Action (Crossing-Point Action Space)
Action (IV.D115) is the τ-categorical Crossing-Point Action Space: the integrated CR-tension along a τ-trajectory, evaluated at every crossing point of the underlying defect-graph. It is the natural quantity for τ-variational principles, the ledger that ties (energy)·(time) into the action quantum (IV.D294).
τ-Definition
Action (IV.D115) is the τ-categorical Crossing-Point Action Space: the integrated CR-tension along a τ-trajectory, evaluated at every crossing point of the underlying defect-graph. It is the natural quantity for τ-variational principles, the ledger that ties (energy)·(time) into the action quantum (IV.D294).
Categorical invariant. Action(γ) := ∫_γ E_CR · dτ = sum over crossing points of CR-tension·time-step; an E2 invariant whose extremum yields the τ-equations of motion.
Primary registry anchor:
IV.D115
τ-Derivation Chain
-
I.K0— Universe Postulate establishes τ -
IV.D21— Energy Index — the integrand at each τ-step -
IV.D76— Energy as CR-Tension supplies the operational integrand -
IV.D115— Crossing-Point Action Space: ∫ E_CR · dτ summed over τ-graph crossings -
IV.D294— Planck's constant in relational units fixes the action quantum h
Lean modules referenced:
TauLib.BookI.Kernel.ActionQuantum
SI Translation
Calibration anchor: PG-P01-neutron
Calibration chain:
- m_n (anchor)
- c² via IV.D23 → energy
- s via Cs hyperfine → time
- ℏ := τ-internal action quantum (IV.D294)
Manuscript reference: manuscript-sources/book-04/part04-quantum-mechanics/ch-action.tex