Shape, Phase, and Forcing in Saturn's Southern Decagon: An Integrated Inference and External-Testing Protocol

Résumé fourni par la source

This deposit contains an analytical methods paper and its companion reproducibility package for studying Saturn’s southern wave-number-10 pattern. It organizes five connected questions about spatial spectrum, physical wavelength, vertical structure, vortex interaction, and persistence into one observation and inference problem. Its primary claim is that mechanism discrimination requires identifiable signal content that admitted nuisance freedoms and competing models cannot absorb. A shared observation model separates atmospheric structure, radiative visibility, sampling, navigation, extracted features, and mechanism claims. Conditional mathematical results establish nuisance-aware estimability, sampling-induced mode mixing, collective phase motion without neighboring spatial modes, rotation-quotient shape comparison with explicit bounds, covariance-weighted vertex decomposition, common-navigation degeneracy, perturbative crest displacement, and vertex-mode aliasing. Deterministic summaries extracted from the same images are not treated as independent confirmations. The vortex-clock analysis supplies a second identifiability boundary. Under a specified fundamental encounter model, the source-reported approximately 32-day modulation requires a relative angular rate of approximately 1.125 degrees per day. This is a conditional requirement, not a measured vortex rate. Under uniform relative drift and freely fitted response phase, the vortex-clock model has the same prediction family as a free sinusoid. An equal-covariance Gaussian projection result quantifies the component of a specified candidate prediction that the declared null model cannot reproduce, directing observation design toward genuinely discriminating information. The companion archive includes the compiled manuscript, complete XeLaTeX source, bibliography and citation files, Python implementation, 32 synthetic and numerical tests, three CSV adapter examples, data dictionaries, an attributed source-value register, separately derived equation evaluations, a claim-to-test matrix, execution receipts, provenance records, and checksum inventories. All 32 scientific tests and all three command-line examples passed in the recorded preparation run. The observational-run template is deliberately not a completed or frozen empirical analysis. The deposit contains no newly acquired Saturn observations, fitted physical vortex coupling, completed atmospheric simulation, or empirical confirmation of a mechanism. Numerical verification concerns the supplied implementation and does not constitute independent scientific replication. The discovery observations and source simulations remain attributed to Sánchez-Lavega and collaborators. Comprehensive review of the discovery article and supplements, validated observational extraction, and real-data testing remain open burdens. Within Structura Reditus, this work is a local Tier-2 methodological witness under Summa Reditus, Architecture Freeze v1.0, the completed canon-facing treatise. It supports RCFT candidate development and ULRC clarification without redefining the Tier-1 kernel, claiming an adopted UMCP evaluation, or granting canonical return credit or welded continuity. Manuscript, original documentation, original synthetic fixtures, and the original compilation of data registers are licensed under CC BY 4.0. Python source, build and reproduction scripts, and tests are licensed under MIT. External sources and preserved historical artifacts retain their applicable rights and notices.