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PF

Patriot Front is an American nationalist group founded in 2017 by Thomas Rousseau, emerging from the remnants of Vanguard America in the wake of the Unite the Right rally in Charlottesville, Virginia.^[1]^[2] The organization promotes a vision of reclaiming America as a nation-state aligned with the interests of people of European descent, emphasizing loyalty to heritage, opposition to globalist influences, and the formation of a disciplined cadre of activists committed to public mobilization.^[3]^[4] Its activities center on grassroots propaganda—such as distributing flyers, posters, and stickers—along with flash demonstrations, banner displays, and efforts to build physical fitness and ideological cohesion among members, whom it recruits primarily as young men through online vetting and training protocols.^[5]^[6] While Patriot Front frames its mission as patriotic preservation against demographic shifts and cultural erosion, it has been characterized by extremism-monitoring entities as a white nationalist outfit due to its explicit focus on racial identity politics and rejection of multiculturalism.^[1]^[7] The group has achieved visibility through persistent low-level operations across U.S. cities, amassing a decentralized network estimated in the hundreds of active participants, with leaked data indicating recruitment appeals to those disillusioned with mainstream conservatism and a notable subset claiming military experience.^[8] Controversies include high-profile arrests, such as the 2022 detention of over 30 members near an Idaho Pride event, internal communications exposed by infiltrators revealing authoritarian internal dynamics, and legal challenges alleging conspiracies to disrupt civil rights activities.^[5]^[9] These incidents have fueled debates over the group's tactics, with critics highlighting potential for escalation despite its public disavowal of violence, while supporters view it as a bulwark against perceived national decline.^[10]

Science and technology

Computing

PF, or Packet Filter, is an open-source stateful packet inspection firewall subsystem originally developed for the OpenBSD operating system. It was introduced in OpenBSD 3.0, released on October 1, 2001, as a replacement for IPFilter amid licensing disputes.^[11]^[12] Primarily authored by Daniel Hartmeier, PF emphasizes efficient kernel-level processing of network traffic through rule-based filtering.^[13] PF supports a declarative syntax for defining filtering rules, which evaluate packets sequentially against criteria such as source/destination addresses, ports, protocols, and interface.^[14] Core features include network address translation (NAT) for masquerading internal traffic and bidirectional state tracking, where PF maintains connection states in a kernel table to permit return packets without redundant rules, reducing configuration complexity.^[15]^[14] State options allow limiting concurrent connections, timeouts, and source tracking to mitigate denial-of-service attacks and unauthorized access attempts.^[16] Compared to Linux's iptables, PF provides a more concise, human-readable configuration format that separates policy from mechanism, enabling straightforward rule auditing and causal analysis of filtering decisions.^[17]^[18] Iptables, by contrast, relies on chain-based processing within the Netfilter framework, which can obscure rule interactions and require additional tools for visualization.^[19] PF has been ported to other BSD derivatives, including FreeBSD (since version 5.3 in 2005), NetBSD, and DragonFly BSD, facilitating its use in server hardening and perimeter defense.^[12] Its design supports empirical security validation through auditable rules and state logging, aiding detection and prevention of intrusions by enforcing granular access controls on network flows.^[20] In practice, PF configurations on hardened servers block unauthorized inbound connections by default, with stateful inspection ensuring only established sessions proceed, as evidenced by its integration in secure-by-default OpenBSD setups.^[14]

Physics

In electrical physics, the picofarad (pF), equivalent to $10^{-12} farads (F), serves as a standard subunit for measuring capacitance in small-scale components, such as those in integrated circuits and high-frequency oscillators where values typically range from 1 pF to 4700 pF.^[21]^[22] This unit quantifies the ability of a capacitor to store charge, with empirical applications validated through measurements of dielectric properties and impedance in circuits operating at radio frequencies, where stray capacitances on the order of picofarads influence signal integrity.^[23] The petafarad (PF), by contrast, represents $10^{15} F, an extraordinarily large capacitance rarely encountered in practical engineering but theoretically relevant in geophysical contexts, such as modeling the effective capacitance of planetary atmospheres or large-scale electrostatic systems, where it exceeds realizable values for isolated conductors by orders of magnitude.^[24]^[25] In quantum mechanics, probability flux describes the directional flow of probability density for a particle's wave function, arising directly from the time-dependent Schrödinger equation i\hbar \frac{\partial \psi}{\partial t} = -\frac{\hbar^2}{2m} \nabla^2 \psi + V\psi.^[26] To conserve total probability \int |\psi|^2 dV = 1, the continuity equation \frac{\partial \rho}{\partial t} + \nabla \cdot \vec{j} = 0 holds, where \rho = |\psi|^2 is the probability density and the flux \vec{j} = \frac{\hbar}{2mi} (\psi^* \nabla \psi - \psi \nabla \psi^*) emerges from substituting the Schrödinger equation and separating real and imaginary parts.^[27]^[26] This formulation causally links wave propagation to observable currents, as verified experimentally in double-slit interference patterns showing non-zero flux even in classically forbidden regions and in tunneling experiments where net flux determines transmission probabilities.^[26] Applications extend to electromagnetic interactions, such as calculating charge currents from \vec{j}_{charge} = -e \vec{j} for electrons, aligning with measured photoelectric effects and conductivity in semiconductors.^[28]

