Extended Data 3; SI: anatomy

Resolution and finite-size response

A bounded effective-dimension response predicts held-out damping observations more accurately than an equal-parameter unbroken power law on all 80 tested curves.

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When does the spectrum inherit the probability slope?

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A local power law does not describe the whole spectrum

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Calibration of uncertainty

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Methods and interpretation

Four fit anchors and three held-out damping values per curve. Continuous effective dimension is the primary endpoint; discrete threshold counts have distinct estimator coverage.

Procedure in the paper: Reproduce the exact reference spectra and estimator checks, fit each candidate response at the four frozen damping anchors, and score the three held-out settings with the recorded aggregation.

Code and data

Spectral response, model selection and coverageZIP

v0.1.0 · 101 KB · View source on GitHub ↗

Ten-model/eight-prompt response and dense-spectrum closure, plus six-model/12-prompt spectral selection and four-model/12-prompt exact-spectrum estimator coverage.

Stiff modes and inheritance controlsZIP

v0.1.0 · 57 KB · View source on GitHub ↗

The 24 reference spectra, three damping ratios, probability controls, five-model inheritance check and 45 generated read-out cases.

Spectral frame and tail controlsZIP

v0.1.0 · 431 KB · View source on GitHub ↗

Native and standardized frame certificates and the probability/readout/width tail factorial.

Spectral core and vocabulary coverageZIP

v0.1.0 · 68 KB · View source on GitHub ↗

Eight-model local-core/crossover study and four-model nested-support/full-vocabulary audit.

Each standalone package includes code, shared helpers, required small inputs and reference results, with setup and commands in its README. Model weights and public datasets are obtained separately where needed.

Download complete source (v0.1.0) for all experiments and the companion website.