IndisputableMonolith.Econ.LedgerEconomics
The Econ.LedgerEconomics module applies the eight-tick octave to ledger systems and shows that this structure forces exactly eight economic phases. Researchers extending Recognition Science to cyclic economic models would cite the phase count and associated bounds. The module imports the base time quantum and derives the phase multiplicity plus conservation properties directly from the octave.
claimThe 8-tick octave forces exactly eight economic phases, with business cycle period bounded in an interval derived from the octave and ledger conservation ratio equal to one.
background
The module sits in the Econ domain and imports the fundamental RS time quantum τ₀ = 1 tick from IndisputableMonolith.Constants. It introduces economicPhases as the set of phases induced by the octave, businessCyclePeriod as the duration of one economic cycle, ledgerConservationRatio as the balance preservation factor in ledgers, and octaveGrowthMultiplier as the scaling factor over the full octave. These objects rest on the eight-tick structure of period 2^3.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module realizes the doc-comment claim that the 8-tick octave forces exactly eight economic phases, extending T7 of the forcing chain into economics. It supplies the phase count, positivity, bounds, and conservation equality that later economic applications would build upon, though no downstream theorems are recorded yet.
scope and limits
- Does not incorporate empirical economic time series or calibration.
- Does not address economic behaviors outside the octave structure.
- Does not derive numerical values for growth rates beyond the multiplier bounds.
- Does not connect to physical constants such as alpha or G.
depends on (1)
declarations in this module (11)
-
def
economicPhases -
def
businessCyclePeriod -
def
ledgerConservationRatio -
def
octaveGrowthMultiplier -
theorem
eight_economic_phases -
theorem
businessCyclePeriod_pos -
theorem
businessCyclePeriod_lower -
theorem
businessCyclePeriod_upper -
theorem
ledgerConservation_eq_one -
theorem
octaveGrowth_bounds -
theorem
businessCycle_bounds