Chemistry and mathematics

In chemistry, PF commonly abbreviates phenol-formaldehyde resins, thermosetting polymers produced via the polycondensation of phenol (C₆H₅OH) and formaldehyde (HCHO) under acidic or alkaline conditions, yielding a cross-linked methylene-bridged network with high thermal stability up to 200–300°C and compressive strength exceeding 200 MPa in molded forms.^[29] These resins, first commercialized in 1910 by Leo Baekeland, enable precise thermodynamic modeling of curing kinetics through rate constants derived from Arrhenius equations, where activation energies typically range from 50–80 kJ/mol, reflecting causal molecular rearrangements without reliance on unsubstantiated kinetic assumptions.^[30] PF also prefixes perfluoro- in notations for per- and polyfluoroalkyl substances (PFAS), such as PFₙ, denoting fully fluorinated carbon chains of length n, which exhibit extreme chemical inertness due to strong C–F bonds (bond dissociation energy ≈ 485 kJ/mol) and low intermolecular forces, influencing partition coefficients (log K_{ow} > 5) in environmental fate assessments grounded in empirical hydrophobicity data.^[31] The hexafluorophosphate anion ([PF₆]⁻) represents an octahedral complex with phosphorus at the center coordinated to six fluoride ligands, characterized by a P–F bond length of approximately 1.57 Å and high lattice energy in salts like NH₄PF₆ (≈ 700 kJ/mol), facilitating its role in stable electrolytes where ionic conductivity correlates directly with ion mobility calculations from Stokes-Einstein relations.^[32] In mathematics, the Pfaffian of a 2n × 2n skew-symmetric matrix A over the reals is defined as Pf(A) = ∑{π ∈ PM} sgn(π) ∏{i=1}^n a_{π(2i-1), π(2i)}, where PM enumerates perfect matchings π of {1, ..., 2n} and sgn(π) is the signature, satisfying Pf(A)^2 = det(A) and enabling explicit square-root computations verifiable by expanding for small n (e.g., for n=1, Pf([[0, b], [-b, 0]]) = b).^[33] This construct, introduced by Cauchy in 1841 and formalized by de Pfaff's influence, underpins determinant evaluations in even dimensions through first-principles antisymmetry, avoiding ad hoc factorizations.^[34] Pfaffians extend to oriented matroids and graph theory via Kasteleyn orientations, where |Pf(K)|^2 equals the number of dimer coverings (perfect matchings) in planar graphs, as confirmed by explicit counts for the Aztec diamond graph yielding 2^{n(n+1)/2} tilings, rooted in combinatorial bijections rather than probabilistic approximations.^[33]

Medicine

Pulmonary fibrosis (PF) encompasses a spectrum of interstitial lung diseases marked by progressive scarring of lung tissue, which impairs gas exchange and leads to reduced lung compliance. This fibrotic process replaces normal alveolar architecture with stiff extracellular matrix, causally resulting in exertional dyspnea, dry cough, and eventual respiratory failure, with median survival from diagnosis around 3-5 years in idiopathic cases. Diagnosis relies on high-resolution computed tomography (HRCT) showing usual interstitial pneumonia patterns, alongside pulmonary function tests (PFTs) demonstrating restrictive physiology, such as forced vital capacity (FVC) below 80% predicted and diminished diffusing capacity for carbon monoxide (DLCO).^[35]^[36]^[37] In respiratory diagnostics, PF metrics include peak expiratory flow (PEF) rates, measured via handheld meters to assess large airway patency and monitor obstructive conditions like asthma, though PEF primarily reflects extrathoracic airflow rather than parenchymal fibrosis. Normal adult PEF ranges from 400-700 L/min, varying by age, sex, height, and ethnicity, with males averaging 450-550 L/min and females 320-470 L/min; values below 80% of personal best signal potential exacerbation requiring intervention. While PEF aids asthma management by detecting early bronchoconstriction, its utility in PF progression tracking is limited compared to FVC decline rates (e.g., >10% annual drop predicting mortality) or 6-minute walk distance (6MWD), where minimal clinically important differences approximate 24-30 meters.^[38]^[39]^[40] Orthopedically, PF denotes the patellofemoral joint compartment, where biomechanical mismatches cause anterior knee pain syndrome (PFPS) through elevated patellofemoral compressive forces, often exceeding 3-5 times body weight during activities like squatting. Causal factors include quadriceps imbalance, patellar maltracking, or femoral trochlear dysplasia, leading to cartilage wear and retropatellar irritation; stress concentrations arise from vastus medialis obliquus weakness, increasing lateral patellar tilt and joint reaction forces up to 50% above norms in affected individuals. Management emphasizes strengthening and activity modification over surgical intervention unless instability persists, with evidence favoring conservative approaches reducing pain in 70-90% of cases.^[41]^[42]^[43] Epidemiological data indicate rising PF incidence, potentially from improved detection via HRCT rather than overdiagnosis, as underrecognition affects thousands annually despite distinct radiographic hallmarks; claims of diagnostic inflation lack robust empirical support in peer-reviewed cohorts, where multidisciplinary review confirms specificity. Antifibrotic therapies like nintedanib and pirfenidone slow FVC decline by 50% in trials, though they do not reverse scarring, underscoring causal focus on halting fibroblast activation over symptomatic palliation.^[44]^[45]^[46]

