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Disc

DiSC is a commercial behavioral assessment tool designed to categorize individuals' observable styles across four quadrants—Dominance (D), Influence (I), Steadiness (S), and Conscientiousness (C)—through self-reported responses to situational prompts, emphasizing practical applications in communication and team dynamics over deep psychological traits. Originating from psychologist William Moulton Marston's 1928 theory linking emotions to interpersonal behaviors, it diverges from his original framework by focusing on self-perception in professional contexts rather than normal vs. abnormal emotional states. The model posits that people exhibit blends of these styles, with D types prioritizing results and assertiveness, I types favoring and , S types emphasizing and stability, and C types stressing accuracy and , purportedly aiding workplaces in tailoring interactions for better . Proponents highlight its and reported in training programs, where millions of assessments have been administered globally since commercial adaptations in the , often yielding consistent self-categorizations with test-retest reliabilities exceeding 0.80. However, its empirical standing is contested, as the foundational theory predates modern personality research like the model, and studies show limited for outcomes such as academic or job performance, with one analysis finding no significant links between DiSC styles and first-year GPA in professional programs. Critics argue that while is strong in validated versions, broader causal claims lack robust, post-1920s evidence, positioning it more as a for than a scientifically predictive , though commercial providers maintain favorable correlations within their datasets.

Etymology and Usage

Historical Origins and Spelling Variations

The English word disc originates from the Latin discus, denoting a flat, round plate or quoit used in throwing sports, which itself derives from the Ancient Greek δίσκος (dískos), referring to a disc-shaped object such as a platter or athletic implement. This Greek term is attested in Homeric epics and classical literature, where it describes objects thrown for distance or used in competitions, with archaeological evidence of stone and later bronze discuses dating to the 8th century BCE in Minoan and Mycenaean contexts. The discus throw, a core event in the ancient Olympic Games from at least 688 BCE, involved athletes hurling lead- or iron-weighted discs weighing 1.3 to 6.6 kg and measuring 17 to 35 cm in diameter, emphasizing rotational technique for maximum distance. The word entered English in the mid-17th century, initially spelled disk to align with native English patterns like whisk or risk, reflecting a phonetic rather than strict classical . By the , the Latinate disc variant gained traction, influenced by direct borrowings from disque and revived classical scholarship during the , which prioritized etymological purity over anglicized forms. Both spellings coexisted, but regional and contextual divergences emerged: standardized disc for general circular objects and optical media (e.g., compact discs developed by in the 1970s using European conventions), while favored disk for mechanical and technologies pioneered by in the 1950s. These preferences persist in style guides, with no semantic distinction but varying frequency in edited prose—disk appearing more in U.S. technical contexts since the 19th-century gramophone era.

Mathematics and Geometry

The Mathematical Disk

In geometry, a is the set of all points in the at a less than or equal to a fixed r from a given point, forming a closed disk; the open disk excludes the boundary points exactly at r. The boundary itself constitutes a , distinguishing the disk as the filled two-dimensional region rather than the one-dimensional . Disks exhibit key topological and metric properties: a closed disk is compact and , while an open disk is an in the , meaning every point admits a smaller disk neighborhood entirely contained within it./02%3A_Analytic_Functions/2.02%3A_Open_Disks_Open_Deleted_Disks_and_Open_Regions) The area of a disk of radius r is \pi r^2, derived from in polar coordinates over the . In complex analysis, the open unit disk \{z \in \mathbb{C} : |z| < 1\} is fundamental, modeling domains for holomorphic functions; it supports the Riemann mapping theorem, which asserts that any simply connected domain in the (excluding the entire ) is conformally equivalent to this disk. Properties like the Schwarz lemma, which bounds holomorphic self-maps of the unit disk, rely on its hyperbolic and automorphism group, consisting of Möbius transformations preserving the disk. Punctured or deleted disks, excluding isolated interior points, arise in studying singularities of analytic functions./02%3A_Analytic_Functions/2.02%3A_Open_Disks_Open_Deleted_Disks_and_Open_Regions) In higher dimensions, the term "disk" generalizes to the n-ball for n \geq 3, but the two-dimensional case retains the specific planar connotation; disks also feature in integral geometry and potential theory for computing volumes and solving boundary value problems.

