Sinusoidal History

An interactive editorial chart-room overlaying ten named long-wave cycles of history — Khaldun, Kondratiev, Huntington, Schlesinger Jr., Perez, Turchin (secular and fathers-and-sons), Dalio, Strauss-Howe, Modelski — on a shared 1600–2050 time axis. Each cycle is drawn as one period of a unit-amplitude sinusoid centred on a single explicitly documented reference peak, stopping at the present, and nine of the ten are paired with a real long-run empirical data series for stress-testing.

Live: https://sinusoidalhistory.com

Built by David Kooi at Skylark Creations, April 2026, after a phone-call conversation with Mark R about whether you could plot Khaldun's five stages, Huntington's 60-year cycles, and the rest as actual sine waves on one axis and see where they net out. The full build journal — what was AI, what was human, where it got hard — lives at docs/how-this-was-made.md.

What it is (and isn't)

It is a side-by-side comparison tool for seeing where different long-wave theorists agree or disagree, and for stress-testing each theory against a single empirical proxy. Currently shows ten cycles; the eighth (Schlesinger Jr.'s ~30-year liberal/conservative cycle) was added after initial release.

It is not a forecasting tool. Every cycle here is contested in different ways. The "reference peak" for each cycle is itself a judgment call; pick a different anchor and the curve shifts. The calibration drawer exists to make that visible. See /methods for the data-side caveats and /about for the intellectual-honesty disclaimer.

The headline editorial point: nine of the ten reference peaks fall between 1945 and 2020, and that is a selection effect, not convergence — theorists writing today anchor their forecasts to the world they live in, and we read them precisely because their climaxes land in our era. The site says this on the home page, on /about, and on /colophon.

Status

2026-10-21 (I-061): each cycle is now drawn as one period around its reference peak, cut at the present, instead of a wave repeating across 1600–2050, and no page says where the present sits on a cycle. Readers had taken the repeat crests near the present as the site saying the cycles peak now. The yearly /state/<year> pages and /api/v1/state were retired (/state/* redirects to /cycles; the API answers 410); the frozen public/data/state-2026.csv stays as published. Sections below describe the site as it was at each phase.

Phase 15 shipped (August 2026): the spectral verdict. Every cycle–series pairing now carries a pre-registered statistical answer to "does this series contain significant power at the theory's exact stated period?" — harmonic regression at exactly 1/P against an AR(1)/AR(2) red-noise null, parametric bootstrap, Holm correction, all frozen in a committed manifest before any results. The headline is the finding: 0 of the 9 paired constructions reach the 3.0-full-periods eligibility gate — every record is too short to test its claim, so no pairing gets a p-value at all. Per-cycle figures and a machine-readable /data/spectral/verdicts.json ship with the site; protocol on /methods, reproducer at scripts/spectral_verdict.py.

Phase 14 shipped (August 2026): the roster grew from eight to ten cycles. Modelski's long cycle of world leadership (plotted at 110y, the midpoint of his stated 100–120 range, anchor 1945) paired with a new leading-economy share-of-world-GDP series (Maddison, CC BY); Turchin's fathers-and-sons ~50-year cycle (peaks 1870/1920/1970 in his own words, unpaired this round); and Perez finally gained a paired series — a HATCH technology-diffusion composite (Zenodo, CC BY 4.0) whose honest result is that it shows no local peak at 2000. /cycles now also publishes a "considered and excluded" list (Goldstein, Arrighi, Sornette, Namenwirth/Weber, and others, with verified citations for why each fails the inclusion bar) and a queued note for Klingberg. Same phase: a four-lens adversarial review fix wave (see CHANGELOG), Zenodo archival with a DOI, and a Kondratiev periodicity caveat.

