive income, even though SBA rules say the loans WaterStation benefited from can only be used to fund actively managed franchises, according to the complaint. The state regulator also said WaterStation exploited the SBA’s preferred lender program.

The SBA was “left in the dark” and relied on lenders to verify that funds for the WaterStation loans were being used for approved purposes, Washington authorities said.

Enter Jefferies

In need of fresh capital, Wear turned to the bond market. In 2022, a Jefferies hedge fund called 352 Capital purchased roughly $100 million in WaterStation bonds earmarked for machine purchases. The fund was run by Chirico, who had bought hundreds of machines prior to joining 352 Capital as portfolio manager, according to federal prosecutors. Chirico didn’t fully disclose to Jefferies his personal stake in WaterStation, according to the indictment, which he disputes.

The bonds have spawned a separate Jefferies lawsuit against First Fed, which the firm claims became aware in the summer of 2022 that many machines didn’t exist. The lender, a unit of First Northwest Bancorp, had serial numbers for machines purchased with loans it gave franchisees, as well as machines WaterStation claimed ownership of that served as collateral for the bonds, “and hundreds of machines appeared on both lists,” according to Jefferies’ suit.

First Fed has denied wrongdoing and last year sought a receiver to take over Wear’s business. In a July bankruptcy settlement, the bank also agreed to pay $2.87 million to creditors and make additional payments and concessions to benefit franchisees, according to court papers.

First Fed in a statement this month said the bankruptcy settlement will benefit creditors because the bank released claims against WaterStation as well as liens on properties owned by an affiliate company. Proceeds from those assets will “become available for ratable distribution” to creditors, the bank said.

‘Going to Jail’

As for Chirico, prosecutors allege he had “learned of serious issues at WaterStation” by the summer of 2023. Then, in a phone call the following January, Wear admitted that thousands of machines supporting the bonds didn’t exist. But instead of telling Jefferies, Chirico allegedly directed the fund to purchase more WaterStation bonds which Wear partly used to repay a debt to Chirico, according to the indictment.

At Wednesday’s arraignment, Rodriguez, the prosecutor, told a federal judge that a “lengthy recorded phone call” is among the evidence law enforcement collected along with messages from Wear’s business email account. An investor who was also on the recorded phone call told Wear this was the “largest franchise fraud case in the history of the United States” and that he was “going to jail,” according to the indictments.

As the legal process plays out, borrowers are still responsible for SBA loans even if they are victims of an alleged scam, said Paul Midzak, a lawyer who advises small business owners. However, borrowers like the WaterStation franchisees can raise the alleged fraud as a defense against their loans and challenge lenders in court, Midzak said. The SBA, meanwhile, can be slow in responding to borrowers and working with the agency can be “like dealing with a woolly mammoth,” he said.

An SBA spokesman directed Bloomberg News to the Department of Justice. The DOJ in its press release announcing the criminal charges this month said that the SBA’s Office of Inspector General was among the federal agencies that assisted law enforcement in the criminal investigation.

Outside court proceedings, the physical markers that remain of Wear’s business include the water dispensers that actually were deployed in places like Pahrump, Nevada, where a Hylyte machine sits near the Lakeside Casino & RV Park, serving water to travelers who stop at the casino for a $12 plate of steak and eggs before heading east to Las Vegas or west to Death Valley.

Another 4,000-plus machines are sitting idle in two dozen abandoned warehouses stretching from Everett to Missoula, Montana, and Fort Meyers, Florida. Liquidation firm TAGeX Brands was hired to inventory machines. It discovered that people have broken into the warehouses to harvest copper wiring from the walls and that some packaged food left inside has attracted rats, according to court papers.

The facilities “stand out as among the most disorganized warehouses I have encountered in my 38-year career,” TAGeX Chief Executive Officer Neal Sherman said in an August court filing. The machines lack insulation and pipes inside dispensers left in cooler climates often burst, making them impossible to sell.

“The water machines were in poor condition,” Sherman said, “and were poorly made.”

–With assistance from Nicola M White and Katanga Johnson.

