One signature, three different questions

A signature that travels across constructions

A finite spectral-ratio profile can recur strongly across very different operators without picking out a single physical mechanism or a privileged set of constants. In the comparisons here, five reconstructed image graphs agree strongly with the minimum-normalized hydrogen profile. The embryo profile is a persistent exception. Kerr damping modes relate more moderately to the other views, and their incidence discriminates against some references much more strongly than against others.

The experiment asks three distinct questions:

1. Which finite profile shapes recur across the specified native constructions?
2. Which changes leave those profiles intact, and which conditional references discriminate the observed incidence?
3. Does the original library of window centers enjoy an exclusive simultaneous advantage over alternatives?

The first two questions yield positive results with explicit boundaries. The third fails its frozen criterion: the joint paired-library reference fraction is $0.2339$ against a maximum of $0.05$.

Fifteen fixed centers, including familiar irrational constants and rational fractions, define the measurement. The vector of window incidences is a structural signature: an operational descriptor of the chosen construction, spectrum, readout, and counting rule. It has no built-in claim to identify geometry, to classify unseen objects, or to serve as a universal physical fingerprint. Library specificity must be measured separately, against the same retained alternative libraries in every domain.

This edition builds the native operators and paired comparisons, shows both successful and unsuccessful controls, and derives the exact connection between all-pair value ratios and log-spectrum autocorrelation. Consecutive-gap statistics [1] and correlated covariance modeling [2] identify complementary tests and a route toward independent explanation. Neither a new density-model experiment nor a new gap-statistics experiment was completed for these data.