Minimal-Lifting Structural Completion of a p17/p29 Finite-Field Packet Endpoint

A Toy-Level Operator Readout Based on Exact-Neutral First Deformation and Relative Spectral Disturbance

抄録

We report a toy-level structural completion chain that connects a finite-field packet construction based on the p17/p29 framework to a minimal operator-level readout description.
The construction begins with the p17 packet backbone, which defines a discrete transition spectrum with a distinguished lowest-gap transition channel. We then impose a minimal lifting principle: the first nontrivial centered deformation must preserve one transition channel as exactly neutral. Within the resulting class of exact-neutral deformations, a relative spectral-disturbance criterion uniquely selects the deformation that preserves the lowest-gap structure of the original p17 spectrum.
The selected deformation defines a preferred structural axis associated with the p29 sector. This axis supports two complementary toy completions. On the mass side, it generates a residual correction channel that improves the downstream flavor endpoint. On the bosonic side, it produces a minimal neutral block structure with rank-one characteristics, providing a simple operator-level realization of the same underlying geometric direction.
The resulting framework establishes a toy-level connection between finite-field packet geometry and operator-based readout structures, illustrating how discrete packet data may be extended into a minimal spectral description.
The proposed construction should be interpreted as a structural completion principle rather than a physical derivation. It does not derive fermion masses, CKM or PMNS mixing, gauge bosons, gauge couplings, the Higgs sector, or the Standard Model Lagrangian. Instead, it provides a limited and reproducible toy framework for exploring how packet-level structures may propagate into higher-level operator descriptions.