Energy Filament Theory · EFT Full KB
Alignment Between Satellite Co-rotation Planes and the Host Filament Axis
V33-33.17 · F 证据节 / 显影节 ·
33.17 turns satellite-plane debates into a skeleton-first orientation audit: for hosts with preregistered significant co-rotating planes, the plane major axis a_plane must show a small-angle bias to the local filament axis f_host, the bias must strengthen with filament strength and node proximity, and it must co-vary with f_corot; under V08/V09-compatible retain, this remains a local node-inheritance direction ledger rather than a global small-scale-structure verdict.
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Keywords: satellite co-rotation planes, host filament axis, a_plane, f_host, ϕ, f_align, f_corot, p_plane, filament strength, membership contamination, footprint control, retain boundary
Section knowledge units
thesis
33.17 says that a co-rotating satellite plane is not just a local geometric curiosity. If the host lives inside a stable filament direction field, then the plane’s major axis should not choose an arbitrary three-dimensional orientation. It should show a reproducible small-angle preference relative to the host filament axis, and the preference should strengthen where the filament is stronger and the host sits closer to a node. The chapter therefore does not ask only whether satellite planes exist. It asks whether their orientation and their co-rotation quality belong to the same direction-field ledger. Under the V33 guardrail that makes the section a retain-level local orientation card, not a chapter that settles every satellite-plane or small-scale-structure dispute.
mechanism
The measurement package is intentionally geometric and kinematic at the same time. For each host the chapter builds a membership catalog with positions, distances, and velocities where available. It fits a best-fit plane, records its normal n_plane and major in-plane axis a_plane, and reports thickness and scale summaries such as h_rms and R_rms. Co-rotation consistency is then quantified either from full angular-momentum sign agreement or from a frozen projected rule when only line-of-sight velocities exist, producing f_corot and its permutation significance. On the structure side the host is assigned a local filament-axis vector f_host and a filament-strength indicator S_fil. The comparison observable is the acute angle ϕ between a_plane and f_host, together with an aligned fraction f_align under a preregistered threshold ϕ0.
mechanism
Execution is arranged to stop the skeleton and the plane from leaking into each other. The filament direction field is built and frozen first, with one algorithm, one smoothing scale, one redshift-slice thickness, and one environment window. Membership rules are then frozen separately, with explicit completeness and contamination reporting and no permission to retune thresholds after seeing alignment scores. Only after that does the chapter test plane significance: each host is compared to isotropic controls that preserve radial distributions and selection masks, yielding a plane-significance score p_plane. Hosts must pass that gate before entering the alignment court. Filament directions, plane parameters, and adjudication are kept in separate pipelines, with a held-out host set or sky region reserved for final confirmation.
evidence
The null suite attacks every obvious way to fake alignment. Filament-direction permutation rotates or relabels the host filament axis while keeping host positions fixed; under that null, ϕ should become near-uniform and f_align should return to random expectations. Satellite phase randomization keeps each host’s radial profile and mask while scrambling angular positions, so both plane significance and plane–filament alignment should weaken. Membership permutation replaces or reweights satellites with background pseudo-members, and significant co-rotation plus alignment should disappear. Finally, void-matched and footprint/completeness controls ask whether the signal collapses in low-filament-strength environments and whether it follows survey geometry instead of physical structure. Only when those artifact routes break can the alignment claim remain in court.
boundary
The pass line again has three linked parts. First, among plane-significant hosts, the alignment-angle distribution must be biased toward small values and the aligned fraction must exceed both filament-axis permutation baselines and isotropic expectations, including in the holdout set. Second, that alignment must strengthen monotonically with filament strength or decreasing node distance, with void-tier hosts materially weaker than filament and node hosts. Third, stronger alignment must travel with stronger co-rotation consistency after controlling for host mass, redshift, and satellite count. Failure is declared if orientations stay consistent with uniformity, if the signal disappears once completeness and contamination are controlled, or if planes remain significant but unrelated to filament directions. The main systematics are membership contamination and projection mixing, distance and velocity uncertainties, and skeleton-reconstruction noise.
interface
So 33.17 survives only as a local node-inheritance direction ledger. If co-rotating satellite planes repeatedly choose small ϕ relative to the host filament axis, strengthen with filament power and node proximity, and lose significance under the permutation and membership nulls, then the chapter is allowed to retain one structured orientation card. If not, it returns to geometry, contamination, or footprint review. Even on a pass, the section does not settle the entire satellite-plane controversy. It routes forward into 33.32’s later synthesis map as one local direction input, while remaining inside V33’s protocol-layer boundary.