Neutrinos as Informational Hyper-Elements: Flavor-Entropy Mapping and Weak-Correlation Scales in the Hyper-Element System

Neutrinos are recast as informational hyper‑elements within the Hyper‑Element System (HES), a three‑axis framework spanned by Binding Energy (BE), Correlation Energy (Ce), and Informational Symmetry (IS). We formalize weak‑interaction correlations during propagation via the matter potential and introduce a normalized flavor‑entropy, IS_hat(L/E), as an operational measure of the informational content carried and transformed by oscillations. In this representation neutrinos occupy a distinctive locus—BE ≈ 0, Ce ≈ 0, IS > 0—explaining, in a single geometrical placement, their lack of nuclear binding, extreme transparency, and oscillation‑driven state evolution. We quantify the weak‑correlation scale (|V|/E) to be ~10^(-18)–10^(-23) across realistic environments, demonstrate how the normalized flavor‑entropy maps onto observable flavor distributions, and outline anomaly‑detection tools (e.g., Mahalanobis distance and kernel density estimation) that separate neutrinos from dense nuclear clusters in BE–Ce space. The framework yields testable predictions: (i) entropy‑versus‑L/E informational tomography with medium‑baseline reactors (e.g., JUNO) to pin down mass ordering and calibrate IS_hat(L/E); (ii) time‑domain probes using supernova bursts (e.g., SNEWS 2.0) to track entropy transport; and (iii) complementarity with neutrinoless double‑beta searches (e.g., nEXO) for assessing the Majorana paradigm. Beyond unifying known phenomenology, HES is predictive: it delineates a nearby region for prospective low‑BE, low‑Ce, finite‑IS states (e.g., sterile neutrinos) and motivates viewing neutrinos as robust, decoherence‑resistant channels for concurrent transport of energy and information across otherwise opaque media.