module module high

`IndisputableMonolith.Information.ChurchTuringPhysicsStructure`

The module defines the 8-tick phase space with phases 0 through 7 and builds discrete ledger states that embed Church-Turing computability into RS physics. Information theorists and physicists working on fundamental computation bounds cite this structure when linking discrete transitions to recognition costs. It consists of type definitions for Phase and LedgerTransition together with finiteness results for the phase space and ledger states.

claimLet $P = 8$ denote the number of phases. The phase space is the finite set $S = {0,1,2,3,4,5,6,7}$ with $|S| = 8$. A discrete ledger state is a map from $S$ to a finite set of states, and the Church-Turing physics structure asserts that all physical transitions remain within this finite phase space and therefore obey the computation limits induced by the recognition cost function.

background

This module sits in the Information domain and imports the RS time quantum from Constants together with the computation-limits framework from ComputationLimitsStructure. The upstream module states that computation limits emerge from three sources in Recognition Science. The 8-tick phase space realizes the octave period $2^3$ required by the forcing chain T0-T8 and supplies the discrete substrate on which ledger transitions are defined.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the 8-tick phase space and ledger structures required by the SimulationHypothesisStructure. There the simulation hypothesis is described as meaningless (dissolved, not refuted) because every physical process is already confined to finite, computable transitions inside the phase space. It directly implements the T7 eight-tick octave landmark and provides the discrete foundation for embedding Church-Turing limits into physical law.

scope and limits

Does not derive explicit numerical bounds such as Bremermann's limit.
Does not treat continuous-time or infinite-state models.
Does not prove full equivalence between physical processes and Turing machines.
Does not address quantum computation beyond the discrete ledger model.

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

IndisputableMonolith.Information.SimulationHypothesisStructure module_import

depends on (3)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import
IndisputableMonolith.Information.ComputationLimitsStructure module_import

declarations in this module (21)

abbrev Phase L46
def numPhases L49
theorem phase_space_finite L52
theorem phase_functions_finite L57
def DiscreteLedgerState L64
def LedgerTransition L68
theorem discrete_ledger_computable L74
def numLedgerStates L83
theorem ledger_state_space_finite L86
theorem has_computation_limits_structure L93
def church_turing_physics_from_ledger L97
theorem church_turing_physics_structure L106
theorem church_turing_implies_limits L110
theorem phase_space_bounded L118
theorem tick_rate_bounded L124
theorem computation_takes_time L128
theorem finite_function_is_computable L136
theorem eight_tick_step_computable L147
theorem rs_dynamics_beyond_rational L158
theorem rs_dynamics_approximable L164
def ic003_certificate L171