IndisputableMonolith.Complexity.CellularAutomata
This module defines core structures for Boolean cellular automata including cell states, tapes, neighborhoods and local rules as part of an exploratory complexity model. Researchers studying discrete dynamical systems or ledger-based dual complexity would reference these definitions. The module consists entirely of type and function definitions with no theorems or proofs.
claimCellState := {0,1}; Tape := ℤ → CellState; Neighborhood := finite window of radius r; localRule : Neighborhood → CellState; step : Tape → Tape applies the rule synchronously.
background
The module sits inside the Complexity domain and imports the ComputationBridge scaffold. That upstream file explicitly states it is a SCAFFOLD MODULE — NOT PART OF CERTIFICATE CHAIN and explores a hypothetical P vs NP resolution framework based on ledger-style dual complexity (computation vs recognition). The present module supplies the concrete Boolean CA objects (CellState, Tape, Window, Neighborhood, extractNeighborhood, localRule, step, ca_is_local, dependency_cone, ClauseGadget) needed to instantiate such models.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the cellular-automaton substrate for the hypothetical dual-complexity framework described in ComputationBridge. No parent theorems in the verified certificate chain (UltimateClosure, CPMClosureCert, etc.) are fed by it; the connection remains exploratory.
scope and limits
- Does not belong to the verified certificate chain.
- Does not contain any theorems or proofs.
- Does not claim a P vs NP resolution.
- Does not define dynamics beyond Boolean CA.
depends on (1)
declarations in this module (23)
-
inductive
CellState -
def
Tape -
def
Window -
def
radius -
structure
Neighborhood -
def
extractNeighborhood -
def
localRule -
def
step -
theorem
ca_is_local -
theorem
ca_k_local -
theorem
dependency_cone -
structure
ClauseGadget -
def
encodeClause -
structure
SATGadget -
def
sat_eval_time -
def
H_SATCARuntime -
structure
TMSimulator -
def
tm_simulation_time -
theorem
tm_simulation_bound -
def
H_SATTMRuntime -
theorem
sat_computation_time -
theorem
sat_recognition_time -
theorem
computation_recognition_separation