module module high

`IndisputableMonolith.Information.ChurchTuringPhysicsStructure`

The module defines the 8-tick phase space with phases 0 through 7 together with discrete ledger states and transitions that embed Church-Turing limits inside Recognition Science. Researchers tracing information bounds or simulation arguments cite it when moving from the RS time quantum to computability structures. The module is definitional, establishing finiteness of the phase space and ledger without deductive proofs.

claimThe 8-tick phase space $\Phi = \{0,1,\dots,7\}$ equipped with finite phase functions, discrete ledger states, and transitions that satisfy the computation limits derived from RS.

background

Constants supplies the RS time quantum $\tau_0 = 1$ tick. ComputationLimitsStructure shows that Bremermann's limit, Landauer's bound, and quantum computation limits arise from three RS sources. The present module sits in the Information domain and introduces Phase as the 8-element set together with numPhases, phase_space_finite, DiscreteLedgerState, and LedgerTransition to make the ledger computable.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the phase-space and ledger objects required by church_turing_physics_structure, which is imported by SimulationHypothesisStructure. That downstream module dissolves the simulation hypothesis rather than refuting it, using the finite 8-tick structure to show that real and simulated physics are indistinguishable inside RS. The construction directly instantiates the eight-tick octave (T7) of the forcing chain.

scope and limits

Does not derive any physical constants or mass ladder.
Does not treat continuous time or spacetime geometry.
Does not prove Turing completeness or equivalence results.
Does not model quantum measurement or collapse.

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