simulation_hypothesis_structure
The theorem establishes that the simulation hypothesis structure holds under Recognition Science assumptions. Researchers examining Bostrom-style arguments or the it-from-bit requirement would cite it to show the ledger-reality distinction collapses. The proof is a one-line term application of the Church-Turing physics structure theorem.
claimThe simulation hypothesis structure holds, where this structure is the Church-Turing physics structure derived from the ledger.
background
In the module on the simulation hypothesis in Recognition Science, the ledger is treated as the unique physical substrate with no external computer or outside possible. Existence is governed by the J-cost: an entity x exists if and only if its J-cost vanishes, which occurs precisely when x equals 1. The immediate upstream result is the theorem that Church-Turing physics follows from the ledger, which itself rests on the cost framework determining what counts as real.
proof idea
The proof is a direct term-mode application of the has_ct_structure theorem, which reduces the simulation hypothesis structure to the Church-Turing physics structure.
why it matters in Recognition Science
This result completes the IC-004 sequence by confirming that the simulation hypothesis structure is identical to the Church-Turing physics structure. It supports the module claim that the simulation/reality distinction carries no semantic content once the ledger is taken as reality itself. The placement aligns with the broader Recognition Science dissolution of external-substrate questions while leaving the phi-ladder and eight-tick octave machinery untouched.
scope and limits
- Does not supply an empirical test capable of distinguishing a simulated ledger from a non-simulated one.
- Does not address whether other physical frameworks could retain a meaningful simulation distinction.
- Does not quantify the computational resources required to simulate the ledger.
- Does not engage with quantum or relativistic extensions of the simulation question.
formal statement (Lean)
136theorem simulation_hypothesis_structure : simulation_hypothesis_from_ledger :=
proof body
Term-mode proof.
137 has_ct_structure
138
139/-- Church-Turing physics implies simulation-hypothesis structure. -/