IndisputableMonolith.Foundation.PathIntegralDeep
This module defines the path integral weight as exp(-J(r)/ℏ) for use in the Recognition Science foundation. It equips path sums with the J-cost exponential in RS-native units. Researchers constructing quantum amplitudes from the forcing chain would reference these objects when weighting trajectories. The module consists of direct definitions and basic properties drawn from the imported Cost and Constants modules.
claimThe path weight is given by $w(r) = e^{-J(r)/ℏ}$, with positivity $w(r) > 0$ and a maximum attained when the argument satisfies the equality condition.
background
The module operates inside the Recognition Science foundation and imports the fundamental time quantum τ₀ = 1 tick. The Cost module supplies the J-cost function that enters the exponential weight. This places the construction inside the single-functional-equation derivation of physics, with J defined via the self-similar fixed point and the phi-ladder.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The definitions supply the weight that feeds the deep path integral certification and later applications of path sums. They connect the J-cost formalism to the forcing chain steps that produce three spatial dimensions and the alpha band.
scope and limits
- Does not derive the path integral measure from the forcing chain.
- Does not prove convergence of the weighted sum.
- Does not connect the weight to specific observables or renormalization.