IndisputableMonolith.Foundation.QRFT.GaugeTreeAmplitudesCert
The module establishes the three canonical gauge tree processes in the QRFT sector of Recognition Science. Researchers deriving gauge amplitudes from the J-cost and phi-ladder would cite these definitions for symmetry and positivity properties. It consists of a collection of definitions and lemmas on process counts and amplitude relations.
claimThe three canonical gauge tree processes with amplitudes $A$ obeying $A(\text{threshold})=0$, reciprocal symmetry $A(x)=1/A(1/x)$, non-negativity, and positivity off threshold, together with a process count of three.
background
The module sits in the Foundation.QRFT domain and imports the RS time quantum $\tau_0=1$ tick from Constants together with cost structures. It introduces the enumeration of the three processes and amplitude functions whose properties follow from the Recognition Composition Law. The setting uses the J-cost to constrain tree-level gauge amplitudes on the phi-ladder.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies amplitude certifications that support QRFT constructions in Recognition Science. It supplies concrete instances for the J-uniqueness and eight-tick octave steps of the forcing chain. No downstream theorems are recorded in the current dependency graph.
scope and limits
- Does not derive the three processes from the unified forcing chain.
- Does not compute numerical amplitude values.
- Does not address loop corrections or higher-order diagrams.
- Does not link processes to specific particle species or mass rungs.
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