Data Storage and Computing

Evolution of Disk Storage Technologies

The first commercial hard disk drive, designated the IBM Model 350, debuted in 1956 as part of the IBM 305 Random Access Method of Accounting and Control (RAMAC) system, featuring 50 rotating aluminum platters coated with magnetic oxide, each 24 inches in diameter, to store approximately 5 megabytes of data across all surfaces. This innovation marked the shift from sequential-access media like magnetic tape to random-access disk storage, enabling faster data retrieval for business applications, though the unit weighed over a ton and rented for $3,200 monthly. Early designs relied on vacuum-tube amplifiers and contact read/write heads that physically touched the platter surface, limiting reliability due to wear. Advancements in the 1960s reduced size and improved access times; the IBM 1301, introduced in 1961, employed aerodynamic slider heads that floated above the platters without contact, boosting storage density to 2.5 megabytes per module using finer-grained magnetic materials. By 1970, IBM's 3340 "Winchester" drive sealed the heads and platters in a contamination-free enclosure with lubricated surfaces, enhancing reliability and paving the way for non-removable media in fixed installations, with capacities reaching 70 megabytes per spindle. Concurrently, flexible magnetic disks emerged: IBM's 8-inch floppy disk in 1971 stored 80 kilobytes on a single side, providing removable, low-cost storage for minicomputers and early personal systems. The 1980s saw disk storage proliferate in personal computing; Seagate's ST-506 in 1980 delivered 5 megabytes in a 5.25-inch form factor, while the 3.5-inch standard by 1984, pioneered by and adopted by Apple and IBM, fit desktop machines and scaled to hundreds of megabytes by decade's end through thinner platters and zoned bit recording. Capacity growth accelerated in the 1990s via thin-film heads and magnetoresistive (MR) sensors, which detected smaller magnetic domains; by 1991, drives exceeded 1 gigabyte, and the 1997 introduction of giant magnetoresistive (GMR) heads further quadrupled areal density, enabling terabyte-scale enterprise arrays. Into the 2000s and beyond, perpendicular magnetic recording (PMR) in 2005 aligned bits vertically for higher density, pushing consumer drives past 1 terabyte by 2009; subsequent innovations like shingled magnetic recording (SMR) in 2013 overlapped tracks for efficiency, and heat-assisted magnetic recording (HAMR) in 2020 prototypes heated platters to stabilize ultra-small bits, targeting 20+ terabytes per drive amid ongoing helium-filled sealing and laser-based writing to counter superparamagnetic limits. Despite solid-state alternatives, rotating disk technologies persist for cost-effective bulk storage, with annual areal density doublings sustaining petabyte-scale systems in data centers.

Anatomy and Medicine

The intervertebral disc is an avascular, fibrocartilaginous structure situated between adjacent vertebral bodies in the spinal column, comprising two primary components: the central and the peripheral . The nucleus pulposus consists of a gel-like matrix rich in proteoglycans and type II collagen, maintaining high water content (up to 88% in youth) that enables hydrostatic pressure resistance to compressive forces. The annulus fibrosus forms a multilayered ring of concentrically arranged collagen fibers (type I dominant), providing tensile strength and constraining the nucleus while permitting controlled vertebral motion. These discs occupy approximately 25% of the spinal column's length in adults and are thickest in the lumbar region (7-10 mm), thinning cranially. Functionally, intervertebral discs facilitate spinal flexibility, distribute axial loads, and absorb shock during dynamic activities such as walking or jumping, with the nucleus generating intradiscal pressure up to 1.5-2 MPa under load to prevent vertebral bony contact. Nutrition occurs via diffusion from vertebral endplates due to avascularity, relying on mechanical pumping from cyclic loading to sustain proteoglycan integrity and hydration. Discs adapt to forces through viscoelastic properties, exhibiting creep under sustained compression and recovery via fluid imbibition, but chronic overload leads to microstructural fatigue. Degenerative disc disease (DDD), characterized by progressive loss of disc height, hydration, and structural integrity, affects an estimated 403 million people globally with symptomatic degeneration (5.5% prevalence), rising sharply with age—disc disease diagnosis reaches 66% in those over 65 versus 2.7 times higher in older versus younger adults overall. Risk factors include aging (proteoglycan depletion and dehydration), genetic predispositions (e.g., collagen gene variants), mechanical overload from heavy lifting or vibration exposure, smoking (reduces nutrient diffusion), obesity, and diabetes, which accelerate matrix catabolism via inflammatory cytokines like IL-1 and TNF-α. Symptoms often manifest as chronic low back pain from endplate irritation or instability, though many cases remain asymptomatic; prevalence of diagnosed spinal degeneration is 27.3%, with disc-specific issues contributing to 40% of cases in prospective MRI studies over 5 years. Lumbar disc herniation, where nucleus material displaces through annular tears (protrusion or extrusion), is the most common related condition, causing radiculopathy in 95% of symptomatic cases via nerve root compression; incidence peaks at 30-50 years, with L4-L5 and L5-S1 levels involved in 90%. Causes include acute trauma, repetitive microtrauma, or degenerative weakening, leading to symptoms of sciatica (leg pain), numbness, weakness, and rarely cauda equina syndrome (bowel/bladder dysfunction in <1%). Over 90% resolve spontaneously within 6-12 weeks via resorption mechanisms involving macrophage-mediated inflammation and neovascularization, though factors like large extrusions (>6 mm) predict slower recovery. Conservative management is first-line for both DDD and herniation, encompassing activity modification, NSAIDs for , physical therapy to strengthen core stabilizers, and epidural steroids for , yielding 80-90% improvement in 3 months. Surgery, such as microdiscectomy, is indicated for persistent deficits (e.g., motor weakness >6 weeks) or , with success rates of 85-95% for leg pain relief but higher reherniation risk (5-10%) than conservative approaches long-term. Emerging evidence questions routine for DDD, favoring motion-preserving options amid debates on , as natural history shows frequent without intervention.

