article = "https://physicslibrary.org/encyclopedia/PeriodicFunctionsHarmonicsAndWhyFourierSeriesExist.html"
article_alias = "FS01"
article_id = 1517
julia_version = "1.10.12"
reference_generator = "julia --startup-file=no --project=. harmonics-fourier-lab.jl"
reference_method = "complex exponential finite sums using cispi; analytic orthogonality RMS and integer gcd periods; independent PCM WAV synthesis"
browser_method = "real sine/cosine finite sums; vertical projections of complex harmonic vectors; D3 scales and Canvas2D"
audio_method = "Web Audio PeriodicWave with cosine real and sine imaginary coefficients, disableNormalization=true; DC excluded; gain bounded by sum of harmonic amplitudes"
renderer = "D3 7.9.0 and Lucide 0.468.0, bundled offline without runtime requests"
scope = "finite synthesis and Fourier previews, not coefficient derivation or a general convergence theorem"
phase_convention = "R_n cos(n omega_0 t - delta_n), A_n=R_n cos(delta_n), B_n=R_n sin(delta_n)"
period = "T_0 / gcd(nonzero harmonic numbers); coefficients below amplitude 1e-10 treated as zero for period classification; constants have no smallest positive period"
audio_limits = "user gesture required; sound initially off; volume up to 0.3 full scale divided by L1 harmonic-amplitude bound; components at or above 0.45 sampleRate omitted from sound only; visual clock slowed independently"
wav = "48000 Hz, mono signed 16-bit little-endian PCM, 2 seconds, linear 25 ms start/end fades; Julia generated square-wave reference"
reference_cases = 14
reference_samples = 1806
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julia_square_wav_sha256 = "6a8f8650328cfd1bd6e71f1510dab200b6387dfcc6de526efd85f58fdb5d51d8"
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audio_js_sha256 = "08e982dbe8dab97cc696ddf0b75c381106e11f3a03d8f2d14308082494e30219"
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pnpm_lock_yaml_sha256 = "74cf4af8287380f3f5fbbfced59dfd65b15abb38783c36911d88893cf49b97f7"
viewer_sha256 = "ddfb9f665a4e67de20596f9956e33a884ae4088a58f798e87502beb2b224c651"