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Participants

We recruited 36 young participants from southern Taiwan through advertisements on the Internet and bulletin boards. We conducted a power analysis (G*Power 3.1.9.7¹², power = 0.95, effect size f = 0.25, α = 0.05, within-between subjects’ design, correlation among repeat measures = 0.5). The analysis indicated that a sample size of 36 participants would be sufficient to detect an estimated medium effect size. All participants were right-handed and without evidence of neurological or psychiatric disorders based on self-reports. This study was reviewed and approved by the Human Research Ethics Committee at National Cheng Kung University (NCKU), Tainan, Taiwan, R.O.C., authorized by the Ministry of Education, Taiwan. All experimental procedures and the informed consent were obtained from all the participants and were approved under Approval No. NCKU HREC-E-112-120-2. All research was performed in accordance with the relevant guidelines and regulations, including the Declaration of Helsinki. Upon completion of all experiments — including computerized span tasks conducted outside the MRI scanner and a visual discrimination task performed inside the MRI scanner — participants received compensation of 1,500 New Taiwan Dollars (NTD). Detailed demographic characteristics are presented in Table 1.

Span tasks outside an MRI scanner

We assessed participants’ span capacity (individual differences) using computerized span tasks developed by Stone and Towse (2015) in JAVA¹³. The tasks included three complex span tasks and corresponding simple span tasks in both the verbal and visuo-spatial domains.

Verbal domain

Operation span task (complex span)

The Operation Span task was chosen as the complex span task for the verbal domain (see Supplementary Figure S1). This task involved a repetitive sequence of memory and processing components. In each trial, participants were presented with an integer to memorize and recall in its original serial position at the end of the trial. Following each memory element (the integer), there was a processing phase where participants encountered a mathematical operation, such as ‘9 + 9 = 27’. They had to determine whether the presented answer was correct. Digits and operations were generated randomly for each trial, with digits ranging from 1 to 99. Each operation had an equal 50% chance of being correct, and the types of operations (multiplication, division, addition, subtraction) each had a 25% probability, ensuring a diverse range of operation types requiring both correct and incorrect responses. Digit span (simple span). Digit span corresponded to the simple span task for Operation Span. Essentially, it was Operation Span without the processing phase. Participants only needed to remember the digits and recall them in sequence at the end of the trial.

Visuo-spatial domain

Symmetry span task (complex span)

The Symmetry Span task is a type of visuo-spatial complex span task where participants were required to recall grid locations in a 4 × 4 grid in the correct serial order (see Supplementary Figure S2). Following the presentation of each To-Be-Remembered (TBR) grid, participants engaged in a processing operation where they judged whether the presented pattern was symmetrical along the vertical axis, using the left/right arrow keys. Patterns were displayed on an 8 × 8 grid for this assessment. The recall phase began once the required number of storage-processing elements had been completed for a trial. Participants were prompted to recall by presenting them with the 4 × 4 grid, allowing them to click on the boxes in the order they remembered seeing them. Upon selection, a box turned blue, helping participants keep track of their responses. Matrix span (simple span). The matrix span task served as the simple span counterpart to the symmetry span task. Its procedure closely mirrored that of the symmetry span task, except for omitting the processing element.

Rotation span task (complex span)

The Rotation Span task was another visuo-spatial complex span task (see Supplementary Figure S3). The To-Be-Remembered (TBR) stimuli consisted of arrows characterized by two features: length (long or short) and angle of rotation (0°, 45°, 90°, 135°, 180°, 225°, 270°, or 315°). Participants were tasked with remembering these arrows presented in their correct serial order during the storage phase. In this complex span task, the processing operation involved presenting participants with a letter (F, G, or R) that could appear in its standard form or as a mirror image, and it could also be rotated at one of the 45-degree angles. Participants had to mentally rotate the image to determine whether the letter was presented normally or as a mirror image, using the left/right keys for their judgment. During the recall phase, participants were shown a 2 × 8 grid displaying all 16 possible arrows. The top row displayed all the long arrows, while the bottom row displayed all the short arrows. Participants used the mouse to select the arrows they recalled seeing in the correct sequential order. Arrow span (simple span). The processing phase was omitted in the arrow span task, which served as the memory span equivalent to the rotation span task. Consequently, the arrow span task focused on the participant’s ability to remember the arrows in their correct serial positions.

Visual discrimination tasks with difficulty manipulation in an MRI scanner

Participants engaged in a visual discrimination task featuring four distinct conditions, as outlined in Fig. 1. The task was programmed using OpenSesame¹⁴. Inside the MRI scanner, the stimulus display was projected onto a mirror affixed to the head coil. The task design was adapted from difficulty manipulations reported by Crittenden and Duncan (2014). These tasks varied in cognitive demands, ranging from simple perceptual discrimination to complex rule-based tasks¹¹.