Advances in Artificial Disc Replacement

Artificial disc replacement (ADR), also known as total disc arthroplasty, involves surgically implanting prosthetic devices to replace degenerated intervertebral discs, aiming to restore motion and alleviate pain while avoiding the rigidity of . Unlike fusion, which eliminates segmental motion and risks adjacent segment degeneration, seeks to mimic natural disc through designs typically featuring a mobile core between endplates made of materials like cobalt-chromium alloy, (UHMWPE), or . Early devices faced issues with wear debris and , but advances have focused on enhancing durability, , and surgical precision. In the lumbar spine, FDA-approved devices remain limited to activL (Aesculap) and ProDisc-L (Centinel Spine), both cleared via premarket approval pathways demonstrating noninferiority to fusion in randomized controlled trials for single-level degenerative disc disease. Recent material innovations include next-generation UHMWPE cores with improved wear resistance and titanium alloy endplates coated for , reducing rates observed in earlier metal-on-metal designs. Meta-analyses of lumbar ADR versus fusion report superior outcomes in Disability Index (ODI) scores (mean difference -4.2 points at 2 years) and visual analog scale (VAS) pain reduction, with lower reoperation rates ( 0.56) due to preserved motion mitigating adjacent segment stress. However, long-term data beyond 7 years show comparable complication profiles, including device migration in 2-5% of cases, underscoring selection criteria like preserved facet . Cervical ADR has seen more rapid evolution, with devices like Mobi-C, Prestige LP, and Simplify approved for two contiguous levels since 2013-2021, expanding indications from single-level or . A pivotal 2025 advancement was the FDA approval on October 14 for two-level implantation of prodisc C Vivo and prodisc C SK, featuring unconstrained ball-and-socket designs that better replicate physiological and reduce heterotopic compared to constrained semiconstrained models. enhancements, such as coatings and vitamin E-stabilized , have lowered particulate wear by up to 50% in bench testing, correlating with sustained Neck Disability Index (NDI) improvements (mean 20-point reduction at 5 years) over fusion in meta-analyses. These outperform (ACDF) in motion preservation ( >3 degrees postoperatively) and adjacent segment disease incidence ( 0.42 at 7 years). Ongoing research emphasizes hybrid constructs combining with for multilevel disease and minimally invasive approaches using systems for precise endplate preparation, reducing operative time by 20-30% and radiation exposure. Despite these gains, 's broader adoption is tempered by exclusion of patients with or , with meta-analytic evidence levels rated moderate due to trial heterogeneity and industry funding biases in some studies. Future directions include viscoelastic replacements and 3D-printed customizable implants to address facet-mediated pain, though randomized trials beyond 10 years remain needed for validation.

