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MCP Connector Setup: No Demo Edits & Credit Non-Transfer Audit
Audit Scoped OAuth Onboarding Rules for the Arte Sheets ChatGPT Connector (0.1.0, In review / Not published): Read-Only Setup Discovery via list_workbooks and list_lessons, Zero Speculative Demo Edits or Invitations, Neutral Access-Denial Reporting, and Zero ChatGPT Credit Transfer.
Read the guide →Connected Apps & Collaboration GovernanceMCP list_workbooks Pagination & Connected Apps Audit
Audit list_workbooks (<=100 cloud documents per page), why local browser-only workbooks require cloud collaboration before external MCP reads/writes, and OAuth revocation via Profile -> Connected apps.
Read the guide →AI Connector Security, OAuth Hygiene & Setup GovernanceMCP OAuth Hygiene, Cloud Visibility & Lesson Prompt Audit
Audit Arte Sheets ChatGPT 0.1.0 setup and teaching guardrails: host OAuth without chat passwords/tokens (revokable in Profile -> Connected apps), no ChatGPT credit transfer claims, cloud collaboration visibility vs local browser sheets, and lesson-text prompt-injection quarantine.
Read the guide →Spreadsheet Security & Collaborative AI GovernanceMCP Public Link Rotation & Cell Prompt-Guard Formula
Audit manage_public_link owner/Pro rotation vs named invitations, 20-row by 10-column anonymous pagination tiles, and strict untrusted-data isolation for cell/comment prompt strings.
Read the guide →Spreadsheet Governance, Collaboration Permissions & External OAuth AuditingMCP share_workbook In-App Invite, emailSent=false & Replay Audit
Audit External OAuth share_workbook Governance in Arte Sheets: Owner + Active Pro Gate, Ambiguous Recipient/Role Hold, In-App Invitation Disclosure (emailSent=false), Zero Arte AI Credit Usage, and Idempotent Replay Semantics.
Read the guide →Spreadsheet Automation, AI Governance & MCP ReliabilityMCP Structural Step Coordinate Shift & Readback Audit
Audit 1-based row/column coordinate shifts R_shifted = R_0 + Ins_Above - Del_Above inside execute_steps (<= 10 steps, <= 20 structural ops, <= 100 cells), enforce post-mutation read_range verification, and reject unsupported file-create/export/macro requests.
Read the guide →Engineering & ScienceMears Criterion: External Boundary-Layer Mass Transfer Check (< 0.15)
Test whether external fluid-film mass transfer limits heterogeneous catalytic reaction rates (< 5% error) via David Mears’ observable criterion Ω_Mears = (-r_A')_obs * ρ_b * R * n / (k_c * C_Ab) < 0.15.
Read the guide →API 682 Rotating Equipment, Centrifugal Pump Mechanical Seals & Tribology PV LimitsMechanical Shaft Seal Balance Ratio, PV & Heat Formula
Calculate Net Seal-Face Contact Pressure Pf (MPa), Mean Sliding Velocity v (m/s), Tribological PV Factor (MPa·m/s), and Seal-Chamber Flush Heat Generation (W).
Read the guide →StatisticalMedian Absolute Deviation (MAD) & Iglewicz-Hoaglin Modified Z-Score outlier formula
Calculate median absolute deviation and a modified Z-score, including the zero-MAD case, to flag observations for investigation.
Read the guide →Descriptive statisticsMEDIAN function: summarize typical values without outlier distortion
Find the middle value of a dataset when one extreme spike pulls AVERAGE upward, and verify how MEDIAN handles both odd and even observation counts.
Read the guide →Healthcare Revenue Cycle & Medical EconomicsMedicare Physician RVU, GPCI & Payment Formula
Calculate CMS Resource-Based Relative Value Scale (RBRVS) Unadjusted RVUs, Geographic Practice Cost Index (GPCI) Adjusted RVUs, Medicare Allowed Fee-Schedule Payment, and 80% Part B Plan Reimbursement.
Read the guide →International Trade & Firm DynamicsMelitz Export Productivity Cutoff & Exporter Share Formula
Calculate the Melitz-Chaney export cutoff hurdle phi_X* / phi_D* = tau * (f_X / f_D)^(1/(sigma - 1)), Pareto exporter share, and domestic survival cutoff elevation.