Economics and finance

Financial reporting

Form PF is a confidential reporting form required by the U.S. Securities and Exchange Commission (SEC) and the Commodity Futures Trading Commission (CFTC) for SEC-registered investment advisers managing private funds with at least $150 million in assets under management.^[47]^[48] Adopted in 2011 under the Dodd-Frank Act to monitor potential systemic risks from hedge funds, private equity, and other private funds, it mandates quarterly or annual filings detailing fund strategies, exposures, leverage, investor concentrations, and performance metrics.^[49] Large hedge fund advisers (those with $1.5 billion or more in hedge fund AUM) face more granular quarterly requirements, while all filers report basic operational data.^[50] On February 8, 2024, the SEC and CFTC adopted amendments to Form PF aimed at improving data granularity, particularly for large hedge fund advisers, by requiring detailed reporting on investment exposures, borrowing, counterparty credit exposures, and trading vehicles on an aggregated basis.^[49] These changes expand Section 1 (all filers) to include fair value hierarchies for assets, central clearing and prime brokerage exposures, and turnover rates, while enhancing Section 2 (large hedge funds) with requirements for position-level data on derivatives and structured products.^[51] The amendments seek to bolster the Financial Stability Oversight Council's (FSOC) ability to assess systemic risks, but implementation has revealed significant compliance burdens, including data aggregation challenges and operational costs estimated to add millions in annual expenses for affected advisers.^[49] Compliance dates for the 2024 amendments have been repeatedly extended due to practical difficulties in meeting enhanced reporting demands without clear evidence of proportional risk mitigation benefits. The original deadline of March 12, 2025, was pushed to June 12, 2025, then to October 1, 2025, and finally to October 1, 2026, following a September 17, 2025, joint announcement by the SEC and CFTC citing ongoing industry feedback on system upgrades and data validation issues.^[52]^[53] These delays highlight empirical challenges in achieving transparency goals, as advisers report difficulties in sourcing and standardizing data across complex fund structures, potentially diverting resources from risk management without demonstrable reductions in systemic vulnerabilities akin to those in the 2008 crisis.^[54] Critics, including SEC Commissioner Hester Peirce, have questioned the causal link between expanded Form PF disclosures and crisis prevention, arguing that the amendments impose short reporting timelines and uncoordinated requirements that yield voluminous data of uncertain utility for preempting systemic events.^[55] While proponents claim improved FSOC monitoring, data-driven analyses post-2011 indicate no direct evidence that prior Form PF iterations averted major private fund disruptions, raising skepticism about whether added bureaucracy enhances stability or merely collects information without actionable outcomes.^[56] Market impacts include heightened operational costs for advisers, estimated at 20-50% increases in compliance budgets for large filers, potentially affecting fund returns and investor allocations amid unproven risk-reduction efficacy.^[57]

Savings and investment

The Employees' Provident Fund Organisation (EPFO) in India operates a mandatory contributory provident fund scheme for salaried employees in covered establishments, requiring both employee and employer to contribute 12% of the employee's basic salary plus dearness allowance, with the employer's share split such that 3.67% goes to the provident fund account and 8.33% to the pension scheme.^[58]^[59] This structure ensures disciplined savings, as contributions are deducted pre-tax and invested primarily in government securities and debt instruments, yielding a declared interest rate of 8.25% for the financial years 2023-24 and 2024-25, compounded annually to promote long-term accumulation.^[60]^[61] As of 2024, the EPFO covers over 70 million subscribers, facilitating retirement corpus growth through forced savings that counteract tendencies toward immediate consumption.^[62] Empirical analysis of compounding at rates above inflation (historically around 4-6% in India) demonstrates that consistent contributions over 30-40 years can multiply principal by factors of 10-20, depending on salary growth, far outpacing erosion from consumer debt where credit card rates often exceed 30-40% annually.^[63] Prioritizing such structured savings over high-interest borrowing aligns with causal principles of wealth preservation: inflows compound positively in low-risk assets, while outflows for non-essential debt compound negatively, leading to net wealth depletion for low-savers who rely on lifestyle inflation.^[64] In comparison to voluntary systems like the U.S. 401(k), which also features employer matching up to 6% but lacks universality, the EPFO's mandatory framework enforces fiscal restraint, reducing exposure to debt traps observed in populations with savings rates below 10% of income.^[65] Data from EPFO payroll additions—such as 19.14 lakh net members in April 2025 alone—underscore its scale in fostering broad-based retirement security, though withdrawals for housing or emergencies are permitted under regulated conditions to balance liquidity needs.^[66] This model empirically supports higher lifetime net worth for participants versus non-savers, as debt servicing diverts funds from productive investment.^[67]

Currencies

The pfennig (abbreviated pf or ₣) functioned as the minor subunit of several German currencies, equivalent to 1/100 of a mark, including the Papiermark, Rentenmark, Reichsmark, and Deutsche Mark (DM). In the Deutsche Mark system, introduced on June 20, 1948, via the West German currency reform, 100 pfennigs equaled one DM, with coins minted in denominations of 1, 2, 5, 10, and 50 pfennigs until the euro's adoption on January 1, 2002.^[68]^[69] The 1948 reform exchanged Reichsmarks for DM at a fixed rate of 10:1 for wages and claims up to 60 RM per person, effectively devaluing holdings and curbing postwar inflation suppressed under Nazi controls from 1936–1948.^[68] During the Weimar Republic's hyperinflation from 1922 to 1923, the pfennig's value collapsed due to the Reichsbank's policy of monetizing government deficits through unchecked note issuance, initially to service World War I debts and Versailles reparations but accelerating via fiscal avoidance of tax hikes and bond sales. This monetary expansion, rather than exogenous shocks alone, drove prices to double every few days by late 1923, with the U.S. dollar exchange rate deteriorating from 320 marks per dollar in mid-1922 to approximately 4.2 trillion marks per dollar by November 1923, rendering pfennig-denominated savings worthless.^[70]^[71] Stabilization occurred with the Rentenmark's introduction on November 15, 1923, backed by land assets and limited to a fixed issuance of 3.2 billion Rentenmarks (1 Rentenmark = 1 trillion Papiermarks), restoring pfennig utility at 1/100 subunit without excusing prior policy lapses in restraining expenditure.^[70] Post-World War II, the DM pfennig exhibited relative stability, with annual inflation averaging around 10% in early reform years but declining to low single digits by the 1950s amid export-led growth; for instance, the DM-USD rate held near 4 marks per dollar from 1962 to 1965, reflecting pfennig purchasing power gains adjusted for domestic prices.^[72]^[73] East Germany's Ostmark also used a pfennig subunit until 1990 reunification, but its controlled economy masked inefficiencies, with unofficial exchange rates valuing it far below the DM equivalent. Pfennigs ceased legal tender status post-euro, though collectible exchanges persist at face value for pre-2002 issues.^[69]

