Protocol-Relative Quotient Observability in Adaptive Oscillator Networks

This record accompanies the paper “Protocol-Relative Quotient Observability: Temporal, Spatial, and Active Refinement of Hidden Winding in Adaptive Oscillator Networks”. The deposit contains the final author manuscript and supplementary material in PDF and editable DOCX formats, together with a README, a SHA-256 checksum manifest, and five reproducibility archives covering the primary reconstruction, independent-seed replication, distributed observation, active intervention, and phase-noise sensitivity analyses. The paper develops protocol-relative quotient observability in a noisy nearest-neighbour oscillator ring with history-dependent couplings. An exact clean-ring calculation identifies the relaxation mode selected by the complex order parameter. Numerical experiments then demonstrate that a finite scalar temporal protocol can distinguish some winding sectors while leaving others operationally aliased; sparse distributed observations refine the residual quotient; and a structurally aligned intervention reveals distinctions that a broadband perturbation does not reliably disclose. A prospectively frozen sensitivity test examines whether the principal findings survive a change in phase-noise amplitude. The results support a graded account of observability in which temporal depth, spatial distribution and active intervention define different statistical experiments and different operational quotients. The claims are protocol-, decoder- and finite-sample-relative and do not imply complete state reconstruction or parameter invariance. The accompanying files are supplied to support independent checking, computational reproduction and journal peer review.