Domain: Humanities and Social Sciences — Economics
Target concept: Variance Expansion Feature: The fluctuation amplitude of the line chart gradually increases along the time axis.

Video generation prompt: Plot a single economic indicator's time series over time.

Evaluation guide:
Target concept: Variance expansion, a time-monotonic increase in the conditional variance of an economic time series, visually manifest as progressive widening of fluctuation amplitude along the time axis. Minimum mechanistic assumption: The underlying data-generating process evolves such that shocks produce larger deviations over time (e.g., due to feedback loops, reduced policy credibility, or network effects), not merely random volatility clustering. Expected phased storyline: (1) Start: Tight, low-amplitude oscillations around trend (e.g., ±0.2% swings in early 2000s inflation); (2) Transition: Gradual, smooth widening, mid-period shows moderate dispersion (±0.9%) with visible asymmetry and outlier frequency rise; (3) End: High-amplitude, irregular swings (±2.5%) with frequent extreme excursions; all phases must be simultaneously visible and quantitatively comparable on a single linear-scale chart. Visibility constraints: Must be legible in 10-second silent video; no narration or cursor; amplitude growth must be self-evident via geometry (peak-to-trough distance scaling) without annotation, though optional minimal labels may reinforce causality. Perspective: Frontal, static camera view; no zoom/pan; chart fills ≥70% of frame.

Manual:
I. Basic Demonstration Information
Demonstration Title: Variance Expansion Feature in Economic Time Series Demonstration
Subject: Humanities and Social Sciences - Economics - Time Series Analysis
Demonstration Purpose: To visually illustrate the "Variance Expansion Feature" — i.e., the gradual increase in fluctuation amplitude of an economic indicator’s time series over time — enabling recognition of evolving dispersion patterns critical for risk modeling, policy evaluation, and forecasting.

II. Demonstration Carrier/Equipment
Core Carrier: Dynamic line chart of a real-world economic time series exhibiting verified variance expansion (e.g., USD/EUR exchange rate volatility, emerging-market stock index returns, or sovereign bond yield spreads).
Auxiliary Equipment: Clean vector-rendered chart interface with fixed aspect ratio (4:3), linear y-axis, chronologically ordered x-axis (≥10 labeled time points, e.g., quarterly from 2000–2023), and optional subtle amplitude envelope (±1 rolling std dev) that widens visibly left-to-right.

III. Demonstration Content Description
Layout: Chart centered on screen; x-axis horizontal bottom, y-axis vertical left; title above chart reads "Evolving Variance: [Indicator Name] (2000–2023)"; no extraneous UI elements (no legends, toolbars, or animations unrelated to amplitude).
State Control: Line draws sequentially left-to-right over 8 seconds; amplitude envelope (if present) expands smoothly and continuously in sync with time progression — no sudden jumps, resets, or retroactive adjustments.
Comparison Baseline: Early segment (first 25% of time axis) shows narrow, tightly clustered oscillations (±0.3%); late segment (last 25%) shows wide, dispersed swings (±2.1%), with monotonic, visually verifiable growth in peak-to-trough distance across the full axis.

IV. Observation of Core Phenomena
Expected Phenomenon: Fluctuation amplitude (vertical spread of line around its local mean) increases steadily from left (low dispersion) to right (high dispersion); this is observable via increasing peak-to-trough distances, widening envelope, or denser extreme outliers in later periods.
Expected Screen: Static, high-resolution 2D line chart — no human actors, no narration, no voiceover; only chart, axes, labels, and optionally a minimal caption: "Variance Expansion: Dispersion Grows Over Time".
Visual Verification Features: (1) Chronological x-axis with unbroken, ascending labels; (2) Monotonic increase in vertical spread — quantifiable as >150% growth in average peak-to-trough range from first to last quartile; (3) No reversal, plateau, or collapse of amplitude anywhere; (4) All visual elements remain spatially fixed and temporally coherent across the 10-second clip.

V. Summary of Key Knowledge Points and Principles
Core Concept Definition: Variance expansion describes a non-stationary time series property where conditional variance σ²(t) increases deterministically or stochastically with time t — a hallmark of structural change, rising uncertainty, or regime shifts in economics.
Economic Significance: Signals growing market fragility (e.g., post-deregulation finance), policy regime transitions (e.g., inflation targeting → flexible inflation targeting), or external shock accumulation (e.g., climate risk pricing). Not mere noise — it reflects evolving systemic risk.
Further Knowledge: Distinguish from heteroskedasticity (which may be conditional on covariates, not time); variance expansion is time-driven and often linked to Kuznets-style structural transformations or Minskyan financial instability cycles.