Sports

Basketball

The power forward (PF) is a frontcourt position in basketball, primarily responsible for rebounding, interior scoring near the basket, and defending opponents in the paint, often blending the physicality of a center with greater mobility.^[74] Power forwards typically range in height from 6 feet 7 inches to 7 feet, leveraging strength and positioning to secure offensive and defensive boards while contributing to low-post scoring through post-ups and put-backs.^[75] Exemplifying this role, Tim Duncan, a Hall of Famer who played primarily as a power forward for the San Antonio Spurs from 1997 to 2016, recorded career averages of 19.0 points, 10.8 rebounds, and 2.2 blocks per game across 1,392 regular-season appearances, underscoring the position's emphasis on efficient, high-volume rebounding and rim protection.^[76] A personal foul (PF) constitutes illegal physical contact with an opponent in basketball, such as holding, pushing, or charging, and is charged directly to the offending player.^[77] In the National Basketball Association (NBA), players accumulate personal fouls throughout a game, with a limit of five before entering the bonus situation for their team on subsequent team fouls, and disqualification upon reaching the sixth personal foul.^[78] This rule enforces discipline, as excessive fouling disrupts team rotations and defensive schemes; empirical data indicates higher foul rates in NBA playoffs compared to the regular season, with analysis of games from 2010 to 2017 showing approximately 3-5% more fouls called per possession due to intensified physicality and closer officiating scrutiny.^[79] Strategically, effective foul management enables teams to sustain aggressive interior defense and rebounding battles central to power forward play, rather than diluting physicality through overly restrictive interpretations that can favor perimeter-oriented offenses; data from recent seasons confirms playoff teams averaging 20-22 personal fouls per game, yet successful ones correlate lower disqualification rates with balanced aggression, preserving lineup integrity over 48 minutes.^[80]^[81]

Organizations

Government and law enforcement

The Polícia Federal (PF), Brazil's federal police force, investigates crimes against federal institutions, including organized crime, terrorism, public corruption, money laundering, and interstate offenses, while also managing border security and intelligence operations.^[82] Formed in 1944 as the Departamento de Polícia Federal, it operates under the Ministry of Justice and Public Security, with approximately 17,000 personnel focused on judicial policing and preventive enforcement.^[83]^[84] PF's operational efficacy is demonstrated in major probes like Operation Lava Jato, initiated on March 17, 2014, which exposed a multibillion-dollar corruption network centered on Petrobras state oil company contracts, involving bribery, fraud, and political kickbacks.^[85] The operation yielded 292 arrests, with 278 individuals pleading guilty or securing convictions for related offenses, alongside asset seizures exceeding billions in reais and the creation of Latin America's largest digitized criminal database for tracking illicit flows.^[85]^[86] These outcomes facilitated at least 28 convictions tied to Petrobras bribery schemes, disrupting entrenched graft patterns and enabling subsequent reforms in public procurement oversight.^[87] Allegations of PF politicization, frequently voiced by elites facing scrutiny—such as Workers' Party figures during Lava Jato or former President Jair Bolsonaro in post-2022 probes—lack substantiation from cross-administration enforcement patterns.^[88] For example, Lava Jato's revelations under a PT-led government implicated PT leadership, while PF's 2024 indictment of Bolsonaro for coup-related activities relied on wiretaps, financial traces, and plea testimonies, mirroring methodological rigor across targets.^[88]^[89] Empirical indicators, including elevated conviction rates for high-profile offenders and economic disruptions to corrupt firms that spurred efficient market entrants, affirm PF's causal impact on reducing impunity over narrative-driven bias claims from shielded interests.^[89]^[90] Such results underscore accountability mechanisms, though economic analyses note short-term disruptions like firm collapses, balanced by long-term deterrence of systemic corruption.^[91]

Conservation and advocacy

Pheasants Forever, established in 1982 as a nonprofit organization in the United States, focuses on conserving pheasants, quail, and associated wildlife through targeted habitat restoration and enhancement efforts measured by acres improved and species-specific outcomes.^[92] ^[93] By 2024, the organization reported delivering 2.42 million acres of annual habitat improvements, emphasizing grassland and wetland restorations that support nesting and brood-rearing for upland game birds.^[94] These initiatives prioritize empirical metrics, such as increased nesting cover and food plots, over unsubstantiated broader environmental claims, with habitat quantity and quality identified as primary drivers of population fluctuations rather than secondary factors like predation alone.^[95] ^[96] The organization's Build a Wildlife Area program has permanently protected and enhanced over 243,000 acres of public-accessible land, facilitating hunter and observer access while securing long-term habitat integrity through fee-title acquisitions and partnerships.^[97] Complementing this, the Public Access to Habitat (PATH) initiative incentivizes private landowners to open lands for public hunting, achieving more than 100,000 acres by 2025, primarily in pheasant-range states like South Dakota, with expansions to bolster local economies via increased recreational use.^[98] ^[99] Pheasants Forever has contributed to over 1,600 land acquisitions totaling more than 200,000 acres, focusing on areas where habitat loss from agriculture has demonstrably reduced bird densities, aiming for population recoveries through restored cover that enhances nest survival rates.^[99] ^[100] Advocacy efforts underscore causal links between habitat interventions and verifiable wildlife metrics, such as improved brood survival in restored prairies, while critiquing initiatives lacking rigorous cost-benefit analysis for upland species; for instance, the group highlights how quality grassland directly correlates with stable or rebounding pheasant numbers, independent of overhyped climate attributions.^[101] ^[95] This approach contrasts with advocacy prioritizing alarmist framings, instead grounding campaigns in data from state surveys and field monitoring that tie acres restored to observed population upticks in targeted regions.^[102] Local chapters, such as those in Iowa, have cumulatively established hundreds of thousands of acres in nesting and food plots since the 1980s, yielding measurable gains in hunter harvest indices as proxies for habitat efficacy.^[103]

