module module high

`IndisputableMonolith.Information.ChurchTuringPhysicsStructure`

This module defines the 8-tick phase space with phases 0-7 together with finite discrete ledger states and computable transitions. Researchers citing IC-002 computation limits or IC-004 simulation dissolution would import it to anchor information structures in the RS eight-tick octave. The module is a pure definition collection that assembles finiteness and computability lemmas from imported constants and cost axioms.

claimThe phase space consists of eight discrete phases indexed $0$ to $7$, with finite cardinality, phase functions, discrete ledger states, and computable ledger transitions, all derived from the RS time quantum and cost structure.

background

The module sits in the Information domain and imports the RS time quantum τ₀ = 1 tick from Constants together with the cost framework. It directly extends ComputationLimitsStructure (IC-002), which derives Bremermann's limit, Landauer's bound, and quantum computation limits from Recognition Science sources. The DOC_COMMENT identifies the core object as the 8-tick phase space phases 0 through 7, realizing the T7 eight-tick octave of period 2³.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the phase space, ledger states, and computability predicates imported by SimulationHypothesisStructure (IC-004). That downstream module uses them to dissolve the simulation hypothesis by rendering the real-versus-simulated distinction meaningless inside RS. It therefore closes the information-theoretic segment of the forcing chain between computation limits and the simulation question.

scope and limits

Does not derive the eight-tick octave from the T0-T8 forcing chain.
Does not prove any computation-limit bounds.
Does not treat continuous-time or non-discrete models.
Does not address physical realizability of the ledger states.

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