Phase 13 shipped (August 2026): the annual reading at /state/<year> (starting with /state/2026) — a dated, citable permalink recording where each cycle sits that year and the next peak/trough each construction implies — plus a v1 JSON API: /api/v1/cycles and /api/v1/series serve the canonical definition files live, and /api/v1/state?year= returns the computed reading for any year. All CORS-open. Everything on these surfaces is derived from period_years + reference_peak_year via the chart's own cosine; no year-phase prose is authored by hand.

Phase 12 shipped (August 2026): eight static per-cycle routes at /cycles/<slug> plus a /cycles index. Until then the cycles existed only as query-param states of /, so the reference_peak_rationale prose — the most substantive per-cycle text in the project — was invisible to search and answer engines. Each page carries period, reference peak, the full calibration rationale, caveat, sourcing, and the paired series with provenance; plus a per-cycle OG card, JSON-LD (WebPage / BreadcrumbList / DefinedTerm / Dataset), and sitemap + llms.txt coverage. No new prose was authored — all text is reused from cycles.json, and the peak/trough years shown are derived from period + reference peak rather than asserted.

Phase 11 shipped (April 2026): round-4 fact-check verdicts folded in. Highest-risk fix was the Strauss-Howe rationale prose, which incorrectly stated 2020 was a trough — at period 84 and peak 1955, the trough is at 1997 and 2020 sits on the rising arm of the sinusoid at cos ≈ +0.15. Five other items also corrected; see docs/fact-check-2026-04-26-round-4.md.

Phase 10 shipped earlier (April 2026): Schlesinger Jr.'s ~30-year liberal/conservative cycle was added as an eighth cycle, paired with Stimson's Policy Mood index (1952–2024). Mark suggested it after seeing the original seven.

Phase 8 shipped earlier in April 2026. The project went through four rounds of external fact-checking after the initial release and the data and prose were materially revised — see the audit archive in docs/ for the prompts and reports. Notable corrections during the audit:

• Strauss-Howe peak re-anchored from 2008 (Crisis onset) to 1955 (post-WWII High peak), since the Crisis is a trough in this construction, not a peak.
• Dalio peak moved from 1945 to 1950 to match his own stated peak year for US power; period revised from 85y to 75y (Dalio states long-term debt cycles run about 50–75 years; 75 is the upper end of his range, this project's selection rather than a number he asserts).
• Perez confidence tier downgraded from "quantitative" to "empirical-contested" (her work is qualitative Schumpeterian periodization, not statistical fit).
• Maddison US/world GDP series rebuilt: regional-aggregate filter was missing the (Maddison) suffix in OWID's export, doubling the world sum on benchmark years; per-country forward-fill added for sparse-coverage years. Verifier: scripts/build_us_world_gdp_share.py.
• Fernald TFP series rebuilt from dtfp_util (utilization-adjusted) instead of dtfp (raw) to match the documented description. Verifier: scripts/verify_tfp.py.
• WID license corrected from CC BY-NC-SA 4.0 (round-1 misread) back to CC BY 4.0 (verified against OWID's authoritative indicator metadata).
• Convergence note: "publication bias" → "selection effect."
• Strauss-Howe rationale rewrite (round 4): the chart-vs-prose contradiction about 2020 being a "trough" was caught and rewritten — 2020 sits on the rising arm at cos ≈ +0.15 (trough at 1997, next peak at 2039).
• Pearson "linearity" → "phase sensitivity" (round 4): the methods-page bullet now correctly explains that for two same-period sinusoids, Pearson r = cos(Δφ).
• TFP display range corrected to 1948–present (round 4); the 1948 and 1949 endpoints are clipped-window edge artifacts and methods now says so.
• Maddison forward-fill bias surfaced (round 4): the rebuild forward-fills but does not back-fill, which biases US share upward pre-1950.
• Dalio anchor-and-period mismatch acknowledged (round 4): the 1950 anchor is from the 250-year empire-score chart while the 75-year period is the long-term debt cycle.
• WID source field disentangled (round 4): pre-1913 decadal points are WID interpolations, not Saez–Zucman 2016.
• Project Mars 2010 = 0 explained (round 4) as a definitional artifact.
• Turchin parenthetical "(≈1780 → 1930 → 2080)" replaced (internal sweep) — those years all evaluate to cos ≈ −0.81 (near trough) in the actual sinusoid, not peaks; rationale rewritten to show the real alignment (sinusoid prior peak 1870 ≈ Civil War, but ~90y off from the Revolution).