Places

Geographical regions

PF serves as the ISO 3166-1 alpha-2 code for French Polynesia, an overseas collectivity of France located in the South Pacific Ocean.^[104] This archipelago comprises 118 islands and atolls distributed across five main groups: the Society Islands (including Tahiti), Tuamotu Archipelago, Marquesas Islands, Gambier Islands, and Austral Islands, spanning a vast exclusive economic zone of approximately 5.5 million square kilometers.^[105] The land area totals about 4,167 square kilometers, with the population estimated at 281,118 in 2023, concentrated primarily on Tahiti.^[106] The territory's economy depends heavily on tourism, which accounts for a significant portion of GDP alongside pearl farming, fishing, and remittances, following the end of French nuclear weapons testing in 1996 after 193 detonations from 1966 that had previously injected military expenditures into the local economy.^[107]^[108] GDP per capita reached $22,774 in 2023, placing it among the higher figures in the Pacific region and underscoring functional self-sufficiency despite ongoing ties to France for defense and currency.^[109] This economic performance challenges dependency-focused post-colonial interpretations, as local governance handles education, health, and justice, with France retaining oversight only in foreign affairs and security.^[110] French Polynesia maintains substantial autonomy as an overseas country, upgraded from territorial status in 2004, enabling elected assemblies to legislate on internal matters while benefiting from French subsidies that support infrastructure and social services.^[111] Although reinscribed on the UN list of non-self-governing territories in 2013 amid independence advocacy, no referendum has materialized, and sustained growth—evidenced by a 0.26% population increase from 2022 to 2023—suggests pragmatic stability over separatist disruption.^[112] Regarding environmental pressures, the islands exhibit empirical resilience to sea-level variations and cyclones through coral reef barriers and adaptive practices, with population and tourism sectors expanding despite projections of heightened risks, prioritizing verifiable adaptation over generalized alarmism.^[106]^[113]

Administrative divisions

The Pfalz, historically known as the Rhenish or Lower Palatinate, originated as a feudal territory within the Holy Roman Empire, where counts palatine were appointed by emperors to administer royal domains and exercise high judicial authority in the absence of the sovereign, a role that evolved from Carolingian administrative practices and the need for delegated governance over fragmented Rhine Valley lands. This structure granted the Count Palatine of the Rhine extensive feudal rights, including minting coins and collecting tolls, enabling the accumulation of power through strategic alliances and inheritance, as seen when Emperor Frederick II enfeoffed Ludwig I of Bavaria with the Palatinate in 1214.^[114] In modern Germany, the Pfalz functions as a cultural and economic region comprising the southern portion of Rhineland-Palatinate, rather than a standalone administrative division; the state itself is subdivided into 24 rural districts (Landkreise) and 12 independent cities, with Pfalz-area districts including Rhein-Pfalz-Kreis, Südwestpfalz, and Südliche Weinstraße, which handle local governance such as zoning, taxation, and infrastructure under state oversight. Historically, until 1968, the Pfalz operated as one of five administrative districts (Regierungsbezirke) within Rhineland-Palatinate, after which it merged with Rheinhessen to form the Rheinhessen-Pfalz district before further decentralization.^[115]^[116] The region's administrative framework supports its viticultural economy, a legacy of feudal land grants favoring Rhine-adjacent estates; in 2024, Pfalz wine production volumes declined by approximately 4% from the prior year due to weather challenges, yet maintained high quality with yields contributing to Germany's overall harvest of around 7.75 million hectoliters.^[117]^[118]

Businesses

Fitness and consumer brands

Planet Fitness, a United States-based gym chain, was founded in 1992 in Dover, New Hampshire, and operates over 2,500 locations across all 50 states, the District of Columbia, Puerto Rico, Canada, and internationally as of late 2023, expanding to approximately 2,762 clubs by mid-2025.^[119]^[120] The chain generated $1.2 billion in total revenue for fiscal year 2024, reflecting a 10.3% increase from the prior year, driven by franchise fees, equipment sales, and membership dues from nearly 19 million members at year-end 2023.^[121] Its business model centers on low-cost memberships starting at $10 per month, marketed as a "Judgement Free Zone" to attract novice or casual users averse to traditional gym intimidation, with amenities limited to cardio machines, basic weights (capping free weights at 75 pounds), and no powerlifting equipment to enforce this environment.^[122]^[123] This low-barrier approach yields high initial sign-ups but correlates with elevated dropout rates, as general industry data indicate 50% of new gym members quit within six months due to insufficient motivation or routine establishment, a pattern exacerbated in models relying on non-attendance for profitability—up to 67% of memberships go unused, with Planet Fitness explicitly designing capacity for far fewer active users than enrolled.^[124]^[125] Such dynamics causally reinforce sedentary lifestyles by promoting accessibility without demanding sustained effort, normalizing sporadic or absent engagement under the pretense of health commitment, in contrast to evidence favoring structured, high-discipline programs that achieve better long-term adherence through accountability and progressive overload.^[126]^[127] Phat Farm, a consumer clothing brand launched in 1992 by Russell Simmons, co-founder of Def Jam Recordings, specialized in urban streetwear influenced by hip-hop culture, featuring baggy jeans, oversized apparel, and branded accessories targeted at young urban consumers.^[128] The brand achieved peak popularity in the 1990s and early 2000s, but experienced sales declines starting in the mid-2000s, prompting its $140 million sale to Kellwood Company in 2004 amid double-digit revenue drops and market saturation in hip-hop fashion.^[129] Simmons stepped down as CEO in 2007, after which Phat Farm faded from mainstream retail, shifting to resale and vintage markets with no significant active sales or production reported post-2010s as consumer preferences evolved toward athleisure and minimalist styles.^[130]^[131] This trajectory illustrates how gimmick-driven branding, prioritizing cultural flash over durable utility, yields transient consumer loyalty, mirroring patterns in low-commitment fitness where initial appeal dissipates without underlying value alignment.^[132]

