KAM torus corridor around 3D-lifted Earth-Moon L1 Lyapunov family member 5/7 (x0=0.876482, z0=0.191973)

lyapunov3d-l1-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 = 2.1711834495519042 TU = 9.441125046826864 d. 3D-lift (seed_route 'lyapunov3d', winding k1=0/k2=1/k_z=2) of the generic Earth-Moon L1 spatial Lyapunov family, NOT a Braik-Ross common-energy resonant cycler lineage (a DIFFERENT Jacobi regime, C~2.998, vs the Braik-Ross common C=3.1294). No literature parent orbit -- see corroborating_sources / data_gaps. 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: Earth-Moon L1 spatial Lyapunov family, 3D lift (winding k1=0, k2=1, k_z=2; #438 seed_route='lyapunov3d')
Mass ratio (μ): 0.012150584270572
Libration point: L1
Jacobi constant: 2.9981
Period (non-dim): 2.1712
Stability index: —

3D CR3BP rotating-frame periodic orbit (out-of-plane, z0=0.191973); 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 -- 3D-lifted Earth-Moon L1 Lyapunov family (7 stratified members) · cyclerfinder internal (lyapunov3d 3D-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 (this is a generic CR3BP L1 spatial-Lyapunov family member, not tied to any specific paper's tabulated orbit). state_nd is DERIVED by the 3D-lift corrector, self-consistency-checked (corrector_residual=8.718885342929877e-15, independent_closure_residual=2.9252350287672864e-13). Never a golden.

source: data/scan_434_3d_broken_plane_em.jsonl; scripts/census_682_cycler_corridors.py
orbit_elements.cr3bp.stability_index [unknown]
the scan records only the qualitative Floquet stability tag ('stable') for this member, not a numeric Barden-nu-style stability index.

source: scripts/census_682_cycler_corridors.py::measure_corridor; scripts/scan_434_3d_broken_plane_em.py

Primary citation

undefined et al. (0). . .

Notes

cycler-corridor CHARACTERIZATION, NOT a discovery. This row measures the quasi-periodic (KAM) torus corridor surrounding an ALREADY-KNOWN, already-stability- classified periodic orbit: 3D-lifted member 5 of 7 (stratified sample) of the generic Earth-Moon L1 spatial Lyapunov family (seed_route='lyapunov3d'). This is a DIFFERENT lineage from the Braik-Ross common-energy resonant cyclers (C21/C32 sibling rows in this same writeback) -- no Braik-Ross Table 2 entry corresponds to this family, and it has NO literature parent at all (a generic, well-known CR3BP structural class -- spatial Lyapunov orbits bifurcating from the planar L1 Lyapunov family -- computed in-repo, not itself individually published). 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. 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 2598.8 km / 8.76 m/s at amplitude rung 0.005 (nondim), independent closure residual 1.304e-05 (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: identical GMOS amplitude-ladder census as the C21/C32 sibling rows in this same writeback -- see those rows' notes for the full method + positive-control paragraph (genome.qp_tori.correct_qp_torus; positive control tests/search/test_variational_qp_torus.py::test_l2_positive_control_reproduces_gmos_torus). 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; see the C21/C32 sibling rows' identical schema-note paragraph for the full rationale).