Read the guide →Ground Improvement & Reclamation, Ménard Dynamic Compaction Energy & DepthMénard Dynamic Compaction Depth & Specific Energy Formula
Calculate Crane Drop-Tamper Impact Energy W*H (tonne·m & MJ), Ménard-Lukas Effective Densification Depth n*SQRT(W*H) (m), and Grid Applied Specific Energy (kJ/m²).
Read the guide →Statistical & Clinical AnalysisMentzer Index (MCV / RBC) & Green-King Index: Beta-Thalassemia Trait vs. Iron Deficiency
Differentiate microcytic beta-thalassemia minor (< 13 Mentzer, < 65 Green-King) from iron-deficiency anemia (> 13 Mentzer, >= 65 Green-King) directly from routine CBC indices.
Read the guide →Manufacturing Mechanics & Metal CuttingMerchant Shear-Plane Angle & Cutting Force Formula
Calculate M.E. Merchant’s Minimum-Power Shear-Plane Angle phi = 45 + alpha/2 - beta/2, Rake-Face Friction Coefficient TAN(beta), Shear-Plane Area, and Tangential Cutting Force F_c.
Read the guide →Lookup & ReferenceMerge two tables by ID: Left Join, Inner Join, and Orphan Key audit
Join an Orders fact table to a Customers master table using XLOOKUP enrichment columns and FILTER for Inner Join vs unmatched Anti-Join audits.
Read the guide →FinancialMerton distance to default: lognormal model and a one-year linear buffer
Calculate an illustrative distance to default from asset value, debt, annual asset drift and volatility, with explicit model assumptions and input checks.
Read the guide →Quantitative Finance & DerivativesMerton Jump-Diffusion Option Pricing via Poisson-Weighted Black-Scholes
Price European options under sudden lognormal jumps using Merton’s (1976) jump-compensated Poisson-weighted Black-Scholes sum and verify convergence to pure Black-Scholes at lambda = 0.
Read the guide →Quantitative Finance & Portfolio ChoiceMerton Optimal Portfolio Share & Consumption-Wealth Formula
Calculate Merton’s continuous-time risky-asset allocation pi* = (mu - r_f)/(gamma * sigma^2), certainty-equivalent return r_CE, and optimal CRRA payout propensity c*/W.
Read the guide →Quantitative FinanceMerton Structural Credit Distance-to-Default (DD) Formula
Calculate Merton’s (1974) / KMV structural credit Distance-to-Default DD = (LN(V_A / D) + (mu_A - 0.5 * sigma_A^2) * T) / (sigma_A * SQRT(T)) in asset standard deviations.
Read the guide →Network Economics & Tech ValuationMetcalfe vs Odlyzko-Tilly Network Value & Critical Mass
Compare Metcalfe pair count N*(N - 1)/2 against Odlyzko-Tilly Zipf network value N * LN(N) and solve Rohlfs’s (1974) critical-mass tipping penetration f_crit*.
Read the guide →Precision Dimensional Metrology, GD&T Gage Uncertainty, Calipers & CMM ProbingMetrology Cosine Error & Abbe Offset Angular Error Formula
Calculate Indicator Tilt Cosine Error E_cos (um), Ernst Abbe’s First-Principle Offset Sine/Tangent Error E_Abbe (um), Combined Systematic Gage Error (um), and Error-to-Length PPM.
Read the guide →Clinical Medicine & PhysiologyMETS-IR Calculator: Bello-Chavolla Non-Insulin Metabolic Score for Insulin Resistance
Quantify peripheral insulin sensitivity without fasting serum insulin assays using Omar Yaxmehen Bello-Chavolla et al.’s (2018) clamp-validated METS-IR = (LN(2 * FPG_mg_dL + TG_mg_dL) * BMI) / LN(HDL_mg_dL).
Read the guide →Civil, Structural & Geotechnical EngineeringMeyer-Peter & Muller (1948) Bedload Sediment Transport Formula: Shields Excess & q_b
Calculate gravel- and coarse-sand river bedload transport intensity Phi = 8 * MAX(0, theta_prime - 0.047)^1.5 and volumetric unit bedload rate q_b (m^2/s) using Eugen Meyer-Peter and Robert Muller’s (1948, ETH Zurich) flume law.
