KAM torus corridor around Braik-Ross C32 (2,1)-family 3D-lifted Earth-Moon cycler member 5/5 (x0=-0.416792, z0=0.302950)

braik-ross-c32-3d-corridor-05-2026 · source: this-project · validation: V0 · known-class

Signature

Bodies: E-Moon
Primary: Earth
Sequence (canonical): E-Moon
Sense: n/a
Orbit class: Quasi-cycler
quasi-cycler (epoch-locked, finite returns)
Cycler class: non-keplerian (CR3BP)
Returns: ∞ — finite for epoch-locked classes
Validity window: — (not published)
Trajectory regime: ballistic
Maintenance ΔV band: unclassified
Model assumption: cr3bp
CR3BP — Jacobi-constant-conserved; signature not patched-conic comparable.
Period: — yr (1 × E-Moon synodic)
T_PO = 31.317958757874642 TU = 136.18230412795552 d (this specific 3D-lifted member's OWN reproduced period, distinct from the planar braik-ross-c32-cycler-2026 anchor's own T^stable). broken-plane continuation lift of the planar Braik-Ross 2026 common-energy (3,2) Earth-Moon cycler at winding (k1=8, k2=0, k_z=26); z0=0.302950 is the out-of-plane amplitude signature. years: null (CR3BP).
Priority date: 2026-07-22

V∞ at encounters

E (encounter 1): — (not published)
CR3BP periodic orbit: conserved quantity is the Jacobi constant, not V_inf.
Moon (encounter 2): — (not published)
Same -- Jacobi-constant model.

CR3BP orbit identity

Family: Braik-Ross C32 (2,1)-family, 3D out-of-plane broken-plane lift (winding k1=8, k2=0, k_z=26); continuation of the planar braik-ross-c32-cycler-2026
Mass ratio (μ): 0.012150584270572
Jacobi constant: 3.0603
Period (non-dim): 31.3180
Stability index: —

3D CR3BP rotating-frame periodic orbit (genuinely out-of-plane, z0=0.302950); Keplerian elements inapplicable. CR3BP identity tuple below.

Orbit view 2.5D ecliptic projection

Not renderable from current data. This is a rotating-frame (CR3BP-family — CR3BP, CCR4BP, or CRNBP) periodic or quasi-periodic orbit. A faithful render requires numerical propagation of the synodic-frame state, which the catalogue does not yet publish as a sampled path — so no stand-in ellipse is drawn (drawing a heliocentric ellipse here would misrepresent the dynamics). Whatever identity fields the model supports (Jacobi constant, period, stability — not all apply to every model in this family; see "Model assumption" above) are tabulated above.

model: CR3BP (rotating frame)

3D view not available for rotating-frame (CR3BP-family) orbits.

Definition status

incomplete — core fields missing or known-unknowns tracked below

Family: cycler-corridor census -- Braik-Ross C32 3D-lifted family (z0_0.24 branch, 5 stratified members) · cyclerfinder internal (broken-plane lift + corridor census)

Known-unknowns (2)

Values we expect to exist but have not yet filled (distinct from "not applicable"). Tracked per upstream docs/spec.md §16.6.4.

orbit_elements.cr3bp.state_nd [not-applicable]
No published IC exists for this specific 3D-lifted member (Braik-Ross 2026 publishes only the planar family at the common Jacobi C=3.1294; the 3D out-of-plane lift is our own broken-plane continuation). state_nd is DERIVED by the continuation corrector, self-consistency-checked (corrector_residual=1.0721120602624904e-13, independent_closure_residual=3.149725975042153e-12). Never a golden. Matches the precedent already recorded for the sibling row em-cycler-21-3d-spatial-2026.

source: data/scan_434_3d_broken_plane_em.jsonl; scripts/census_682_cycler_corridors.py
orbit_elements.cr3bp.stability_index [unknown]
the scan (data/scan_434_3d_broken_plane_em.jsonl) records only the qualitative Floquet stability tag ('stable') for this member, not a numeric Barden-nu-style stability index. the family's first-documented member's own census recomputes the monodromy/Floquet eigenpairs internally (to select the widest-rotation center pair for the GMOS torus) but does not persist a scalar stability index either.

source: scripts/census_682_cycler_corridors.py::measure_corridor (floquet_multipliers/monodromy calls); scripts/scan_434_3d_broken_plane_em.py

Primary citation

undefined et al. (0). . .