Each trial began with a uniform gray screen in the baseline 4-line (4 L) condition. Participants were required to select the one odd line out of four based on length, considered the baseline or least demanding condition involving simple perceptual discrimination. At the start of each trial, a small fixation cross appeared at the center of the screen for 200 ms. Subsequently, four vertical lines were briefly presented (100 ms), aligned along the middle of the screen with their midpoints distributed symmetrically on either side of the fixation cross (total width 8.3° visual angle). Among these lines, three were equal in length (13.4°), while the fourth was consistently 50% shorter (6.7°). Participants indicated the position of the shorter line by pressing the corresponding key on an 8-button response box (e.g., Fig. 1, leftmost line shortest, response with the left middle finger). Responses were recorded only within the time window of the fixation cross, which persisted for 1000 ms after the lines disappeared from the display. Following a response, there was a jittered interstimulus interval of 500 to 1500 ms before the onset of the subsequent trial.

The remaining conditions exhibited similarities with some alterations as described below. In the 8 L condition, similar to the 4 L condition but with eight lines instead of four, two additional vertical lines were presented on either side of the original four lines (total display width 16.7°; see Fig. 1). This required participants to use each hand’s little and ring fingers for a response. The 8 L condition increased the perceptual load by doubling the number of lines, thereby raising the cognitive demand compared to the 4 L condition.

In the fine discrimination (FD) condition, similar to the 4 L condition, there were still four lines, but the shortest line was reduced to only 10% shorter than the other three lines (see Fig. 1). Participants had to discriminate between lines of very similar lengths, necessitating fine perceptual judgments. This condition heightened the cognitive demand further by requiring precise discrimination of line lengths, adding to the perceptual load.

In the mapping switch (MS) condition, the stimulus-response mapping was modified from the natural one to the alternative illustrated in Fig. 1. Participants were still required to discriminate between lines of very similar lengths, making fine perceptual judgments. This condition was considered the most demanding, as participants had to select the right-most odd line but press the left-most button. This complex rule introduced higher-order cognitive processing involving working memory and response inhibition. It placed significant demands on executive functions and was generally regarded as the most challenging^15,16. Participants practiced this condition until their accuracy rate reached 70% or higher.

Trials were grouped into blocks, each dedicated to one task condition. Each block displayed a schematic similar to Fig. 1 indicating the upcoming condition in the middle of the screen for 2,000 ms. Following the cue, there was a 3,800 ms pause before the onset of the first trial. Each block consisted of 8 trials, with a total duration of 18,400 milliseconds. There was a 10-second interval between blocks. To maintain task engagement, the accuracy of each block was displayed at the end.

The experiment was divided into three scanning sessions, each separated by a 30-second break. Within each session, there were 20 task blocks, comprising five blocks for each of the four conditions (4 L, 8 L, FD, and MS). The sequence of blocks was arranged in a pseudorandom order.

Behavioral data analysis

Span task performance

For each span task, we calculated their Full-Trial Accuracy (FTA) score. In the case of simple span tasks, points were awarded only when all Target-to-Be-Remembered (TBR) stimuli within a trial were correctly recalled. The score for each trial was determined by the loading of that particular trial, and the sum of scores across all trials constituted the FTA score for that task. In the case of complex span tasks, the calculation method was similar to that of simple span tasks, with the distinction that points were awarded only for trials where the response to the processing component was correct.

Grouping participants based on a median split of the FTA score

Our study employed the complex span task total scores to perform a median split, grouping participants into high-span and low-span groups based on individual differences in span task performances. This decision was based on the higher complex span scores compared to simple span scores, making them more effective for distinguishing individual differences in span capacity. However, we acknowledge that this approach may inadvertently capture differences in perceptual abilities, as evidenced by significant differences in simple span performance between groups (p <.005; see Results). Complex span tasks, which involve both storage and processing components, are known to be more sensitive measures of working memory capacity compared to simple span tasks that only require storage¹⁷. Given that our participant sample consisted of young adults, the complex span tasks were particularly effective in capturing individual differences in working memory capacity, which is critical for examining PFC activation patterns under varying cognitive demands^18,19.