Sports and Recreation

Flying Discs and Disc Sports

Flying discs, lightweight aerodynamic objects typically made of , are thrown for or competitive purposes in disc , which emphasize precision, strategy, and athleticism without bodily contact in most variants. The modern flying disc emerged from post-World War II experimentation, with inventor developing a molded version in 1948 alongside partner Warren Franscioni, initially marketed as the "Flyin-Saucer" amid public fascination with unidentified flying objects. By 1955, Morrison refined the design into the "Pluto Platter," which Manufacturing Company acquired and rebranded as the in 1957, capitalizing on the existing popularity of tossing pie tins from the bakery, a practice dating back to the early 20th century in . This commercialization propelled flying discs into widespread use, with annual sales reaching millions by the , evolving from casual play to structured . Disc sports encompass team-based and individual activities governed internationally by the , established in 1985 with 126 member associations across over 120 countries as of 2025, focusing on sanctioning events and standardizing rules. , one of the most popular variants, originated in 1968 when high school students in , adapted elements of , , and into a non-contact game using a flying disc; formal rules were codified in 1970, emphasizing self-officiation via the "spirit of the game" principle to resolve disputes without referees. Played on a rectangular field with s, teams of seven players advance the disc by passing—pivoting in place without traveling—and score by catching in the opponent's ; turnovers occur on incomplete passes, interceptions, or out-of-bounds throws, with games typically to 15 points. The first intercollegiate match occurred on November 6, 1972, between Rutgers and Princeton Universities, where Rutgers prevailed 29-27 in a contest resembling unstructured . Disc golf, another prominent discipline, simulates traditional by throwing discs toward chain-link baskets on courses of 9 or 18 holes, scoring based on the fewest throws needed, with early informal versions appearing in the using trees or barrels as targets. Inventor "Steady" , a former executive, standardized the sport in the early 1970s by patenting the Disc Pole Hole—a metal basket catching mechanism—in 1975, which addressed inconsistent targets and enabled precise play; he founded the (PDGA) in 1976, growing the sport to over 10,000 courses worldwide by 2025. Players select from specialized discs varying in weight (typically 150-175 grams), rim width, and flight paths—drivers for distance, mid-ranges for control, and putters for accuracy—adhering to rules prohibiting running while holding the disc and penalizing hazards like out-of-bounds areas. Additional disc sports include , involving acrobatic routines with catches and throws judged on difficulty and form; guts, a high-speed precision-passing game across a hip-high net emphasizing rapid volleys; and double disc court, where opponents defend zones against targeted throws. These activities have expanded globally, with WFDF-sanctioned world championships drawing thousands of competitors; participation surged in the 1970s era but achieved mainstream traction through organized leagues, underscoring the disc's inherent in flight due to its molded rim and flat profile, which enables predictable trajectories governed by rather than propulsion variability.

Music and Audio

Disc-Based Audio Formats

The Compact Disc Digital Audio (CD-DA), standardized in the Philips-Sony Red Book specification finalized in 1982, marked the first widespread optical disc format for consumer audio, utilizing pulse-code modulation (PCM) at a 44.1 kHz sampling rate and 16-bit depth to achieve approximately 74 minutes of stereo playback on a 120 mm polycarbonate disc read by a 780 nm laser. Commercial production began with the pressing of Billy Joel's 52nd Street album on August 17, 1982, at a Polygram facility in Germany, followed by market release in Japan that October. This format displaced analog vinyl and cassette tapes due to its durability, random access capabilities, and immunity to wear from playback, though it faced criticism for introducing digital artifacts like quantization noise absent in analog media. High-resolution formats emerged in the late 1990s to address CD limitations, with (SACD) developed by and and introduced in 1999 using (DSD) encoding at a 2.8224 MHz sampling rate and 1-bit depth for multilayer discs supporting up to 120 minutes of stereo or multichannel audio. SACD discs employ a 650 nm for reading a high-density layer beneath a standard CD-compatible layer in hybrid variants, enabling , but adoption remained niche among audiophiles owing to high costs, limited catalog (fewer than 10,000 titles by 2010), and debates over audible benefits beyond CD's Nyquist limit for human hearing around 20 kHz. , finalized by the around 1999 for release in 2000, offered PCM or (MLP) compression up to 192 kHz/24-bit resolution and 5.1 channels on standard DVD media, yet it achieved minimal market penetration—estimated at under 1% of high-res audio sales—due to format wars with SACD, copy-protection restrictions limiting playback to proprietary players, and the rise of digital downloads. Recordable magneto-optical formats like Sony's , launched in 1992, provided portable digital audio storage using 68 mm discs with compression for about 74 minutes of near-CD quality, gaining popularity in with over 20 million units sold by 2000 but declining globally after 2000 as writable drives offered cheaper, uncompressed alternatives and players eroded demand for physical media. ceased MiniDisc player production in 2013 and announced end of media manufacturing in 2025, reflecting obsolescence amid streaming dominance. In the Blu-ray era post-2005, audio-only discs leverage the format's 25 GB (single-layer) or higher capacity for lossless codecs like or , supporting up to 192 kHz/24-bit multichannel content without dedicated "Blu-ray Audio" branding, though releases remain sporadic for classical and surround-sound genres due to preference for video-inclusive Blu-rays and digital alternatives. These formats collectively shifted audio from analog grooves to laser-read pits, prioritizing precision and longevity but yielding to non-physical distribution as bandwidth improved.