Corroborating sources

Braik, A. & Ross, S. D. (2026). Orbital Networks in the Three-Body Problem. arXiv preprint arXiv:2605.31543 (29 May 2026). · link
The published CLASS + PLANAR-parent source (braik-ross-c32-cycler-2026, C32-cycler Table 2 row). Supplies NO 3D out-of-plane IC (planar-only paper) -- this row's specific 3D-lifted member and its corridor measurement are both entirely this-project computation; see data_gaps above and notes below.

Notes

cycler-corridor CHARACTERIZATION, NOT a discovery. This row measures the quasi-periodic (KAM) torus corridor -- the volume of natural, station-keeping-free drift -- surrounding an ALREADY-KNOWN, already-stability-classified periodic orbit: 3D-lifted member 5 of 5 (stratified sample, stride-selected across the family's z0/Jacobi range) of the Braik-Ross C32 (2,1)-family broken-plane continuation, itself bifurcated from the planar braik-ross-c32-cycler-2026 (Braik-Ross 2026 common-energy (3,2) Earth-Moon cycler). KAM theory GUARANTEES some quasi-periodic torus family exists around any linearly-stable periodic orbit -- the open question this measurement answers is purely how BIG that corridor is, not whether it exists. This is explicitly NOT conflated with this project's one confirmed novel finding (the Uranian symmetric-closure family); see data/OUTSTANDING.md's [[project_novel_findings_status]] note. Measurement result: corridor tube half-width 1792.5 km / 9.45 m/s at amplitude rung 0.005 (nondim), independent closure residual 1.661e-06 (nondim; gate 1.0e-4 = ~38.44 km equivalent). This is a genuine WALL -- the independent closure residual crossed the closure gate (or the Newton corrector failed to converge) at the next amplitude rung up, so this value IS the measured corridor edge. Method (reused GMOS torus machinery the bootstrap from): per member, monodromy -> Floquet center eigenpairs -> GMOS invariant-circle torus (genome.qp_tori.correct_qp_torus, the Olikara-Scheeres benchmark corrector) built at each rung of a geometric amplitude ladder (3e-4, 1e-3, 5e-3, 2e-2, 6e-2 nondim), recording the INDEPENDENT closure residual (a non-circular short-time nonlinear-flow check, not the algebraic invariance residual) at each rung. Corrector-choice honesty: the 2D pseudospectral corrector under-resolves these long-period, high-winding STABLE cycler center-manifolds at tractable mode counts; GMOS resolves the longitudinal angle EXACTLY by stroboscopic integration, so it is the correct tool here. Positive control: the family's first-documented member's own fallback (Olikara-Scheeres 2012 is not in the corpus) is the in-repo L2 GMOS positive control (tests/search/test_variational_qp_torus.py::test_l2_positive_control_reproduces_gmos_torus), which validates this EXACT corrector directly. Schema note: admitted as orbit_class=quasi_cycler under the schema v5.2 epoch-free CR3BP KAM-corridor carve-out (data/catalogue.schema.json v5.2 description; tests/data/test_schema_v47_orbit_class.py) -- NOT the real-ephemeris "cycler of opportunity" semantics the class was originally built for (contrast the Uranian moon-pair quasi_cycler rows, which carry a genuine SPICE-validated calendar validity_window). This row is instead epoch_locked=false / n_returns=infinite, like cycler/resonant_po, because a KAM torus around a linearly-stable CR3BP orbit winds quasi-periodically forever with no calendar launch window to speak of.