Read the guide →Operations, Logistics & EngineeringMeyerhof & Vesić Ultimate Bearing Capacity Formula: Exact N_q, N_c & N_gamma Strip Footing
Calculate shallow strip-footing ultimate bearing capacity q_u = c'*N_c + q*N_q + 0.5*gamma*B*N_gamma from friction angle phi' using exact Prandtl-Reissner N_q, N_c and Vesić (1973) vs. Meyerhof (1963) N_gamma.
Read the guide →EngineeringMichaelis-Menten enzyme kinetics formula: reaction velocity v, Km & kcat
Calculate a simple Michaelis-Menten initial rate, its fraction of Vmax, and kcat from compatible enzyme concentration units.
Read the guide →High-Speed PCB Design, RF/SerDes Controlled Impedance & IPC-2141 Microstrip LinesMicrostrip PCB Impedance (Z0) & Propagation Delay Formula
Calculate Quasi-TEM Effective Dielectric Constant epsilon_eff, IPC-2141 Microstrip Characteristic Impedance Z_0 (Ohms), Propagation Delay (ps/mm), and Phase Velocity (% of c).
Read the guide →Cleaning imported dataMID function: extract a middle code segment while keeping leading zeros
Slice a fixed-position middle segment such as 482 or 035 out of product codes like AA-482-Z using one-based character positions.
Read the guide →Statistical & Clinical AnalysisMiettinen Test-Based Confidence Interval Formula: OR^(1 ± z / SQRT(Chi-Square))
Reconstruct 95% confidence limits for any Odds Ratio, Risk Ratio, or Hazard Ratio published with only a point estimate and Mantel-Haenszel chi-square statistic using Olli S. Miettinen’s 1976 test-based formula OR^(1 ± z / SQRT(chi²)).
Read the guide →MathMifflin-St Jeor resting energy estimate: a spreadsheet exercise
Practice the adult Mifflin-St Jeor resting-energy equation with fictional inputs and an explicitly assumed activity multiplier.
Read the guide →Industrial Organization & Game TheoryMilgrom-Roberts Limit-Pricing Separating Formula
Calculate Paul Milgrom and John Roberts’s (1982) least-cost separating limit quantity Q_sep = MAX(Q_m(L), Q_m(H) + SQRT(Delta_H / b)), limit price P_sep, and signaling profit distortion.
Read the guide →Treasury & Corporate FinanceMiller-Orr Stochastic Cash Control Bands: Return Point and Upper Limit
Compute the Miller-Orr cube-root cash control spread Z, asymmetric one-third return point RP = L + Z/3, and upper sweep threshold H = L + Z for volatile daily cash flows.
Read the guide →Descriptive statisticsMIN and MAX in Excel: find the extremes and calculate the range
Use a short temperature log to find the lowest and highest readings, calculate their difference, and avoid reporting missing data as zero.
Read the guide →Financial & AccountingMincer Earnings Function Formula: Return to Schooling & Concave Experience Wage Profile
Model human-capital earnings EXP(beta_0 + r_s*S + beta_1*X + beta_2*X²), marginal return to work experience (beta_1 + 2*beta_2*X), and peak-earnings career horizon X* = -beta_1 / (2*beta_2) using Jacob Mincer’s 1974 log-wage equation.
Read the guide →Mechanical & Structural EngineeringMindlin-Reissner Thick Circular Plate Bending + Shear Deflection
Extend Kirchhoff thin-plate formulas to thick viewports and flange blinds using Mindlin-Reissner transverse shear deflection q*R^2 / (4*kappa*G*h) and exact (h/R)^2 scaling.
Read the guide →Statistical & Clinical AnalysisMini Nutritional Assessment Short-Form (MNA-SF 0–14) Formula: BMI & Calf Fallback
Calculate the revised 6-item Mini Nutritional Assessment Short-Form (MNA-SF, 0–14 points — Rubenstein et al., 2001 / Kaiser et al., 2009) with automatic Calf Circumference (>= 31 cm = 3 pts, < 31 cm = 0 pts) fallback when standing BMI is unavailable.
Read the guide →Healthcare & Clinical FormulasMini-Cog Rapid Cognitive & Dementia Screen (0–5 Composite)
Compute Soo Borson’s 3-minute Mini-Cog score (0–5) from Delayed 3-Word Recall (0–3 pts) + All-or-None Clock Drawing Test (Normal = 2 pts, Abnormal = 0 pts), flagging 0–2 for formal dementia workup.