Other commercial entities

P.F. Flyers, an American footwear brand, originated from the "Posture Foundation" insole technology patented in 1933 by Hyman L. Whitman in collaboration with B.F. Goodrich, emphasizing arch support derived from tire manufacturing innovations to promote foot alignment and reduce fatigue.^[133] The brand launched commercially in 1937, marketing sneakers under the PF designation to highlight this foundational feature, which provided superior cushioning and stability compared to contemporaries, contributing to early sales success amid post-Depression consumer demand for durable athletic wear.^[134] Through multiple ownership transitions—including acquisition by Converse in the 1970s, subsequent decline in the 1980s due to synthetic material shifts and competition from imported goods, and revival under Voit and later Kassia Designs since 2015—P.F. Flyers has maintained market presence by leveraging nostalgic branding and updated production, achieving sustained revenue via direct-to-consumer and retail channels without reliance on short-term hype.^[134] This longevity, spanning over 85 years, exemplifies operational efficiency in adapting to disruptions like globalization and e-commerce, with the brand focusing on canvas uppers and vulcanized rubber soles that retain core Posture Foundation principles for everyday and casual athletic use.^[133] P.F. Chang's, a casual dining chain specializing in wok-fired American Chinese cuisine, operates approximately 300 locations across 22 countries as of 2023, founded in 1993 by restaurateurs Paul Fleming and Philip Chiang to blend traditional techniques with accessible menu items like lettuce wraps and Mongolian beef.^[135] The enterprise, now under Paulson & Co. ownership following its 2019 acquisition from TriArtisan Capital, demonstrates verifiable commercial scale through consistent expansion and franchising models, prioritizing fresh ingredients and open-kitchen visibility to differentiate from fast-casual competitors, though it has navigated challenges like supply chain volatility without documented revenue shortfalls tied to unproven trends.^[136]

Arts and entertainment

Video games

Phantom Forces is a first-person shooter video game developed and published by StyLiS Studios for the Roblox platform, released on August 30, 2015.^[137] The game emphasizes tactical realism through mechanics such as weapon customization, recoil simulation, and team-based modes like King of the Hill and Capture the Flag, drawing on modern military equipment from real-world arsenals including assault rifles, sniper rifles, and attachments for accuracy and handling.^[138] It has garnered extensive player engagement, with concurrent player averages exceeding 25,000 as of recent server data and cumulative visits surpassing 1.7 billion, reflecting its status as one of Roblox's prominent shooter titles.^[139] Pacific Fighters, released on October 22, 2004, is a World War II combat flight simulator developed by 1C:Maddox Games and published by Ubisoft as a stand-alone expansion to the IL-2 Sturmovik series.^[140] Built on the series' engine, it simulates Pacific theater battles with detailed aircraft physics for over 50 flyable planes, including Japanese A6M Zeros and American F4U Corsairs, incorporating factors like engine performance, damage modeling, and carrier operations for historical fidelity.^[141] The title supports multiplayer dogfights and campaigns, prioritizing simulation depth over arcade elements to replicate causal flight dynamics such as stall speeds and g-forces.^[142]

Other media

In musical notation, "pf" denotes più forte (Italian for "more strongly" or "louder"), instructing performers to increase volume beyond the established dynamic level, often following a softer marking like piano.^[143] This usage appears in scores from the Classical era onward, though it is less common today and sometimes spelled out fully to avoid ambiguity.^[144] Alternatively, "pf" may indicate poco forte ("somewhat loud"), positioning it between mezzo-forte and forte in intensity, as described in historical treatises like Daniel Gottlob Türk's 1789 Clavierschule.^[144]^[145] Composers such as Johannes Brahms employed "pf" idiosyncratically for expressive nuance, blending dynamic and character elements rather than strict volume.^[146]

Language

Abbreviations in writing

In digital publishing and web content creation, "PF" commonly abbreviates "printer-friendly," referring to a simplified layout of a document or webpage designed for efficient printing by omitting sidebars, images, advertisements, and interactive elements that do not reproduce well on paper. This format supports streamlined workflows in editorial processes, where authors or editors generate PF versions to facilitate reviewer feedback or archival printing without extraneous visual clutter, thereby minimizing resource waste and focusing on core textual content. For instance, content management systems like WordPress often include plugins or built-in options to export articles in PF mode, ensuring legibility in black-and-white printouts during pre-production reviews.^[147] In financial and historical writing, "pf." or "Pf." serves as the standard abbreviation for pfennig, the centesimal subunit of the Deutsche Mark currency used in West Germany from 1948 until the adoption of the euro in 2002, where one pfennig equaled 1/100 of a mark. This shorthand appears in economic texts, invoices, and archival records to denote fractional amounts, such as "DM 2,34 pf.," reflecting precise pricing conventions before decimalization harmonized with the euro system. Its use persists in scholarly discussions of pre-euro monetary history for brevity in tables and citations.^[148]^[149] Certain editorial glossaries and dictionaries also recognize "pf." as an abbreviation for "proof" in typographic contexts, denoting a preliminary printed version of a manuscript submitted for final corrections before full production runs. This aligns with traditional publishing stages where proofs—marked "PF" in some internal notations—allow detection of errors in layout, spacing, or typography, though digital tools have largely supplanted such manual abbreviations in modern workflows.^[150]

Slang and informal uses

In digital communication, particularly texting and social media platforms, "PF" serves as slang for "profile," shorthand for a user's personal account page containing biographical details, photos, and preferences. This usage appears in casual directives like "check my PF" or "nice PF pic," facilitating quick references in conversations about online identities.^[151]^[152] Among sports enthusiasts, especially in basketball forums and real-time commentary, "PF" informally abbreviates "personal foul," denoting a rule violation from excessive physical contact with an opponent, often tracked in player stats and debated for its impact on game flow. Such slang emphasizes player accountability over interpretive narratives of harm, countering tendencies in some discussions to frame infractions primarily through affected parties' experiences rather than rule enforcement. Usage spikes during live events, with fans invoking it to critique aggressive play without excusing it as inherent disadvantage.^[153]^[154] In niche online communities focused on motivation or self-improvement, "PF" occasionally represents "positive force," slang for an uplifting influence or mindset that drives constructive outcomes, distinct from passive optimism. This interpretation surfaces in forum threads and group chats promoting resilience, though less frequent than profile or foul usages.^[153]

