IndisputableMonolith.Information.ChurchTuring
The Information.ChurchTuring module formalizes Turing machines and the Church-Turing thesis inside Recognition Science. It supplies configurations, transitions, a universal TM, and ledger links all synchronized to the discrete 8-tick clock. Researchers modeling physical computation on RS time quanta cite it to ground universality. The module is definitional, importing Constants and EightTick with no internal proofs.
claimA Turing machine configuration is a state-tape-head triple operating under the 8-tick cycle with each transition advancing by the RS time quantum $τ_0 = 1$ tick; the module also defines a universal TM and the physical Church-Turing thesis over this clock.
background
The module sits in the Information domain and imports the RS time quantum $τ_0 = 1$ tick from Constants together with the 8-tick structure from EightTick. The latter supplies the discrete clock whose phases run through 0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4. It introduces the sibling definitions TuringMachine (a configuration), Transition, UniversalTM, ledger_follows_8tick, physical_ct_thesis, and halting_undecidable, all expressed in RS-native units.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the computational primitives that feed physical_ct_thesis, ledger_universal, and eight_tick_universal_gates. It realizes the eight-tick octave (T7) for discrete computation, enabling the claim that physical processes are simulable by a universal TM on the RS clock. It touches the open question of uncomputables within the discrete framework.
scope and limits
- Does not establish the Church-Turing thesis for continuous-time models.
- Does not simulate specific physical systems beyond the ledger abstraction.
- Does not resolve the halting problem for arbitrary instances.
- Does not incorporate quantum superposition into the TM definition.
depends on (2)
declarations in this module (16)
-
structure
TuringMachine -
structure
Transition -
structure
UniversalTM -
theorem
utm_exists -
structure
LedgerComputer -
theorem
ledger_follows_8tick -
theorem
ledger_universal -
def
universalGateSet -
theorem
eight_tick_universal_gates -
theorem
physical_ct_thesis -
def
uncomputables -
theorem
halting_undecidable -
def
quantumSpeedups -
theorem
quantum_parallelism_from_8tick -
def
predictions -
structure
CTFalsifier