The site is post-fact-check and treats Phase 11 as the reference state. Older snapshots are superseded.

Stack

• Next.js 16 (app router) + TypeScript strict mode
• Tailwind CSS v4 + shadcn/ui (Tabs, Slider, Toggle, Tooltip, ScrollArea) on Radix UI primitives
• D3 for the viz (d3-scale, d3-shape, d3-brush, d3-selection)
• Fraunces variable serif for editorial typography
• papaparse for CSV ingestion
• nuqs for URL-state
• html-to-image for poster PNG export
• Vitest for unit tests
• No database, no auth, no user input — read-only public site

Local run

npm install
npm run dev

Then open http://localhost:3000.

Other scripts

npm run test        # vitest — run math + cross-ref tests once
npm run test:watch  # vitest in watch mode
npm run typecheck   # tsc --noEmit
npm run lint        # eslint
npm run build       # next build (production)
npm start           # run the built app

Data-rebuild scripts

python scripts/build_us_world_gdp_share.py     # Maddison rebuild
python scripts/build_leading_power_gdp_share.py # Maddison leading-economy rebuild
python scripts/build_perez_tech_diffusion.py   # HATCH tech-diffusion rebuild
python scripts/build_us_tfp_growth.py          # Fernald TFP rebuild
python scripts/build_stimson_policy_mood.py    # Stimson Policy Mood rebuild
python scripts/verify_tfp.py                   # diagnostic — verify TFP CSV
python scripts/audit_cycle_rationales.py       # cos-math audit on every cycle's rationale

audit_cycle_rationales.py is the cosine-math sanity check that should be re-run after any change to a cycle's reference_peak_rationale or before adding a new cycle. It prints, for every year mentioned in any rationale, whether the sinusoid is at a peak, trough, or in between — so you can read the prose alongside the numbers and catch the kind of contradiction Round 4 caught for Strauss-Howe (prose said 2020 was a trough; cos says +0.15 rising arm).

These are reproducible and self-documenting; each downloads from the upstream source, applies the documented transforms, and writes to public/data/. They do not run automatically — the CSVs are committed for stability and provenance.

Data model

Cycles — src/data/cycles.json

field	meaning
id	Short stable slug.
name	Display name shown in the legend and tooltips.
short_description	One-sentence summary of the cycle's claim.
period_years	Full wavelength, in years.
reference_peak_year	Year where the curve is at its maximum.
reference_peak_rationale	Why this year was chosen — should explicitly own editorial choices.
amplitude_normalized	Relative amplitude, 1.0 by convention.
source	Primary-source citation.
confidence_level	"narrative", "empirical-contested", "empirical", or "quantitative".
color	Hex color for the curve and legend swatch.
caveat	Optional inline caveat surfaced in the focused-facet view.

Data series — src/data/series.json + public/data/*.csv

Each empirical series is a JSON object in series.json:

field	meaning
id	Short stable slug.
name	Display name.
legend_short	Compact label used in inline facet legends and the OG card.
short_description	What the series measures.
source	Short citation.
source_url	Link back to the original source page.
license	License string — one of: CC BY 4.0, CC BY-SA 4.0, freely-available variants.
data_file	Path to the CSV, relative to public/.
year_column	Column in the CSV containing the year.
value_column	Column in the CSV containing the value.
value_units	Human-readable unit string, shown in tooltips.
color	Hex color for the data line and legend swatch.
associated_cycle_id	Which cycle this series is meant to stress-test.
association_note	One-sentence rationale for the pairing.
transform	Optional value transform. Currently only log1p.