Additionally, using the median split method allowed for a clear and balanced division of participants into two groups, facilitating the analysis of how these differences associate with neural activation patterns during task performance²⁰. Specifically, using a median split ensured an equal distribution of participants into high- and low-span groups, facilitating balanced and well-built statistical comparisons. This approach also mitigated potential biases that could arise from uneven group sizes, enhancing the validity and reliability of our findings²¹. By employing a median split on complex span scores, we aimed to provide a clear delineation of how varying levels of individual differences impact neural activation patterns and cognitive control processes. However, we acknowledge that treating individual differences as a continuous covariate in a regression analysis might offer greater statistical power and a more profound understanding of its relationship with PFC activation. To address this, we conducted an additional regression analysis using complex span FTA scores as a continuous covariate, confirming that the observed patterns of PFC activation remained significant (p <.001; see Figure S4 in Supplementary Information).

Visual discrimination task performance

Behavioral performance (reaction time [RT] and accuracy) was measured separately for each of the four conditions (4 L, 8 L, FD, MS). Subsequently, we conducted a one-way analysis of variance (ANOVA) on the four conditions to determine if the behavioral performance replicated previous findings reported by Duncan and colleagues¹¹. To test the hypothesis regarding whether individual differences would be associated with primary contrasts between conditions of interest in task performance, we initially compared the 8 L, FD, and MS conditions with the 4 L condition to identify any increase in reaction time (RT) and/or decrease in accuracy resulting from manipulation difficulty. Tasks with higher task demands, such as increased perceptual load in the 8 L condition, finer discrimination in the FD condition, or complex rule mapping in the MS condition, require greater working memory resources. High-span individuals typically exhibit superior cognitive control in these contexts²². In contrast, low-span individuals exhibited broader neural recruitment, which may reflect the additional engagement of brain regions under increased task demands²³.

Subsequently, we contrasted the conditions of interest. We used the 4 L condition as a baseline to evaluate how the 8 L, FD, and MS conditions demanded greater performance costs. The three contrast pairs were as follows:

8 L–4 L (Perceptual Load): The primary difference lies in the number of items to be processed. The 8 L condition has double the items of the 4 L condition, increasing perceptual load and cognitive demand.

FD-4 L (Precision of Discrimination): While both conditions involve selecting an odd line, the FD condition requires finer perceptual judgments, thereby increasing cognitive load compared to the broader discrimination required in the 4 L condition.

MS-4 L (Complexity of Rule Application): The MS condition introduces a complex rule that reverses the typical response mapping, significantly increasing cognitive demands compared to the straightforward perceptual discrimination in the 4 L condition.

We then employed mixed-design repeated-measures 2 (high- and low-span groups) x 3 (paired-contrasts: 8 L–4 L, FD-4 L, MS-4 L) ANOVAs on RT and accuracy, respectively, to examine the effects of the three contrasted conditions and determine if they interacted across two groups of individuals with high versus low span performances. Following the initial statistical testing, post hoc analyses were conducted using the Holm correction to further explore and compare the significant differences identified among the conditions.

Imaging acquisition and analysis for the visual discrimination task

The imaging data was gathered utilizing a General Electric (GE) Discovery MR750 3 Tesla scanner (General Electric Medical Systems, Milwaukee, USA) equipped with a 32-channel receive-only phased-array head coil at the Mind Research Imaging Center, National Cheng Kung University. High-resolution structural images were obtained using a fast-SPGR sequence comprising 166 axial slices (TR/TE/flip angle 7.6 ms/3.3 ms/12°; field of view (FOV) 22.4 × 22.4 cm²; matrix size 224 × 224; slice thickness 1 mm). Functional EPI images were acquired through an interleaved T2* weighted gradient-echo planar imaging (EPI) pulse sequence (TR/TE/flip angle, 2000 ms/30 ms/78°; matrix size, 64 × 64; FOV, 22 × 22 cm²; slice thickness, 3 mm; voxel size, 3.4375 × 3.4375 × 3 mm). Each run comprised 368 volumes, with the initial eight being dummy scans discarded to mitigate T1 equilibrium effects.

