Phase-Stabilised Periodicity Reconstructing the Eight-Second Signal Hypothesis

S This restricted Version 2 manuscript reconstructs and supersedes the active claim set of the 2025 paper Structural Stabilization of Periodicity: Reframing the Eight-Second Signal. The earlier concept of “structural stabilisation” is reformulated within the current phase-based framework: lawful phase organisation is treated as foundational, compatibility relations and stable basins constrain admissible organisation, observer geometry represents that organisation relationally, and periodicity is the recurrence registered within that geometry. The paper incorporates the completed MRCG-01–03 development programme as a limited mathematical precedent. Under a frozen toy-model construction and declared calibration assumptions, lawful phase organisation reproduces selected observer-level weak-field results, including a Newtonian potential, inverse-square acceleration, a first-order clock relation and orbital closure. These findings establish conditional mathematical possibility only. They do not constitute empirical validation, derive a complete spacetime theory, or demonstrate that gravity or any astronomical periodic signal physically originates in phase organisation. The original eight-second observational case is also re-audited. The retained 2025 paper does not securely identify its intended source, and its earlier claim that the signal exhibited no systematic spin-down is withdrawn. SGR 0526−66 is retained only as the strongest provisional reconstruction candidate, while conventional magnetar rotation and magnetospheric dynamics remain the required baseline explanation unless a distinct phase-based prediction survives controlled comparison. The manuscript establishes the restricted PSP-P01–PSP-P06 validation architecture, covering source provenance, conventional timing reconstruction, pulse-profile and harmonic relations, interruption and recovery behaviour, multiwavelength phase relations, held-out prediction and independent replication. This work remains restricted because source provenance, preregistered discriminatory testing, reproducibility and independent validation have not yet been completed. Its theoretical claims and test architecture remain open to revision, narrowing or rejection as part of the living Phase Compatibility research programme.