LIGONoiseFloor
plain-language theorem explainer
Packages the three observables needed to test whether LIGO's noise floor carries a metric-aliasing imprint: reference PSD, reference frequency, and the measured spectral slope above Nyquist. Downstream falsifiers and consistency checks cite this bundle. As a plain structure there is no proof body; it is a data carrier for the RS spectral-shape prediction.
Claim. A LIGO noise-floor record is a triple $(S_{\mathrm{ref}}, f_{\mathrm{ref}}, \gamma)$ of real numbers: noise power spectral density at a reference frequency, that reference frequency in hertz, and the measured spectral slope above the Nyquist frequency. Recognition Science predicts a steep falloff above Nyquist from metric aliasing of the eight-tick cadence.
background
The LedgerHum module packages discrete-spacetime signatures that should appear as a low-level "hum" in precision timing and interferometry. The fundamental tick $\tau_0$ and the eight-tick period $\tau_8 = 8\tau_0$ set the Nyquist scale for metric sampling. Metric aliasing is the claim that continuous spacetime measurements fold discrete ledger updates into a characteristic noise floor.
LIGO's reported quantum noise floor is reinterpreted here as partly aliasing of that eight-tick structure. The predicted shape is flat below Nyquist, steep falloff above it, and phase structure locked to the eight-tick cadence (forcing-chain landmark T7). Sibling structures such as MetricAliasing and the pulsar residual signature supply the parallel timing-array channel.
This structure does not compute the floor; it only holds the three numbers an experiment must report so that the slope test ligoConsistentWithAliasing can run.
proof idea
No proof: the declaration is a structure with three real fields and field doc-strings. It is inhabited by supplying measured PSD, reference frequency, and spectral slope. Downstream, consistency is the predicate that the measured slope lies within absolute distance 1 of the RS target slope (steep falloff above Nyquist).
why it matters
Feeds the combined LedgerHum falsifier bundle, which requires (1) pulsar stacked residual at nanosecond scale, (2) LIGO spectral slope $f^{-4}$-class above Nyquist, and (3) cross-correlation of timing arrays at $\tau_8$. The status string ledgerHumStatus lists this structure among the minimal protocol items. The eight-tick octave (T7) is the framework landmark: if spacetime is discrete on that cadence, interferometric noise cannot be purely continuous quantum shot noise. Closing or failing the slope test is one of three independent routes to falsify or support the ledger-hum prediction.
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