fMRI imaging preprocessing

Functional imaging data were analyzed using the FMRIB Software Library (FSL)²⁴ software. The analysis process comprised several specific steps at the 1 st level: Initially, preprocessing involved correcting head motion artifacts using the Motion Correction FMRIB’s Linear Image Registration Tool (MCFLIRT)^25,26,27. Subsequently, the brain extraction tool eliminated non-brain tissue from the preprocessed MR images (BET²⁷. The FSL Motion Outliers tool^25,27 accessible at https://fsl.fmrib.ox.ac.uk/fsl/fslwiki/FSLMotionOutliers, was then employed to detect outlier volumes based on frame displacement between volumes (exceeding the 75th percentile + 1.5 times the interquartile range). The results of this process were utilized to reduce the influence of those volumes in subsequent analyses. Individual brain functional images underwent registration to the high-resolution T1 structural image via linear transformation, followed by registration of the individual structural image to the standard MNI152 template via linear transformation²⁸. The first-level General Linear Model (GLM) in FEAT tool^29,30,31 was then established, incorporating a 9 mm full-width half-maximum (FWHM) Gaussian kernel for spatial smoothing.

Statistical analysis: fMRI blocked analyses for the visual discrimination task

A general linear model (GLM) was used to estimate parameter values reflecting the mean difference between experimental conditions of the visual discrimination task. Contrasts were performed to identify the regions recruited more for the 8 L, FD, and MS conditions relative to the 4 L condition.

The start time of each condition block’s stimulus to the endpoint of the block was captured and used to generate the onset file. The onset files for the four conditions were incorporated into the model as EVs (explanatory variables) and convolved with the double gamma hemodynamic response function. The six head motion parameters and the motion outlier data obtained in the previous step were included as covariates in the model for control.

The second-level analysis integrated data from the three runs, and the results of the three paired-contrasts (8 L–4 L, FD-4 L, MS-4 L) obtained at the first level were averaged separately.

To investigate our hypotheses regarding the high- and low-span groups, the subject-level files of the two groups were compared by averaging them separately according to the three paired-contrasts. We further examined the significant clusters for the combinations with simple main effects based on the ANOVA results of behavioral data, separately contrasting high span > low span and low span > high span.

Whole-brain univariate analysis

All group-level analyses involved computing the activation level across the whole brain region for each participant and submitting each of those to a group-level t-test, treating the participant as a random effect. We identified clusters of activity that were significant at a cluster-level rate of 0.01, using a 3.1 z-threshold to define contiguous clusters³². Subsequently, the estimated significance level of each cluster (derived from Gaussian Random Field theory) was compared with the probability threshold³³. To account for potential confounding factors, weperformed a partial regression analysis to control for gender effects between the high- and low-span groups. This step aimed to isolate the specific contributions of individual differences observed in neural activation patterns between the two groups.

fMRI preprocessing and GLM for multivoxel pattern analysis (MVPA)

The fMRI data were preprocessed using Statistical Parametric Mapping (SPM) 12^34,35 implemented in MATLAB (The MathWorks, Inc., Natick, MA). The preprocessing steps included slice-time correction and realignment to correct head motion using a rigid-body transformation³⁶. The T1 image was co-registered to the mean EPI image, and then both the T1 image and functional volumes were normalized to the MNI template. All images were resliced to a 2 × 2 × 2 mm voxel size, resulting in a data cube of 79 × 95 × 79 voxels. The onset files, marked with the start times for three runs and four conditions, were input into the GLM model. Head motion parameters obtained from realignment were included as regressors. After preprocessing, we obtained the beta maps and SPM.mat files for subsequent MVPA analysis.

MVPA

MVPA was conducted using the Decoding Toolbox (TDT, version 3.999 F) implemented in MATLAB, following standard preprocessing procedures. A whole-brain searchlight analysis was performed to identify regions whose activation patterns allowed classification between higher difficulty conditions and the 4 L condition used as the baseline³⁷. The input data for the classifier were the beta maps obtained from preprocessing and GLM analysis, normalized to MNI standard space. For every voxel in the brain, a sphere with a radius of 5 voxels centered on that voxel was used to train and test a linear support vector machine (SVM) using leave-one-run-out cross-validation within each participant^38,39. The classification accuracy of each sphere was assigned to the center voxel, resulting in a subject-level accuracy map. Accuracy maps were then entered into group-level analysis to identify regions where decoding accuracy was significantly above chance (50%). To ensure independence between training and testing phases, cross-validation was performed within each participant’s functional space. This method avoids assumptions of voxel-wise anatomical correspondence across participants^38,40.