modal_geometry_status
plain-language theorem explainer
This definition supplies a formatted string summarizing the geometry of the possibility space in the modal layer. Readers of the Modal module would consult it for an overview of topology, metric, and resolution limits drawn from Recognition Science. The body assembles the report directly as a concatenated literal without computation or external calls.
Claim. The status report for modal geometry is the string describing a star topology in dimension 2 (value plus time) with metric $d(x,y)$ given by the J-cost at transition states, curvature formula $1/c^2 + 1/c^4$, eight-tick period limiting resolution to one tick, and interference between equal-cost paths.
background
The ModalGeometry module sits inside the modal domain and imports Possibility and Actualization. It draws on the J-cost function, where J_transition(x*) returns the value of J at a transition state, and on the octave defined as the ratio 2. Upstream results include the statement that the octave ratio equals 2 and that J_transition supplies the dimensionless activation energy as J(x*) minus J(reactant).
proof idea
As a definition this is a direct string literal. The body concatenates fixed text blocks that list the star topology, the metric using J_transition, the curvature expression, the eight-tick Nyquist limit, and the interference rules; no lemmas or tactics are applied.
why it matters
The definition consolidates a human-readable summary of modal geometry properties that rest on the eight-tick octave and J-uniqueness from the forcing chain. It references the octave and tick constants and the J_transition cost. With zero downstream uses it functions as module documentation rather than a theorem feeding further results.
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