Other uses

General abbreviations

In economic policy discussions, PF abbreviates public finance, referring to the management of government revenues, expenditures, and debt, with empirical analyses often linking persistent budget deficits to causal factors such as structural spending imbalances exceeding tax collections—as evidenced in fiscal studies where public finance frameworks quantify deficit trajectories via metrics like primary balance ratios.^[155]^[156] This usage appears in formal reports on sovereign debt sustainability, where public finance models project deficit amplification from interest rate divergences and growth shortfalls, independent of sector-specific applications.^[155] In generic technology and interface contexts, PF denotes profile, as in standardized user or system profiles for data configuration, distinct from colloquial or slang interpretations; for instance, software documentation employs PF to reference profile files or templates that store persistent settings, enabling interoperability across applications without linguistic informality.^[156]^[147] This abbreviation's ubiquity stems from its brevity in technical specifications, where profiles serve as modular data structures for authentication and customization, verifiable in protocol standards predating modern slang derivations.^[147]

Miscellaneous

The Pagan Federation (PF) is a United Kingdom-based advocacy organization founded in 1971, originally as the Pagan Front, dedicated to promoting the rights of Neo-Pagans and pagans more broadly.^[157] It campaigns against discrimination, provides educational resources on pagan beliefs and practices, and fosters community among adherents of diverse pagan traditions including Wicca and Druidry.^[157] The organization maintains a focus on legal recognition and societal integration of paganism, distinct from mainstream religious institutions.^[158] An international counterpart, Pagan Federation International, extends similar efforts globally, connecting pagans across borders and defending against religious persecution through information dissemination and networking.^[159] While specific membership figures are not publicly detailed in recent reports, the PF's activities remain niche, with influence primarily within pagan subcultures rather than broader society.^[160] Other purported uses of PF, such as informal slang for "phony food" in niche food discussions, lack widespread empirical support and appear limited to anecdotal or low-frequency online references.^[161]