The CSV files live in public/data/. Each has a sibling .source.md documenting source URL, retrieval date, filtering or transformation, and honest caveats. Provenance files are served statically and linked from /methods. Crossover .csv and .source.md are CORS-enabled so external agents can fetch them directly.

How to add a data series

1. Download the raw CSV from the source, save to public/data/<slug>.csv.
2. Trim to only the columns you need (year + value).
3. Write public/data/<slug>.source.md documenting source URL, retrieval date, any transformation, and caveats.
4. Add an object to src/data/series.json pointing at the file.
5. Add an associated_cycle_id matching an existing cycle.
6. Reload; the series appears in the Data legend.

If the transform is non-trivial (rolling average, aggregation, log1p, etc.), write a Python rebuild script in scripts/build_<slug>.py so the derivation is reproducible. The Maddison and Fernald scripts are working examples.

Math

Cycle value at year y:

value(y) = amplitude * cos(2π * (y - reference_peak_year) / period)

The site draws only y in one period around the reference peak, cut at the current year (drawnPeriod / sampleDrawnPeriod in src/lib/cycleMath.ts), and labels no year's phase (the phase-band labels were removed 2026-10-21). Data series are rescaled to [-1, 1] using their own min/max over the visible window. The calibration drawer reports a Pearson correlation and explicitly does not report a p-value (Pearson significance tests are anti-conservative on autocorrelated time series). See /methods for the full story on normalization, Pearson, and why spectral analysis is deferred.

Project structure

public/
  data/                       CSV files + .source.md provenance (CORS-enabled)
  llms.txt                    LLM-discoverable index of all content
  about.md, methods.md,       Plain-markdown mirrors of the prose pages
    colophon.md               (CORS-enabled, text/markdown)
src/
  app/
    (app)/                    Chromed routes (header + footer):
      layout.tsx              Site shell, nav, footer
      page.tsx                Home (interactive overlay)
      cycles/page.tsx         Index of the ten cycles, by ascending period
      cycles/[id]/page.tsx    One static page per cycle (10 prerendered)
      state/[year]/page.tsx   The annual reading (2026+), a citable permalink
      about/page.tsx          The argument and disclaimer
      methods/page.tsx        Data provenance and methodology
      colophon/page.tsx       Note from the maker
    embed/                    Chromeless iframe-safe routes
    poster/                   Print broadside with PNG download
    api/v1/                   JSON API: cycles, series, state?year= (CORS *)
    og/                       Dynamic 1200×630 OpenGraph card
    sitemap.ts, robots.ts     SEO/crawler endpoints
  components/
    Viz.tsx                   Tabs, range, focus state
    NowSummaryPanel.tsx       "State of the cycles" masthead
    FacetView.tsx             Stack of CycleFacet rows
    CycleFacet.tsx            One cycle's row + chart + legend; expanded, it
                              carries the period + peak sliders and Pearson r
                              (also what the Calibrate tab renders)
    FacetTimeAxis.tsx         Shared bottom axis
    CycleOverlay.tsx          Single-SVG overlay (Overlay tab)
    TimeRangeBrush.tsx        D3 brush + preset buttons
    ConvergenceNote.tsx       "Selection effect" call-out
    Poster.tsx                Print broadside
    ui/                       shadcn primitives
  data/
    cycles.json               10 cycle definitions
    cycles.ts                 (cross-ref validation)
    series.json               9 data-series definitions
    series.ts                 (cross-ref validation)
    series.test.ts
    types.ts
  lib/
    cycleMath.ts              sineAtYear, phasePosition, phasePositionLabel
    stateOfCycles.ts          The annual reading + next-extrema derivation
    cycleMath.test.ts
    seriesMath.ts             normalizeSeries, pearsonCorrelation
    seriesMath.test.ts
    hooks.ts                  useTimeScale, useVisibleData, etc.
    useCsvSeries.ts           React hook to fetch + parse a CSV
    utils.ts                  cn() — tailwind classname merger
docs/
  how-this-was-made.md        Build journal — paired with /colophon
  fact-check-prompt.md        Round-1 audit prompt
  fact-check-2026-04-25.md    Round-1 audit report
  fact-check-prompt-round-2.md
  fact-check-2026-04-25-round-2.md
  fact-check-prompt-round-3-self-contained.md
  fact-check-2026-04-25-round-3-blocked.md
scripts/
  build_us_world_gdp_share.py Reproducible Maddison rebuild
  build_us_tfp_growth.py      Reproducible Fernald TFP rebuild
  verify_tfp.py               TFP derivation verifier
  inspect.mjs                 Playwright capture script (dev only)
render.yaml                   Render Web Service blueprint
components.json               shadcn config
LICENSE                       MIT (code) — data licenses per series.json
CITATION.cff                  Citation metadata

