IndisputableMonolith.Foundation.QRFT.GaugeTreeAmplitudesCert
This module certifies amplitudes for the three canonical gauge tree processes in the Recognition Science QRFT setting. Researchers modeling elementary quantum processes in RS-native units cite it to access verified amplitude properties such as threshold vanishing and non-negativity. The module assembles these objects from the imported Cost and Constants primitives without internal proofs.
claimDefines the three canonical gauge tree processes together with their amplitudes $A$ obeying $A=0$ at threshold, the reciprocity relation $A(x)=A(1/x)$, and $A>0$ off threshold.
background
The module sits inside the Foundation.QRFT portion of the Recognition Science monolith and imports the fundamental time quantum from Constants together with cost functionals from the Cost module. It introduces gauge tree processes as the elementary objects whose amplitudes are built from J-cost evaluations on the phi-ladder. The setting inherits the Recognition Composition Law and the eight-tick octave structure from upstream modules.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the base gauge-tree amplitude objects that support higher-level QRFT constructions on process enumeration and amplitude certification. It directly instantiates the J-uniqueness and phi-fixed-point steps of the forcing chain by grounding amplitudes in the cost formalism.
scope and limits
- Does not compute explicit numerical amplitude values.
- Does not treat loop-level or higher-order diagrams.
- Does not define non-gauge or non-tree processes.
- Does not address renormalization or running couplings.
depends on (2)
declarations in this module (10)
-
inductive
GaugeTreeProcess -
theorem
gauge_tree_process_count -
def
processAmplitude -
theorem
amplitude_zero_at_threshold -
theorem
amplitude_reciprocal_symm -
theorem
amplitude_nonneg -
theorem
amplitude_pos_off_threshold -
theorem
process_count_equals_3 -
structure
GaugeTreeAmplitudesCert -
def
gaugeTreeAmplitudesCert