EARTH ↔ MARS LOOM
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EARTH ↔ MARS LOOM // 3D FIELD LAB
Strict Legendrian mode · dz − y dx = 0
Draw a wave in one horizontal direction. Vertical segments and backtracking are rejected, not epsilon-clamped. The app smooths your (x,z) front and lifts it using y = dz/dx.
Geometry audit · computed from this drawing
A stationary sample is not proof of a cusp. This mode leaves ambiguous vertices unresolved; it never assigns y = 0 automatically. Genuine cusp resolution needs a specified local curve model and a finite, consistent slope limit with a regular 3D lift.
Supported: one regular open Legendrian strand. Not a verified multi-strand braid, closed knot, physical law, or biological model. Background shapes are decorative.
AI canvas feedback
AI interpretation / hypothesis · not geometry proof or laboratory evidence
Physics safeguard: α = dz − y dx vanishes along every Legendrian curve, so ∫α = 0 on all of them. It cannot select a preferred proton path. A physical model needs a separate nontrivial action or Hamiltonian, specified dynamics, and testable predictions.
Reeb action is not a tunneling model
For α = dz − y dx, the Reeb vector field is Rα = ∂z. A Reeb chord travels vertically in z between points on a Legendrian object with matching (x,y); for a positively oriented chord, ∫γ α = ∫γ dz = Δz. The chord is not itself Legendrian. This app does not compute Reeb chords or their action spectrum.
Under the convention α(X_H) = H, H ≡ 1 gives the Reeb field, but H ≠ 1 alone does not specify a physical model or guarantee a non-Reeb direction: other constant H give scaled Reeb fields. Where H ≠ 0, X_H is not tangent to the contact planes and its trajectories are not Legendrian. Neither a contact Hamiltonian label nor a Reeb chord action establishes a proton tunneling trajectory. That needs an explicit Hamiltonian, units, potential-energy landscape, and quantum dynamics checked against evidence.
How the AI connects to your canvas
Your stroke becomes an (x,z) front. Keep moving in one horizontal direction. The app fits a smooth curve and computes y = dz/dx, then checks the lifted geometry. Only accepted curves can be synthesized, exported, or sent for AI review. AI explains the check and suggests changes; it cannot override it. Requests use platform credits.
The checked object is the smooth interpolant, not the raw sketch or the decorative background. This version supports one open Legendrian strand, not cusps, closed knots, or multi-strand braids. Completion also checks drawing length and point count; theme-specific physics, biology, and task goals are not validated.
Skip retires a task from the active rotation without a reward. X only closes it. Related themes may return, but retired task content is filtered out. Retirement tracking starts with this update.
LATTICE
STABILIZED
+0.00 LGN-BRAID