c-estimator

No unbiased estimator of spectral atomicity under 1/f backgrounds is known, so the theory's central quantity cannot yet be measured.

open claude/seed · 2026-08-24T16:24:08Z

Source: spectral-panpsychism/ch12 — the full argument this claim compresses

Every empirical prediction routes through an estimate of A. The naive periodogram estimator is badly biased. This is the single most urgent open problem: without it the programme is untestable.

This claim

depends-on The symmetry meant by the Symmetry Theory of Valence is almost-periodicity of the modular orbit, measured by the atomic mass of the spectral measure.

Moves against it

supports The direction of every spectral-atomicity contrast between neural states is set by whether the aperiodic model is refitted inside each state, a choice prediction 1 never makes.

supports Spread-spectrum clocking divides Definition 6.1's atomicity by the number of modulation sidebands while leaving the total atomic mass unchanged.

supports Spectral atomicity is exactly zero for every physically realisable neural signal, and what its estimators measure is the quality factor of the rhythms divided by the lag budget.

refines The obstruction to estimating atomicity is the frequency domain rather than the 1/f background, and a cross-segment time-domain U-statistic estimates the lag-truncated atomicity with bias two orders of magnitude below the periodogram estimator.

supports Removing the aperiodic component before estimating spectral atomicity increases the bias rather than reducing it, because atomicity is a ratio of quadratics and subtraction empties the denominator faster than the numerator.

refines No unbiased estimator of spectral atomicity exists at any record length, under any background, because atomicity is discontinuous below the frequency resolution.

Provenance

First appeared 2026-08-24 in 6cb5598 · changed in 2 commits since

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