Read the guide →Descriptive statisticsMINIFS and MAXIFS: find lowest and highest values by category
Compare the lowest and highest supplier quotes within one material group, and avoid mistaking a 0 unmatched result for a free quote.
Read the guide →StatisticalMinimum value if unique: find the lowest non-tied bid and winning bidder
Disqualify tied low values and extract the smallest strictly unique number (and its owner) using COUNTIF, FILTER, MIN, and XLOOKUP.
Read the guide →Mineral Processing & Smelter OfftakeMining Net Smelter Return (NSR) & TC/RC Formula
Calculate Concentrate Mass Pull, Minimum-Unit-Deducted Payable Copper Grade, Smelter Value per Dry Metric Tonne of Concentrate after Treatment/Refining/Freight Charges, and Mine-Mouth NSR per Tonne Milled.
Read the guide →Agricultural Economics & Soil FertilityMitscherlich-Baule Fertilizer Yield & Optimum Formula
Calculate Mitscherlich-Baule Crop Yield Y = A_max * (1 - 2^(-(N_0 + N_app) / b_Baule)), Unfertilized Check Yield, Net Agronomic Profit Lift ($/ha), and Profit-Maximizing Economic Optimal Nitrogen Rate.
Read the guide →Numbers and totalsMOD function: calculate leftover items after filling complete packs
Find how many loose items remain when packing whole quantities into fixed-size sleeves or cartons, and check exact multiples and zero-divisor errors.
Read the guide →StatisticalMODE.SNGL and MODE: find the most frequent number in a dataset
Identify the most common pack size or order quantity with MODE.SNGL, and handle all-unique ranges where no value repeats (#N/A).
Read the guide →Healthcare & Clinical CalculationsModified Aldrete Score for Phase-I PACU Post-Anesthesia Discharge
Calculate J. Antonio Aldrete’s 5-domain Modified PACU Recovery Score (0–10 across Activity, Respiration, Circulation, Consciousness, and Pulse Oximetry SpO2) with zero-subscore safety hold.
Read the guide →Clinical Medicine & PhysiologyModified Brooke Burn Fluid Resuscitation (2 mL/kg/%TBSA) & Curreri Calorie Formula
Calculate ATLS / ABA initial 24-hour Modified Brooke Lactated Ringer’s resuscitation volume (2 mL * kg * %TBSA, first-8h hourly infusion rate) to prevent "fluid creep," alongside P. William Curreri’s adult burn hypermetabolic nutrition formula (25 * kg + 40 * %TBSA).
Read the guide →Healthcare & Clinical CalculationsModified CT Severity Index (MCTSI / Balthazar) for Acute Pancreatitis
Calculate Koenraad Mortele’s 0–10 Modified CT Severity Index (even integers 0–10) from Pancreatic Inflammation (0/2/4), Parenchymal Necrosis Percentage (0%, <= 30%, > 30%), and Extrapancreatic Complications (0/2).
Read the guide →FinancialModified Dietz portfolio return with day-weighted external cash flows
Calculate investment performance across mid-month deposits and withdrawals without daily portfolio valuations via R = (EMV - BMV - SUM(CF)) / (BMV + SUM(w_i * CF_i)).
Read the guide →Healthcare & ClinicalModified Early Warning Score (MEWS 0–14): Ward Rapid-Response Escalation Formula
Calculate Subbe's 5-parameter bedside Modified Early Warning Score (MEWS, 0 to 14 points) directly from Systolic BP, Heart Rate, Respiratory Rate, Temperature (°C), and AVPU level (0–3) to trigger Rapid Response Team escalation at >= 5.
Read the guide →Healthcare & ClinicalModified Fisher CT Scale (0–4) & Hunt-Hess Subarachnoid Hemorrhage (SAH) Grade
Determine the Modified Fisher CT Grade (0 to 4) for delayed cerebral ischemia / vasospasm risk from subarachnoid blood thickness and bilateral intraventricular hemorrhage (IVH), alongside Hunt & Hess SAH clinical severity (Grades 1–5).
Read the guide →Financial & AccountingModified Internal Rate of Return (MIRR): Separate Finance & Reinvestment Rates
Compute the exact Modified Internal Rate of Return (MIRR) by discounting negative cash outflows at your cost of capital and compounding positive cash inflows at realistic treasury reinvestment rates.
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