The core insight was that all four images are the same mathematical object seen four ways: three are renderings of the reverse (predecessor) tree of the 3n+1 map, and one is a single long orbit. From shared building blocks — a forward orbit function, the predecessor-tree builder, and the "proportional power ratio" mapping — each figure adds its own layout and styling: Figure 1 (green/red neuron): the predecessor tree under a vectorized Fruchterman–Reingold force layout, with quadratic-Bézier curved edges for the organic loops and the longest root-to-leaf paths highlighted red. Figure 2 (rainbow fan): a faithful line-for-line port of the Processing "Collatz Tree" sketch — fixed branch geometry, depth-cycled palette, green leaf dots. Deterministic, so essentially an exact match. Figure 3 (purple/orange lobed tree): the same tree under the force layout to get the graphviz-neato look — central spine, lobes with white gaps, dark-red→plum→orange depth colouring. This one we corrected mid-project after you flagged that my first radial version filled the circle too uniformly. Figure 4 (polar web): one long orbit (n = 670617279) plotted with θ = index in radians and r = power-ratio base 6, which produces the star/spoke pattern. Also deterministic and near-exact.

Time-Series Econometrics, FAU Oct 2024 – Feb 2025 • Built a full R Markdown time-series pipeline modelling sales and GDP-growth dynamics across FDL and ADL specifications, deriving impact, interim, and long-run multipliers • Selected and estimated an ARMA(1,3) via AIC/AICc/BIC search; evaluated accuracy through recursive out-of-sample 4-quarter forecasts (RMSE/MAE/ MAPE) against a naïve benchmark • Tested stationarity with ADF and KPSS; fit a GARCH volatility model, diagnosing volatility clustering and a persistence parameter of 0.991 with Ljung– Box / Shapiro–Wilk residual checks

• Replicated the BRAC ELA cluster-RCT (150 communities; 100 treatment / 50 control; three-wave panel of 5,966 adolescent girls), estimating Intent-to-Treat effects via OLS ANCOVA with baseline-covariate and branch fixed-effect controls • Constructed z-scored empowerment indices; ran balance checks (two-sample t-tests, standardised mean differences), flagging 5 of 15 imbalanced baseline covariates; produced a discrepancy report against the published estimates • Bounded attrition with Lee bounds, clustered SEs at village level, trimmed the top 1% of expenditure outliers; extended with a Treatment × StillGoing interaction for heterogeneous treatment effects, deriving conditional effects analytically • Built a reproducible R Markdown pipeline with reusable functions automating variable construction, regression output, and tables; added cost-effectiveness comparisons against the Jóvenes programmes and unconditional cash transfers

Assembled post-war disposable-income series (Finland 1966–2024; Estonia 1990–2024) and Gini trajectories from OECD, WID, and UNU-WIDER (WIID) • Diagnosed inclusive vs. top-heavy growth through mean–median divergence; traced Finland’s U-shaped Gini and Estonia’s post-transition spike to institutional drivers (progressive taxation, Nokia skill premium, privatisation, flat-tax reform) • Reconciled Soviet-era data-suppression gaps in the Estonian series

• Analysed a 35-year (1980–2015) panel of US beef exports via difference-in-differences and event-study OLS, controlling for EU GDP, US beef production, and the US–EU exchange rate • Specified event dummies for the 1989 ban, 1998 ruling, and 2009 settlement; found the ruling insignificant (p = 0.42) while the settlement raised export value by ≈88%, quantifying the “compliance gap”, with a 44% contraction in EU specialty imports under retaliation • Integrated multi-source trade data (USDA FAS, UN COMTRADE, Eurostat Comext, USITC, World Bank WDI); linked results to Bagwell & Staiger and Ederington & Ruta

• Replicated and audited Excel-computed market-model parameters (α, β) in R, reconciling both sets of estimates to the decimal across all 10 OMXH25 firms a direct reproducibility and code-review check • Estimated two-way (firm × year) fixed-effects panel regressions of Tobin’s Q on ROA, size, leverage (unbalanced 24-firm, 127-observation panel; plm), validated with F-tests, Hausman tests, firm-clustered robust SEs • Ran a market-model event study of profit warnings: AR, CAR, CAAR over a [−10, +10] window, with cross-sectional t-tests; delivered a cross-sectional OLS of CAR on firm size with HC3 robust SEs and residual diagnostics (Shapiro–Wilk) • Packaged as a reproducible R Markdown / RPubs pipeline regenerating every table and figure from raw data in one kni