Psychology and Behavioral Assessment

DISC Personality Assessment Model

The DISC personality assessment model, also known as DiSC, categorizes observable behaviors into four primary styles: Dominance (D), Influence (I), Steadiness (S), and Compliance (C). Developed as a tool for understanding interpersonal dynamics, it posits that individuals exhibit blends of these traits in response to environmental demands, rather than fixed types. The model originated from the theoretical work of psychologist , who in his 1928 book Emotions of Normal People described how normal emotions drive adaptive behaviors influenced by perceptions of one's environment as favorable or antagonistic and others as hostile or compliant. Marston's framework did not initially include a formal instrument; instead, it emphasized four emotional-behavioral factors—Dominance (overcoming opposition), Inducement (influencing others), Submission (cooperating with others), and (adhering to rules)—as responses to situational pressures. The first practical DISC-based assessments emerged in the mid-20th century, with Walter Vernon Clarke adapting Marston's ideas into a forced-choice in the to measure these dimensions empirically. Commercial versions proliferated from the onward, often through publishers like Inscape Publishing (now Wiley), focusing on self-reported profiles for practical application rather than deep psychological diagnosis. The four factors are defined as follows: Dominance involves direct, decisive, and results-oriented behaviors, often seen in competitive or challenging settings; encompasses sociable, persuasive, and enthusiastic interactions aimed at building relationships; Steadiness reflects patient, supportive, and team-focused tendencies, prioritizing harmony; (or ) emphasizes accuracy, rule-following, and analytical caution to ensure quality and compliance with standards. Assessments typically yield a showing relative strengths across these factors, with 12 possible blends (e.g., , IS) derived from combinations, though individuals score on a rather than categories. Primarily applied in organizational contexts, DISC tools support , , sales training, and by highlighting communication preferences and potential blind spots. For instance, high-D individuals may be coached to temper for better , while high-C profiles might focus on flexibility. Usage spans corporations, with millions of assessments administered annually, but it is not endorsed for high-stakes decisions like clinical or unaided hiring due to limitations in . Psychometric evaluation reveals moderate test-retest reliability, with coefficients often exceeding 0.80 for factor scores over short intervals, indicating consistency in self-perceptions. However, convergent validity with established models like the is partial at best, and for job performance remains weakly supported by independent research. Proprietary validity reports from providers claim correlations with outcomes like sales success, but peer-reviewed studies are sparse and do not robustly confirm causal links between DISC profiles and behavioral predictions beyond descriptive utility. Critics, including psychologists, argue the model oversimplifies into quadrants lacking empirical grounding, akin to typologies dismissed in for ignoring trait continua and contextual variability. Claims of pseudoscientific elements arise from its divergence from factor-analytic traditions, with insufficient evidence tying Marston's emotional theory to measurable outcomes; for example, no large-scale, replicated studies validate DISC's incremental utility over simpler behavioral observations. Commercial interests may inflate reported validities, as independent scrutiny highlights risks of stereotyping or in applications, underscoring its role as a rather than a rigorous diagnostic instrument.