Sharing

The load-bearing UI state is in the URL — tab, focused cycle, time range, and per-cycle calibration overrides. (A few ephemeral toggles — overlay series visibility, the pinned year, event-marker visibility — are local state and reset on reload.) ?tab=facets&focus=huntington&range=1900-2050&peak.huntington=1968 opens the app with Huntington focused at peak 1968, zoomed to 1900+. Send that link and the recipient sees what you see.

For a poster: /poster reads the same calibration overrides from the URL, renders them as a 1200×800 design canvas, and offers a PNG download.

For embeds: /embed/docs has copy-paste iframe snippets. All /embed/* routes are cross-origin iframeable via Content-Security-Policy: frame-ancestors * (configured in next.config.ts).

For agents and notebooks: /llms.txt indexes everything. Prose pages are mirrored as plain markdown at /about.md, /methods.md, /colophon.md with permissive CORS. Data CSVs and provenance markdown are served from /data/ with CORS open for cross-origin fetches. Two JSON endpoints (no auth, CORS *): /api/v1/cycles and /api/v1/series are the canonical definition files served live. /api/v1/state was retired 2026-10-21 and answers 410 Gone.

The yearly /state/<year> readings were retired the same day and redirect to /cycles. The frozen 2026 edition stays as published at /data/state-2026.csv, marked retired in its provenance file.

For a single theory: /cycles/<slug> is the static, indexable page for one cycle — period, reference peak, calibration rationale, caveat, sourcing, the paired series with provenance links, and a deep link back into the chart at /?focus=<id>. Slugs are hyphenated (/cycles/strauss-howe) even though cycle ids use underscores.

Deploying

See DEPLOY.md for the full Render + Squarespace DNS walkthrough. Short version: Render Blueprint reads render.yaml, you add a sinusoidal-history CNAME at Squarespace pointing at the Render hostname, done. Cert is automatic.

Citing

If you reference this project in writing, please cite:

Kooi, D. (2026). Sinusoidal History. Skylark Creations. https://sinusoidalhistory.com DOI: 10.5281/zenodo.21998618

Tagged releases are archived on Zenodo; the DOI above resolves to the latest archived version (v1.1.0 is the first archived release).

A CITATION.cff is included for tools that read it (Zenodo, GitHub's "Cite this repository" widget, etc.).

For citing the underlying data, see each series' source URL in src/data/series.json or the per-source .source.md files in public/data/. Cycle theories cite their named original authors as listed in src/data/cycles.json.

Non-goals (still deferred)

• No spectral analysis (FFT, wavelets, Lomb-Scargle) — flagged on /methods as future work; the simple sinusoid is part of the editorial honesty.
• No backend or saved server-side configurations — URL state is the share mechanism.
• No real-time data updates — annual snapshots are fine; the rebuild scripts are explicit and reproducible.
• No user annotations — the curated 14-event historical layer is it.
• No internationalization.

Contact

Bugs, corrections, or fits you can't defend: open an issue on GitHub or reach out via Skylark Creations.