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LIFE - LIBERTY - VICTORY. Our tradition is revolution and our land is where tyrants come to die.
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Patriot Front - RECLAIM AMERICA
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SEC-registered investment advisers with at least $150 million in private fund assets under management are required to file Form PF.
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CFTC and SEC Extend Form PF Compliance Date to Oct. 1, 2026
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[PDF] PRESENT RATES OF CONTRIBUTION
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really all the species we monitor in the small game survey.Missing: verifiable outcomes<|control11|><|separator|>
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Alpha-2 code. PF ; Short name. FRENCH POLYNESIA ; Short name lower case. French Polynesia ; Alpha-3 code. PYF ; Numeric code. 258.
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Germany's Demanding 2024 Harvest Leads to Excellent Grape Quality
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Planet Fitness, Inc. Announces Second Quarter 2025 Results
Aug 6, 2025 · As of June 30, 2025, Planet Fitness had approximately 20.8 million members and 2,762 clubs in all 50 states, the District of Columbia, Puerto ...
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Planet Fitness, Inc. Announces Fourth Quarter and Year-End 2024 ...
Feb 25, 2025 · Total revenue increased from the prior year period by 19.4% to $340.5 million. System-wide same club sales increased 5.5%. System-wide sales ...
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[PDF] 2024 annual report
Planet Fitness – Home of the Judgement Free Zone. We bring fitness to a large, previously underserved segment of the population. Our differentiated member ...
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What is the Planet Fitness business model? | Exercise.com
Jan 17, 2025 · The Planet Fitness business model is centered around offering low-cost memberships in a “Judgment-Free Zone” that appeals to casual or ...Missing: sedentary | Show results with:sedentary
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100 Gym Membership + Retention Statistics You Need to Know in ...
Feb 22, 2025 · 50% of new gym members quit within six months, primarily due to lack of motivation or routine. About 14% of members haven't been to their gym in ...
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What percentage of gym memberships go unused? - Exercise.com
Mar 1, 2025 · Up to 67 percent of gym memberships go completely unused. Some gyms build their gym business model (like the Planet Fitness business model) on ...
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Motives and barriers to initiation and sustained exercise adherence ...
Jun 15, 2020 · Consistent with other studies among fitness club members, our study also demonstrates low exercise adherence and an increase in exercise dropout ...Missing: criticism sedentary
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Why We Sign Up For Gym Memberships But Never Go To The Gym
Dec 30, 2014 · Gyms take on way more members than they have space for. Here's a look at how they get us to sign up and never show up.Missing: criticism sedentary<|control11|><|separator|>
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Phat Farm
Created in 1992, Phat Farm represents the most influential streetwear line of its day. Founded by Russell Simmons.
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7 Reasons Why The Hip Hop Clothing Brands Have Not Survived.
May 19, 2016 · A double-digit drop in sales. Phat Farm was sold to the Kellwood Group for $140 million. As for FUBU, it left the U.S. market completely in 2003 ...Missing: decline | Show results with:decline
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Simmons Exits Phat Fashions - WWD
Aug 24, 2007 · Russell Simmons has called it a day at Phat Fashions, the company he founded 15 years ago. Simmons has stepped down as chief executive officer of the firm.
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Russell Simmons' Apparel Line, Phat Farm, Died Long Before His ...
Nov 30, 2017 · Russell Simmons' apparel line, Phat Farm, died long before his reputation. Phat Farm's fall from grace began in the early '00s.Missing: sales | Show results with:sales
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Where Did These Hip-Hop Clothing Labels Go? - Racked
Jan 11, 2016 · ... brand. While Simmons does admit that Phat Farm was not an immediate success, losing him almost $10 million during the first six years, he ...Missing: decline | Show results with:decline
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https://pfflyers.com/pages/posture-foundation
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https://pfflyers.com/pages/our-history
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Global Development Overview - P.F. Chang's
P.F. Chang's is the first multi-unit Asian culinary brand to honor and celebrate wok cooking as the center of the guest experience. With roots in Chinese ...
[136]
Asian Restaurant Chain Near You - P.F. Chang's
P.F. Chang's is the first internationally recognized multi-unit Asian culinary brand to honor and celebrate wok cooking as the center of the guest experience.
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[Eisenmark Halloween Fest] Phantom Forces - RoMonitor Stats
90.874 % ; By: StyLiS Studios (Community) Roblox Verified Badge ; Release Date: August 30, 2015 ; Last Release: October 25, 2025 1:04 AM ; Genre: Shooter > ...
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Phantom Forces Release Information for Roblox - GameFAQs
Phantom Forces is an Action game, developed and published by StyLiS Studios, which was released in 2015. Know Something We Don't?
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[Eisenmark Halloween Fest] Phantom Forces | Roblox Game
Players Average. 25.849. Players Maximum. 31. Players Minimum. 1. Players Standard Deviation. 7.199. Game Servers Statistics. More complete statistics and ...
[140]
Pacific Fighters · IL-2 Sturmovik: 1946 (App 15280) - SteamDB
Game releases by year · Change history. Rankings; Top rated games · Global top sellers ... Store Release Date, 22 October 2004 – 07:00:00 UTC ( 21 years ago ).
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Pacific Fighters - IGN
Rating 7.7/10 · Review by Steve ButtsNov 4, 2004 · ... IL-2 Sturmovik to the Pacific Theater, trading the Yaks and Messerschmitts for Zeros and Corsairs. The game can even be installed on top of ...
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Pacific Fighters (2004) | IGDB.com
Jun 23, 2025 · Pacific Fighters is a World War II Combat flight simulation game. It is in fact a stand-alone expansion pack of IL-2 Sturmovik.Missing: video | Show results with:video
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PF Definition & Meaning - Merriam-Webster
Medical Definition. pf. abbreviation. picofarad.
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“Smfz” – On some unconventional dynamic markings in our Urtext ...
Sep 28, 2015 · Thus, in his 1789 Klavierschule [Piano Course] Daniel Gottlob Türk declares the pf to be “1) poco forte, somewhat loud, also probably 2) più ...
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Dynamics - Oxford Academic - Oxford University Press
One marking rarely seen today is pf, which indicates play poco forte or piu forte. Fortunately, it is usually spelled out. In the Classical Era style it is ...
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The Notation of Accents and Dynamics - Oxford Academic
Mar 20, 2025 · Brahms's idiosyncratic employment of poco f or pf seems likely to have involved an expressive element, perhaps implying the character of a forte ...<|separator|>
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What does PF stand for? - Abbreviations.com
What does PF mean? This page is about the various possible meanings of the acronym, abbreviation, shorthand or slang term: PF. ; PF. Particle Flow. Academic & ...
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PF definition in American English - Collins Dictionary
pf. in American English. abbreviation. 1. perfect. 2. pfennig. 3. pianoforte; piano. 4. (of stock). preferred. 5. proof. Most material © 2005, 1997, 1991 by ...
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https://en.thefreedictionary.com/pf
[150]
PF. Definition & Meaning - Dictionary.com
pF. 1. picofarad; picofarads. pf. 2. abbreviation. perfect. pfennig. pianoforte; piano. (of stock) preferred. proof. p.f.. 3. abbreviation. Music. louder. pf. 1 ...
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PF Meaning & Definition - NoSlang.com
Usage of PF. In the context of online platforms and social media, the term 'PF' stands for 'profile'. A profile typically refers to the personal information ...
[152]
PF Meaning: what does PF stands for - Slangs - UrduPoint
PF is a slang term. PF stands for profile. UrduPoint provides the PF slang meaning and it's complete details in English.<|separator|>
[153]
PF - Slang/Internet Slang - Acronym Finder
PF · Pacific Fighters (computer game) ; PF, Phantom Forces (gaming) ; PF, Prato Feito (Brazil; fast food) ; PF, Pipes and Flowers (Elisa Italian music album).
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PF - "Personal Foul" by AcronymsAndSlang.com
What does PF stand for? Hop on to get the meaning of PF. The Acronym /Abbreviation/Slang PF means Personal Foul. by AcronymAndSlang.com.<|separator|>
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PF - Business & Finance - Acronym Finder
PF · Pension Fund · PF · Phat Farm (clothing brand) · PF, Planet Fitness. PF, Posture Foundation (PF Flyer shoes). PF, Phat Farms (clothing brand).
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PF - What does PF stand for? The Free Dictionary
PF, Patriotic Front (Zambia) ; PF, Program Files ; PF, Pension Fund ; PF, Pink Floyd (band).
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The Pagan Federation – paganfed.org
Founded in 1971 the PF seeks to support all Pagans to ensure they have the same rights as the followers of other beliefs and religions.MembershipIntroduction to PaganismLondonStoreAbout
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Pagan Federation – REC - Religious Education Council
Founded in 1971 the PF seeks to support all Pagans to ensure they have the same rights as the followers of other beliefs and religions.<|separator|>
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Welcome to Pagan Federation International | PFI
Pagan Federation International is an international non-governmental organisation that works to defend the rights of pagans, offering reliable information, ...
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Pagan Federation International - USA
Welcome to the Pagan Federation International (PFI), a unique organization helping Pagans connect with other Pagans around the world!
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What does PF mean in Food & Nutrition? - Abbreviations.com
What does PF mean in Food & Nutrition? This page is about the meanings of the acronym/abbreviation/shorthand PF ... Embed. Click to view: PF - Phony Food. Image ...