Other Technical and Scientific Uses

Disc Brakes in Automotive Engineering

Disc brakes in automotive engineering utilize a rotating metal disc, or rotor, attached to the wheel hub, against which brake pads are pressed by a caliper to generate friction and decelerate the vehicle. This system operates on hydraulic principles, where pressure from the brake pedal activates a master cylinder to force fluid through lines to the calipers, clamping the pads onto the disc. Unlike drum brakes, which enclose components in a drum, disc brakes expose the rotor to air for enhanced cooling, reducing thermal buildup during prolonged use. The invention of the caliper-type disc brake is attributed to English engineer Frederick William Lanchester, who patented it in 1902 for use on Lanchester automobiles produced in . Early adoption was limited, with drum brakes dominating due to simplicity and cost, but disc brakes gained traction in racing; the employed them in 1953 for improved performance at , followed by the in 1955 for production cars. Widespread implementation occurred in the , with front disc brakes becoming standard on many U.S. models by the early , driven by demands for better amid rising vehicle speeds and weights. Key components include the brake rotor, typically or , which rotates with the and withstands frictional heat; the caliper, housing pistons that push pads via hydraulic force; friction pads made of semi-metallic or ceramic composites for grip and durability; and support hardware such as clips and shims to maintain alignment and reduce noise. The system integrates with the and fluid reservoir for pressure modulation, often incorporating anti-lock braking sensors in modern setups. Ventilated rotors, featuring internal vanes for airflow, emerged in the mid-20th century to further mitigate fade. During operation, pedal application transmits force hydraulically to the caliper pistons, which extend to clamp pads against the , converting to via ; release allows retraction springs or seals to pull pads away, preventing drag. This clamping action provides linear response and consistent , with stopping distances 17-33% shorter than brakes at typical highway speeds due to efficient force application and minimal expansion under . Disc brakes outperform drum systems in heat dissipation—exposed rotors cool 20-30% faster, minimizing fade during repeated stops—and resist water-induced loss of efficacy, as rotation sheds moisture. They require less maintenance, with self-adjusting and easier pad replacement, yielding lower long-term costs despite higher initial expense. Drawbacks include greater susceptibility to warping from uneven heating and higher noise from pad material, though mitigated in ventilated designs. In high-performance vehicles, carbon-ceramic discs, introduced commercially in the late , offer extreme durability under loads exceeding 1,000°C, as seen in Ferrari models from onward.

Astronomical and Natural Discs

In astronomy, discs refer to flattened, rotating structures of gas, dust, or stars formed by conservation of angular momentum during gravitational collapse or accretion processes. These structures are ubiquitous in the universe, ranging from circumstellar environments around individual stars to large-scale galactic components. Protoplanetary discs, for instance, surround young stars and serve as the birthplaces of planetary systems, consisting primarily of dense gas and dust that persists for several million years while material accretes onto the central star or coalesces into planetesimals. Accretion discs form when diffuse material orbits a massive central object, such as a or , spiraling inward due to and , which heats the disc and generates intense across X-ray to wavelengths. These discs are geometrically thin and optically thick, with their inner regions reaching temperatures exceeding 10^7 K, enabling observations of phenomena like quasars and X-ray binaries. Debris discs, by contrast, represent later evolutionary stages, comprising and remnants around mature stars, often sculpted by unseen that clear gaps or confine the material, as inferred from excesses detected by telescopes like Spitzer and . Galactic discs characterize spiral and lenticular galaxies, forming thin, distributions of stars, gas, and in near-circular orbits around a central bulge or bar, with typical scale heights of 300-500 parsecs and radial extents spanning tens of kiloparsecs. The Milky Way's disc, for example, rotates differentially with velocities around 220 km/s at the Sun's position, 8 kpc from the center, and its structure evolves through internal dynamical processes like density waves and mergers, rather than monotonic growth. On , natural disc-like formations arise from and thermal gradients, such as discs in rivers, which develop in cold climates where eddy currents create rotating vortices that freeze surface water into large, flat pans up to 100 meters in . These phenomena, observed in locations like the in on January 15, 2019, result from differential cooling where water at 4°C sinks, sustaining the spin and eroding edges into circular shapes. Similar hydrodynamic principles underpin lenticular clouds, stationary disc-shaped formations over mountains caused by stable atmospheric layers and , mimicking some astronomical disc stability but on vastly smaller scales.

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