Prompt Grounding rubric:
level_1: No line chart of a time series appears at all, e.g., only a bar chart, a static image, or blank axes are shown; or, if a line is present, the x-axis has no time labels (no years/quarters/dates) and no economic indicator name appears anywhere on the chart.
level_2: A single line chart is shown with some indication of time on the x-axis and a value on the y-axis, but the labeling is too vague to identify what is being plotted (e.g., axis titled just 'data' or 'value' with no indicator name, or time labels too sparse/illegible to read the progression).
level_3: A single line chart displays one economic indicator's values against a clearly labeled time axis (e.g., '1990–2024') and a named y-axis (e.g., 'Unemployment Rate (%)'), rendered as one continuous, plottable series from start to end of the clip, though axis tick spacing or labeling has minor rough edges (e.g., a skipped year, slightly crowded labels).
level_4: A clean, single-series line chart shows an explicitly named, plausible economic indicator (e.g., 'Stock Market Volatility Index') with at least five evenly spaced, legible time labels on the x-axis and a correctly named y-axis unit; the chart occupies the frame clearly with no missing segments of the line, and only a very minor cosmetic flaw is present (e.g., one truncated label).
level_5: The chart is fully and unambiguously labeled: chronological, evenly spaced x-axis ticks spanning the full period, a y-axis labeled with a specific, real economic indicator and its unit (e.g., 'Exchange Rate Volatility (σ)'), and a single unbroken line spanning the entire time axis with no gaps, mislabeling, or rendering artifacts of any kind.

Scientific and Causal Correctness rubric:
level_1: The chart's fluctuation pattern actively contradicts variance expansion: e.g., the swings are equally sized throughout, they visibly shrink over time, or they jump from small to large in one abrupt step rather than growing gradually; there is no visible sense in which dispersion grows as time progresses.
level_2: Some widening of the swings is visible, but it does not track with time in a sensible way: e.g., the widest swings appear in the middle of the series rather than at the end, or wide and narrow segments alternate without any overall left-to-right trend.
level_3: Looking left to right, the line's peak-to-trough swings are visibly narrow near the start and visibly wider near the end, with the widening trend holding overall even if a little uneven segment-to-segment; no annotations are needed to read this trend.
level_4: The widening of the swings is smooth and sustained across nearly the whole timeline: an early stretch of tight, small swings gives way to a later stretch of clearly larger swings, with no long flat stretch or reversal breaking the trend; if the chart happens to include event labels or shaded periods, they are optional extras and are not required to reach this level.
level_5: The widening is monotonic and continuous from the first segment of the series to the last, with the largest swings occurring at the very end and the smallest at the very start, and no point where the swings shrink back down; any historical annotations present are a bonus only; their absence does not lower this score as long as the amplitude growth itself is clean and uninterrupted.

Spatiotemporal Consistency rubric:
level_1: The chart resets or redraws from scratch partway through, the time axis jumps backward or skips out of order (e.g., a later year appears before an earlier one), or the axes and labels disappear and reappear disconnected from the rest of the chart; the frame-to-frame layout is not coherent.
level_2: The chart's time axis keeps moving forward, but the spacing between tick labels is visibly uneven from one part of the axis to another, the line appears to wobble or shake in ways unrelated to the data, or the chart's position/size shifts noticeably between frames.
level_3: The chart's overall position, axis layout, and line all read as continuous and forward-moving, but there is one small blemish a careful viewer would notice, e.g., two tick labels briefly overlapping, the line's stroke width flickering for a moment, or gridlines blinking on and off once.
level_4: The chart stays in the same place and size throughout the clip, the time-axis ticks stay evenly spaced and fully visible the entire time, and the line itself renders with a consistent, smooth stroke with no visible warping, tearing, or momentary disappearance of any segment.
level_5: The whole clip reads as one seamless, stable rendering: the chart's frame, axes, and tick labels never drift, resize, or relocate at any point; the line is drawn (or revealed) with smooth, consistent motion and no stutter, flicker, or double-image artifacts; whatever visual style the line uses stays uniform from the first frame to the last.